Spatial synchrony in population dynamics: The effects of demographic stochasticity and density regulation with a spatial scale

Seasonality in Environment and Population Processes Alters Population Spatial Synchrony

AbstractPopulation spatial synchrony-the tendency for temporal population fluctuations to be correlated across locations-is common and important to metapopulation stability and persistence. One common cause of spatial synchrony, termed the Moran effect, occurs when populations respond to environmental fluctuations, such as weather, that are correlated over space. Although the degree of spatial synchrony in environmental fluctuations can differ between seasons and different population processes occur in different seasons, the impact on population spatial synchrony is uncertain because prior work has largely assumed that the spatial synchrony of environmental fluctuations and their effect on populations are consistent over annual sampling intervals. We used theoretical models to examine how seasonality in population processes and the spatial synchrony of environmental drivers affect population spatial synchrony. We found that population spatial synchrony can depend not only on the spatial synchrony of environmental drivers but also on the degree to which environmental fluctuations are correlated across seasons, locally, and across space. Moreover, measurements of synchrony from "snapshot" population censuses may not accurately reflect synchrony during other parts of the year. Together, these results show that neglecting seasonality in environmental conditions and population processes is consequential for understanding population spatial synchrony and its driving mechanisms.

Generation time and seasonal migration explain variation in spatial population synchrony across European bird species

Spatial population synchrony is common among populations of the same species and is an important predictor of extinction risk. Despite the potential consequences for metapopulation persistence, we still largely lack understanding of what makes one species more likely to be synchronized than another given the same environmental conditions. Generally, environmental conditions in a shared environment or a species' sensitivity to the environment can explain the extent of synchrony. Populations that are closer together experience more similar fluctuations in their environments than those populations that are further apart and are therefore more synchronized. The relative importance of environmental and demographic stochasticity for population dynamics is strongly linked to species' life-history traits, such as pace of life, which may impact population synchrony. For populations that migrate, there may be multiple environmental conditions at different locations driving synchrony. However, the importance of life history and migration tactics in determining patterns of spatial population synchrony have rarely been explored empirically. We therefore hypothesize that increasing generation time, a proxy for pace of life, would decrease spatial population synchrony and that migrants would be less synchronized than resident species. We used population abundance data on breeding birds from four countries to investigate patterns of spatial population synchrony in growth rate and abundance. We calculated the mean spatial population synchrony between log-transformed population growth rates or log-transformed abundances for each species and country separately. We investigated differences in synchrony across generation times in resident (n = 67), short-distance migrant (n = 86) and long-distance migrant (n = 39) bird species. Species with shorter generation times were more synchronized than species with longer generation times. Short-distance migrants were more synchronized than long-distance migrants and resident birds. Our results provide novel empirical links between spatial population synchrony and species traits known to be of key importance for population dynamics, generation time and migration tactics. We show how these different mechanisms can be combined to understand species-specific causes of spatial population synchrony. Understanding these specific drivers of spatial population synchrony is important in the face of increasingly severe threats to biodiversity and could be key for successful future conservation outcomes.

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.

Spatial synchrony in sub-arctic geometrid moth outbreaks reflects dispersal in larval and adult life cycle stages

Spatial synchrony in population dynamics can be caused by dispersal or spatially correlated variation in environmental factors like weather (Moran effect). Distinguishing between these mechanisms is challenging for natural populations, and the study of dispersal-induced synchrony in particular has been dominated by theoretical modelling and laboratory experiments. The goal of the present study was to evaluate the evidence for dispersal as a cause of meso-scale (distances of tens of kilometres) spatial synchrony in natural populations of the two cyclic geometrid moths Epirrita autumnata and Operophtera brumata in sub-arctic mountain birch forest in northern Norway. To infer the role of dispersal in geometrid synchrony, we applied three complementary approaches, namely estimating the effect of design-based dispersal barriers (open sea) on synchrony, comparing the strength of synchrony between E. autumnata (winged adults) and the less dispersive O. brumata (wingless adult females), and relating the directionality (anisotropy) of synchrony to the predominant wind directions during spring, when geometrid larvae engage in windborne dispersal (ballooning). The estimated effect of dispersal barriers on synchrony was almost three times stronger for the less dispersive O. brumata than E. autumnata. Inter-site synchrony was also weakest for O. brumata at all spatial lags. Both observations argue for adult dispersal as an important synchronizing mechanism at the spatial scales considered. Further, synchrony in both moth species showed distinct anisotropy and was most spatially extensive parallel to the east-west axis, coinciding closely to the overall dominant wind direction. This argues for a synchronizing effect of windborne larval dispersal. Congruent with most extensive dispersal along the east-west axis, E. autumnata also showed evidence for a travelling wave moving southwards at a speed of 50-80 km/year. Our results suggest that dispersal processes can leave clear signatures in both the strength and directionality of synchrony in field populations, and highlight wind-driven dispersal as promising avenue for further research on spatial synchrony in natural insect populations.

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.