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The Evolution of Patch Selection in Stochastic Environments

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The Evolution of Patch Selection in Stochastic Environments vol. 180, no. 1 the american naturalist july 2012 The Evolution of Patch Selection in Stochastic Environments Sebastian J. Schreiber* Department of Evolution and Ecology and the Center for Population Biology, University of California, Davis, California 95616 Submitted July 25, 2011; Accepted February 8, 2012; Electronically published May 17, 2012 1969; Sutherland 1983, 1996; Tregenza et al. 1996; Ksha- abstract: A null model for habitat patch selection in spatially triya and Cosner 2002; Cosner 2005; Cantrell et al. 2007, heterogeneous environments is the ideal free distribution (IFD), which assumes individuals have complete knowledge about the en- 2010; Morris 2011), the combined effects of temporal and vironment and can freely disperse. Under equilibrium conditions, spatial variation on the evolution of patch selection is less the IFD predicts that local population growth rates are zero in all understood (Holt and Barfield 2001; Morris 2011). Given occupied patches, sink patches are unoccupied, and the fraction of the ubiquity of temporal variation and its notable impacts the population selecting a patch is proportional to the patch’s car- on demography (Boyce et al. 2006) and the evolution of rying capacity. Individuals, however, often experience stochastic fluc- passive dispersal (Johnson and Gaines 1990; Ronce 2007), tuations in environmental conditions and cannot respond to these fluctuations instantaneously. An evolutionary stability analysis for I examine the evolution of habitat patch selection for freely fixed patch-selection strategies reveals that environmental uncer- dispersing individuals in a stochastic environment. tainty disrupts the classical IFD predictions: individuals playing the In their seminal article, Fretwell and Lucas (1969) in- evolutionarily stable strategy may occupy sink patches, local growth troduced the ideal free distribution (IFD), which describes rates are negative and typically unequal in all patches, and individuals the patch distribution of freely dispersing individuals that prefer higher-quality patches less than predicted by their carrying have complete knowledge about spatial variation in in- capacities. Spatial correlations in environmental fluctuations can en- hance or marginalize these trends. The analysis predicts that contin- dividual fitness. For population exhibiting this distribu- ually increasing environmental variation first selects for range ex- tion, individual fitness is equal in all occupied habitat pansion, then selects for persisting coupled sink populations, and patches and individuals would decrease their fitness by ultimately leads to regional extinction. In contrast, continually in- moving into unoccupied patches. This distribution has creasing habitat degradation first selects for range contraction and been explored under a variety of conditions, including may select for persisting coupled sink populations before regional interference competition (Sutherland 1983, 1996; Tregenza extinction. These results highlight the combined roles of spatial and temporal heterogeneity on the evolution of habitat selection. et al. 1996), exploitative competition (Sutherland 1983; Milinski and Parker 1991; Oksanen et al. 1995; Krˇivan Keywords: habitat selection, evolutionarily stable strategies, environ- 2003), and multispecies interactions (van Baalen and Sa- mental stochasticity, spatial heterogeneity, source-sink dynamics, belis 1993, 1999; Krˇivan 1997; Cressman et al. 2004; Schrei- ideal free distribution. ber and Vejdani 2006). Surprisingly, while many of these studies assert that the ideal free distribution is an evolu- Introduction tionarily stable strategy (ESS), only recently has a delicate nonlinear analysis verified the ESS conditions (Cressman Habitat selection by individuals can profoundly influence et al. 2004; Cressman and Krˇivan 2006, 2010; Cantrell et population persistence in heterogenous landscapes (Pul- al. 2007, 2010). Under equilibrium conditions, the IFD liam and Danielson 1991; Greene 2003; Schmidt 2004), predicts that the fraction of individuals selecting a source stability of predator-prey interactions (van Baalen and Sa- patch is proportional to the carrying capacity of the source belis 1993; Krˇivan 1997; Schreiber and Vejdani 2006), and patch (Holt and Barfield 2001). Consequently, all sink geographical shifts in species distributions in response to patches are unoccupied as their carrying capacity is zero climate change (Morris 2011). While there are significant (Holt 1985). Neither of these predictions, however, agrees and extensive advances in the evolutionary theory of patch selection for populations living in spatially heterogeneous fully with empirical observations. environments (Morisita 1952, 1969; Fretwell and Lucas Observed patch distributions are frequently less extreme than predicted by the IFD: individuals underexploit * E-mail: [email protected]. higher-quality patches (i.e., undermatching) than pre- dicted by the IFD and overuse lower-quality patches (i.e., Am. Nat. 2012. Vol. 180, pp. 17–34. ᭧ 2012 by The University of Chicago. 0003-0147/2012/18001-53211$15.00. All rights reserved. overmatching; Milinski 1979, 1994; Abrahams 1986; Ken- DOI: 10.1086/665655 nedy and Gray 1993; Tregenza 1995). Explanations for This content downloaded from 169.237.045.004 on August 02, 2019 16:55:12 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 18 The American Naturalist these deviations include perceptual constraints (Abrahams lead to shifts in species distributions (Allen and Breshears 1986; Gray and Kennedy 1994), demographic stochasticity 1998), it is becoming increasingly important to understand (Regelmann 1984; Miller and Coll 2010), sampling vari- how environmental fluctuations influence species’ habitat ation (Regelmann 1984; Earn and Johnstone 1997), and choices. As a step toward this understanding, I present a environmental stochasticity (Hakoyama 2003; Jonze´n et general analysis of the evolution of patch selection strat- al. 2004). Of greatest relevance here, Hakoyama (2003) egies for freely dispersing populations living in spatially showed that if stochastic variation in resource availability and temporally heterogeneous landscapes. For these pop- in higher-quality patches is sufficiently greater than sto- ulations, I derive an analytic characterization for the ESS chastic variation in lower-quality patches, populations in these stochastic environments. Using this characteri- playing the ESS for patch selection undermatch the higher- zation, I examine how spatial correlations and temporal quality patches. This study, however, does not account for fluctuations inhibit or enhance the evolution of sink pop- population growth or resource depletion due to con- ulations, result in undermatching of higher-quality sumption. Consequently, ecological feedbacks on the evo- patches, determine local stochastic growth rates, and in- lution of patch selection are missing. In another study, fluence the evolution of species ranges in response to in- Jonze´n et al. (2004) examined the effects of environmental creased environmental variation or habitat destruction. stochasticity and population dynamics on patch distri- butions using a heuristic stochastic patch selection rule. However, Jonze´n et al. (2004, p. E110) readily admit that Model and Methods it “is not clear to what extent the stochastic habitat selec- Local and Regional Population Dynamics tion rule implemented here would also be [an] ESS.” Hence, it remains to be understand how environmental I model a population with overlapping generations living stochasticity and ecological feedbacks determine the ESS in a spatially heterogeneous environment consisting of k for patch selection. distinct patches. These patches may represent distinct hab- Contrary to the predictions of the classical IFD theory, itats, patches of the same habitat type, or combinations sink populations exist in a diversity of taxa, including vi- thereof. The abundance of the population in the ith patch i ruses (Sokurenko et al. 2006), plants (Anderson and Geber at time t isNt . Its rate of change is determined by a mixture 2010), birds (Tittler et al. 2006; Møller et al. 2006), fish of deterministic and stochastic environmental forces. More iip Ϫ i (Barson et al. 2009), and mammals (Naranjo and Bodmer specifically, the changeDNttN ϩDttN in small time 2007; Sulkava et al. 2007; Robinson et al. 2008). These stepDt satisfies population exhibit an extreme form of overmatching, as tϩDt sink patches cannot sustain population growth in the ab- ޅ D iiF p ͵ ޅ iiiF sence of immigration. Under equilibrium conditions, one [ NttN ] [fis(N )N sN t]ds explanation for the existence of these sink populations is t (1) maladaptive patch choice (Holt 1997). Alternatively, the- ≈ f (N ii)N Dt, ory suggests that sink populations may evolve when tem- it t poral variation is sufficiently great in source patches (Holt wherefi is the average per capita growth rate in patch i 1997; Jansen and Yoshimura 1998; Holt and Barfield 2001). andޅ[XFY] denotes the conditional expectation of a ran- When this occurs, numerical simulations by Holt and Bar- dom variable X given the random variable Y. To account field (2001) show that the geometric mean of fitness, a for intraspecific competition and population regulation natural measure of fitness in fluctuating environments, is within the patch, I assume thatfi is a decreasing function not equal in all occupied patches. In contrast, if all patches of local population abundance
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