Spatial synchrony and harvesting in fluctuating populations:Relaxing the small noise assumption

Effects of local density dependence and temperature on the spatial synchrony of marine fish populations

Disentangling empirically the many processes affecting spatial population synchrony is a challenge in population ecology. Two processes that could have major effects on the spatial synchrony of wild population dynamics are density dependence and variation in environmental conditions like temperature. Understanding these effects is crucial for predicting the effects of climate change on local and regional population dynamics. We quantified the direct contribution of local temperature and density dependence to spatial synchrony in the population dynamics of nine fish species inhabiting the Barents Sea. First, we estimated the degree to which the annual spatial autocorrelations in density are influenced by temperature. Second, we estimated and mapped the local effects of temperature and strength of density dependence on annual changes in density. Finally, we measured the relative effects of temperature and density dependence on the spatial synchrony in changes in density. Temperature influenced the annual spatial autocorrelation in density more in species with greater affinities to the benthos and to warmer waters. Temperature correlated positively with changes in density in the eastern Barents Sea for most species. Temperature had a weak synchronizing effect on density dynamics, while increasing strength of density dependence consistently desynchronised the dynamics. Quantifying the relative effects of different processes affecting population synchrony is important to better predict how population dynamics might change when environmental conditions change. Here, high degrees of spatial synchrony in the population dynamics remained unexplained by local temperature and density dependence, confirming the presence of additional synchronizing drivers, such as trophic interactions or harvesting.

Age-dependent patterns of spatial autocorrelation in fish populations

The degree of spatial autocorrelation in population fluctuations increases with dispersal and geographical covariation in the environment, and decreases with strength of density dependence. Because the effects of these processes can vary throughout an individual's lifespan, we studied how spatial autocorrelation in abundance changed with age in three marine fish species in the Barents Sea. We found large interspecific differences in age-dependent patterns of spatial autocorrelation in density. Spatial autocorrelation increased with age in cod, the reverse trend was found in beaked redfish, while it remained constant among age classes in haddock. We also accounted for the average effect of local cohort dynamics, i.e. the expected local density of an age class given last year's local density of the cohort, with the goal of disentangling spatial autocorrelation patterns acting on an age class from those formed during younger age classes and being carried over. We found that the spatial autocorrelation pattern of older age classes became increasingly determined by the distribution of the cohort during the previous year. Lastly, we found high degrees of autocorrelation over long distances for the three species, suggesting the presence of far-reaching autocorrelating processes on these populations. We discuss how differences in the species' life history strategies could cause the observed differences in age-specific variation in spatial autocorrelation. As spatial autocorrelation can differ among age classes, our study indicates that fluctuations in age structure can influence the spatio-temporal variation in abundance of marine fish populations.

A general mathematical method for predicting spatio-temporal correlations emerging from agent-based models

Agent-based models are used to study complex phenomena in many fields of science. While simulating agent-based models is often straightforward, predicting their behaviour mathematically has remained a key challenge. Recently developed mathematical methods allow the prediction of the emerging spatial patterns for a general class of agent-based models, whereas the prediction of spatio-temporal pattern has been thus far achieved only for special cases. We present a general and mathematically rigorous methodology that allows deriving the spatio-temporal correlation structure for a general class of individual-based models. To do so, we define an auxiliary model, in which each agent type of the primary model expands to three types, called the original, the past and the new agents. In this way, the auxiliary model keeps track of both the initial and current state of the primary model, and hence the spatio-temporal correlations of the primary model can be derived from the spatial correlations of the auxiliary model. We illustrate the agreement between analytical predictions and agent-based simulations using two example models from theoretical ecology. In particular, we show that the methodology is able to correctly predict the dynamical behaviour of a host–parasite model that shows spatially localized oscillations.

Hidden similarities in the dynamics of a weakly synchronous marine metapopulation

Populations of many marine species are only weakly synchronous, despite coupling through larval dispersal and exposure to synchronous environmental drivers. Although this is often attributed to observation noise, factors including local environmental differences, spatially variable dynamics, and chaos might also reduce or eliminate metapopulation synchrony. To differentiate spatially variable dynamics from similar dynamics driven by spatially variable environments, we applied hierarchical delay embedding. A unique output of this approach, the "dynamic correlation," quantifies similarity in intrinsic dynamics of populations, independently of whether their abundance is correlated through time. We applied these methods to 17 populations of blue crab (Callinectes sapidus) along the US Atlantic coast and found that their intrinsic dynamics were broadly similar despite largely independent fluctuations in abundance. The weight of evidence suggests that the latitudinal gradient in temperature, filtered through a unimodal response curve, is sufficient to decouple crab populations. As unimodal thermal performance is ubiquitous in ectotherms, we suggest that this may be a general explanation for the weak synchrony observed at large distances in many marine species, although additional studies are needed to test this hypothesis.

The effect of harvesting on the spatial synchrony of population fluctuations

Harvesting in space affects, in general, the spatial scale of the synchrony in the population fluctuations, which determines the size of the areas subjected to simultaneous quasi-extinction risk. Here we show that harvesting reduces the population synchrony scale if it depends more strongly on population fluctuations than the density dependence of the growth rate in the absence of harvesting. We show that constant and proportional harvesting always increases the spatial scale, using a theta-logistic model for density regulation. We also provide exact scaling results under harvesting for the Beverton-Holt and the Ricker stock-recruitment models that are commonly applied, e.g. in fisheries. Our results indicate that harvest in areas with large abundances should be encouraged to avoid increase of the spatial scale of synchrony in the population fluctuations that can lead to unexpected quasi-extinction of populations over large areas. Our results quantify this harvesting impact giving the resulting scales of spatial synchrony of population fluctuations. This emphasizes the importance of estimating the form of density dependence as well as the dependency of harvest upon population density of exploited populations, in order to get reliable predictions of the size of areas that can undergo simultaneous quasi-extinction.

Spatial distribution and optimal harvesting of an age-structured population in a fluctuating environment

We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities. A general result is that the squared scale has an additive term equal to the squared scale of the environmental noise, corresponding to the Moran effect, as well as additive terms proportional to the dispersal rate and variance of dispersal distance for the age classes and approximately inversely proportional to the strength of density regulation. We show that the optimal harvesting strategy in the deterministic case is to harvest only juveniles when their relative value (e.g. financial) is large, and otherwise only adults. With increasing environmental stochasticity there is an interval of increasing length of values of juveniles relative to adults where both age classes should be harvested. Harvesting generally tends to increase all spatial scales of the autocovariances of densities.