TY - JOUR
T1 - Evolution of natal dispersal in spatially heterogenous environments
AU - Cantrell, Robert Stephen
AU - Cosner, Chris
AU - Lou, Yuan
AU - Schreiber, Sebastian J.
N1 - Funding Information:
We would like to thank the editor and two anonymous referees for their helpful comments which improve the manuscript. This research was partially supported by the NSF grants DMS-0816068 , DMS-1118623 , and DMS-1514752 (RSC, CC), DMS-1411476 (YL), DMS-1022639 and DMS-1313418 (SJS) and by National Natural Science Foundation of China grants No. 11571363 and No. 11571364 (YL).
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a “source-sink” spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.
AB - Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a “source-sink” spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.
KW - Evolution of dispersal
KW - Evolutionary stability
KW - Ideal free distribution
KW - Patchy environments
KW - Source-sink populations
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U2 - 10.1016/j.mbs.2016.11.003
DO - 10.1016/j.mbs.2016.11.003
M3 - Article
C2 - 27840280
AN - SCOPUS:85000500156
VL - 283
SP - 136
EP - 144
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
ER -