Evolution of Site-Selection Stabilizes Population Dynamics, Promotes Even Distribution of Individuals, and Occasionally Causes Evolutionary Suicide

Abstract

Species that compete for access to or use of sites, such as parasitic mites attaching to honey bees or apple maggots laying eggs in fruits, can potentially increase their fitness by carefully selecting sites at which they face little or no competition. Here, we systematically investigate the evolution of site-selection strategies among animals competing for discrete sites. By developing and analyzing a mechanistic and population-dynamical model of site selection in which searching individuals encounter sites sequentially and can choose to accept or continue to search based on how many conspecifics are already there, we give a complete characterization of the different site-selection strategies that can evolve. We find that evolution of site-selection stabilizes population dynamics, promotes even distribution of individuals among sites, and occasionally causes evolutionary suicide. We also discuss the broader implications of our findings and propose how they can be reconciled with an earlier study (Nonaka et al. in J Theor Biol 317:96-104, 2013) that reported selection toward ever higher levels of aggregation among sites as a consequence of site-selection.

Keywords: Adaptive dynamics; Evolution; Evolutionary suicide; First-principles derivation; Mechanistic modeling.

Fig. 1

(Color figure online) Evolution stabilizes population dynamics under pure scramble competition: a a trait substitution sequence initiated with the always settle strategy $(1,1,\dots ,1)$ (thick dashed curve) converging to strategy $(1,0,s_2,s_3,\dots )$ (thick curve). b Discrete-time population models corresponding to the strategies in panel (a). c Discrete-time population models corresponding to the ESS strategy for different values of $b_1$. Points in panels b and c show the population-dynamical attractors. Parameters: Panel a and b: $b_1=16$. All panels: $\mathit{\alpha }T=2.5$

Fig. 2

(Color figure online) Evolution stabilizes population dynamics also under pure scramble competition with Allee effect: a a trait substitution sequence initiated with the always settle strategy $(1,1,\dots ,1)$ (thick dashed curve) converging to strategy $(1,1,0,s_3,s_4,\dots )$ (thick curve). b Discrete-time population models corresponding to the strategies in panel (a). c Discrete-time population models corresponding to the ESS strategy for different values of $b_2$. Points in panels b and c show the population-dynamical attractors. Parameters: Panel a and b: $b_2=8$. All panels: $\mathit{\alpha }T=2.5$

Fig. 3

(Color figure online) Evolution can result in cyclic population dynamics under general scramble competition: a a trait substitution sequence initiated with the always settle strategy $(1,1,\dots ,1)$ (thick dashed curve) converging to strategy $(1,s_1,0,s_3,s_4,\dots )$ with $s_1\approx 0.384$ (thick curve). b Discrete-time population models corresponding to the strategies in panel a. c Discrete-time population models corresponding to the ESS strategy for different values of $b_2$. Points in panels b and c show the population-dynamical attractors. d Evolution of the strategy component $s_2$ as a function of fecundity $b_2$. Curves in panel d show evolutionarily singular strategies. e Population-dynamical attractors corresponding to the evolutionarily attracting singular strategies illustrated in panel d. Parameters: Panel a and b: $b_2=0.2$. All panels: $\mathit{\alpha }T=2.5$, $b_1=8$

Fig. 4

(Color figure online) Evolution typically stabilizes population dynamics under general scramble competition: a Evolved settlement strategy and the corresponding population dynamics for different combinations of fecundities $b_1$ and $b_2$. The evolved strategy is either of the boundary strategies $(1,0,\dots )$ and $(1,1,0,\dots )$, or a singular strategy $(1,s_1,0,\dots )$ with $0<s_1<1$. b Type of the population-dynamical attractor for the always settle strategy $(1,1,1,\dots )$. Shading illustrates different types of population dynamics

Fig. 5

(Color figure online) First route to evolutionary suicide: a a trait substitution sequence initiated with the strategy $s=(1,1,1,0,\dots )$. The strategy component $s_2$ decreases until the population goes extinct. b Explanation of the extinction. As a consequence of the decrease in $s_2$, the return map for the population dynamics changes so that a chaotic attractor collides with an unstable equilibrium, beyond which the population is no longer viable. c Phase diagram illustrating when evolution of strategy component $s_2$ results in collision with an unstable equilibrium and eventual extinction. The interaction function is given by Eq. 17

Fig. 6

(Color figure online) Second route to evolutionary suicide: a a trait substitution sequence results in the strategy $s=(1,1,s_3,0,\dots )$ becoming fixated in the population. b As a consequence, the return map for the population dynamics changes and the stable equilibrium vanishes in a saddle-node bifurcation. This results in the extinction of the population. c Phase diagram illustrating the resulting evolutionary outcomes for different values of $b_2$ and $b_3$. The interaction function is given by Eq. 17

Fig. 7

Evolution promotes even distribution of individuals: dependence of the mean and the variance-mean ratio (the dispersion index) for the distribution of individuals among sites for four site-selection strategies. The always settle strategy results in the Poisson distribution, for which the variance-mean ratio is always one. The other illustrated strategies are of form given by (18), which is the form of evolutionary stable site-selection strategies that the interaction functions we have considered have all given rise to. These site-selection strategies always result in underdispersed (non-aggregated) distributions, for which the variance-mean ratio is less than one