On the Sympatric Evolution and Evolutionary Stability of Coexistence by Relative Nonlinearity of Competition

Abstract

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and evolutionary perspectives for gaining a better understanding of community assembly and biogeographic patterns.

What the paper shows and why it matters

(AI-generated)

Many ways for species to coexist beyond classical niche differences are plausible, and community-level data and ecological models have not settled which of them sustain diversity. Asking whether selection would produce and maintain a given mechanism can complement these approaches. Relative nonlinearity of competition (RNC) is a candidate: species respond differently and nonlinearly to a shared resource, and each shapes the resource’s fluctuations in a way that favours its competitor. Its theory is relatively well understood, and coexistence that is stable on ecological time scales is a plausible contributor to diversity. The paper takes on the step from this dynamic stability to evolutionary stability: whether such a mechanism can also arise and persist under evolution.

The paper asks whether coexistence through relative nonlinearity of competition (RNC) survives evolution and finds that it generally does not: many pairs of species coexist stably, but selection favours a single intermediate strategy that excludes them. The study lets species evolve their “density-compensation strategy” (how strongly growth reacts when numbers depart from the carrying capacity) under a trade-off between growth at high and at low resource availability. Adaptive dynamics theory and individual-based simulations of classical population models show that strongly and weakly compensating strategies coexist stably; in the simulations, times to exclusion are up to four orders of magnitude longer than for two species with identical strategies. Yet evolution, even when started from such a pair, ends at one intermediate strategy near the onset of population cycles, which excludes both. Of the trade-offs examined, only a deliberately modified, irregular one led one strategy to split into a stable pair, and it needed fine-tuning that depends on growth rate and mortality. A flowering-time study parameterised with field data (Metcalf et al. 2008) likewise found coexisting strategies to be evolutionarily unstable.

**Figure 3.** Evolutionary and dynamic stability in the individual-based Maynard Smith and Slatkin model. From Hartig et al. (2014), *PLoS ONE*, licensed under CC BY 4.0. Click the image to enlarge.

The paper concludes that sympatric evolution and evolutionary stability of RNC are possible in principle but unlikely, as nothing suggests that such finely tuned trade-offs are common. It speculates that this may partly explain why empirical demonstrations are rare, although the difficulty of detecting RNC in the field is an equally likely explanation. The results are limited to non-overlapping generations, constant resource supply and unstructured space. More generally, dynamic and evolutionary stability are different properties of a coexistence mechanism and need to be assessed together.

References

Metcalf et al. (2008). Evolution of flowering decisions in a stochastic, density-dependent environment. Proceedings of the National Academy of Sciences 105, 10466–10470. doi:10.1073/pnas.0800777105