The migration game in habitat network: the case of tuna

The Ideal Free Distribution with travel costs

This article studies the effect of travel costs on population distribution in a patchy environment. The Ideal Free Distribution with travel costs is defined in the article as the distribution under which it is not profitable for individuals to move, i.e., the movement between patches ceases. It is shown that depending on the travel costs between patches, the Ideal Free Distribution may be unique, there may be infinitely many possible IFDs, or no Ideal Free Distribution exists. In the latter case, animal distribution can converge to an equilibrium of distributional dynamics at which individuals do disperse, but the net movement between patches ceases. Such distributional equilibrium corresponds to balanced dispersal.

Isotopic life-history signatures are retained in modern and ancient Atlantic bluefin tuna vertebrae

Isotopic, tagging and diet studies of modern-day teleosts lack the ability to contextualise life-histories and trophic dynamics with a historical perspective, when exploitation rates were lower and climatic conditions differed. Isotopic analysis of vertebrae, the most plentiful hard-part in archaeological and museum collections, can potentially fill this data-gap. Chemical signatures of habitat and diet use during growth are retained by vertebrae during bone formation. However, to fulfil their potential to reveal life-history and trophic dynamics, we need a better understanding of the time-frame recorded by vertebrae, currently lacking due to a poor understanding of fish bone remodelling. To address this issue, we serially-sectioned four vertebral centra of the highly migratory Atlantic bluefin tuna (Thunnus thynnus; BFT) captured off Sardinia (Italy) and analysed their isotopic composition. We show how carbon (δ¹³ C), nitrogen (δ¹⁵ N) and sulfur (δ³⁴ S) isotope values can vary significantly across BFT vertebrae growth-axes, revealing patterning in dietary life-histories. Further, we find similar patterns are revealed through incremental isotopic analysis of inner and outer vertebrae centra samples from thirteen archaeological BFT vertebrae dating between the 9^th -13^th century CE. Our results indicate that multi-year foraging signatures are retained in vertebrae and allow for the study of life-histories in both modern and paleo-environments. These novel methods can be extended across teleost taxa owing to their potential to inform management and conservation on how teleost trophic dynamics change over time and what their long-term environmental, ecological, and anthropological drivers are.

Copuling population dynamics and diel migration patterns

The diel vertical migration is one of the main drivers of population dynamics in the ocean. Population dynamical models of the ocean typically do not incorporate the behavioral aspects of the migration. We demonstrate a model with coupled population dynamics and behavior with the diel vertical migration emerging. We study the population dynamics and behavioral dynamics of a predator-prey system. We impose a cost of motion for both consumers and prey, and model each individual as following an Itô stochastic differential equation. We study the fixed-points of the ecosystem. Our modeling shows that as we increase the basal resource load, the strength of the diel vertical migration increases, as well as maximal velocity. In addition, a bimodal pattern emerges both for predators and consumers. The increase in the magnitude of the diel vertical migration causes a change in the allocation of copepod resources.

A regime shift in the Southeast Greenland marine ecosystem

Two major oceanographic changes have recently propagated through several trophic levels in coastal areas of Southeast Greenland (SEG). Firstly, the amount of drift-ice exported from the Fram Strait and transported with the East Greenland Current (EGC) has decreased significantly over the past two decades, and a main tipping element (summer sea ice) has virtually disappeared since 2003 leading to a regime shift in oceanographic and ecological conditions in the region. The following 20-year period with low or no coastal sea ice is unique in the 200-year history of ice observations in the region, and the regime shift is also obvious in the volume of ice export through the Fram Strait after 2013. In the same period, the temperature of the EGC south of 73.5 N has increased significantly (>2°C) since 1980. Secondly, the warm Irminger Current, which advects warm, saline Atlantic Water into the region, has become warmer since 1990. The lack of pack ice in summer together with a warming ocean generated cascading effects on the ecosystem in SEG that are manifested in a changed fish fauna with an influx of boreal species in the south and the subarctic capelin further north. At higher trophic levels there has been an increase in the abundance of several boreal cetaceans (humpback, fin, killer, and pilot whales and dolphins) that are either new to this area or occur in historically large numbers. It is estimated that the new cetacean species in SEG are responsible for an annual predation level of 700,000 tons of fish. In addition, predation on krill species is estimated at >1,500,000 tons mainly consumed by fin whales. Simultaneously, there has been a reduction in the abundance and catches of narwhals and walruses in SEG and it is suggested that these species have been impacted by the habitat changes.

First tagging data on large Atlantic bluefin tuna returning to Nordic waters suggest repeated behaviour and skipped spawning

Atlantic bluefin tuna (Thunnus thynnus; ABFT) is one of the most iconic fish species in the world. Recently, after being very rare for more than half a century, large bluefin tunas have returned to Nordic waters in late summer and autumn, marking the return of the largest predatory fish in Nordic waters. By tagging 18 bluefin tunas with electronic tags (pop-up satellite archival tags), we show that bluefin tuna observed in Nordic waters undertake different migration routes, with individuals migrating into the western Atlantic Ocean, while others stay exclusively in the eastern Atlantic and enter the Mediterranean Sea to spawn. We additionally present evidence of possible skipped spawning inferred from behavioural analyses. In Nordic waters, ABFT are primarily using the upper water column, likely reflecting feeding activity. The results support the hypothesis that ABFT migrating to Nordic waters return to the same general feeding area within the region on an annual basis. These observations may have important implications for management because (1) tunas that come into Nordic waters might represent only a few year classes (as evidenced by a narrow size range), and thus may be particularly vulnerable to area-specific exploitation, and (2) challenge the assumption of consecutive spawning in adult Atlantic bluefin tuna, as used in current stock assessment models. Without careful management and limited exploitation of this part of the ABFT population, the species’ return to Nordic waters could be short-lived.

Solving multispecies population games in continuous space and time

Game theory has emerged as an important tool to understand interacting populations in the last 50 years. Game theory has been applied to study population dynamics with optimal behavior in simple ecosystem models, but existing methods are generally not applicable to complex systems. In order to use game-theory for population dynamics in heterogeneous habitats, habitats are usually split into patches and game-theoretic methods are used to find optimal patch distributions at every instant. However, populations in the real world interact in continuous space, and the assumption of decisions based on perfect information is a large simplification. Here, we develop a method to study population dynamics for interacting populations, distributed optimally in continuous space. A continuous setting allows us to model bounded rationality, and its impact on population dynamics. This is made possible by our numerical advances in solving multiplayer games in continuous space. Our approach hinges on reformulating the instantaneous game, applying an advanced discretization method and modern optimization software to solve it. We apply the method to an idealized case involving the population dynamics and vertical distribution of forage fish preying on copepods. Incorporating continuous space and time, we can model the seasonal variation in the migration, separating the effects of light and population numbers. We arrive at qualitative agreement with empirical findings. Including bounded rationality gives rise to spatial distributions corresponding to reality, while the population dynamics for bounded rationality and complete rationality are equivalent. Our approach is general, and can easily be used for complex ecosystems.

Environmental Conditions along Tuna Larval Dispersion: Insights on the Spawning Habitat and Impact on Their Development Stages

Estimated larval backward trajectories of three Tuna species, namely, Atlantic Bluefin Tuna (Thunnus thynnus, Linnaeus, 1758), Bullet Tuna (Auxis Rochei, Risso, 1801) and Albacore Tuna (Thunnus alalunga, Bonnaterre, 1788) in the central Mediterranean Sea, were used to characterize their spawning habitats, and to assess the impact of changes due to the major environmental parameters (i.e., sea surface temperature and chlorophyll-a concentration) on larval development during their advection by surface currents. We assumed that the environmental variability experienced by larvae along their paths may have influenced their development, also affecting their survival. Our results showed that the Tuna larvae underwent an accelerated growth in favorable environmental conditions, impacting on the notochord development. In addition, further updated information on spawning and larval retention habitats of Atlantic Bluefin Tuna, Bullet and Albacore Tunas in the central Mediterranean Sea were delivered.

Consequences of barriers and changing seasonality on population dynamics and harvest of migratory ungulates

Many animal populations providing ecosystem services, including harvest, live in seasonal environments and migrate between seasonally distinct ranges. Unfortunately, two major sources of human-induced global change threaten these populations: climate change and anthropogenic barriers. Anthropogenic infrastructure developments present a global threat to animal migrations through increased migration mortality or behavioral avoidance. Climate change alters the seasonal and spatial dynamics of resources and therefore the effects of migration on population performance. We formulated a population model with ideal-free migration to investigate changes in population size and harvest yield due to barriers and seasonal dynamics. The model predicted an increasing proportion of migrants when the difference between areas in seasonality or carrying capacity increased. Both migration cost and behavioral avoidance of barriers substantially reduced population size and harvest yields. Not surprisingly, the negative effects of barriers were largest when the population benefited most from migration. Despite the overall decline in harvest yield from a migratory population due to barriers, barriers could result in locally increased yield from the resident population following reduced competition from migrants. Our approach and results enhance the understanding of how global warming and infrastructure development worldwide may change population dynamics and harvest offtake affecting livelihoods and rural economies.

Models and measures of animal aggregation and dispersal

The dispersal of individuals within an animal population will depend upon local properties intrinsic to the environment that differentiate superior from inferior regions as well as properties of the population. Competing concerns can either draw conspecifics together in aggregation, such as collective defence against predators, or promote dispersal that minimizes local densities, for instance to reduce competition for food. In this paper we consider a range of models of non-independent movement. We include established models, such as the ideal free distribution, but also develop novel models, such as the wheel. We also develop several ways to combine different models to create a flexible model of addressing a variety of dispersal mechanisms. We further devise novel measures of movement coordination and show how to generate a population movement that achieves appropriate values of the measure specified. We find the value of these measures for each of the core models described, as well as discuss their use, and potential limitations, in discerning the underlying movement mechanisms. The movement framework that we develop is both of interest as a stand-alone process to explore movement, but also able to generate a variety of movement patterns that can be embedded into wider evolutionary models where movement is not the only consideration.

Stochastic optimal switching model for migrating population dynamics

An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

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.

A simple game-theoretic model for upstream fish migration

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.