Many plant and animal species produce seeds or eggs that do not emerge when their development is achieved and the environmental conditions are favorable (Evans and Dennehy 2005). Instead, the propagules may stay in a dormant stage, sometimes a long time before they hatch, thereby forming seed banks or egg banks. Such delay in early life development might be viewed as a form of temporal dispersal (Venable and Brown 1988), which suggests that the evolution of dormancy and dispersal might be driven by very similar selective forces.
Both dispersal and dormancy entail some costs, because these two strategies require the development of physiological and morphological attributes that are necessary to disperse or to enter a dormant stage. There are also mortality costs incurred from dispersal (owing, e.g., to increased predation risk) and from dormancy (owing, e.g., to seed burial and soil disturbance). Last, there are costs associated with the variation of environmental conditions: just like a disperser may land in an unsuitable habitat if there is spatial variability, a dormant individual may face harsh conditions after emergence if there is temporal variability. On the other hand, both traits are associated with very similar benefits (Venable and Brown 1988; Venable et al. 1993). First, considering density-independent processes only, dispersal and dormancy may provide a means to hedge one's bets, that is, to avoid the risks associated with the spatio-temporal variation of environmental conditions (Slatkin 1974; Philippi and Seger 1989). For example, with a temporal variation in survival and/or fecundity due to the succession of good years and bad years, producing dormant seeds spreads the risk of reproductive failure by distributing the emergence of the propagules across several years (Cohen 1966; Venable 2007). Dispersal may also evolve as a bet-hedging strategy, but in less straightforward ways. For example, although dispersal responds to the between-year variation of the rate of extinction of local populations, it may not respond to between-year local variation in fecundity (Metz et al. 1983). Both dormancy and dispersal will also respond to stochastic variation in fecundity between generations, but only if the number of patches is finite (Venable and Brown 1988; Venable et al. 1993; Ronce 2007). The second category of benefits associated with dispersal and dormancy relies on the fact that with density dependence, both strategies allow a reduction in crowding (Levin et al. 1984; Ellner 1985aa,b). Dispersal and dormancy may help reduce the impact of local competition that occurs among relatives (Hamilton 1964; Hamilton and May 1977; Ellner 1986; Frank 1986; Taylor 1988; Kobayashi and Yamamura 2000), although some recent experiments challenge the idea that competition among siblings is a major force driving the evolution of dormancy (Eberhart and Tielbörger 2012). Last, both strategies may also contribute to avoiding reduced fitness caused by inbreeding depression (Waser et al. 1986; Gandon 1999; Perrin and Mazalov 1999; Morgan 2002; Roze and Rousset 2005, 2009), as illustrated empirically for dispersal (see, e.g., Richards 2000; Ebert et al. 2002; Paland and Schmid 2003; Busch 2006).
Because dispersal and dormancy presumably respond to similar evolutionary forces, it is tempting to consider that these strategies may substitute for each other. One would expect in that case to observe a negative covariation between these traits. Several theoretical studies looking at the evolution of dormancy indeed confirmed the prediction that, in general, increasing dispersal tends to decrease the evolutionarily stable (ES) rate of dormancy (Kobayashi and Yamamura 2000; Satterthwaite 2010). Several studies analyzing the evolution of dispersal also found that, in general, increasing dormancy selects for lower ES rates of dispersal (Levin et al. 1984; Cohen and Levin 1991; Snyder 2006). Yet to predict the outcome of the evolution of dispersal and dormancy, and to characterize the emerging covariation between both traits, it is necessary to consider models where dispersal and dormancy evolve jointly. Some models have been developed to study, numerically, the joint evolution of dispersal and dormancy under various ecological scenarios (Cohen and Levin 1987; Klinkhamer et al. 1987; Venable and Brown 1988; Tsuji and Yamamura 1992; Wiener and Tuljapurkar 1994; McPeek and Kalisz 1998; Olivieri 2001). Although these models differ in their assumptions (see Table 12.1 in Olivieri 2001, for a detailed summary), they found that increased dispersal would usually select for less dormancy and vice versa. However, Cohen and Levin (1987) emphasized that different patterns of covariation between the ES rates of dispersal and dormancy may emerge. When the relative costs of dispersal and dormancy vary, then the ES rates of dispersal and dormancy are negatively correlated (Cohen and Levin 1987). However, when the temporal variability of the environment varies (keeping the intrinsic costs fixed), then dispersal and dormancy are selected for in the same direction, which leads to a positive covariation between these traits (Cohen and Levin 1987). Yet none of these models considered the potential effect of kin competition on the evolutionary dynamics of these traits.
Here, we use an analytical model to analyze the joint evolution of dispersal and dormancy in a metapopulation with kin competition and local extinctions. We assume that the metapopulation is made up of an infinitely large number of patches, so that the global stochastic variance in mean performance between generations vanishes for all genotypes (Venable and Brown 1988; Venable et al. 1993; Ronce 2007). Hence, in our analytical model, neither dispersal nor dormancy evolve as a risk reduction, or bet-hedging, strategy. Our model is based on the computation of selection gradients in a metapopulation. The formal derivation of the gradients relies on standard results for class-structured populations (see, e.g., Hamilton 1966; Taylor 1990; Charlesworth 1994) completed by the results of Rousset and Ronce (2004), which take into account the feedback of individual behavior on allele frequency change, through the effect of this behavior on the demography of the local populations. However, the exact calculation of the gradient in our model was impractical, so we used some analytical approximations to find the convergence stable (CS) strategies for dispersal and dormancy. We show that our predictions are remarkably consistent with individual-based simulations. In the following, we first detail the assumptions of our model and derive the gradients of selection for dispersal and dormancy. Then we provide the results of our analyses for the evolution of each trait when they evolve independently from the others. Finally, because in reality selection acts simultaneously on all phenotypic traits, we examine the outcome of the joint evolution of all the traits. At each step of these analyses, we emphasize the connection with previous models devoted to the evolution of dispersal and dormancy. The originality of the present study lies in the fact that it reconciles some results obtained with simpler evolutionary scenarios, generates new quantitative and testable predictions, and paves the way toward a better understanding of the evolution of delayed emergence in variable environments.