Sex-biased dispersal and the speed of two-sex invasions

American Naturalist

Volumn 177, Issue 5, 2011, Pages 549-561

  Miller, Tom E X ^a   Shaw, Allison K ^b   Inouye, Brian D ^c   Neubert, Michael G ^d  

^a RICE UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c FLORIDA STATE UNIVERSITY   (United States)

^d WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

Integrodifference equations; Invasion speed; Marriage squeeze; Mating functions; Sex biased dispersal; Spatial spread

Indexed keywords

BIOLOGICAL INVASION; DEMOGRAPHY; DISPERSAL; EQUATION; MAGNITUDE; MATING BEHAVIOR; NUMERICAL MODEL; POPULATION DENSITY; POPULATION GROWTH; POPULATION MODELING; SENSITIVITY ANALYSIS; SEX RATIO;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; FEMALE; INTRODUCED SPECIES; MALE; POPULATION DYNAMICS; SEXUAL DEVELOPMENT;

ANIMALS; FEMALE; INTRODUCED SPECIES; MALE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; SEX CHARACTERISTICS;

ANIMALIA;

EID: 79955400987     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/659628     Document Type: Article

References (51)

1. Abramowitz, M., and I. A. Stegun, eds. 1972. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New York.
2. Andow, D., P. Kareiva, S. Levin, and A. Okubo. 1990. Spread of invading organisms. Landscape Ecology 4:177-188.
3. Ashih, A. C., and W. G. Wilson. 2001. Two-sex population dynamics in space: effects of gestation time on persistence. Theoretical Population Biology 60:93-106.
4. Buckley, Y., E. Brockerhoff, L. Langer, N. Ledgard, H. North, and M. Rees. 2005. Slowing down a pine invasion despite uncertainty in demography and dispersal. Journal of Applied Ecology 42:1020-1030.
5. Bullen, P. S. 2003. Handbook of means and their inequalities. Kluwer Academic, Dordrecht.
6. Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation. 2nd ed. Sinauer, Sunderland, MA.
7. Caswell, H., and D. Weeks. 1986. Two-sex models: chaos, extinction, and other dynamic consequences of sex. American Naturalist 128:707-735.
8. Clarke, A., B. E. Sæther, and E. Roskaft. 1997. Sex biases in avian dispersal: a reappraisal. Oikos 79:429-438.
9. Crozier, L., and G. Dwyer. 2006. Combining population-dynamic and ecophysiological models to predict climate-induced range shifts. American Naturalist 167:853-866.
10. Dale, S. 2001. Female-biased dispersal, low female recruitment, unpaired males, and the extinction of small and isolated bird populations. Oikos 92:344-356.
11. Dobson, F. 1982. Competition for mates and predominant juvenile dispersal in mammals. Animal Behavior 30:1183-1192.
12. Fagan, W., M. Lewis, M. Neubert, and P. van den Driessche. 2002. Invasion theory and biological control. Ecology Letters 5:148-157.
13. Fagan, W., M. Lewis, M. Neubert, C. Aumann, J. Apple, and J. G. Bishop. 2005. When can herbivores slow or reverse the spread of an invading plant? a test case from Mount St. Helens. American Naturalist 166:669-685.
14. Fisher, R. 1930. The genetical theory of natural selection. Clarendon, Oxford.
15. Franklin, A. B., D. R. Anderson, E. D. Forsman, K. P. Burnham, and F. W. Wagner. 1996. Methods for collecting and analyzing demographic data on the northern spotted owl. Avian Biology 17:12-20.
16. Greenwood, P. 1980. Mating systems, philopatry and dispersal in birds and mammals. Animal Behaviour 28:1140-1162.
17. Hadeler, K. 1989. Pair formation in age-structured populations. Acta Applicandae Mathematicae 14:91-102.
18. Hardy, G., J. E. Littlewood, and G. Polya. 1952. Inequalities. 2nd ed. Cambridge University Press, Cambridge.
19. Hastings, A., K. Cuddington, K. Davies, C. Dugaw, S. Elmendorf, A. Freestone, S. Harrison, et al. 2005. The spatial spread of invasions: new developments in theory and evidence. Ecology Letters 8:91-101.
20. Iannelli, M., M. Martcheva, and F. A. Milner. 2005. Gender-structured population modeling: mathematical methods, numerics, and simulations. SIAM, Philadelphia.
21. Keitt, T., M. Lewis, and R. Holt. 2001. Allee effects, invasion pinning, and species' borders. American Naturalist 157:203-216.
22. Kot, M. 1992. Discrete-time travelling waves: ecological examples. Journal of Mathematical Biology 30:413-436.
23. Kot, M. 2002. Do invading organisms do the wave? Canadian Applied Mathematics Quarterly 10:139-170.
24. Kot, M., and W. M. Schaffer. 1986. Discrete-time growth-dispersal models. Mathematical Biosciences 80:109-136.
25. Kot, M., M. Lewis, and P. van den Driessche. 1996. Dispersal data and the spread of invading organisms. Ecology 77:2027-2042.
26. Kotz, S., and J. Van Dorp. 2004. Beyond beta: other continuous families of distributions with bounded support and applications. World Scientific, Singapore.
27. Legendre, S., J. Clobert, A. Møller, and G. Sorci. 1999. Demographic stochasticity and social mating system in the process of extinction of small populations: the case of passerines introduced to New Zealand. American Naturalist 153:449-463.
28. Lindstrom, J., H. Kokko. 1998. Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences. Proceedings of the Royal Society B: Biological Sciences 265:483-488.
29. Maron, J., and S. Harrison. 1997. Spatial pattern formation in an insect host-parasitoid system. Science 278:1619-1621.
30. Miller, T., and B. Tenhumberg. 2010. Contributions of demography and dispersal parameters to the spread of a stage-structured insect invasion. Ecological Applications 20:620-633.
31. Neubert, M., and H. Caswell. 2000. Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations. Ecology 81:1613-1628.
32. Neubert, M., M. Kot, and M. Lewis. 1995. Dispersal and pattern formation in a discrete-time predator-prey model. Theoretical Population Biology 48:7-43.
33. Neubert, M., and I. Parker. 2004. Projecting rates of spread for invasive species. Risk Analysis 24:817-831.
34. Okubo, A. 1980. Diffusion and ecological problems: mathematical models. Biomathematics 10. Springer, Berlin.
35. Olsson, M., and R. Shine. 2003. Female-biased natal and breeding dispersal in an alpine lizard, Niveoscincus microlepidotus. Biological Journal of the Linnean Society 79:277-283.
36. Pollak, R. A. 1986. A reformulation of the two-sex problem. Demography 23:247-259.
37. Potapov, A. B., and M. Lewis. 2004. Climate and competition: the effect of moving range boundaries on habitat invasibility. Bulletin of Mathematical Biology 66:975-1008.
38. Rankin, D., and H. Kokko. 2007. Do males matter? the role of males in population dynamics. Oikos 116:335-348.
39. Ranta, E., V. Kaitala, and J. Lindstrom. 1999. Sex in space: population dynamic consequences. Proceedings of the Royal Society B: Biological Sciences 266:1155-1160.
40. Rosen, K. 1983. Mathematical models for polygynous mating systems. Mathematical Modelling 4:27-39.
41. Schoen, R. 1983. Measuring the tightness of a marriage squeeze. Demography 20:61-78.
42. Sharov, A. A., A. M. Liebhold. 1998. Bioeconomics of managing the spread of exotic pest species with barrier zones. Ecological Applications 8:833-845.
43. Skellam, J. 1951. Random dispersal in theoretical populations. Biometrika 38:196-218.
44. Smith, M. H. 1968. Dispersal of the old-field mouse, Peromyscus polionotus. Bulletin of the Georgia Academy of Science 26:45-51.
45. South, A., and R. Kenward. 2001. Mate finding, dispersal distances, and population growth in invading species: a spatially explicit model. Oikos 95:53-58.
46. Tinker, M., D. Doak, and J. Estes. 2008. Using demography and movement behavior to predict range expansion of the southern sea otter. Ecological Applications 18:1781-1794.
47. Van Dorp, J., and S. Kotz. 2002. The standard two-sided power distribution and its properties: with applications in financial engineering. American Statistician 56:90-99.
48. Weinberger, H. 1978. Asymptotic behavior of a model of population genetics. Pages 47-98 in J. Chadam, ed. Nonlinear partial differential equations and applications. Vol. 648. Lecture Notes in Mathematics. Springer, New York.
49. Weinberger, H. 1982. Long-time behavior of a class of biological models. SIAM Journal on Mathematical Analysis 13:353.
50. Wilson, W., S. Harrison, A. Hastings, and K. McCann. 2002. Exploring stable pattern formation in models of tussock moth populations. Journal of Animal Ecology 68:94-107.
51. Zhou, Y. and Kot, M. 2010. Discrete-time growth-dispersal models with shifting species ranges. Theoretical Ecology 4:13-25.