Abstract

The transformation of ecosystems proceeds at unprecedented rates. Recent studies suggest that high rates of environmental change can cause rate-induced tipping. In ecological models, the associated rate-induced critical transition manifests during transient dynamics in which populations drop to dangerously low densities. In this work, we study how indirect evolutionary rescue—due to the rapid evolution of a predator’s trait—can save a prey population from the rate-induced collapse. Therefore, we explicitly include the time-dependent dynamics of environmental change and evolutionary adaptation in an eco-evolutionary system. We then examine how fast the evolutionary adaptation needs to be to counteract the response to environmental degradation and express this relationship by means of a critical rate. Based on this critical rate, we conclude that indirect evolutionary rescue is more probable if the predator population possesses a high genetic variation and, simultaneously, the environmental change is slow. Hence, our results strongly emphasize that the maintenance of biodiversity requires a deceleration of the anthropogenic degradation of natural habitats.

Highlights

  • Today, the world’s ecosystems are faced with unprecedented rates of climate change, habitat fragmentation and destruction (Travis 2003; Teyssèdre and Robert 2014; Oliver et al 2015; Trathan et al 2015; Frishkoff et al 2016; Lee et al 2017; Selwood et al 2015; Parmesan 2006)

  • We find three different transient dynamics: tracking, R-tipping and indirect evolutionary rescue depending on the relation of the rate of environmental change rK and the genetic variation rV

  • We highlighted this relationship by deriving a critical rate of environmental change, above which R-tipping can be expected, depending on the genetic variation which determines the rate of evolution

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Summary

Introduction

The world’s ecosystems are faced with unprecedented rates of climate change, habitat fragmentation and destruction (Travis 2003; Teyssèdre and Robert 2014; Oliver et al 2015; Trathan et al 2015; Frishkoff et al 2016; Lee et al 2017; Selwood et al 2015; Parmesan 2006). The mostly negative signed lag-load τα(K(t), ε) (Fig. 5) means that predators are less aggressive than in the optimum for most of the time which lowers the predation pressure on the prey and prevents its rate-induced collapse As it is the predator whose adaptation secures the prey’s survival, it is a case of indirect evolutionary rescue. Initial conditions with α0 > eopt,α(K0, ε) are less prone to exhibit R-tipping In this case, the prey population experiences lower predation pressure because (i) initial predator densities are lower and (ii) the attack rate decreases sufficiently fast (see Fig. 7F). The prey population experiences lower predation pressure because (i) initial predator densities are lower and (ii) the attack rate decreases sufficiently fast (see Fig. 7F) As expected, these initial conditions experience indirect evolutionary rescue when the genetic variation is increased from rV = 0.2 (A) to rV = 0.9 (B).

Discussion
Conclusion

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