Interspecific differences in stochastic population dynamics explains variation in Taylor's temporal power law

Taylor's power law for freshwater fishes: Functional traits beyond statistical inevitability

Taylor's power law (TPL) describes the expected range of parameters of the mean-variance scaling relationship and has been extensively used in studies examining temporal variations in abundance. Few studies though have focused on biological and ecological covariates of TPL, while its statistical inherences have been extensively debated. In the present study, we focused on species-specific features (i.e. functional traits) that could be influential to temporal TPL. We combined field surveys of 180 fish species from 972 sites varying from small streams to large rivers with data on 31 ecological traits describing species-specific characteristics related to three main niche dimensions (trophic ecology, life history, and habitat use). For each species, the parameters of temporal TPL (intercept and slope) were estimated from the log-log mean-variance relationships while controlling for spatial dependencies and biological covariates (species richness and evenness). Then, we investigated whether functional traits explained variations in TPL parameters. Differences in TPL parameters among species were explained mostly by life history and environmental determinants, especially TPL slope. Life history was the main determinant of differences in TPL parameters and thereby aggregation patterns, with traits related to body size being the most influential, thus showing a high contrast between small-sized species with short lifespans and large-bodied migratory fishes, even after controlling for phylogenetic resemblances. We found that life history traits, especially those related to body size, mostly affect TPL and, as such, can be determinants of temporal variability of fish populations. We also found that statistical effects and phylogenetic resemblances are embedded in mean-variance relationships for fish, and that environmental drivers can interact with ecological characteristics of species in determining temporal fluctuations in abundance.

Proximate determinants of Taylor's law slopes

Taylor's law (TL), a commonly observed and applied pattern in ecology, describes variances of population densities as related to mean densities via log(variance) = log(a) + b*log(mean). Variations among datasets in the slope, b, have been associated with multiple factors of central importance in ecology, including strength of competitive interactions and demographic rates. But these associations are not transparent, and the relative importance of these and other factors for TL slope variation is poorly studied. TL is thus a ubiquitously used indicator in ecology, the understanding of which is still opaque. The goal of this study was to provide tools to help fill this gap in understanding by providing proximate determinants of TL slopes, statistical quantities that are correlated to TL slopes but are simpler than the slope itself and are more readily linked to ecological factors. Using numeric simulations and 82 multi-decadal population datasets, we here propose, test and apply two proximate statistical determinants of TL slopes which we argue can become key tools for understanding the nature and ecological causes of TL slope variation. We find that measures based on population skewness, coefficient of variation and synchrony are effective proximate determinants. We demonstrate their potential for application by using them to help explain covariation in slopes of spatial and temporal TL (two common types of TL). This study provides tools for understanding TL, and demonstrates their usefulness.

Heterogeneous 'proportionality constants' - A challenge to Taylor's Power Law for temporal fluctuations in abundance

Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.

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.

Direct evidence that density-dependent regulation underpins the temporal stability of abundant species in a diverse animal community

To understand how ecosystems are structured and stabilized, and to identify when communities are at risk of damage or collapse, we need to know how the abundances of the taxa in the entire assemblage vary over ecologically meaningful timescales. Here, we present an analysis of species temporal variability within a single large vertebrate community. Using an exceptionally complete 33-year monthly time series following the dynamics of 81 species of fishes, we show that the most abundant species are least variable in terms of temporal biomass, because they are under density-dependent (negative feedback) regulation. At the other extreme, a relatively large number of low abundance transient species exhibit the greatest population variability. The high stability of the consistently common high abundance species—a result of density-dependence—is reflected in the observation that they consistently represent over 98% of total fish biomass. This leads to steady ecosystem nutrient and energy flux irrespective of the changes in species number and abundance among the large number of low abundance transient species. While the density-dependence of the core species ensures stability under the existing environmental regime, the pool of transient species may support long-term stability by replacing core species should environmental conditions change.