Stanford University Stanford, California, United States
Abstract: Understanding the effect of fluctuations on populations is crucial in the context of increasing habitat fragmentation, climate change, and biological invasions, among others. Migration is an important strategy in response to environmental disturbances as it enables populations to escape unfavourable conditions, benefit from new environments and thereby ride out fluctuations in environments.
Hypothesis and
Methods:
We start with a basic question: would populations disperse if there is no uncertainty? Karlin showed in his 1982 paper that for sub-populations experiencing differing but fixed growth rates at different sites, greater mixing of populations will lower the overall growth rate relative to the most favorable site. Here we ask when might environmental variability favor migration over no-migration? Specifically, in random environments, would a small amount of migration increase the overall long-run growth rate relative to the zero migration case? We use methods from matrix analysis and large deviation theory as well as simulations to show how long-run growth rate changes with migration rate.
Results:
Our results show that when fitness (dis)advantages fluctuate over time across sites, migration may allow populations to benefit from variability. We show that when there is one best site with highest growth rate (on average), the effect of migration on long-run growth-rate depends on the difference in expected site-specific growth rates, scaled by the variance of the difference. This may be because when fluctuations are large, there is a substantial probability of an inferior site having a higher growth rate than superior site (at some time t). Thus, a high variance can compensate for habitat quality or a fixed difference in growth-rates between sites.
When there are more than 2 sites, we explore the interplay between the length of shortest path from the best site (with highest growth rate on average), the size of fluctuations and the long-run growth rate. We also find positively correlated fluctuations in growth rates lead to reduced rates of migration. Intuitively, populations are less likely to survive through long runs of poor conditions.
Implications:
Our findings indicate that habitat quality and fluctuations are both important determinants of migration evolution and the results have implications for conservation biology and evolution of migration since the system is characterized by variability. When there are superior sites in a sea of poor habitat (such as national parks, wildlife reserves), connectivity and variability across space are key to persistence.
