메뉴 건너뛰기




Volumn 70, Issue 6, 2008, Pages 1790-1826

Saddle-point approximations, integrodifference equations, and invasions

Author keywords

Biological invasions; Integrodifference equations; Invasion speed; Method of steepest descent; Saddle point approximation

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH; STATISTICAL MODEL;

EID: 48449101961     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9325-2     Document Type: Article
Times cited : (10)

References (65)
  • 1
    • 0025815358 scopus 로고
    • Properties of some density-dependent integrodifference equation population models
    • M. Andersen 1991 Properties of some density-dependent integrodifference equation population models Math. Biosci. 104 135 157
    • (1991) Math. Biosci. , vol.104 , pp. 135-157
    • Andersen, M.1
  • 3
    • 0037178717 scopus 로고    scopus 로고
    • Aerial dispersal of pathogens on the global and continental scales and its impact on plant disease
    • J.K.M. Brown M.S. Hovmoller 2002 Aerial dispersal of pathogens on the global and continental scales and its impact on plant disease Science 297 537 541
    • (2002) Science , vol.297 , pp. 537-541
    • Brown, J.K.M.1    Hovmoller, M.S.2
  • 4
    • 0033805460 scopus 로고    scopus 로고
    • Long distance seed dispersal by wind: Measuring and modelling the tail of the curve
    • J.M. Bullock R.T. Clarke 2000 Long distance seed dispersal by wind: measuring and modelling the tail of the curve Oecologia 124 506 521
    • (2000) Oecologia , vol.124 , pp. 506-521
    • Bullock, J.M.1    Clarke, R.T.2
  • 6
    • 0033834648 scopus 로고    scopus 로고
    • Long-distance seed dispersal in plant populations
    • M.L. Cain B.G. Milligan A.E. Strand 2000 Long-distance seed dispersal in plant populations Am. J. Bot. 87 1217 1227
    • (2000) Am. J. Bot. , vol.87 , pp. 1217-1227
    • Cain, M.L.1    Milligan, B.G.2    Strand, A.E.3
  • 7
    • 0344364584 scopus 로고    scopus 로고
    • Demography and dispersal: Life table response experiments for invasion speed
    • H. Caswell R. Lensink M.G. Neubert 2003 Demography and dispersal: life table response experiments for invasion speed Ecology 84 1968 1978
    • (2003) Ecology , vol.84 , pp. 1968-1978
    • Caswell, H.1    Lensink, R.2    Neubert, M.G.3
  • 8
    • 0031823937 scopus 로고    scopus 로고
    • Why trees migrate so fast: Confronting theory with dispersal biology and the paleorecord
    • J.S. Clark 1998 Why trees migrate so fast: Confronting theory with dispersal biology and the paleorecord Am. Nat. 152 204 224
    • (1998) Am. Nat. , vol.152 , pp. 204-224
    • Clark, J.S.1
  • 9
    • 18044404921 scopus 로고    scopus 로고
    • On the estimation of spread rate for a biological population
    • J.S. Clark L. Horvath M. Lewis 2001 On the estimation of spread rate for a biological population Stat. Probab. Lett. 51 225 234
    • (2001) Stat. Probab. Lett. , vol.51 , pp. 225-234
    • Clark, J.S.1    Horvath, L.2    Lewis, M.3
  • 10
    • 13744249456 scopus 로고    scopus 로고
    • How parasitism affects critical patch-size in a host-parasitoid model: Application to the forest tent caterpillar
    • C.A. Cobbold M.A. Lewis F. Lutscher J. Roland 2005 How parasitism affects critical patch-size in a host-parasitoid model: application to the forest tent caterpillar Theor. Popul. Biol. 67 109 125
    • (2005) Theor. Popul. Biol. , vol.67 , pp. 109-125
    • Cobbold, C.A.1    Lewis, M.A.2    Lutscher, F.3    Roland, J.4
  • 11
    • 0000186368 scopus 로고
    • A Padé approximant to the inverse Langevin function
    • A. Cohen 1991 A Padé approximant to the inverse Langevin function Rheol. Acta 30 270 273
    • (1991) Rheol. Acta , vol.30 , pp. 270-273
    • Cohen, A.1
  • 12
    • 0001367156 scopus 로고
    • Saddlepoint approximations in statistics
    • H.E. Daniels 1954 Saddlepoint approximations in statistics Ann. Math. Stat. 25 631 650
    • (1954) Ann. Math. Stat. , vol.25 , pp. 631-650
    • Daniels, H.E.1
  • 14
    • 27844462152 scopus 로고    scopus 로고
    • When can herbivores slow or reverse the spread of an invading plant? a test case from Mount St. Helens
    • W.F. Fagan M. Lewis M.G. Neubert C. Aumann J.L. Apple J.G. Bishop 2005 When can herbivores slow or reverse the spread of an invading plant? A test case from Mount St. Helens Am. Nat. 166 669 685
    • (2005) Am. Nat. , vol.166 , pp. 669-685
    • Fagan, W.F.1    Lewis, M.2    Neubert, M.G.3    Aumann, C.4    Apple, J.L.5    Bishop, J.G.6
  • 16
    • 0001018461 scopus 로고
    • On the empirical saddlepoint approximation
    • A. Feuerverger 1989 On the empirical saddlepoint approximation Biometrika 76 457 464
    • (1989) Biometrika , vol.76 , pp. 457-464
    • Feuerverger, A.1
  • 17
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R.A. Fisher 1937 The wave of advance of advantageous genes Ann. Eugen. 7 355 369
    • (1937) Ann. Eugen. , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 18
    • 34248587478 scopus 로고    scopus 로고
    • Fronts from complex two-dimensional dispersal kernels: Theory and application to Reid's paradox
    • J. Fort 2007 Fronts from complex two-dimensional dispersal kernels: Theory and application to Reid's paradox J. Appl. Phys. 101 094701
    • (2007) J. Appl. Phys. , vol.101 , pp. 094701
    • Fort, J.1
  • 20
    • 0002303732 scopus 로고
    • Saddle-point methods for the multinomial distribution
    • I.J. Good 1957 Saddle-point methods for the multinomial distribution Ann. Math. Stat. 28 861 881
    • (1957) Ann. Math. Stat. , vol.28 , pp. 861-881
    • Good, I.J.1
  • 21
    • 0033409355 scopus 로고    scopus 로고
    • Explaining the saddlepoint approximation
    • C. Goutis G. Casella 1999 Explaining the saddlepoint approximation Am. Stat. 53 216 224
    • (1999) Am. Stat. , vol.53 , pp. 216-224
    • Goutis, C.1    Casella, G.2
  • 22
    • 0002216778 scopus 로고    scopus 로고
    • A spatial model for the spread of invading organisms subject to competition
    • D.R. Hart R.H. Gardner 1997 A spatial model for the spread of invading organisms subject to competition J. Math. Biol. 35 935 948
    • (1997) J. Math. Biol. , vol.35 , pp. 935-948
    • Hart, D.R.1    Gardner, R.H.2
  • 23
    • 0032987501 scopus 로고    scopus 로고
    • Predicting plant migration rates in a changing world: The role of long-distance dispersal
    • S.I. Higgins D.M. Richardson 1999 Predicting plant migration rates in a changing world: the role of long-distance dispersal Am. Nat. 153 464 475
    • (1999) Am. Nat. , vol.153 , pp. 464-475
    • Higgins, S.I.1    Richardson, D.M.2
  • 25
    • 30944457708 scopus 로고    scopus 로고
    • Fire increases invasive spread of Molinia caerulea mainly through changes in demographic parameters
    • H. Jacquemyn R. Brys M.G. Neubert 2005 Fire increases invasive spread of Molinia caerulea mainly through changes in demographic parameters Ecol. Appl. 15 2097 2108
    • (2005) Ecol. Appl. , vol.15 , pp. 2097-2108
    • Jacquemyn, H.1    Brys, R.2    Neubert, M.G.3
  • 27
    • 0026477253 scopus 로고
    • Discrete-time travelling waves: Ecological examples
    • M. Kot 1992 Discrete-time travelling waves: ecological examples J. Math. Biol. 30 413 436
    • (1992) J. Math. Biol. , vol.30 , pp. 413-436
    • Kot, M.1
  • 28
    • 38249039995 scopus 로고
    • Discrete-time growth-dispersal models
    • M. Kot W.M. Schaffer 1986 Discrete-time growth-dispersal models Math. Biosci. 80 109 136
    • (1986) Math. Biosci. , vol.80 , pp. 109-136
    • Kot, M.1    Schaffer, W.M.2
  • 29
    • 0030426365 scopus 로고    scopus 로고
    • Dispersal data and the spread of invading organisms
    • M. Kot M.A. Lewis P. van den Driessche 1996 Dispersal data and the spread of invading organisms Ecology 77 2027 2042
    • (1996) Ecology , vol.77 , pp. 2027-2042
    • Kot, M.1    Lewis, M.A.2    Van Den Driessche, P.3
  • 31
    • 34247568346 scopus 로고    scopus 로고
    • Relating dispersal and range expansion of California sea otters
    • M. Krkosek J.S. Lauzon-Guay M.A. Lewis 2007 Relating dispersal and range expansion of California sea otters Theor. Popul. Biol. 71 401 407
    • (2007) Theor. Popul. Biol. , vol.71 , pp. 401-407
    • Krkosek, M.1    Lauzon-Guay, J.S.2    Lewis, M.A.3
  • 34
    • 84941466161 scopus 로고
    • Probabilité des résultats moyens tirés d'observations répetées
    • N. Lobatschewsky 1842 Probabilité des résultats moyens tirés d'observations répetées J. Reine Angew. Math. 24 164 170
    • (1842) J. Reine Angew. Math. , vol.24 , pp. 164-170
    • Lobatschewsky, N.1
  • 35
    • 0020560243 scopus 로고
    • Existence and stability of travelling wave solutions of a nonlinear integral operator
    • R. Lui 1983 Existence and stability of travelling wave solutions of a nonlinear integral operator J. Math. Biol. 16 199 220
    • (1983) J. Math. Biol. , vol.16 , pp. 199-220
    • Lui, R.1
  • 36
    • 0039364107 scopus 로고
    • Deriving the probability density for sums of uniform random variables
    • E.J. Lusk H. Wright 1982 Deriving the probability density for sums of uniform random variables Am. Stat. 36 128 130
    • (1982) Am. Stat. , vol.36 , pp. 128-130
    • Lusk, E.J.1    Wright, H.2
  • 37
    • 34250790756 scopus 로고    scopus 로고
    • A short note on short dispersal events
    • F. Lutscher 2007 A short note on short dispersal events Bull. Math. Biol. 69 1615 1630
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1615-1630
    • Lutscher, F.1
  • 38
    • 0038638479 scopus 로고
    • A Bessel function distribution
    • A.T. McKay 1932 A Bessel function distribution Biometrika 24 39 44
    • (1932) Biometrika , vol.24 , pp. 39-44
    • McKay, A.T.1
  • 40
    • 0026360188 scopus 로고
    • Dependence of epidemic and population velocities on basic parameters
    • D. Mollison 1991 Dependence of epidemic and population velocities on basic parameters Math. Biosci. 107 255 287
    • (1991) Math. Biosci. , vol.107 , pp. 255-287
    • Mollison, D.1
  • 43
    • 0033923327 scopus 로고    scopus 로고
    • Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations
    • M.G. Neubert H. Caswell 2000 Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations Ecology 81 1613 1628
    • (2000) Ecology , vol.81 , pp. 1613-1628
    • Neubert, M.G.1    Caswell, H.2
  • 44
    • 4544271418 scopus 로고    scopus 로고
    • Projecting rates of spread for invasive species
    • M.G. Neubert I.M. Parker 2004 Projecting rates of spread for invasive species Risk Anal. 24 817 831
    • (2004) Risk Anal. , vol.24 , pp. 817-831
    • Neubert, M.G.1    Parker, I.M.2
  • 45
    • 0029476440 scopus 로고
    • Dispersal and pattern formation in a discrete-time predator-prey model
    • M.G. Neubert M. Kot M.A. Lewis 1995 Dispersal and pattern formation in a discrete-time predator-prey model Theor. Popul. Biol. 48 7 43
    • (1995) Theor. Popul. Biol. , vol.48 , pp. 7-43
    • Neubert, M.G.1    Kot, M.2    Lewis, M.A.3
  • 48
    • 0040060171 scopus 로고    scopus 로고
    • The origin of the method of steepest descent
    • S.S. Petrova A.D. Solov'ev 1997 The origin of the method of steepest descent Hist. Math. 24 361 375
    • (1997) Hist. Math. , vol.24 , pp. 361-375
    • Petrova, S.S.1    Solov'Ev, A.D.2
  • 50
    • 13544273192 scopus 로고    scopus 로고
    • Epidemic spread of a lesion-forming plant pathogen-analysis of a mechanistic model with infinite age structure
    • J.A. Powell I. Slapnicar W. van der Werf 2005 Epidemic spread of a lesion-forming plant pathogen-analysis of a mechanistic model with infinite age structure Linear Algebra Appl. 398 117 140
    • (2005) Linear Algebra Appl. , vol.398 , pp. 117-140
    • Powell, J.A.1    Slapnicar, I.2    Van Der Werf, W.3
  • 51
    • 0031082133 scopus 로고    scopus 로고
    • Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes
    • J. Radcliffe L. Rass 1997 Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes Math. Biosci. 140 101 129
    • (1997) Math. Biosci. , vol.140 , pp. 101-129
    • Radcliffe, J.1    Rass, L.2
  • 52
    • 84972528712 scopus 로고
    • Saddlepoint methods and statistical inference
    • N. Reid 1988 Saddlepoint methods and statistical inference Stat. Sci. 3 213 227
    • (1988) Stat. Sci. , vol.3 , pp. 213-227
    • Reid, N.1
  • 53
    • 0033733290 scopus 로고    scopus 로고
    • Applying the saddlepoint approximation to bivariate stochastic processes
    • E. Renshaw 2000 Applying the saddlepoint approximation to bivariate stochastic processes Math. Biosci. 168 57 75
    • (2000) Math. Biosci. , vol.168 , pp. 57-75
    • Renshaw, E.1
  • 55
    • 0028862561 scopus 로고
    • Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance
    • M.W. Shaw 1995 Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance Proc. R. Soc. Lond. B 259 243 248
    • (1995) Proc. R. Soc. Lond. B , vol.259 , pp. 243-248
    • Shaw, M.W.1
  • 57
    • 0346174871 scopus 로고    scopus 로고
    • Invasion and range expansion of species: Effects of long-distance dispersal
    • Blackwell Malden
    • Shigesada, N., Kawasaki, K., 2002. Invasion and range expansion of species: effects of long-distance dispersal. In J.M. Bullock, R.E. Kenward, R.S. Hails (Eds.) Dispersal Ecology, pp. 350-373. Blackwell, Malden.
    • (2002) Dispersal Ecology , pp. 350-373
    • Shigesada, N.1    Kawasaki, K.2    Bullock, J.M.3    Kenward, R.E.4    Hails, R.S.5
  • 58
    • 34548184646 scopus 로고    scopus 로고
    • Dispersal patterns, dispersal mechanisms, and invasion wave speeds for invasive thistles
    • O. Skarpaas K. Shea 2007 Dispersal patterns, dispersal mechanisms, and invasion wave speeds for invasive thistles Am. Nat. 170 421 430
    • (2007) Am. Nat. , vol.170 , pp. 421-430
    • Skarpaas, O.1    Shea, K.2
  • 59
    • 0009636209 scopus 로고
    • Random dispersal in theoretical populations
    • J.G. Skellam 1951 Random dispersal in theoretical populations Biometrika 38 196 218
    • (1951) Biometrika , vol.38 , pp. 196-218
    • Skellam, J.G.1
  • 60
    • 34548057205 scopus 로고    scopus 로고
    • A parametric model for estimation of dispersal patterns applied to five passerine spatially structured populations
    • J. Tufto T.H. Ringsby A.A. Dhondt F. Adriaensen E. Matthysen 2005 A parametric model for estimation of dispersal patterns applied to five passerine spatially structured populations Am. Nat. 165 E13 E26
    • (2005) Am. Nat. , vol.165
    • Tufto, J.1    Ringsby, T.H.2    Dhondt, A.A.3    Adriaensen, F.4    Matthysen, E.5
  • 62
    • 0001047828 scopus 로고
    • Long-time behavior of a class of biological models
    • H.F. Weinberger 1982 Long-time behavior of a class of biological models SIAM J. Math. Anal. 13 353 396
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 353-396
    • Weinberger, H.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.