Abstract:Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology. The spatial distribution of fish populations observed in the wild results from the complex interactions of multiple controls both external or internal to the fish populations. Whilst species distribution models (SDMs) have been mostly concerned with static description of species distribution as a function of environmental constraints, models of animal movements (MAMs) have focussed on the dynamic nature of spatial distribution of groups of individuals under a number of constraints external and internal to the population. Besides SDMs and MAMs, modelling the spatial distribution of fish populations can be achieved by models that are fundamentally static (like SDMs) but can also incorporate many hypotheses on the control of fish spatial distribution (like MAMs). The hypotheses underlying these models need to make sense at the population level -rather than at the individual or species level -we term these 'population distribution models' (PDMs). PDMs are statistical models that rely on several hypotheses, which include: (i) control through geographical attachment, (ii) environmental conditions, (iii) density-dependent habitat selection, (iv) spatial dependency, (v) population demographic structure, (vi) species interactions and (vii) population memory. We review the basis behind each of these conceptual models and we examine corresponding numerical applications. We argue that the conceptual models are complementary rather than competing, that existing numerical applications are still rarely compared and combined, and that PDMs can offer a statistical framework to achieve this. We recommend that the numerical models associated with different hypotheses be constructed within such a common general framework. This will permit evaluation, comparison and combination of the multiple hypotheses on fish spatial distribution. It will ultimately lead to a more comprehensive understanding of the factors controlling the spatial distribution of fish populations and to more accurate predictions in which model uncertainty is accounted for.

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Cod, harp seal and minke whale are the main top predators in the Barents Sea ecosystem. In the last decade, the abundance of cod has increased considerably, and is at a record high level. In spite of this, the growth and condition of cod has remained rather stable, although some decrease is seen in size at age of large, mature cod. During the same period, the abundance of harp seals has declined whereas the minke whale stock has been at a stable level. The body condition (blubber thickness) of these two mammal stocks has, however, decreased, with the strongest decrease observed for harp seals. A possible hypothesis for explaining this is that cod outperform the marine mammal stocks in the competition for food. The main advantages for cod are most likely larger availability of food (mainly capelin) during winter-spring than for marine mammals, as well as a wider range of prey species being available to cod than to marine mammals. Harp seals are more dependent on prey items found close to the ice edge than the other two predator stocks are, which could partly explain why the performance of harp seals is worse than that of the two other main top predators in the area.

Atlantic minke whales are important predators in the Barents Sea ecosystem; capelin Mallotus villosus, krill Thysanoessa sp. and Meganyctephanes norvegica and herring Clupea harengus are their major prey. Their consumption of commercial species may present an economic problem for the local fishery. In order to estimate this consumption and understand the potential consequences for prey dynamics, it is essential to determine the multispecies functional response of the whales. The parameterisation of a functional response requires measurements of consumption rates and prey availability. In this localised study, undigested stomach contents were used to assess the amount of each prey that had been consumed immediately prior to capture. To determine the availability of prey to the whales, standard acoustic surveys were run in the same area within 2 d of the capture of the whales. The spatial distribution of prey was modelled using generalised additive models (GAMs). In order to generate a measure of prey availability and the uncertainty in this value, a simple model was assumed for whale movement, and prey abundance was sampled over space according to a Gaussian kernel. A multispecies functional response (MSFR) model was then fitted to the consumption and prey availability data using Bayesian methods. Simple simulations, based on the fitted MSFR, indicate that minke whales may deplete local capelin aggregations at small spatial scales. This is the first time that a multispecies functional response has been fitted for a cetacean predator, and the methods outlined here may prove useful for modelling marine mammal-fish interactions in other systems.