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

Evolutionary game of environmental investment under national environmental regulation in China

With the rapid development of social economy, the deterioration of environment has become more and more serious; it is urgent to find a balance between economic development and environmental protection. Therefore, enterprises are appealed to invest in environmental protection, and local municipalities are appealed to supervise the environmental behaviors of enterprises, while central government plays a role of regulation. In order to study the preconditions for a better environmental strategy combination of local municipalities and enterprises, an evolutionary game theory was first constructed in this paper, then the evolutionary stable strategy (ESS) of local municipalities and enterprises under different scenarios was examined, and finally a simulation was used to test the results of the analysis. The results indicate that central government's regulation has influence on the strategies chosen by local municipalities and enterprises, the larger the degree of central government's incentives are, the more possible local municipalities and enterprises would choose environment-friendly strategies; and the intensity of central government's regulation, the cost and benefits of local municipalities' supervision, and the cost and benefits of enterprises' environmental investment are the key influence factors.

Evolution and Adaptation of Anti-predation Response of Prey in a Two-Patchy Environment

When perceiving a risk from predators, a prey may respond by reducing its reproduction and decreasing or increasing (depending on the species) its mobility. We formulate a patch model to investigate the aforementioned fear effect which is indirect, in contrast to the predation as a direct effect, of the predator on the prey population. We consider not only cost but also benefit of anti-predation response of the prey, and explore their trade-offs together as well as the impact of the fear effect mediated dispersals of the prey. In the case of constant response level, if there is no dispersal and for some given response functions, the model indicates the existence of an evolutionary stable strategy which is also a convergence stable strategy for the response level; and if there is dispersal, the analysis of the model shows that it will enhance the co-persistence of the prey on both patches. Considering the trait as another variable, we continue to study the evolution of anti-predation strategy for the model with dispersal, which leads to a three-dimensional system of ordinary differential equations. We perform some numerical simulations, which demonstrate global convergence to a positive equilibrium with the response level evolving towards a positive constant level, implying the existence of an optimal anti-predation response level.

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

Landscape permeability is often explored spatially, but may also vary temporally. Landscape permeability, including partial barriers, influences migratory animals that move across the landscape. Partial barriers are common in rivers where barrier passage varies with streamflow. We explore the influence of partial barriers on the spatial and temporal distribution of migration‐linked genotypes of Oncorhynchus mykiss, a salmonid fish with co‐occurring resident and migratory forms, in tributaries to the South Fork Eel River, California, USA, Elder and Fox Creeks. We genotyped >4,000 individuals using RAD‐capture and classified individuals as resident, heterozygous or migratory genotypes using life history‐associated loci. Across four years of study (2014–2017), the permeability of partial barriers varied across dry and wet years. In Elder Creek, the largest waterfall was passable for adults migrating up‐river 4–39 days each year. In this stream, the overall spatial pattern, with fewer migratory genotypes above the waterfall, remained true across dry and wet years (67%–76% of migratory alleles were downstream of the waterfall). We also observed a strong relationship between distance upstream and proportion of migratory alleles. In Fox Creek, the primary barrier is at the mouth, and we found that the migratory allele frequency varied with the annual timing of high flow events. In years when rain events occurred during the peak breeding season, migratory allele frequency was high (60%–68%), but otherwise it was low (30% in two years). We highlight that partial barriers and landscape permeability can be temporally dynamic, and this effect can be observed through changing genotype frequencies in migratory animals.

Migration to freshwater increases growth rates in a facultatively catadromous tropical fish

Diadromy is a form of migration where aquatic organisms undergo regular movements between fresh and marine waters for the purposes of feeding and reproduction. Despite having arisen in independent lineages of fish, gastropod molluscs and crustaceans, the evolutionary drivers of diadromous migration remain contentious. We test a key aspect of the 'productivity hypothesis', which proposes that diadromy arises in response to primary productivity differentials between marine and freshwater habitats. Otolith chemistry and biochronology data are analysed in a facultatively catadromous tropical fish (barramundi, Lates calcarifer) to determine the effect of freshwater residence on growth rates. Individuals that accessed freshwater grew ~ 25% faster on average than estuarine residents in the year following migration, suggesting that catadromy provides a potential fitness advantage over non-catadromous (marine/estuarine) life histories, as predicted by the productivity hypothesis. Although diadromous barramundi exhibited faster growth than non-diadromous fish, we suggest that the relative reproductive success of diadromous and non-diadromous contingents is likely to be strongly influenced by local environmental variability such as temporal differences in river discharge, and that this may facilitate the persistence of diverse life history strategies within populations.

A stochastic differential game approach toward animal migration

A stochastic differential game model for animal migration between two habitats under uncertain environment, a new population dynamics model, is formulated. Its novelty is the use of an impulse control formalism to naturally describe migrations with different timings and magnitudes that the conventional models could not handle. Uncertainty of the environment that the population faces with is formulated in the context of the multiplier robust control. The optimal migration strategy to give the maximized minimal profit is found through a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). A key message from HJBQVI is that its free boundary determines the optimal migration strategy. Solving the HJBQVI is carried out with a specialized stable and convergent finite difference scheme. This paper theoretically suggests that the sub-additivity of the performance index, the index to be optimized through the migration, critically affects the resulting strategy. The computational results with the established scheme are consistent with the theoretical predictions and support importance of the sub-additivity property. Social interaction to reduce the net mortality rate is also quantified, suggesting a linkage between the present and existing population dynamics models.

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature.

Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.