Collective behavior as a driver of critical transitions in migratory populations

This study focuses on the population dynamics of species that utilize collective navigation during their migrations. Theory and experimental evidence suggest that social interactions may help animals traveling in groups to find their way when navigating through challenging environments, and that these effects should increase for larger groups [6, 7, 10–16, 20–23, 62, 63]. The potential effects, from these individual-level mechanisms, at the population or community level are, however, not well studied or described. With the current study we offer insight into the ecological dynamics that may result from individuals in migratory populations traveling in groups. Rather than using individual-based models and assuming specific interaction rules, we bestow individuals in ODE population models with generic group-level benefits, based on empirical studies of collective behavior. We use these models to investigate to what extent group level benefits affect the possible population-level dynamics of social species. We find that while collective behavior can positively affect migratory populations, it can also result in non-linear effects and sudden collapses under broad environmental conditions.

The types of migrations we have studied here represent two of the most prevalent types of migrations: travel to specific breeding sites, and movement to track regions of favorable conditions. Our models were based stylistically on the movement ecology of salmon (Models 1 2) and wildebeests (Model 3); however, they should apply in a generic sense to a wide array of taxa. Moreover, the specific choice of population model, outfitted with a collective accuracy term, should not qualitatively change our results. This is because our results are a product of the feedback between migratory ability and population density, rather than a feature of any system-specific biology. For example, one could modify our model of breeding migrations, in which individuals travel one way to discrete fixed end-points to breed, to fit many species of migratory birds, by adding another equivalent movement stage reflecting the navigational challenges on their return journey back to the feeding grounds. Alternately, one could assume that our navigational accuracy term, a(U), applies, as is, to the round trip to the feeding grounds and then back to the breeding grounds and simply remove the assumption of semelparity.

Migratory populations may face a multitude of external perturbations to their survival. In our models we have accounted for such processes by implementing a generic mortality term, h. This term represents effects such as additional mortality due to harvesting, the introduction of new diseases or predators, or climate change. It could also represent impedances to migration such as dams, roads, buildings or reduction of migration corridors, which in addition to causing mortality, may restrict the ability, or tendency, of animals to move.

We have focused on collective navigation as the main group benefit during migrations, and include this benefit as a monotonic increase in accuracy (breeding migrations) or resource tracking ability (feeding migrations) as a function of population size (Eq. (3)). One could, in principle, recast the a(U) term as a general benefit of collective behavior, such as an increase in probability to properly time a migration [64–66] or survive predation en route, or a boost in efficiency due to aerodynamic benefits [67] or by collectively navigating a more efficient route [12].

We implicitly assume that greater population density results in larger typical group sizes. This is supported by empirical [68] and theoretical [9, 69] results that suggest that this is the case for social species. For simplicity, in the breeding migration model we assume that the population is limited by resources on the feeding grounds. Though not shown, we confirmed numerically that assuming that the limiting resource is on the breeding grounds does not change our results. Also for simplicity, in the feeding migrations we assume that the group tracks only a single favorable region, does so indefinitely and breeds continuously along the way. We stress that a population needs only to be limited by a dynamic resource field for a portion of their life-cycle (or the season) for this model to qualitatively apply.

Populations of migratory schooling fishes, including striped bass, capelin, herring, sardine, anchovy and cod, subject to intense fishing pressure have collapsed and may be slow to recover (see [70] and references therein). Though there are other explanations for such collapses [71], this is consistent with the Allee effect predicted by our models. Similarly, caribou herds have ceased to migrate after population declines and only started again once the population recovered [72]. Associations between numbers of migrants and migration distance have been observed in wildebeest [73] and there are many historical examples of migration collapse for both the blue and black wildebeest [74], however little is known about the exact nature of these events.

More subtly, our multi-site model (Model 2) suggests that there may be critical levels of additional mortality at which local adaptation and population genetic structure collapses (Fig. 4). Our model did not explicitly consider interbreeding between locally adapted and non-locally adapted types, which could further erode local adaptation at a site, so the collapse we observe should perhaps be considered an upper bound on local adaptation. Feedbacks between local adaptation and dispersal may strengthen such a collapse [75]. This may be particularly relevant when we consider anadromous salmon, which do home more accurately in years of greater density [11, 30] and are locally adapted to their natal streams [48–50], however, they do not appear to suffer Allee effects when looking at population size [76, 77]. Though it might not be observable to stock managers with their eye on population enumeration and straying rates, this sudden shift in percentage of locally adapted fish could erode portfolio effects [78] which play an important role in stabilizing populations on larger scales [79].