Best Ways for Species to Spread Across Two Habitats for Stability

Greg Howard
23rd February, 2024

Best Ways for Species to Spread Across Two Habitats for Stability

A new model shows how population sizes in connected habitats are shaped by dispersal and growth rates, highlighting a critical transition (black curve) where increased dispersal makes the entire system more resilient to extinction.

Image adapted from: Jorba-Cuscó et al. / CC BY (Source)
Populations in nature are rarely found as a single, large group. More often, they exist as smaller, separate groups – what ecologists call metapopulations – linked by the movement of individuals between them. Understanding how this movement, known as dispersal, affects the long-term survival of a species is a central challenge in ecology, particularly as human activities increasingly fragment natural habitats. A key question is whether dispersal consistently helps or hinders population persistence. Researchers at the Centre de Recerca Matemàtica (CRM) have recently investigated this issue using mathematical models[1]. Their work focuses on a simplified scenario: a metapopulation divided into just two patches, or sub-populations, where individuals move between them. The study builds upon the “standard model” frequently used in ecology, which represents population growth within each patch using a logistic equation – a formula describing how population size increases when resources are plentiful, but slows down as it approaches the environment’s carrying capacity[2]. The CRM team’s research addresses how dispersal influences the stability of these two-patch systems, particularly in the face of random fluctuations – what’s known as stochastic perturbations. These fluctuations can represent unpredictable events like changes in weather or the outbreak of disease, which can drive populations towards extinction. The researchers began by examining the behaviour of the system around the point where both populations die out completely – the extinction equilibrium. They found that the rate of dispersal is critical. At low dispersal rates, the model showed that the extinction point acted as a ‘repeller’ – meaning that any population starting near extinction would be pushed away from it, but in a way that made them vulnerable to stochastic events. Essentially, the populations were quickly driven away from zero, but along paths that didn’t necessarily lead to long-term survival. However, as dispersal increased, this repeller transitioned into a ‘saddle point’. This change in behaviour meant that populations were still pushed away from extinction, but now along paths that rapidly converged towards a more stable state, significantly reducing the risk of extinction. This highlights how dispersal can enhance the robustness of a metapopulation. Previous research has suggested that a balance between dispersal and local population dynamics is crucial[3]. While dispersal can promote stability, it can also lead to synchrony – where populations in different patches rise and fall at the same time. This synchrony can be detrimental, as a negative event affecting one patch is likely to affect all patches simultaneously, increasing the risk of a widespread extinction[3]. However, the CRM study suggests that, at least in this simplified two-patch model, dispersal can simultaneously promote both stability and reduce the likelihood of complete metapopulation collapse. The study also investigated the impact of asymmetric dispersal – where the rate of movement between patches isn’t equal in both directions. It confirmed earlier findings that unequal conditions between patches can be beneficial for the overall population size[4]. The CRM team went further, providing a complete mathematical formula for the optimal dispersal rate that maximizes the total population size, regardless of the dispersal rate. This is a significant advance, as previous work had only addressed optimal dispersal for very high or very low dispersal rates. Interestingly, the findings align with research showing that chaotic dynamics within subpopulations can sometimes be stabilized by dispersal[5]. While chaotic fluctuations might seem inherently dangerous, the CRM study, like the earlier work, suggests that dispersal can reduce synchrony between patches, lessening the chance of all populations crashing at the same time. This is particularly relevant given that many real-world species consist of multiple, weakly connected populations[5].

EnvironmentEcologyAnimal Science

References

Main Study

1) Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters.

Published 21st February, 2024

https://doi.org/10.1007/s12064-023-00411-2

Related Studies

2) Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation.

https://doi.org/10.1016/j.tpb.2015.10.001

3) A dispersal-induced paradox: synchrony and stability in stochastic metapopulations.

https://doi.org/10.1111/j.1461-0248.2011.01670.x

4) Effects of symmetric and asymmetric dispersal on the dynamics of heterogeneous metapopulations: two-patch systems revisited.

https://doi.org/10.1016/j.jtbi.2013.12.005

5) Chaos reduces species extinction by amplifying local population noise.

Journal: Nature, Issue: Vol 364, Issue 6434, Jul 1993


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