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.

Random sampling of skewed distributions implies Taylor's power law of fluctuation scaling

Taylor's law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species' population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)(b), a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared.