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Volumn , Issue , 2008, Pages 1-500

Modeling Differential Equations in Biology

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EID: 77951456296     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511811364     Document Type: Book
Times cited : (11)

References (621)
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    • For the salmonids, there were two statistically significant estimates of the depensation parameter that were greater than 1 and two that were less than 1. The most convincing case of depensation is that of pink salmon in, population abundance of less than 100 females; it is perhaps at this level that depensation is expected to occur for salmonids
    • For the salmonids, there were two statistically significant estimates of the depensation parameter that were greater than 1 and two that were less than 1. The most convincing case of depensation is that of pink salmon in Sashin Creek, AK, at a population abundance of less than 100 females; it is perhaps at this level that depensation is expected to occur for salmonids.
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    • We repeated the analyses assuming gammainstead of log-normally distributed residuals; the results were almost identical, Lognormal errors in the estimation of spawners (cr = 0.2) and first-order autocorrelation of 0.4 in recruitment did not increase type 1 errors if 5 was held at 1. As expected, the power was reduced if depensation was present (<5 = 2); for the 26 high-power stocks, with errors in the estimation of spawners, the power was reduced by approximately 3% on average, whereas with autocorrelation, the power was reduced by approximately 1% on average. In addition, we tested the adequacy of the chi-square approximation to the distribution of the likelihood ratio statistic by calculating the type 1 error rate when 6 = 1 (approximately 3% on average for the 26 highpower stocks)
    • We repeated the analyses assuming gammainstead of log-normally distributed residuals; the results were almost identical. Robustness to estimation error in spawners and serial correlation in recruitment were investigated by introduction of these effects into the procedure used to estimate power. Lognormal errors in the estimation of spawners (cr = 0.2) and first-order autocorrelation of 0.4 in recruitment did not increase type 1 errors if 5 was held at 1. As expected, the power was reduced if depensation was present (<5 = 2); for the 26 high-power stocks, with errors in the estimation of spawners, the power was reduced by approximately 3% on average, whereas with autocorrelation, the power was reduced by approximately 1% on average. In addition, we tested the adequacy of the chi-square approximation to the distribution of the likelihood ratio statistic by calculating the type 1 error rate when 6 = 1 (approximately 3% on average for the 26 highpower stocks).
    • Robustness to estimation error in spawners and serial correlation in recruitment were investigated by introduction of these effects into the procedure used to estimate power
  • 37
    • 84931441564 scopus 로고    scopus 로고
    • We thank the many fish population biologists who generously provided their data and the Canadian Department of Fisheries and Oceans Northern Cod Science Program for financial assistance
    • We thank the many fish population biologists who generously provided their data and the Canadian Department of Fisheries and Oceans Northern Cod Science Program for financial assistance.
  • 52
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    • Cambridge Univ. Press, Cambridge, 1990)] with the help of J. J. Sepkoski Jr. to adjust the beginning times of the Cambrian and Ordovician periods
    • Data for the Figure came from the following sources: Ages and durations from [W. Harland et al, A Geologic Time Scale, 1989 (Cambridge Univ. Press, Cambridge, 1990)] with the help of J. J. Sepkoski Jr. to adjust the beginning times of the Cambrian and Ordovician periods.
    • (1989) A Geologic Time Scale
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    • Rock areas and unadjusted diversities came from [D. M. Raup, Paleobiology 279 (1976a)
    • (1976) Paleobiology , vol.279
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  • 55
    • 84931429141 scopus 로고
    • Raup counted 71, 112 species entries in the zoological record from 1900 to 1970. He extrapolated 73, 139 more from these 71, 112. of these 144, 251 species, 7416 were insects, or uncertain, or lived in more than one period, or lived in the Pre-Cambrian; I excluded the latter. The remaining 136, 835 species represent a substantial fraction of all known fossil forms. The adjusted number of species in a period is the number (of the 136, 835) attributed to it divided by A0383, where A is the period's rock area divided by that of the Cenozoic.
    • (1970) The adjusted number of species in a period is the number
  • 58
    • 84931455853 scopus 로고    scopus 로고
    • First, arrange the data in order of declining accumulation rates, so that the “first” period has the highest rate and the “last” has the lowest. This imposes the largest possible negative second derivative on the data. Second, reverse the order (so that the one with the lowest rate is first). This imposes the largest possible positive second derivative on the data. The results are, in the first case, an exponent of 0.866 in a power fit, and in the second, an exponent of 1.204. The Figure 1 shows the polynomial approximations of these curves
    • First, arrange the data in order of declining accumulation rates, so that the “first” period has the highest rate and the “last” has the lowest. This imposes the largest possible negative second derivative on the data. Second, reverse the order (so that the one with the lowest rate is first). This imposes the largest possible positive second derivative on the data. The results are, in the first case, an exponent of 0.866 in a power fit, and in the second, an exponent of 1.204. The Figure 1 shows the polynomial approximations of these curves.
  • 62
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    • S. L. Pimm, The Balance of Nature (Univ. of Chicago Press, Chicago, IL, 1992), chap. 14.
    • (1992) The Balance of Nature , vol.14
    • Pimm, S.L.1
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  • 69
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    • thesis, Michigan Technological University
    • K. L. Risenhoover, thesis, Michigan Technological University (1987), p. 49.
    • (1987) , pp. 49
    • Risenhoover, K.L.1
  • 71
    • 84931446701 scopus 로고    scopus 로고
    • unpublished data (figures are for the west end of Isle Roy ale)
    • B.E. McLaren, unpublished data (figures are for the west end of Isle Roy ale).
    • McLaren, B.E.1
  • 73
    • 84931390476 scopus 로고    scopus 로고
    • Suppression of balsam fir growth on Isle Royale by moose foraging occurs because of continuous removal of upper branches in winter. Trees remain alive in the forest understory for several decades, because lateral branches are protected from browsing by snow cover and because balsam fir is tolerant of shade. Trees in this study (except those represented in Fig. 4A) ranged from 34 to 68 years of age but came from a consistent height interval of 1 to 3 m at the time of sampling. The age variation made no contribution to variation in growth rates
    • Suppression of balsam fir growth on Isle Royale by moose foraging occurs because of continuous removal of upper branches in winter. Trees remain alive in the forest understory for several decades, because lateral branches are protected from browsing by snow cover and because balsam fir is tolerant of shade. Trees in this study (except those represented in Fig. 4A) ranged from 34 to 68 years of age but came from a consistent height interval of 1 to 3 m at the time of sampling. The age variation made no contribution to variation in growth rates.
  • 78
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    • A harmonic function fitted with an ordinary least squares approach, period 17.8 years, matched the west-end chronology with R2 = 0.38; a function with period 16.1 years matched the east-end chronology with R2 = 0.70
    • functions incorporating both a harmonic term and a first-order autoregressive term were matched to the series, with improved fits of R2^= 0.68 and R2 = 0.81, respectively
    • A harmonic function fitted with an ordinary least squares approach, period 17.8 years, matched the west-end chronology with R2 = 0.38; a function with period 16.1 years matched the east-end chronology with R2 = 0.70. Following M. G. Bulmer Anim. Ecol. 43, 701 (1978)], functions incorporating both a harmonic term and a first-order autoregressive term were matched to the series, with improved fits of R2^= 0.68 and R2 = 0.81, respectively.
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    • Bulmer, M.G.1
  • 79
    • 84931380018 scopus 로고    scopus 로고
    • The cycle period inferred from empirical consideration of the three-trophic-level system is shorter than a period cited earlier, which was derived from a body-mass regression [6]. However, the confidence interval for the allometric Equation also included the shorter period of 16 to 18 years
    • The cycle period inferred from empirical consideration of the three-trophic-level system is shorter than a period cited earlier, which was derived from a body-mass regression [6]. However, the confidence interval for the allometric Equation also included the shorter period of 16 to 18 years.
  • 80
    • 84931306227 scopus 로고    scopus 로고
    • Ring-width suppression followed heightgrowth suppression in both samples by about 3 years
    • Ring-width suppression followed heightgrowth suppression in both samples by about 3 years.
  • 81
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    • The plant with the inferior growth rate lags behind herbivore density more than does the plant with the superior growth rate
    • G. Caughley, Oecologia 54, 309 (1976). The plant with the inferior growth rate lags behind herbivore density more than does the plant with the superior growth rate.
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    • unpublished data; R. M. Linn, thesis, Duke University
    • B. E. McLaren, unpublished data; R. M. Linn, thesis, Duke University (1957).
    • (1957)
    • McLaren, B.E.1
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    • unpublished data
    • R. O. Peterson, unpublished data.
    • Peterson, R.O.1
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    • Our result is new primarily because studies of long-term processes in terrestrial food chains are rare, especially studies of those in which top carnivores still exist. A. R. E. Sinclair and colleagues [Am. Nat. 141, 173 (1993)] recently described the well-known snowshoe hare (Lepus amehcana) cycle in the Yukon Territory, Canada, as generating cyclic suppression of white spruce (Picea glauca). These authors, however, favored an explanation in meteorological driving forces. Other studies [for example
    • Our result is new primarily because studies of long-term processes in terrestrial food chains are rare, especially studies of those in which top carnivores still exist. A. R. E. Sinclair and colleagues [Am. Nat. 141, 173 (1993)] recently described the well-known snowshoe hare (Lepus amehcana) cycle in the Yukon Territory, Canada, as generating cyclic suppression of white spruce (Picea glauca). These authors, however, favored an explanation in meteorological driving forces. Other studies [for example, L. B. Keith, A. W. Todd, C. J. Brand, R. S. Adamcik, D. H. Rusch, Int. Congr. Game Biol. 13, 151 (1976)
    • (1976) Int. Congr. Game Biol. , vol.13 , pp. 151
    • Keith, L.B.1    Todd, A.W.2    Brand, C.J.3    Adamcik, R.S.4    Rusch, D.H.5
  • 85
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    • have considered plant-herbivore and herbivore-carnivore relations for the snowshoe hare, but in different study areas. The third trophic level in the fox-prey system studied by E. R. Lindstroem and colleagues [Ecology 75, 1042 (1994)] was a parasite
    • L.B. Keith and L. A. Windberg, Midi. Monogr. 58, 70 (1978)] have considered plant-herbivore and herbivore-carnivore relations for the snowshoe hare, but in different study areas. The third trophic level in the fox-prey system studied by E. R. Lindstroem and colleagues [Ecology 75, 1042 (1994)] was a parasite.
    • (1978) Midi. Monogr , vol.58 , Issue.70
    • Keith, L.B.1    Windberg, L.A.2
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    • for other contrasting published ideas concerning predator-prey cycles on Isle Royale, see [6] and
    • for other contrasting published ideas concerning predator-prey cycles on Isle Royale, see [6] and J. Pastor and R. J. Naiman, Am. Nat. 139, 690(1992).
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    • Pastor, J.1    Naiman, R.J.2
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    • The index was calculated with the use of daily records from Thunder Bay, Ontario
    • M. L. Rosenzweig, Am. Nat. 102, 67 (1968). The index was calculated with the use of daily records from Thunder Bay, Ontario.
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    • Rosenzweig, M.L.1
  • 94
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    • Understory fir density exceeds 250 ha"1 over about 70% of Isle Royale's land area and exceeds 10, 000 ha"1 in many shoreline forests. Values were obtained by averaging density estimates for stems < 2 m in 0.01-ha plots at the corners of each (square-mile) township section
    • Understory fir density exceeds 250 ha"1 over about 70% of Isle Royale's land area and exceeds 10, 000 ha"1 in many shoreline forests. Values were obtained by averaging density estimates for stems < 2 m in 0.01-ha plots at the corners of each (square-mile) township section.
  • 95
    • 84931376455 scopus 로고    scopus 로고
    • The ring-width index is the ratio of increments calculated as a summation of volume differences for a series of stacked conic sections representing the stems of sampled trees, divided by the cambial surface area at the beginning of each growing season for each year. An aggregate index, comprising ring-width measurements (±10~2 mm) averaged for four radii at 5-to 10-cm increments along stems, is presented. This intensity of sampling permits an accurate height-growth reconstruction of the trees and measurement of the wood volume increment throughout the trees' stems
    • The ring-width index is the ratio of increments calculated as a summation of volume differences for a series of stacked conic sections representing the stems of sampled trees, divided by the cambial surface area at the beginning of each growing season for each year. An aggregate index, comprising ring-width measurements (±10~2 mm) averaged for four radii at 5-to 10-cm increments along stems, is presented. This intensity of sampling permits an accurate height-growth reconstruction of the trees and measurement of the wood volume increment throughout the trees' stems.
  • 96
    • 84931401807 scopus 로고    scopus 로고
    • We acknowledge the National Park Service (NPS) for permission to sample trees; V. G. Smith, University of Toronto, for the design of the ring-width index; R. J. Miller, Ontario Ministry of Natural Resources, for the development of analytic software and loan of measurement equipment; Environment Canada for supplying weather records; and the following for financial support: National Geographic Society, NPS Earthwatch, the Boone and Crockett Club, and NSF grant DEB-9317401
    • We acknowledge the National Park Service (NPS) for permission to sample trees; V. G. Smith, University of Toronto, for the design of the ring-width index; R. J. Miller, Ontario Ministry of Natural Resources, for the development of analytic software and loan of measurement equipment; Environment Canada for supplying weather records; and the following for financial support: National Geographic Society, NPS Earthwatch, the Boone and Crockett Club, and NSF grant DEB-9317401. W. C. Kerfoot and F. H. Wagner kindly reviewed this manuscript and offered many helpful suggestions.
    • Kindly Reviewed This Manuscript and Offered Many Helpful Suggestions
    • Kerfoot, W.C.1    Wagner, F.H.2
  • 98
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    • Centers for Disease Control
    • This plateau was obscured after January 1993 by the expansion of case definition to include HIV-infected persons with severe CD4 depletion [Centers for Disease Control, 41 (no. RR-17) (1992)]
    • Centers for Disease Control, Morb. Mortal. Wkly. Rep. 43 826 (1994). This plateau was obscured after January 1993 by the expansion of case definition to include HIV-infected persons with severe CD4 depletion [Centers for Disease Control, 41 (no. RR-17) (1992)].
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    • The analysis was based on all cases in the United States and its territories, including Puerto Rico, who were older than 13 years at diagnosis and who were reported to CDC as of March 1994. The AIDS incidence and mortality data for individuals who met the 1987 case definition [6] were adjusted for reporting delays with standard CDC adjustment weights. Incidence counts were inflated by 18%, an approximate figure, to account for unreported cases and for infected individuals who died before meeting the case definition. Adjusted totals of 336, 000 incident cases of AIDS and 227, 000 AIDS deaths as of 1 January 1993 were stratified by month of diagnosis, single year of age at diagnosis, gender, and race and ethnicity (non-Hispanic whites, non-Hispanic blacks, Hispanics, and others). Use of the 1987 definition maintains consistency between the AIDS data and available estimates of the incubation distribution
    • The analysis was based on all cases in the United States and its territories, including Puerto Rico, who were older than 13 years at diagnosis and who were reported to CDC as of March 1994. The AIDS incidence and mortality data for individuals who met the 1987 case definition [6] were adjusted for reporting delays with standard CDC adjustment weights. Incidence counts were inflated by 18%, an approximate figure, to account for unreported cases and for infected individuals who died before meeting the case definition. Adjusted totals of 336, 000 incident cases of AIDS and 227, 000 AIDS deaths as of 1 January 1993 were stratified by month of diagnosis, single year of age at diagnosis, gender, and race and ethnicity (non-Hispanic whites, non-Hispanic blacks, Hispanics, and others). Use of the 1987 definition maintains consistency between the AIDS data and available estimates of the incubation distribution.
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    • Technical details of the fitting procedures are described elsewhere [5]
    • Technical details of the fitting procedures are described elsewhere [5].
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    • This fast model may yield conservative estimates because the natural history hazard function may level off around 7 years after infection, The Weibull hazard, in contrast, continues to increase. To reflect that progression rates appear to be slower with infection at younger ages, the age-specific hazard of progression for the fast model was assumed to increase (decrease) by the factor 1.042 (0.960) per year increase (decrease) in the age at infection compared to a person aged 30 years at infection, as derived in [9]
    • This fast model may yield conservative estimates because the natural history hazard function may level off around 7 years after infection [J. C. M. Hendriks et al., AIDS 7, 231 (1993)]. The Weibull hazard, in contrast, continues to increase. To reflect that progression rates appear to be slower with infection at younger ages, the age-specific hazard of progression for the fast model was assumed to increase (decrease) by the factor 1.042 (0.960) per year increase (decrease) in the age at infection compared to a person aged 30 years at infection, as derived in [9].
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    • The estimated linear slope effect was 0.01 per year at 2.6 years after infection and the corresponding age effect was 1.037 [9]. Both the fast and slow estimates of the incubation distribution were derived from a large cohort study of HIV-infected homosexual men [R. J. Biggar and the International Registry of Seroconverters, AIDS 4, 1059 (1990)]
    • The estimated linear slope effect was 0.01 per year at 2.6 years after infection and the corresponding age effect was 1.037 [9]. Both the fast and slow estimates of the incubation distribution were derived from a large cohort study of HIV-infected homosexual men [R. J. Biggar and the International Registry of Seroconverters, AIDS 4, 1059 (1990)].
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    • Concorde Coordinating Committee
    • Therapy was assumed to reduce the hazard of AIDS among treated individuals by the factor 0.50 for persons infected for about 5 years, and then to wear off [15]. The estimated cumulative proportion in treatment before AIDS was 40% for white males and 20% for other demographic groups. Therapy was assumed to have been introduced in April 1987 among white men and women and in April 1988 among other groups. These parameters are broadly consistent with clinical trial results, and with estimates of the extent of therapy use in different groups [N. M. H. Graham et al, J-AIDS 4, 267 (1991)
    • Therapy was assumed to reduce the hazard of AIDS among treated individuals by the factor 0.50 for persons infected for about 5 years, and then to wear off [15]. The estimated cumulative proportion in treatment before AIDS was 40% for white males and 20% for other demographic groups. Therapy was assumed to have been introduced in April 1987 among white men and women and in April 1988 among other groups. These parameters are broadly consistent with clinical trial results [Concorde Coordinating Committee, Lancet 343, 871 (1994)] and with estimates of the extent of therapy use in different groups [N. M. H. Graham et al, J-AIDS 4, 267 (1991)
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    • To estimate age-specific prevalence at time T, note that individuals aged k years represent the surviving members of the cohort born at time T-k. Prevalence is estimated as the cumulative probability that a member of this cohort becomes infected as of T minus the cumulative probability that a member dies of AIDS as of r. These quantities can be estimated with actuarial formulas applied to census and AIDS mortality data and the results from the backcalculations
    • To estimate age-specific prevalence at time T, note that individuals aged k years represent the surviving members of the cohort born at time T-k. Prevalence is estimated as the cumulative probability that a member of this cohort becomes infected as of T minus the cumulative probability that a member dies of AIDS as of r. These quantities can be estimated with actuarial formulas applied to census and AIDS mortality data and the results from the backcalculations.
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    • I gratefully acknowledge M. Morgan for providing national AIDS surveillance data, T. Green for calculating the reporting delays, J. Smith of Information Management Systems for data management, and J. M. Karon and R. J. Biggar for many helpful discussions
    • I gratefully acknowledge M. Morgan for providing national AIDS surveillance data, T. Green for calculating the reporting delays, J. Smith of Information Management Systems for data management, and J. M. Karon and R. J. Biggar for many helpful discussions.
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    • Power, M.E.1    Parker, M.S.2
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    • 84931369170 scopus 로고    scopus 로고
    • (six replicates per predator species; 10 grazers and one predator per tub) experienced no mortality over 24 hours, whereas a representative grazer, the mayfly Centroptilum, experienced 50.7 ± 24.5% (SD) mortality due to predation pooled across all replicates of all predator species
    • Dicosmoecus exposed to seven predator species in 12.6-liter tubs (six replicates per predator species; 10 grazers and one predator per tub) experienced no mortality over 24 hours, whereas a representative grazer, the mayfly Centroptilum, experienced 50.7 ± 24.5% (SD) mortality due to predation pooled across all replicates of all predator species.
    • Dicosmoecus Exposed to Seven Predator Species in 12.6-Liter Tubs
  • 156
    • 84931477605 scopus 로고    scopus 로고
    • We visually counted all fish (Hesperoleucas symmetricus and Gasterosteus aculeatus) and odonates (primarily Aeshna californica and Archilestes californica) in the entire channel and counted all grazing insects [predominantly Centroptilum, Nixe, and Paroleptophlebia (Ephemeroptera); Mysticides, Lepidosoma, Tinodes, and Gumaga (Trichoptera); Ferrissia and Physella (Pulmonata); and Eubrianix (Psephenidae)], except for midge (Chironomidae) larvae, on the top and bottom of each tile. Midges were counted on only one tile because of their high abundance. We collected benthic algae (largely a mixture of Cladophora glomerata, Nostoc spp., and Epithemia spp.) from one randomly selected tile in each treatment by scraping the tile with a razor blade and measuring ashfree dry weight in the laboratory. All floating algal mats in a channel were collected with an aquarium net, spun in a salad spinner for a standard 50 turns to remove excess water, and weighed. Subsamples of floating algae were collected, dried, weighed, and analyzed through measurement of ash-free dry weight to calibrate wet mass with ashfree dry weight. We used a blocked, two-way MANOVA to test for community-wide differences among treatments, and then tested for the specific differences predicted a priori by the model, using one-tailed paired t tests
    • We visually counted all fish (Hesperoleucas symmetricus and Gasterosteus aculeatus) and odonates (primarily Aeshna californica and Archilestes californica) in the entire channel and counted all grazing insects [predominantly Centroptilum, Nixe, and Paroleptophlebia (Ephemeroptera); Mysticides, Lepidosoma, Tinodes, and Gumaga (Trichoptera); Ferrissia and Physella (Pulmonata); and Eubrianix (Psephenidae)], except for midge (Chironomidae) larvae, on the top and bottom of each tile. Midges were counted on only one tile because of their high abundance. We collected benthic algae (largely a mixture of Cladophora glomerata, Nostoc spp., and Epithemia spp.) from one randomly selected tile in each treatment by scraping the tile with a razor blade and measuring ashfree dry weight in the laboratory. All floating algal mats in a channel were collected with an aquarium net, spun in a salad spinner for a standard 50 turns to remove excess water, and weighed. Subsamples of floating algae were collected, dried, weighed, and analyzed through measurement of ash-free dry weight to calibrate wet mass with ashfree dry weight. We used a blocked, two-way MANOVA to test for community-wide differences among treatments, and then tested for the specific differences predicted a priori by the model, using one-tailed paired t tests.
  • 158
  • 160
    • 84931341809 scopus 로고    scopus 로고
    • Methods are described in [6]. Data were taken from survey locations described in [6] and from surveys of reaches of the Mad River (regulated) and Van Duzen River (unregulated) in Six Rivers National Forest, CA, conducted throughout the summer of 1994. All variables except algal occurrence were logtransformed before analysis to stabilize the variance
    • Methods are described in [6]. Data were taken from survey locations described in [6] and from surveys of reaches of the Mad River (regulated) and Van Duzen River (unregulated) in Six Rivers National Forest, CA, conducted throughout the summer of 1994. All variables except algal occurrence were logtransformed before analysis to stabilize the variance.
  • 180
    • 0003603864 scopus 로고
    • Chapman and Hall, London
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    • (1994) Rarity
    • Gaston, K.J.1
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    • I. Hanski, Oikos 62, 88 (1991).
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    • Hanski, I.1
  • 188
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    • To our knowledge, the only reference to a possible connection between the SA and DA curves is by, in Species Diversity in Ecological Communities: Historical and Geographical Perspectives, R. E. Ricklefs and D. Schluter, Eds. (Univ. of Chicago Press, Chicago
    • To our knowledge, the only reference to a possible connection between the SA and DA curves is by I. Hanski, J. Kouki, and A. Halkka [in Species Diversity in Ecological Communities: Historical and Geographical Perspectives, R. E. Ricklefs and D. Schluter, Eds. (Univ. of Chicago Press, Chicago, 1993), p. 108.
    • (1993)
    • Hanski, I.1    Kouki, J.2    Halkka, A.3
  • 189
    • 84931389120 scopus 로고    scopus 로고
    • We use the term "island" to refer both to true and habitat islands, and to what are called habitat patches, or fragments, in the metapopulation literature [7]
    • We use the term "island" to refer both to true and habitat islands, and to what are called habitat patches, or fragments, in the metapopulation literature [7].
  • 190
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    • Without any loss of generality, we assume that mw equals unity
    • Without any loss of generality, we assume that mw equals unity.
  • 193
    • 0028173771 scopus 로고
    • the latter two references, the more general relation m, = e/Kfj is used, but we assume here for simplicity that x = 1, which is a good approximation for many species. The rate parameter e has been here absorbed in the unit of island area, to give the per-year extinction probability 1-e~]/A for species with w = 1. A scaling constant d is given by d = A' I A, where A' is island area in (say) kilometers squared, d may be calculated from knowledge of the per-year extinction probability and A
    • J.Anim. Ecol. 63, 151 (1994). In the latter two references, the more general relation m, = e/Kfj is used, but we assume here for simplicity that x = 1, which is a good approximation for many species. The rate parameter e has been here absorbed in the unit of island area, to give the per-year extinction probability 1-e~]/A for species with w = 1. A scaling constant d is given by d = A' I A, where A' is island area in (say) kilometers squared, d may be calculated from knowledge of the per-year extinction probability and A'.
    • (1994) J.Anim. Ecol , vol.63 , Issue.151
  • 194
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    • Schoener, T.W.1
  • 195
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    • Somewhat confusingly, the classical metapopulation scenario, where there is no external mainland, is referred to as the "mainland" regression in the species-area literature
    • Somewhat confusingly, the classical metapopulation scenario, where there is no external mainland, is referred to as the "mainland" regression in the species-area literature.
  • 196
    • 84931476223 scopus 로고    scopus 로고
    • The equilibrium probability of species i occupying island j, p*-, which is called the incidence, Jij, is obtained from Equation 1 as [Equation Found] In the metapopulation model, the incidences can be calculated only numerically. Substituting Equation 2 into the expression C* = cWiXJijAj, which gives the equilibrium value of Ci(t) in the metapopulation model, we obtain[Equation Found] from which C* can be solved provided that cwf X A2-> 1, which is a necessary and sufficient condition for species i to persist in the network of islands. The incidences can then be calculated from Equation 2
    • The equilibrium probability of species i occupying island j, p*-, which is called the incidence, Jij, is obtained from Equation 1 as [Equation Found] In the metapopulation model, the incidences can be calculated only numerically. Substituting Equation 2 into the expression C* = cWiXJijAj, which gives the equilibrium value of Ci(t) in the metapopulation model, we obtain[Equation Found] from which C* can be solved provided that cwf X A2-> 1, which is a necessary and sufficient condition for species i to persist in the network of islands. The incidences can then be calculated from Equation 2.
  • 202
    • 84931334499 scopus 로고    scopus 로고
    • The nonlinear logistic model can be linearized with the logit-transformation, log[P/(l-P)] = a + blogiv, which we apply throughout this report
    • The nonlinear logistic model can be linearized with the logit-transformation, log[P/(l-P)] = a + blogiv, which we apply throughout this report.
  • 203
    • 84931364200 scopus 로고    scopus 로고
    • Assuming that Q (species number in the pool) is large and that log if is uniformly distributed with zero mean, we obtain after some calculation the expected number of species on island j as[Equation Found] 20.
    • Assuming that Q (species number in the pool) is large and that log if is uniformly distributed with zero mean, we obtain after some calculation the expected number of species on island j as[Equation Found] 20.
  • 204
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    • Denoting the per-year colonization and extinction probabilities by A and /u, we obtain[Equation Found] where E denotes the expected value. That the slope of the SA curve depends on the ratio of colonization to extinction probabilities has been suggested by
    • Denoting the per-year colonization and extinction probabilities by A and /u, we obtain[Equation Found] where E denotes the expected value. That the slope of the SA curve depends on the ratio of colonization to extinction probabilities has been suggested by R. E. Ricklefs and G. W. Cox [Am. Nat. 106, 195 (1972)]
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    • [Equation Found] 23. We derived the slope values [19] also for backto-back exponential and lognormal distributions of w. The expressions are more complicated in these cases, but the results are very similar
    • M. P. Johnson and D. S. Simberloff [Biogeogr. 1, 149 (1974)]. [Equation Found] 23. We derived the slope values [19] also for backto-back exponential and lognormal distributions of w. The expressions are more complicated in these cases, but the results are very similar.
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    • The moth example includes 46 islands located about 15 km off the mainland in southwest Finland. Moths were trapped with sugar-bait traps in summer 1993. The parameter log w gives the abundance on mainland
    • M. Nieminen, Oecologia 108, 643 (1996). The moth example includes 46 islands located about 15 km off the mainland in southwest Finland. Moths were trapped with sugar-bait traps in summer 1993. The parameter log w gives the abundance on mainland.
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    • The bird examples are from studies in Poland (Witkowski and Plonka) and The Netherlands (Harms and Opdam). "Islands" in this instance are habitat islands on mainland. The parameter logw in Figure 1H gives the estimated density of territories
    • The bird examples are from studies in Poland (Witkowski and Plonka) and The Netherlands (Harms and Opdam). "Islands" in this instance are habitat islands on mainland. The parameter logw in Figure 1H gives the estimated density of territories.
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    • for comments on the manuscript. W. W. Murdoch and National Center for Ecological Analysis and Synthesis (NCEAS) in Santa Barbara are thanked for supporting this research
    • We thank F. Adler, J. Brown, M. Camara, E. Connor, M. Kuussaari, J. Lawton, A. Moilanen, and T. Schoener for comments on the manuscript. W. W. Murdoch and National Center for Ecological Analysis and Synthesis (NCEAS) in Santa Barbara are thanked for supporting this research.
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    • The deep borehole is located in a building, and the liquid surface in the borehole is found at a depth of 40 m. The temperatures measured in the top 40 m are very disturbed, so we used measurements from an air-filled shallow borehole (100 m) near the borehole
    • The deep borehole is located in a building, and the liquid surface in the borehole is found at a depth of 40 m. The temperatures measured in the top 40 m are very disturbed, so we used measurements from an air-filled shallow borehole (100 m) near the borehole.
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    • Between 50 and 20 ka, the ice thickness was 50 m less than at present, even though the ice sheet covered a larger area. The maximum ice thickness of 3230 m is found at 10 ka, after which the ice thickness gradually has decreased to the present 3028.6 m. The depression and uplift of the bedrock influences the elevation of the surface
    • Between 50 and 20 ka, the ice thickness was 50 m less than at present, even though the ice sheet covered a larger area. The maximum ice thickness of 3230 m is found at 10 ka, after which the ice thickness gradually has decreased to the present 3028.6 m. The depression and uplift of the bedrock influences the elevation of the surface [S. J. Johnsen, D. Dahl-Jensen, W. Dansgaard, N. S. Gundestrup, Tellus 5 47, 624(1995)].
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    • Johnsen, S.J.1    Dahl-Jensen, D.2    Dansgaard, W.3    Gundestrup, N.S.4
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    • The past accumulation rates are determined by coupling them to the past (unknown) temperature through the relation A(T) = Ao exp[0.0467(T-To)-0.000227(7-7b)2], where A(T) is the accumulation rate at the surface temperature T, Ao is the present ice accumulation rate, which is 0.23 m/year at GRIP and 0.49 m/year at Dye 3, and To is the present surface temperatures at the sites:-31.7°C at GRIP and-20.1°C at Dye 3, respectively [9]
    • The past accumulation rates are determined by coupling them to the past (unknown) temperature through the relation A(T) = Ao exp[0.0467(T-To)-0.000227(7-7b)2], where A(T) is the accumulation rate at the surface temperature T, Ao is the present ice accumulation rate, which is 0.23 m/year at GRIP and 0.49 m/year at Dye 3, and To is the present surface temperatures at the sites:-31.7°C at GRIP and-20.1°C at Dye 3, respectively [9].
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    • Our Monte Carlo scheme is a random walk in the high dimensional space of all possible models, m (temperature histories and geothermal heat flow densities). The temperature history has been divided in 125 intervals (interval length is 25 ky at 450 ka and 10 years at present). Including the geothermal heat flow density as an unknown the model space is 126-dimensional. In each step of the random walk, a perturbed model, wipert of the current model vector m1 is proposed. The next model becomes equal to mpert with an acceptance probability ^accept = min{l, exp(-[5(TOpert)-Sim1)])}, where S(m) = Zj(gHm)-dJ obs)2, which is the misfit function measuring the difference between g{m), the calculated borehole temperatures, and dObS, the observed temperatures. If the perturbated model is rejected, the next model becomes equal to ml and a new perturbed model is proposed. To ensure an efficient sampling of all possible models, we developed ways of choosing the temperature histories and geothermal heat flow densities to be tested. The main scheme to perturb the models is to randomly select one of the 126 temperature/heat flow density parameters and change its value to a new value chosen uniformly at random within a given interval. A singular value decomposition (SVD) of the matrix G = {dgj/dnii}, evaluated in a near-optimal model, yields a set of eigenvectors in the model space whose orientations reveal efficient directions of perturbation for the random walk. The SVD method is included as a possible method of perturbing models especially in the start of the process as it speeds the Monte Carlo scheme significantly
    • Our Monte Carlo scheme is a random walk in the high dimensional space of all possible models, m (temperature histories and geothermal heat flow densities). The temperature history has been divided in 125 intervals (interval length is 25 ky at 450 ka and 10 years at present). Including the geothermal heat flow density as an unknown the model space is 126-dimensional. In each step of the random walk, a perturbed model, wipert of the current model vector m1 is proposed. The next model becomes equal to mpert with an acceptance probability ^accept = min{l, exp(-[5(TOpert)-Sim1])}, where S(m) = Zj(gHm)-dJ obs)2, which is the misfit function measuring the difference between g{m), the calculated borehole temperatures, and dObS, the observed temperatures. If the perturbated model is rejected, the next model becomes equal to ml and a new perturbed model is proposed. To ensure an efficient sampling of all possible models, we developed ways of choosing the temperature histories and geothermal heat flow densities to be tested. The main scheme to perturb the models is to randomly select one of the 126 temperature/heat flow density parameters and change its value to a new value chosen uniformly at random within a given interval. A singular value decomposition (SVD) of the matrix G = {dgj/dnii}, evaluated in a near-optimal model, yields a set of eigenvectors in the model space whose orientations reveal efficient directions of perturbation for the random walk. The SVD method is included as a possible method of perturbing models especially in the start of the process as it speeds the Monte Carlo scheme significantly.
  • 275
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    • Of the 3.3 x 10(i models tested during the random walk 30% have been accepted by the Monte Carlo scheme [16]. Every 500 is chosen of those where the misfit function S [16] is less than the variance of the observations. The waiting time of 500 has been chosen to exceed the maximum correlation length of the output model parameters. This is a necessary condition for the 2000 models to be uncorrelated. To further ensure that the output models were uncorrelated, the random walk was frequently restarted at several random selected points in the model space
    • Of the 3.3 x 10(i models tested during the random walk 30% have been accepted by the Monte Carlo scheme [16]. Every 500 is chosen of those where the misfit function S [16] is less than the variance of the observations. The waiting time of 500 has been chosen to exceed the maximum correlation length of the output model parameters. This is a necessary condition for the 2000 models to be uncorrelated. To further ensure that the output models were uncorrelated, the random walk was frequently restarted at several random selected points in the model space.
  • 276
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    • The probabilistic formulation of the inverse problem leads to definition of a probability distribution in the model space, describing the likelihood of possible temperature histories and geothermal heat flow densities. The Monte Carlo scheme is constructed to sample according to this probability distribution. The histograms in Figure 2 describe the probability distribution of the geothermal heat flow density and temperatures at times before present. The maxima in the histograms thus describe the most likely values. The method does not constrain the distributions to have a single maximum, indeed there could be histograms with several maxima, reflecting that more than one value of the temperature at this time would give a good fit to the observed temperature in the borehole. The histograms however, are all seen to have a well-defined zone with most likely past temperatures. A soft curve is fitted to the histograms and the maximum value is taken as the most likely value. The standard deviations shown in Figure 3 are derived as deviations from the maximum value
    • The probabilistic formulation of the inverse problem leads to definition of a probability distribution in the model space, describing the likelihood of possible temperature histories and geothermal heat flow densities. The Monte Carlo scheme is constructed to sample according to this probability distribution. The histograms in Figure 2 describe the probability distribution of the geothermal heat flow density and temperatures at times before present. The maxima in the histograms thus describe the most likely values. The method does not constrain the distributions to have a single maximum, indeed there could be histograms with several maxima, reflecting that more than one value of the temperature at this time would give a good fit to the observed temperature in the borehole. The histograms however, are all seen to have a well-defined zone with most likely past temperatures. A soft curve is fitted to the histograms and the maximum value is taken as the most likely value. The standard deviations shown in Figure 3 are derived as deviations from the maximum value.
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    • order to produce a past temperature record from the calculated past surface temperatures, the temperatures have been corrected to the present elevation of the GRIP site (and Dye 3 site respectively) using the surface elevation changes described in [9] and a lapse rate of 0.006 K/m
    • In order to produce a past temperature record from the calculated past surface temperatures, the temperatures have been corrected to the present elevation of the GRIP site (and Dye 3 site respectively) using the surface elevation changes described in [9] and a lapse rate of 0.006 K/m.
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    • The amplitude of the warming at 1930 A.D. must be considered to be more uncertain. The information leading to this result are the measured temperatures in an open shallow borehole, where air movements could influence the measurements.
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    • To comply with this resolution the time steps have been chosen with increasing length back in time. The increasing length of the time steps can be considered as an efficient way of calculating the mean temperatures in the intervals so full available resolution is kept but the calculations are rationalized.
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    • [7], it is argued that parameter combinations of mean glacial temperature, mean glacial accumulation, and geothermal heat flow density can be found that fit the Dye 3 measurements due to the reduced resolution of the climate history reaching further back than 7 ka. A combination with a geothermal heat flow density of 38.7mW/m2 was chosen corresponding to a mean glacial temperature 12 K colder than the present temperatures. If a value of 51 mW/m2 is chosen as that found for our inversion, the mean glacial temperature is 19 K colder than the present, which is well in agreement with the results found for the GRIP reconstruction. Comparison of the Dye 3 temperature history presented in [7] and that presented here shows a general good agreement for the last 7 ky. The history presented in [7] is more intuitive and less detailed, and the history has not been corrected for elevation changes. The ice thickness was assumed constant in this reconstruction
    • In [7], it is argued that parameter combinations of mean glacial temperature, mean glacial accumulation, and geothermal heat flow density can be found that fit the Dye 3 measurements due to the reduced resolution of the climate history reaching further back than 7 ka. A combination with a geothermal heat flow density of 38.7mW/m2 was chosen corresponding to a mean glacial temperature 12 K colder than the present temperatures. If a value of 51 mW/m2 is chosen as that found for our inversion, the mean glacial temperature is 19 K colder than the present, which is well in agreement with the results found for the GRIP reconstruction. Comparison of the Dye 3 temperature history presented in [7] and that presented here shows a general good agreement for the last 7 ky. The history presented in [7] is more intuitive and less detailed, and the history has not been corrected for elevation changes. The ice thickness was assumed constant in this reconstruction. L. K. Barlov, J. C. Rogers, M. C. Serreze, R. C. Barry, J. Geophys. Res. 102, 26333 (1997).
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    • Blocks were spaced at least 1 km apart. Within each block, we surveyed checkerboard grids of 20-by-20 points with 30.5-m spacing and used these grids for snowshoe hare live trapping. Two experimental areas were provided with supplemental food (commercial rabbit chow, 16% protein) year round. In the summer of 1987, we built one electric fence around 1 km2 to exclude mammalian predators, and over the following year we covered 10 ha with monofilament to reduce avian predation. The monofilament was never effective in preventing avian predation inside the electric fences, and consequently we did not rely on it as a part of the treatment. In the summer of 1988, we built a second electric fence around 1 km2 to use for the combined predator reduction-food addition treatment. We modified the design of the electric fences in 1988 to make them more effective, and since then they have worked effectively to prevent mammalian predators from entering the area. The fences are permeable to snowshoe hares. We could not replicate either the predator reduction or the predator reduction-food addition treatment because of maintenance costs and the difficulty of maintaining electric fences in the Yukon winter with-45°C temperatures. The fences had to be checked every day during winter. From 1976 to 1985, we trapped hares in six areas within the main study region and found that their population trajectories were very similar [3]. We thus have no reason to suspect strong area effects on the unreplicated predator reduction plots
    • Blocks were spaced at least 1 km apart. Within each block, we surveyed checkerboard grids of 20-by-20 points with 30.5-m spacing and used these grids for snowshoe hare live trapping. Two experimental areas were provided with supplemental food (commercial rabbit chow, 16% protein) year round. In the summer of 1987, we built one electric fence around 1 km2 to exclude mammalian predators, and over the following year we covered 10 ha with monofilament to reduce avian predation. The monofilament was never effective in preventing avian predation inside the electric fences, and consequently we did not rely on it as a part of the treatment. In the summer of 1988, we built a second electric fence around 1 km2 to use for the combined predator reduction-food addition treatment. We modified the design of the electric fences in 1988 to make them more effective, and since then they have worked effectively to prevent mammalian predators from entering the area. The fences are permeable to snowshoe hares. We could not replicate either the predator reduction or the predator reduction-food addition treatment because of maintenance costs and the difficulty of maintaining electric fences in the Yukon winter with-45°C temperatures. The fences had to be checked every day during winter. From 1976 to 1985, we trapped hares in six areas within the main study region and found that their population trajectories were very similar [3]. We thus have no reason to suspect strong area effects on the unreplicated predator reduction plots.
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    • We used three control areas but were not able to trap hares in all of them every year. We have more detailed data on hares from control area 1. The three control areas had quite different histories during the increase phase from 1986 to 1988. Control area 3 reached its greatest hare density in 1988 and remained at a plateau until 1990. Control area 2 reached its peak density in 1990, and control area 1 reached its peak in 1989. By the late peak in 1990 and during the decline phase, the control areas were much more similar to each other in hare densities
    • We used three control areas but were not able to trap hares in all of them every year. We have more detailed data on hares from control area 1. The three control areas had quite different histories during the increase phase from 1986 to 1988. Control area 3 reached its greatest hare density in 1988 and remained at a plateau until 1990. Control area 2 reached its peak density in 1990, and control area 1 reached its peak in 1989. By the late peak in 1990 and during the decline phase, the control areas were much more similar to each other in hare densities.
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    • The electric fence was 10-stranded, 2.2 m in height, and carried 8600 V. Snow tracking of mammalian predators meeting the fence illustrated its effectiveness. We excluded mammalian predators virtually continuously from January 1989 onward. Our attempts to use monofilament fishing line as a deterrent to birds of prey was largely ineffective because ice formation and snow accumulation on the lines in winter caused them to break or collapse to the ground. We used mononlament on 10 ha of the predator exclosure but did not attempt to use it on the combination treatment area. The predator exclosures thus were mammalian predator exclosures and were still subject to avian predation
    • The electric fence was 10-stranded, 2.2 m in height, and carried 8600 V. Snow tracking of mammalian predators meeting the fence illustrated its effectiveness. We excluded mammalian predators virtually continuously from January 1989 onward. Our attempts to use monofilament fishing line as a deterrent to birds of prey was largely ineffective because ice formation and snow accumulation on the lines in winter caused them to break or collapse to the ground. We used mononlament on 10 ha of the predator exclosure but did not attempt to use it on the combination treatment area. The predator exclosures thus were mammalian predator exclosures and were still subject to avian predation.
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    • We fertilized two 1-km2 blocks of forest with commercial fertilizer. In May 1987, we used ammonium nitrate at 25 g/m2. In May 1988, we switched to NPK fertilizer and used 17.5 g of N/m2, 5 g of P/m2, and 2.5 g of K/m2. In 1989, we used half this amount, and in the years 1990 to 1994 we used the full amount as in 1988. The fertilizer was spread aerially and we did ground checks to make sure it was uniformly spread. We do not present the data here to show the plant growth responses, but all elements of the flora responded dramatically to the added nutrients, unpublished data
    • We fertilized two 1-km2 blocks of forest with commercial fertilizer. In May 1987, we used ammonium nitrate at 25 g/m2. In May 1988, we switched to NPK fertilizer and used 17.5 g of N/m2, 5 g of P/m2, and 2.5 g of K/m2. In 1989, we used half this amount, and in the years 1990 to 1994 we used the full amount as in 1988. The fertilizer was spread aerially and we did ground checks to make sure it was uniformly spread. We do not present the data here to show the plant growth responses, but all elements of the flora responded dramatically to the added nutrients (C. J. Krebs et al., unpublished data).
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    • We thank the Natural Sciences and Engineering Research Council of Canada for supporting this research program through a Collaborative Special Project grant; the Arctic Institute of North America, University of Calgary, for the use of the Kluane Lake research station; and all the graduate students, technicians, and undergraduates who have assisted in this project over the past 9 years, in particular
    • We thank the Natural Sciences and Engineering Research Council of Canada for supporting this research program through a Collaborative Special Project grant; the Arctic Institute of North America, University of Calgary, for the use of the Kluane Lake research station; and all the graduate students, technicians, and undergraduates who have assisted in this project over the past 9 years, in particular V. Nams, S. Schweiger, and M. O'Donoghue.
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  • 442
    • 84931451481 scopus 로고    scopus 로고
    • Voucher specimens are deposited in the Museum of Natural Science, Louisiana State University (LSUMZ) or the New Mexico Museum of Natural History (NMMNH) and are as follows: Orthogeomys underwoodi (LSUMZ 29493), O. hispidus (LSUMZ 29231), O. cavator (LSUMZ 29253), O. cherriei (LSUMZ 29539), O. heterodus (LSUMZ 29501), Geomys breviceps (LSUMZ 33940), G. personatus (LSUMZ 31460), G. bursarius halli (LSUMZ 31463; designated "a" in Fig. 2), G. b. majusculus (LSUMZ 31448; designated "b" in Fig. 2), Cratogeomys castanops (LSUMZ 31455), C. merriami (LSUMZ 34343), Pappogeomys bulleri (LSUMZ 34338), Zygogeomys trichopus (LSUMZ 34340), Thomomys bottae (LSUMZ 29320 and 29569), and T. talpoides (NMMNH 1634 and 1637
    • Voucher specimens are deposited in the Museum of Natural Science, Louisiana State University (LSUMZ) or the New Mexico Museum of Natural History (NMMNH) and are as follows: Orthogeomys underwoodi (LSUMZ 29493), O. hispidus (LSUMZ 29231), O. cavator (LSUMZ 29253), O. cherriei (LSUMZ 29539), O. heterodus (LSUMZ 29501), Geomys breviceps (LSUMZ 33940), G. personatus (LSUMZ 31460), G. bursarius halli (LSUMZ 31463; designated "a" in Fig. 2), G. b. majusculus (LSUMZ 31448; designated "b" in Fig. 2), Cratogeomys castanops (LSUMZ 31455), C. merriami (LSUMZ 34343), Pappogeomys bulleri (LSUMZ 34338), Zygogeomys trichopus (LSUMZ 34340), Thomomys bottae (LSUMZ 29320 and 29569), and T. talpoides (NMMNH 1634 and 1637).
  • 443
    • 0000311591 scopus 로고
    • Pocket gophers were trapped, killed, and immediately brushed to recover lice. Gopher tissues and lice were stored at negative 70°Celsius. DNA extractions from gophers followed the phenol-chloroform technique, D. M. Hillis and C. Moritz, Eds. (Sinauer, Sunderland, MA
    • Pocket gophers were trapped, killed, and immediately brushed to recover lice. Gopher tissues and lice were stored at negative 70°Celsius. DNA extractions from gophers followed the phenol-chloroform technique [D. M. Hillis, A. Larson, S. K. Davis, E. A. Zimmer, in Molecular Systematics, D. M. Hillis and C. Moritz, Eds. (Sinauer, Sunderland, MA, 1990), pp. 318-370].
    • (1990) Molecular Systematics , pp. 318-370
    • Hillis, D.M.1    Larson, A.2    Davis, S.K.3    Zimmer, E.A.4
  • 444
    • 0026822397 scopus 로고
    • DNA extractions from lice followed a modification of the protocol described by
    • DNA extractions from lice followed a modification of the protocol described by H. Liu and A. T. Beckenbach [Mol. Phylogenet. Evol. 1, 41 (1992)]
    • (1992) Mol. Phylogenet. Evol , vol.1 , Issue.41
    • Liu, H.1    Beckenbach, A.T.2
  • 445
    • 84931308101 scopus 로고    scopus 로고
    • used two lice from each gopher. One /JI of the extraction solution was used for DNA amplification in a 50-/J1 reaction. A 379-base pair (bp) region of the mitochondrial COI gene was amplified by polymerase chain reaction (PCR) with two degenerate primers: L6625 (5'-CCGGATCCTTYTGRTTYTTYGGNCAYCC-3') and H7005 (5'-CCGGATCC ACNACRTARTANGTRTCRTG-3')-Primer names refer to the 3' position of each primer relative to the human mitochondrial genome [S. Anderson et ah, Nature 290, 457 (1981)]. Double-stranded amplifications were done by four cycles of 1 min of denaturation (95"Celsius), 1 min of annealing (45"Celsius), and 1 min of extension (72°Celsius), followed by 30 cycles at reduced denaturation temperatures (93°Celsius) and increased annealing temperatures (60° Celsius). Methods for production of single-stranded templates and for sequencing of single-stranded products are given elsewhere [18]. Because no two sequences were identical either within or between lice and gophers, cross-contamination is not suspected. Gopher and louse sequences are available through GenBank (accession numbers L32682 to L32696 for gophers and L32665 to L32681 for lice)
    • and used two lice from each gopher. One /JI of the extraction solution was used for DNA amplification in a 50-/J1 reaction. A 379-base pair (bp) region of the mitochondrial COI gene was amplified by polymerase chain reaction (PCR) with two degenerate primers: L6625 (5'-CCGGATCCTTYTGRTTYTTYGGNCAYCC-3') and H7005 (5'-CCGGATCC ACNACRTARTANGTRTCRTG-3')-Primer names refer to the 3' position of each primer relative to the human mitochondrial genome [S. Anderson et ah, Nature 290, 457 (1981)]. Double-stranded amplifications were done by four cycles of 1 min of denaturation (95"Celsius), 1 min of annealing (45"Celsius), and 1 min of extension (72°Celsius), followed by 30 cycles at reduced denaturation temperatures (93°Celsius) and increased annealing temperatures (60° Celsius). Methods for production of single-stranded templates and for sequencing of single-stranded products are given elsewhere [18]. Because no two sequences were identical either within or between lice and gophers, cross-contamination is not suspected. Gopher and louse sequences are available through GenBank (accession numbers L32682 to L32696 for gophers and L32665 to L32681 for lice).
  • 446
    • 0001140522 scopus 로고
    • D. M. Hillis and C. Moritz, Eds. (Sinauer, Sunderland, MA
    • D. L. Swofford and G. J. Olsen, in Molecular Systematics, D. M. Hillis and C. Moritz, Eds. (Sinauer, Sunderland, MA, 1990), pp. 411-501
    • (1990) Molecular Systematics , pp. 411-501
    • Swofford, D.L.1    Olsen, G.J.2
  • 449
    • 84931299251 scopus 로고
    • We used the PAUP program (Phylogenetic Analysis Using Parsimony, 3.1.1, D. L. Swof ford, Illinois Natural History Survey) for phylogenetic analyses of the sequence data. of the 134 variable sites in pocket gophers (178 in lice), 113 were phylogenetically informative (142 in lice). To compensate for the effects of multiple mutations at nucleotide positions, we used a parsimony analysis in which transitions at first and third codon positions were designated as more likely than transversions (with a 10:1 step matrix for gophers and a 17:1 step matrix for lice). These empirical estimates of transition bias represent maximal values, which were observed between taxa with the most similar sequences (8.7% sequence divergence between the most similar gophers; 4.7% between the most similar lice). Because the effects of multiple mutations should be least for closely related taxa, we consider these to be reasonable approximations of the actual transition bias. For each database (gophers and lice) we conducted 100 heuristic searches, varying the addition order of taxa (using the random addition option of PAUP) and using alternate branch-swapping algorithms (using the TBR and SPR options). All gopher and louse parsimony trees contained significant phylogenetic signal (g\ <-0.54, P < 0.01) [D. M. Hillis and J. P. Huelsenbeck, J. Hered. 83, 189 (1992)]. Gophers in the genus Thomomys and lice of the genus Thomomydoecus were designated as outgroups. The outgroup status of these taxa is supported by previous morphological and molecular analyses [16, 17] [R. A. Hellenthal and R. D. Price
    • We used the PAUP program (Phylogenetic Analysis Using Parsimony, 3.1.1, D. L. Swof ford, Illinois Natural History Survey) for phylogenetic analyses of the sequence data. of the 134 variable sites in pocket gophers (178 in lice), 113 were phylogenetically informative (142 in lice). To compensate for the effects of multiple mutations at nucleotide positions, we used a parsimony analysis in which transitions at first and third codon positions were designated as more likely than transversions (with a 10:1 step matrix for gophers and a 17:1 step matrix for lice). These empirical estimates of transition bias represent maximal values, which were observed between taxa with the most similar sequences (8.7% sequence divergence between the most similar gophers; 4.7% between the most similar lice). Because the effects of multiple mutations should be least for closely related taxa, we consider these to be reasonable approximations of the actual transition bias. For each database (gophers and lice) we conducted 100 heuristic searches, varying the addition order of taxa (using the random addition option of PAUP) and using alternate branch-swapping algorithms (using the TBR and SPR options). All gopher and louse parsimony trees contained significant phylogenetic signal (g\ <-0.54, P < 0.01) [D. M. Hillis and J. P. Huelsenbeck, J. Hered. 83, 189 (1992)]. Gophers in the genus Thomomys and lice of the genus Thomomydoecus were designated as outgroups. The outgroup status of these taxa is supported by previous morphological and molecular analyses [16, 17] [R. A. Hellenthal and R. D. Price, J. Kans. Entomol. Soc. 57, 231 (1984)
    • (1984) Entomol. Soc , vol.57 , pp. 231
    • Kans, J.1
  • 451
    • 84931479497 scopus 로고    scopus 로고
    • We used PHYLIP [Phylogeny Inference Package, 3. 5c, J. Felsenstein, Department of Genetics, University of Washington, Seattle] for maximum-likelihood, Fitch-Margoliash [W. M. Fitch and E. Margoliash, Science 155, 279 (1967)], and neighbor-joining [N. Saitou and M. Nei, Mol. Biol. Evol. 4, 406 (1987)] analyses of the sequence data. Empirical base frequencies and maximal observed transition biases (10:1 for gophers and 17:1 for lice) were used in the maximum-likelihood analysis. The Fitch-Margoliash and neighborjoining analyses were based on distance matrices corrected with the Kimura twoparameter model [substituting maximal observed transition bias values for the default (2:1) value M. Kimura, J. Mol. Evol. 16, 111 (1980)]. We repeated each analysis at least 10 times, varying the input order of taxa using the jumble option of PHYLIP
    • We used PHYLIP [Phylogeny Inference Package, 3. 5c, J. Felsenstein, Department of Genetics, University of Washington, Seattle] for maximum-likelihood, Fitch-Margoliash [W. M. Fitch and E. Margoliash, Science 155, 279 (1967)], and neighbor-joining [N. Saitou and M. Nei, Mol. Biol. Evol. 4, 406 (1987)] analyses of the sequence data. Empirical base frequencies and maximal observed transition biases (10:1 for gophers and 17:1 for lice) were used in the maximum-likelihood analysis. The Fitch-Margoliash and neighborjoining analyses were based on distance matrices corrected with the Kimura twoparameter model [substituting maximal observed transition bias values for the default (2:1) value M. Kimura, J. Mol. Evol. 16, 111 (1980)]. We repeated each analysis at least 10 times, varying the input order of taxa using the jumble option of PHYLIP.
  • 452
    • 84931457751 scopus 로고    scopus 로고
    • the alternative parsimony tree for pocket gophers, the phylogenetic positions of P. bulleri and Z. trichopus were reversed and the two species of Cratogeomys were not depicted as sister taxa
    • In the alternative parsimony tree for pocket gophers, the phylogenetic positions of P. bulleri and Z. trichopus were reversed and the two species of Cratogeomys were not depicted as sister taxa.
  • 453
    • 84931342918 scopus 로고    scopus 로고
    • The neighbor-joining tree differed from the Fitch-Margoliash tree (Fig. IB) only in the placement of P. bulleri (immediately basal to the five-taxon clade containing O. hispidus) and Z. trichopus (basal to the eight-taxon clade containing C. castanops, C. merriami, and P. bulleri)
    • The neighbor-joining tree differed from the Fitch-Margoliash tree (Fig. IB) only in the placement of P. bulleri (immediately basal to the five-taxon clade containing O. hispidus) and Z. trichopus (basal to the eight-taxon clade containing C. castanops, C. merriami, and P. bulleri).
  • 454
    • 0024307824 scopus 로고
    • as used in PHYLIP [12]
    • H. Kishino and M. Hasegawa, J. Mol. Evol. 29, 170 (1989), as used in PHYLIP [12].
    • (1989) J. Mol. Evol , vol.29 , Issue.170
    • Kishino, H.1    Hasegawa, M.2
  • 460
    • 84931472938 scopus 로고    scopus 로고
    • the second parsimony tree, the louse G. actuosi was linked with the oklahomensisgeomydis clade, rather than the texanusewingi clade (as in Fig. 2A). The third tree showed G. thomomyus near the root of the tree between the outgroups T. minor and T. barbarae
    • In the second parsimony tree, the louse G. actuosi was linked with the oklahomensisgeomydis clade, rather than the texanusewingi clade (as in Fig. 2A). The third tree showed G. thomomyus near the root of the tree between the outgroups T. minor and T. barbarae.
  • 461
    • 84931373947 scopus 로고    scopus 로고
    • The neighbor-joining tree was identical to the Fitch-Margoliash tree (Fig. 2B), except that G. thomomyus and G. perotensis were linked as sister taxa (as in the parsimony and maximum-likelihood trees, Fig. 2A) and positioned basal to the G. chapini branch
    • The neighbor-joining tree was identical to the Fitch-Margoliash tree (Fig. 2B), except that G. thomomyus and G. perotensis were linked as sister taxa (as in the parsimony and maximum-likelihood trees, Fig. 2A) and positioned basal to the G. chapini branch.
  • 464
  • 465
    • 84931386846 scopus 로고    scopus 로고
    • The test was based on the criterion of minimum number of independent losses necessary to reconcile the host and parasite trees [22]. Sixteen of the 20 pairwise comparisons were also found to be statistically significant (P <-0.05) according to the criterion of "number of leaves added" [22]. Number of leaves added is equivalent to onehalf the number of "items of error" [G. Nel son and N. Platnick, Systematics and Biogeography: Cladistics and Vicariance (Columbia Univ. Press, New York, 1981)]. The four comparisons that were not statistically significant (according to the criterion of number of leaves added) all involved the louse parsimony tree that depicted the outgroup Thomomydoecus as polyphyletic. The branching structure of this tree is challenged by evidence from previous morphological and allozyme studies [11] supporting monophyly of the louse genus Thomomydoecus
    • The test was based on the criterion of minimum number of independent losses necessary to reconcile the host and parasite trees [22]. Sixteen of the 20 pairwise comparisons were also found to be statistically significant (P <-0.05) according to the criterion of "number of leaves added" [22]. Number of leaves added is equivalent to onehalf the number of "items of error" [G. Nel son and N. Platnick, Systematics and Biogeography: Cladistics and Vicariance (Columbia Univ. Press, New York, 1981)]. The four comparisons that were not statistically significant (according to the criterion of number of leaves added) all involved the louse parsimony tree that depicted the outgroup Thomomydoecus as polyphyletic. The branching structure of this tree is challenged by evidence from previous morphological and allozyme studies [11] supporting monophyly of the louse genus Thomomydoecus.
  • 466
    • 84931423953 scopus 로고    scopus 로고
    • The trees (Fig. 2) were reduced to the largest number of taxa that showed identical branching patterns in the hosts and parasites. All possible combinations of cospeciating taxa were compared. For example, there are four possible combinations of nine cospeciating taxa in Fig. 2A [that is, the nine-taxon gopher tree can include either O. underwoodi or O. cavator (but not both) and G. breviceps or G. personatus (but not both)]. There are 2 possible combinations of 10 cospeciating taxa in Fig. 2B (that is, the tree can include either G. breviceps or G. personatus, but not both). Because most of the uncertainty in the phylogenetic analyses involved branches near the base of the trees, only terminal and subterminal branches were compared between gophers and lice
    • The trees (Fig. 2) were reduced to the largest number of taxa that showed identical branching patterns in the hosts and parasites. All possible combinations of cospeciating taxa were compared. For example, there are four possible combinations of nine cospeciating taxa in Fig. 2A [that is, the nine-taxon gopher tree can include either O. underwoodi or O. cavator (but not both) and G. breviceps or G. personatus (but not both)]. There are 2 possible combinations of 10 cospeciating taxa in Fig. 2B (that is, the tree can include either G. breviceps or G. personatus, but not both). Because most of the uncertainty in the phylogenetic analyses involved branches near the base of the trees, only terminal and subterminal branches were compared between gophers and lice.
  • 467
    • 0014054519 scopus 로고
    • We calculated distance matrices using the maximum-likelihood model [12]. For the 9 cospeciating taxa in Fig. 2A, t = 4.073, P < 0.01. For the 10 cospeciating taxa in Fig. 2B, t = 4.289, P < 0.01. Degrees of freedom were adjusted to n-1, where n = equals number of taxa compared [3]
    • N. Mantel, Cancer Res. 27, 209 (1967). We calculated distance matrices using the maximum-likelihood model [12]. For the 9 cospeciating taxa in Fig. 2A, t = 4.073, P < 0.01. For the 10 cospeciating taxa in Fig. 2B, t = 4.289, P < 0.01. Degrees of freedom were adjusted to n-1, where n = equals number of taxa compared [3].
    • (1967) Cancer Res , vol.27 , Issue.209
    • Mantel, N.1
  • 468
    • 84931478882 scopus 로고
    • Trees for cospeciating taxa (24) were input as user trees into PHYLIP [12] in order to estimate maximum-likelihood branch lengths. Empirical estimates of transition bias, nucleotide frequency bias, and positional bias (first:second:third codon position: 5:1:40 for gophers and 5:1:21 for lice) were incorporated into the maximum-likelihood model [12]. We recognize that the parameters used in maximum-likelihood models will influence rate estimates, Our models use empirical estimates of these parameters (rather than arbitrary or constant values) to obtain a more realistic approximation of the actual mutational dynamics of the gene region being surveyed [12, 28]
    • Trees for cospeciating taxa (24) were input as user trees into PHYLIP [12] in order to estimate maximum-likelihood branch lengths. Empirical estimates of transition bias, nucleotide frequency bias, and positional bias (first:second:third codon position: 5:1:40 for gophers and 5:1:21 for lice) were incorporated into the maximum-likelihood model [12]. We recognize that the parameters used in maximum-likelihood models will influence rate estimates [K. Fukami-Kobayashi and Y. Tateno, J. Mol. Evol. 32, 79 (1991)]. Our models use empirical estimates of these parameters (rather than arbitrary or constant values) to obtain a more realistic approximation of the actual mutational dynamics of the gene region being surveyed [12, 28].
    • (1991) J. Mol. Evol , vol.32 , Issue.79
    • Fukami-Kobayashi, K.1    Tateno, Y.2
  • 469
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    • We used Model II regression analysis (reduced major axis model), which does not permit conventional tests of significance, (W. H. Freeman, San Francisco, 1969)]. However, the nonparametric Mantel's test documents a significant relation between genetic distances in gophers and lice [25], and the non-parametric Wilcoxon sign-rank test shows that louse branches are significantly longer than gopher branches. When the regression analyses were not constrained through the origin, none of the y-intercepts was significantly different from zero
    • We used Model II regression analysis (reduced major axis model), which does not permit conventional tests of significance [R. R. Sokal and F. J. Rohlf, Biometry (W. H. Freeman, San Francisco, 1969)]. However, the nonparametric Mantel's test documents a significant relation between genetic distances in gophers and lice [25], and the non-parametric Wilcoxon sign-rank test shows that louse branches are significantly longer than gopher branches. When the regression analyses were not constrained through the origin, none of the y-intercepts was significantly different from zero.
    • Biometry
    • Sokal, R.R.1    Rohlf, F.J.2
  • 471
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    • Total sequence differences among the five species of Orthogeomys range from 4 to 11.9%. Sequence differences among the parasites of Orthogeomys range from 11.9 to 20.3%
    • R.A. Capaldi, Annu. Rev. Biochem. 59, 569 (1990). Total sequence differences among the five species of Orthogeomys range from 4 to 11.9%. Sequence differences among the parasites of Orthogeomys range from 11.9 to 20.3%.
    • (1990) Annu. Rev. Biochem , vol.59 , Issue.569
    • Capaldi, R.A.1
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    • Differences in nucleotide composition were tested using the B-statistic
    • Differences in nucleotide composition were tested using the B-statistic [A. P. Martin, G. J. P. Naylor, S. P. Palumbi, Nature 357, 153 (1992)].
    • (1992) Nature , vol.357 , Issue.153
    • Martin, A.P.1    Naylor, G.J.2    Palumbi, S.P.3
  • 475
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    • The slope of this relationship is affected very little by use of different nucleotide frequency estimates in the maximum-likelihood model. The slopes are more sensitive, however, to different estimates of transition:transversion bias. Our model used empirical estimates of transition:transversion bias (4:1 in gophers; 10:1 in lice) because such estimates are more likely to reflect the actual mutational dynamics of the gene regions being surveyed [12, 28]
    • The slope of this relationship is affected very little by use of different nucleotide frequency estimates in the maximum-likelihood model. The slopes are more sensitive, however, to different estimates of transition:transversion bias. Our model used empirical estimates of transition:transversion bias (4:1 in gophers; 10:1 in lice) because such estimates are more likely to reflect the actual mutational dynamics of the gene regions being surveyed [12, 28].
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    • for providing PCR primer sequences and protocols. Photography was provided by R. J. Bouchard. D. H. Clayton, S. V. Edwards, D. A. Good, D. J. Hafner, B. D. Marx, R. D. M. Page, S. Scheiner, and two anonymous reviewers provided helpful advice and comments on this manuscript. Supported by NSF grant BSR-8817329 and NSFLouisiana Education Quality Support Fund grant ADP-02
    • We thank D. R. Wolstenholme, R. Okimoto, and C. T. Beakley for providing PCR primer sequences and protocols. Photography was provided by R. J. Bouchard. D. H. Clayton, S. V. Edwards, D. A. Good, D. J. Hafner, B. D. Marx, R. D. M. Page, S. Scheiner, and two anonymous reviewers provided helpful advice and comments on this manuscript. Supported by NSF grant BSR-8817329 and NSFLouisiana Education Quality Support Fund grant ADP-02.
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    • Core samples were collected with precision cutting tools to remove material in narrow slots at centimeter intervals. We avoided sampling the core's outer rind and obvious disturbances such as burrowing. All samples (dry) were weighed, then washed to separate the fine (<62 ^jm) from the coarse sediment fraction. All petrologic analyses were done in the 63-to 150-jjm size range, which consistently contains at least a few hundred lithic grains. A portion of that grain fraction was placed on a glass slide (with glycerin as a mounting medium) and 300 to 500 grains were counted per sample, using a line rather than point counting method. A key factor in our ability to measure certain tracers accurately is a specially prepared microscope. We placed a white reflector on the condenser lens and illuminated the sample slide from above with a halogen light source. By moving the substage reflector up and down, a position can be found that creates a strong impression of relief and brings into striking view details of surface textures and coatings on grains. The technique is especially useful for identifying hematite-stained grains, even when the stain is quite small (Figure 3). Counting of lithic grain concentrations was done in the >150 £/m fraction. To avoid errors introduced by splitting small grain populations, we did not split samples for this procedure. Counting of planktonic foraminiferal concentrations and abundances was done on splits of the >150 ji/m fraction. For the abundance measurements, 300 to 500 individuals were counted. Species in the >150 ji/m fraction were selected for planktonic and benthic isotopic measurements. All isotopic measurements were made at North Carolina State University by W.S. The samples were crushed and washed with reversed-osmosis water and airdried at 65°C, and then 30-to 100-fjg sample aliquots were isotopically analyzed in a Kiel Autocarbonate device attached to a FMAT 251 RMS. NBS-19, NBS-18, and the NCSU CM-1 marble standard were analyzed with every sample run for standard calibration and sample correction. During the period these samples were analyzed, for samples in the 10-to 100-/L/g size range the standard reproducibility was 0.07 per mil for 13C and 0.08 per mil for 18O. Planktonic isotopic analyses for VM 28-14 were made on 18 to 20 individuals per sample and were replicated at a number of depths. For VM 29-191, 10 repli cate analyses were done on two or three individuals from each centimeter depth with the objective of investigating small-sample variability over time. Because those results showed no coherent relation to our other proxies, we combined all measurements from each centimeter with a mass balance Equation using the sample size (micromolar) and the sample isotopic composition per mil, the results of which are shown in Figure 2. The final result is equivalent to isotopically analyzing 20 planktonic individuals at once
    • Core samples were collected with precision cutting tools to remove material in narrow slots at centimeter intervals. We avoided sampling the core's outer rind and obvious disturbances such as burrowing. All samples (dry) were weighed, then washed to separate the fine (<62 ^jm) from the coarse sediment fraction. All petrologic analyses were done in the 63-to 150-jjm size range, which consistently contains at least a few hundred lithic grains. A portion of that grain fraction was placed on a glass slide (with glycerin as a mounting medium) and 300 to 500 grains were counted per sample, using a line rather than point counting method. A key factor in our ability to measure certain tracers accurately is a specially prepared microscope. We placed a white reflector on the condenser lens and illuminated the sample slide from above with a halogen light source. By moving the substage reflector up and down, a position can be found that creates a strong impression of relief and brings into striking view details of surface textures and coatings on grains. The technique is especially useful for identifying hematite-stained grains, even when the stain is quite small (Figure 3). Counting of lithic grain concentrations was done in the >150 £/m fraction. To avoid errors introduced by splitting small grain populations, we did not split samples for this procedure. Counting of planktonic foraminiferal concentrations and abundances was done on splits of the >150 ji/m fraction. For the abundance measurements, 300 to 500 individuals were counted. Species in the >150 ji/m fraction were selected for planktonic and benthic isotopic measurements. All isotopic measurements were made at North Carolina State University by W.S. The samples were crushed and washed with reversed-osmosis water and airdried at 65°C, and then 30-to 100-fjg sample aliquots were isotopically analyzed in a Kiel Autocarbonate device attached to a FMAT 251 RMS. NBS-19, NBS-18, and the NCSU CM-1 marble standard were analyzed with every sample run for standard calibration and sample correction. During the period these samples were analyzed, for samples in the 10-to 100-/L/g size range the standard reproducibility was 0.07 per mil for 13C and 0.08 per mil for 18O. Planktonic isotopic analyses for VM 28-14 were made on 18 to 20 individuals per sample and were replicated at a number of depths. For VM 29-191, 10 repli cate analyses were done on two or three individuals from each centimeter depth with the objective of investigating small-sample variability over time. Because those results showed no coherent relation to our other proxies, we combined all measurements from each centimeter with a mass balance Equation using the sample size (micromolar) and the sample isotopic composition per mil, the results of which are shown in Figure 2. The final result is equivalent to isotopically analyzing 20 planktonic individuals at once.
  • 525
    • 84931473661 scopus 로고    scopus 로고
    • The counting error is the 2a standard deviation for the mean of 20 replicate counts in each of two representative samples
    • The counting error is the 2a standard deviation for the mean of 20 replicate counts in each of two representative samples.
  • 526
    • 84931427108 scopus 로고    scopus 로고
    • That we find any measurable record of drift ice as far south as 54°N is not as extraordinary as it might seem. Between about 1880 and the mid-1960s there were more than 20 iceberg sightings in the eastern North Atlantic between 45°and 60°N, and icebergs have been reported from as far south as Bermuda and the Azores [40]. Even so, keeping in mind that the lithic grain concentrations are very low and that each sample integrates 50 to 100 years of time, the amounts of drifting ice reaching either site, even at peak concentrations, must have been small, and certainly much less than during the glaciation
    • That we find any measurable record of drift ice as far south as 54°N is not as extraordinary as it might seem. Between about 1880 and the mid-1960s there were more than 20 iceberg sightings in the eastern North Atlantic between 45°and 60°N, and icebergs have been reported from as far south as Bermuda and the Azores [40]. Even so, keeping in mind that the lithic grain concentrations are very low and that each sample integrates 50 to 100 years of time, the amounts of drifting ice reaching either site, even at peak concentrations, must have been small, and certainly much less than during the glaciation.
  • 529
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    • Sarnthein et ah, Paleoceanography
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  • 530
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    • G.Wu and C. Hillaire-Marcel, Geochim. Cosmochim. Acta 58, 1303 (1994).
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  • 532
    • 0021618069 scopus 로고
    • N.-A. Morner and W. Karlen, -Eds. (Reidel, Dordrecht, Netherlands
    • T. B. Kellogg, in Climatic Changes on a Yearly to Millennial Basis, N.-A. Morner and W. Karlen, -Eds. (Reidel, Dordrecht, Netherlands, 1984), pp. 123-133.
    • (1984) Climatic Changes on a Yearly to Millennial Basis , pp. 123-133
    • Kellogg, T.B.1
  • 535
    • 84931349138 scopus 로고    scopus 로고
    • Most of the cores (indicated by solid dots in Figure 1) have Holocene sections, documented on the basis of radiocarbon dating, isotopic measurements, or the presence of ash layer 1 (-10, 000 years) at depths of tens of centimeters. The existence of Holocene sections in the remainder, indicated by plus signs, is inferred from distinct color patterns and bulk carbonate measurements [41]. Core top ages likely vary from close to the present to perhaps a few thousand years; on average, then, the core top petrologic data reflect distributions of the tracers over time as well as over a large geographic area. The petrographic analyses of each core top lithic sample were done in the same way as for VM 29-191 and VM 28-14
    • Most of the cores (indicated by solid dots in Figure 1) have Holocene sections, documented on the basis of radiocarbon dating, isotopic measurements, or the presence of ash layer 1 (-10, 000 years) at depths of tens of centimeters. The existence of Holocene sections in the remainder, indicated by plus signs, is inferred from distinct color patterns and bulk carbonate measurements [41]. Core top ages likely vary from close to the present to perhaps a few thousand years; on average, then, the core top petrologic data reflect distributions of the tracers over time as well as over a large geographic area. The petrographic analyses of each core top lithic sample were done in the same way as for VM 29-191 and VM 28-14.
  • 536
    • 84931302565 scopus 로고    scopus 로고
    • There probably were no tidewater glaciers in Iceland, at least during the middle and late parts of the Holocene, ruling out transport of debris to the sites by Icelandic icebergs; direct transport in eruption clouds is also ruled out by the large size of clasts (coarsest grains typically are 0.5 to 1 mm) and by evidence that only two of the six largest Holocene eruptions in Iceland are correlative with the petrologic events [42]. The only plausible mechanism, therefore, is eruption of Icelandic volcanic material onto nearby sea ice (and probably glacier ice as well) and subsequent transport of that ice in surface currents to the coring sites. Explosive eruptions from volcanoes such as Hekla, Katla, and Grimsvotn occur once every 20 to 30 years or so in Iceland [43], and the Icelandic lithic grains at both sites are dominantly (70 to 95%) clear rhyolitic glass shards, the characteristic product of explosive eruptions in silicic volcanoes. The importance of our interpretation of the Icelandic IRD is that its increases at VM 28-14 require increases in drift ice within reach of eruption clouds to the east. Hence, changes in surface hydrography favoring preservation and transportation of drift ice in the western North Atlantic must have taken place, at the very least, from Denmark Strait to the vicinity of Iceland or Jan Mayen
    • There probably were no tidewater glaciers in Iceland, at least during the middle and late parts of the Holocene, ruling out transport of debris to the sites by Icelandic icebergs; direct transport in eruption clouds is also ruled out by the large size of clasts (coarsest grains typically are 0.5 to 1 mm) and by evidence that only two of the six largest Holocene eruptions in Iceland are correlative with the petrologic events [42]. The only plausible mechanism, therefore, is eruption of Icelandic volcanic material onto nearby sea ice (and probably glacier ice as well) and subsequent transport of that ice in surface currents to the coring sites. Explosive eruptions from volcanoes such as Hekla, Katla, and Grimsvotn occur once every 20 to 30 years or so in Iceland [43], and the Icelandic lithic grains at both sites are dominantly (70 to 95%) clear rhyolitic glass shards, the characteristic product of explosive eruptions in silicic volcanoes. The importance of our interpretation of the Icelandic IRD is that its increases at VM 28-14 require increases in drift ice within reach of eruption clouds to the east. Hence, changes in surface hydrography favoring preservation and transportation of drift ice in the western North Atlantic must have taken place, at the very least, from Denmark Strait to the vicinity of Iceland or Jan Mayen.
  • 538
    • 84931363948 scopus 로고    scopus 로고
    • The carbon isotopic composition of C. wuellerstorfi appears to record the 13C of total CO2 of sea water, and therefore is taken as a proxy of the nutrient content of that water [44]. Today, VM 29-191 lies within NADW, which is nutrient-depleted and hence <513C-enriched; below the depth of the core are modified waters of Southern Ocean origin, which are nutrient-enriched and <513Cdepleted [45], Variations in the <513C of that foraminifera are related to shifts in the rate of production of NADW and hence in the rate of convective overturning and thermohaline circulation in the North Atlantic [34, 44]
    • The carbon isotopic composition of C. wuellerstorfi appears to record the 13C of total CO2 of sea water, and therefore is taken as a proxy of the nutrient content of that water [44]. Today, VM 29-191 lies within NADW, which is nutrient-depleted and hence <513C-enriched; below the depth of the core are modified waters of Southern Ocean origin, which are nutrient-enriched and <513Cdepleted [45], Variations in the <513C of that foraminifera are related to shifts in the rate of production of NADW and hence in the rate of convective overturning and thermohaline circulation in the North Atlantic [34, 44].
  • 541
  • 542
    • 84931376927 scopus 로고    scopus 로고
    • The calendar age model in the composite record for the interval between the Younger Dryas and 18, 000 radiocarbon years was constructed by linear interpolation between radiocarbon dates from VM 23-81 calibrated following Bard et al [46] (Table 1). For the remainder of the record, we transferred the GISP2 ages of Heinrich events 2 and 3 (H2 and H3) [47] into their equivalent levels in VM 23-81 (Table 1) [48] and interpolated linearly between the two ages. Our estimate of the age of H3 is corroborated by calibrated radiocarbon measurements in Barbados corals (Table 1) and by paired U-Th-14C measurements in aragonite from Lake Lisan in the Dead Sea Rift [49]. Detrital carbonate at the Younger Dryas level was deposited rapidly and is widespread, extending from the eastern North Atlantic to sources in Hudson Strait and Cumberland Strait [50]; it serves as an excellent chronostratigraphic marker. Calibrations of radiocarbon ages in VM 19-30 (Table 1) at 100 and 150 cm are from [46]. Remaining calibrations are from the age model for the Holocene-glacial composite record as described above
    • The calendar age model in the composite record for the interval between the Younger Dryas and 18, 000 radiocarbon years was constructed by linear interpolation between radiocarbon dates from VM 23-81 calibrated following Bard et al [46] (Table 1). For the remainder of the record, we transferred the GISP2 ages of Heinrich events 2 and 3 (H2 and H3) [47] into their equivalent levels in VM 23-81 (Table 1) [48] and interpolated linearly between the two ages. Our estimate of the age of H3 is corroborated by calibrated radiocarbon measurements in Barbados corals (Table 1) and by paired U-Th-14C measurements in aragonite from Lake Lisan in the Dead Sea Rift [49]. Detrital carbonate at the Younger Dryas level was deposited rapidly and is widespread, extending from the eastern North Atlantic to sources in Hudson Strait and Cumberland Strait [50]; it serves as an excellent chronostratigraphic marker. Calibrations of radiocarbon ages in VM 19-30 (Table 1) at 100 and 150 cm are from [46]. Remaining calibrations are from the age model for the Holocene-glacial composite record as described above.
  • 543
    • 84931292642 scopus 로고    scopus 로고
    • The Heinrich events are tied to welldocumented lowerings of atmospheric and ocean surface temperatures and to large reductions in the rate of NADW formation (Figure 6) [34]. The two distinct ice-rafting peaks between interstadial 1 and the Younger Dryas, dated at-13, 200 and-14, 000 calendar years (-11, 300 and 12, 00014C years), are accompanied by increases in N. pachyderma (s.) measured in the same core [51], and they are coincident with prominent decreases in <518O in Greenland ice (Figure 6). Evidence of coolings at about the same times have been found in other deep sea cores from the North Atlantic [52] and the Nordic Seas [53] and in pollen and glacial records in Europe and North America [53]. From 23, 000 calendar years to the end of the record, the IRDpetrologic episodes between Heinrich events also occur at times of maxima in abundances of N. pachyderma (s.) [7] and at times of prominent cold phases in the ice core <518O records (Figure 6). We also find distinct IRD events punctuating prolonged stadials, such as between interstadials 2 and 3 and interstadials 4 and 5. There, the IRD-petrologic peaks correspond to prominent increases in dissolved Ca (Figure 6) and in the polar circulation index [23], suggesting a close association of the marine events with expansion of polar circulation above the ice cap. Within the long interval between interstadials 1 and 2, we have identified four other IRD-petrologic events in addition to HI. The N. pachyderma (s.) abundances are saturated through the entire interval, preventing reliable estimates of changes in sea surface temperatures. The youngest of the four events, dated at-15, 200 calendar years (-12, 90014C years), however, is correlative with glacial advances in the U.S. midwest [for example, Port Huron Stade [54]], with a glacial readvance on the Scotian shelf [55], and with a Heinrich-like cooling and ice-rafting event identified on the Scotian Slope [56]. The other three events, a, b, and c, previously identified by Bond and Lotti [7] and dated at about 19, 000, 21, 000, and 22, 000 calendar years (-16, 500, 17, 500, and ~18, 60014C years), are present in IRD records from a number of other sites in the subpolar North Atlantic and GIN Seas [57], and they also appear in magnetic susceptibility records from the Labrador Sea [58]. Two of these widespread events, a and c, are correlative with prominent coolings identified in pollen records from a long lacustrine sequence in northern Norway [59]. There is evidence that the two older events, b and c, may even be correlative with glacial advances in the Southern Hemisphere, implying a bihemi
    • The Heinrich events are tied to welldocumented lowerings of atmospheric and ocean surface temperatures and to large reductions in the rate of NADW formation (Figure 6) [34]. The two distinct ice-rafting peaks between interstadial 1 and the Younger Dryas, dated at-13, 200 and-14, 000 calendar years (-11, 300 and 12, 00014C years), are accompanied by increases in N. pachyderma (s.) measured in the same core [51], and they are coincident with prominent decreases in <518O in Greenland ice (Figure 6). Evidence of coolings at about the same times have been found in other deep sea cores from the North Atlantic [52] and the Nordic Seas [53] and in pollen and glacial records in Europe and North America [53]. From 23, 000 calendar years to the end of the record, the IRDpetrologic episodes between Heinrich events also occur at times of maxima in abundances of N. pachyderma (s.) [7] and at times of prominent cold phases in the ice core <518O records (Figure 6). We also find distinct IRD events punctuating prolonged stadials, such as between interstadials 2 and 3 and interstadials 4 and 5. There, the IRD-petrologic peaks correspond to prominent increases in dissolved Ca (Figure 6) and in the polar circulation index [23], suggesting a close association of the marine events with expansion of polar circulation above the ice cap. Within the long interval between interstadials 1 and 2, we have identified four other IRD-petrologic events in addition to HI. The N. pachyderma (s.) abundances are saturated through the entire interval, preventing reliable estimates of changes in sea surface temperatures. The youngest of the four events, dated at-15, 200 calendar years (-12, 90014C years), however, is correlative with glacial advances in the U.S. midwest [for example, Port Huron Stade [54]], with a glacial readvance on the Scotian shelf [55], and with a Heinrich-like cooling and ice-rafting event identified on the Scotian Slope [56]. The other three events, a, b, and c, previously identified by Bond and Lotti [7] and dated at about 19, 000, 21, 000, and 22, 000 calendar years (-16, 500, 17, 500, and ~18, 60014C years), are present in IRD records from a number of other sites in the subpolar North Atlantic and GIN Seas [57], and they also appear in magnetic susceptibility records from the Labrador Sea [58]. Two of these widespread events, a and c, are correlative with prominent coolings identified in pollen records from a long lacustrine sequence in northern Norway [59]. There is evidence that the two older events, b and c, may even be correlative with glacial advances in the Southern Hemisphere, implying a bihemi
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    • We define event pacing as the time separating adjacent peaks placed at the midpoints between the peaks (Figure 6). We define peaks as maxima with at least two points and amplitudes equal to or exceeding the 2a counting error (4% [8]); the measure of separation is made between maxima in peak percentage. At the levels of HI and H2, the sharp decreases in percentages of the two petrologic tracers reflect dilution by massive amounts of IRD discharged from the Labrador Sea [7], and we place the peaks for those two events at maxima in the lithic grain concentrations (Figure 6)
    • We define event pacing as the time separating adjacent peaks placed at the midpoints between the peaks (Figure 6). We define peaks as maxima with at least two points and amplitudes equal to or exceeding the 2a counting error (4% [8]); the measure of separation is made between maxima in peak percentage. At the levels of HI and H2, the sharp decreases in percentages of the two petrologic tracers reflect dilution by massive amounts of IRD discharged from the Labrador Sea [7], and we place the peaks for those two events at maxima in the lithic grain concentrations (Figure 6).
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    • We thank G. Kukla, J. Lynch-Stieglitz, and A. Van Geen for comments on the manuscript. Supported in part by grants from NSF and the National Oceanic and Atmospheric Administration. Support for the core curation facilities of the Lamont-Doherty Earth Observatory Deep-Sea Sample Repository is provided by NSF through grant OCE94-02150 and the Office of Naval Research through grant N00014-96-1-0186.This is L-DEO contribution 5714.
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