The puzzle of partial migration: Adaptive dynamics and evolutionary game theory perspectives

Abstract

We consider the phenomenon of partial migration which is exhibited by populations in which some individuals migrate between habitats during their lifetime, but others do not. First, using an adaptive dynamics approach, we show that partial migration can be explained on the basis of negative density dependence in the per capita fertilities alone, provided that this density dependence is attenuated for increasing abundances of the subtypes that make up the population. We present an exact formula for the optimal proportion of migrants which is expressed in terms of the vital rates of migrant and non-migrant subtypes only. We show that this allocation strategy is both an evolutionary stable strategy (ESS) as well as a convergence stable strategy (CSS). To establish the former, we generalize the classical notion of an ESS because it is based on invasion exponents obtained from linearization arguments, which fail to capture the stabilizing effects of the nonlinear density dependence. These results clarify precisely when the notion of a "weak ESS", as proposed in Lundberg (2013) for a related model, is a genuine ESS. Secondly, we use an evolutionary game theory approach, and confirm, once again, that partial migration can be attributed to negative density dependence alone. In this context, the result holds even when density dependence is not attenuated. In this case, the optimal allocation strategy towards migrants is the same as the ESS stemming from the analysis based on the adaptive dynamics. The key feature of the population models considered here is that they are monotone dynamical systems, which enables a rather comprehensive mathematical analysis.

Temporal dynamics of migration‐linked genetic variation are driven by streamflows and riverscape permeability

“…Once a habitat is occupied by both resident and migratory individuals, the individual decision to migrate is often considered a threshold trait (Pulido, 2011). Furthermore, partial migration can be considered an evolutionary stable strategy such that migration is condition-dependent (Lundberg, 1987), and strongly influenced by the density of conspecifics (De Leenheer, Mohapatra, Ohms, Lytle, & Cushing, 2017). Together, these processes may create feedback loops, such that habitats that can be accessed by migratory animals tend to have higher densities of juveniles (Bohlin et al, 2001;Nilsson, Lindström, Jonzén, Nilsson, & Karlsson, 2006), which can then encourage migration (Kaitala, Kaitala, & Lundberg, 1993;Taylor & Norris, 2007).…”

Partial migration alters population ecology and food chain length: evidence from a salmonid fish

“…, Taylor and Norris , De Leenheer et al. ). This competitive release hypothesis, in which individuals migrate from high‐density habitats to escape competition (Chapman et al.…”

“…Theoretical studies often cite density dependence as a cause, rather than a consequence, of migration (Kaitala et al 1993, Taylor and Norris 2007, De Leenheer et al 2017). This competitive release hypothesis, in which individuals migrate from high-density habitats to escape competition (Chapman et al 2011), has considerable empirical support from birds (Nilsson et al 2006), ungulates (Mysterud et al 2011), andfishes (Olsson et al 2006).…”

“…) or the evolutionary stability of this polymorphism (Lundberg , De Leenheer et al. ). Ecological implications of, rather than as a cause for, migration remain poorly understood, with fewer studies exploring this topic (Fryxell and Sinclair , Palkovacs and Post , Hansen et al.…”

“…Partial migration is common across migratory taxa (Chapman et al 2011), including ungulates (Ball et al 2001, Cagnacci et al 2011, fishes (Chapman et al 2012), birds (Boyle 2008, Jahn et al 2010, Sanz-Aguilar et al 2012, and insects (Attisano et al 2013, Odermatt et al 2017. Past research on partially migratory animals has focused on trade-offs favoring this polymorphism (reviewed in Chapman et al 2011) or the evolutionary stability of this polymorphism (Lundberg 2013, De Leenheer et al 2017. Ecological implications of, rather than as a cause for, migration remain poorly understood, with fewer studies exploring this topic (Fryxell and Sinclair 1988, Palkovacs and Post 2009, Hansen et al 2019.…”