Scaling of the mean and variance of population dynamics under fluctuating regimes

An optimal stopping approach for onset of fish migration

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.

Population dynamics, synchrony, and environmental quality of Hokkaido voles lead to temporal and spatial Taylor's laws

Taylor's law (TL) asserts that the variance in a species' population density is a power-law function of its mean population density: log(variance) = a + b × log(mean). TL is widely verified. We show here that empirical time series of density of the Hokkaido gray-sided vole, Myodes rufocanus, sampled 1962-1992 at 85 locations, satisfied temporal and spatial forms of TL. The slopes (b ± standard error) of the temporal and spatial TL were estimated to be 1.613 ± 0.141 and 1.430 ± 0.132, respectively. A previously verified autoregressive Gompertz model of the dynamics of these populations generated time series of density which reproduced the form of temporal and spatial TLs, but with slopes that were significantly steeper than the slopes estimated from data. The density-dependent components of the Gompertz model were essential for the temporal TL. Adding to the Gompertz model assumptions that populations with higher mean density have reduced variance of density-independent perturbations and that density-independent perturbations are spatially correlated among populations yielded simulated time series that satisfactorily reproduced the slopes from data. The slopes (b ± standard error) of the enhanced simulations were 1.619 ± 0.199 for temporal TL and 1.575 ± 0.204 for spatial TL.

Barn Owl Productivity Response to Variability of Vole Populations

We studied the response of the barn owl annual productivity to the common vole population numbers and variability to test the effects of environmental stochasticity on their life histories. Current theory predicts that temporal environmental variability can affect long-term nonlinear responses (e.g., production of young) both positively and negatively, depending on the shape of the relationship between the response and environmental variables. At the level of the Czech Republic, we examined the shape of the relationship between the annual sum of fledglings (annual productivity) and vole numbers in both non-detrended and detrended data. At the districts’ level, we explored whether the degree of synchrony (measured by the correlation coefficient) and the strength of the productivity response increase (measured by the regression coefficient) in areas with higher vole population variability measured by the s-index. We found that the owls’ annual productivity increased linearly with vole numbers in the Czech Republic. Furthermore, based on district data, we also found that synchrony between dynamics in owls’ reproductive output and vole numbers increased with vole population variability. However, the strength of the response was not affected by the vole population variability. Additionally, we have shown that detrending remarkably increases the Taylor’s exponent b relating variance to mean in vole time series, thereby reversing the relationship between the coefficient of variation and the mean. This shift was not responsible for the increased synchrony with vole population variability. Instead, we suggest that higher synchrony could result from high food specialization of owls on the common vole in areas with highly fluctuating vole populations.