Trait–fitness relationships determine how trade‐off shapes affect species coexistence

Abstract

Trade-offs between functional traits are ubiquitous in nature and can promote species coexistence depending on their shape. Classic theory predicts that convex trade-offs facilitate coexistence of specialized species with extreme trait values (extreme species) while concave trade-offs promote species with intermediate trait values (intermediate species). We show here that this prediction becomes insufficient when the traits translate non-linearly into fitness which frequently occurs in nature, e.g., an increasing length of spines reduces grazing losses only up to a certain threshold resulting in a saturating or sigmoid trait-fitness function. We present a novel, general approach to evaluate the effect of different trade-off shapes on species coexistence. We compare the trade-off curve to the invasion boundary of an intermediate species invading the two extreme species. At this boundary, the invasion fitness is zero. Thus, it separates trait combinations where invasion is or is not possible. The invasion boundary is calculated based on measurable trait-fitness relationships. If at least one of these relationships is not linear, the invasion boundary becomes non-linear, implying that convex and concave trade-offs not necessarily lead to different coexistence patterns. Therefore, we suggest a new ecological classification of trade-offs into extreme-favoring and intermediate-favoring which differs from a purely mathematical description of their shape. We apply our approach to a well-established model of an empirical predator-prey system with competing prey types facing a trade-off between edibility and half-saturation constant for nutrient uptake. We show that the survival of the intermediate prey depends on the convexity of the trade-off. Overall, our approach provides a general tool to make a priori predictions on the outcome of competition among species facing a common trade-off in dependence of the shape of the trade-off and the shape of the trait-fitness relationships.

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

“…Furthermore, the type of defense costs regarding competitiveness (resource uptake affinity or growth rate) plays an important role for coexistence. Theory already showed that predator‐mediated coexistence crucially depends on the environmental conditions (Chase et al., 2002), for example, the enrichment level (Genkai‐Kato & Yamamura, 1999; Leibold, 1996; Proulx & Mazumder, 1998), the prey switching behavior of the predator (Abrams & Matsuda, 1993; Fryxell & Lundberg, 1994; Murdoch, 1969), the magnitude of the trade‐off between defense and competitiveness (Abrams, 1999; Kasada, Yamamichi, & Yoshida, 2014; Tirok & Gaedke, 2010), and the difference in both the defense level and the competitiveness between the prey types (Becks, Ellner, Jones, & Hairston, 2010; Ehrlich, Becks, & Gaedke, 2017; Jones & Ellner, 2007). However, the role of different defense mechanisms and competition costs in prey communities remains unclear but holds promise to be decisive for their coexistence and the occurring population dynamics.…”

The role of stressors in altering eco‐evolutionary dynamics

“…For scenario (d), we assume that the prey defence arises at the cost of reduced competitiveness and the prey population maintains a polymorphism of defended and undefended individuals. This polymorphism can lead to eco-evolutionary feedback dynamics cycles might be stabilized through prey evolution where the defended prey replaces the undefended over time (Figure 1, scenario (c), Becks, Ellner, Jones, & Hairston, 2010;Ehrlich, Becks, & Gaedke, 2017;Jones & Ellner, 2004, Yoshida et al, 2003.…”

“…Depending on the trait-fitness relationship in the specific system, the invader will out-compete the defended prey, the undefended prey or both, which will lead to a change in the population dynamics (see figure 4 in Ehrlich et al, 2017).…”

“…With predator and prey already in a steady state, prey evolution might lead to an increase in the prey and a decrease in the predator population size (Figure , scenario (b)). Alternatively, when the defence incurs a cost of reduced prey population growth, prey densities might remain similar, but the predator population would still decline, or predator–prey cycles might be stabilized through prey evolution where the defended prey replaces the undefended over time (Figure , scenario (c), Becks, Ellner, Jones, & Hairston, ; Ehrlich, Becks, & Gaedke, ; Jones & Ellner, , Yoshida et al, ).…”

“…When local adaptation to the stressor confers at the same time some level of defence against the predator (e.g., through positive pleiotropic effects of a mutation, see below), successful invasion of individuals from patch 1 would be possible. Depending on the trait–fitness relationship in the specific system, the invader will out‐compete the defended prey, the undefended prey or both, which will lead to a change in the population dynamics (see figure 4 in Ehrlich et al, ).…”