Taylor's law, one of the most widely accepted generalizations in ecology, states that the variance of a population abundance time series scales as a power law of its mean. Here we reexamine this law and the empirical evidence presented in support of it. Specifically, we show that the exponent generally depends on the length of the time series, and its value reflects the combined effect of many underlying mechanisms. Moreover, sampling errors alone, when presented on a double logarithmic scale, are sufficient to produce an apparent power law. This raises questions regarding the usefulness of Taylor's law for understanding ecological processes. As an alternative approach, we focus on short-term fluctuations and derive a generic null model for the variance-to-mean ratio in population time series from a demographic model that incorporates the combined effects of demographic and environmental stochasticity. After comparing the predictions of the proposed null model with the fluctuations observed in empirical data sets, we suggest an alternative expression for fluctuation scaling in population time series. Analyzing population fluctuations as we have proposed here may provide new applied (e.g., estimation of species persistence times) and theoretical (e.g., the neutral theory of biodiversity) insights that can be derived from more generally available short-term monitoring data.
Abstract Aim Deterministic niche theory predicts that increasing environmental heterogeneity increases species richness. In contrast, a recent stochastic model suggests that heterogeneity has a unimodal effect on species richness since high levels of heterogeneity reduce the effective area available per species, thereby increasing the likelihood of stochastic extinction (the ‘area–heterogeneity trade‐off’). We tested these contrasting predictions using data on bird distributions in N orth A merica. Location N orth A merica. Methods The effect of heterogeneity on species richness was tested using simultaneous autoregressive regression models based on two measures of heterogeneity (elevational range and land‐cover richness) each quantified at two scales (400 m, 5 km), three measures of species richness (observed, corrected for incomplete detection, and corrected for regional richness) and three variable selection methods [forced entry, A kaike information criterion ( AIC) ‐based and a null‐model approach]. Covariates included precipitation, temperature, elevation and latitude. For all variables, both linear and quadratic terms were included in the analyses. Results Overall, heterogeneity had a weak effect on species richness and the contribution of the quadratic term of heterogeneity to the explained variance was very small (< 1%). Nevertheless, in all 36 models, the coefficients of both the linear and quadratic terms of heterogeneity were statistically significant and the estimated inflection point was within the range of the data, as predicted by the area–heterogeneity trade‐off. Moreover, in 30 out of the 36 models, support for a unimodal effect of heterogeneity on species richness based on information theoretic criteria was strong (Δ AIC > 10), and in 22 of those 30 models the null hypothesis of a monotonically positive relationship could be rejected at the 0.05% significance level. Main conclusions Patterns of bird richness in N orth A merica were predominantly consistent with the predictions of the area–heterogeneity trade‐off. Future attempts to understand the mechanisms affecting species diversity should pay more attention to the potential consequences of this fundamental trade‐off.
File List Neutral_fortran.txt (MD5: 7d5175db22c1bf3d1724b608611568de) Description Neutral_Fortran is a program that simulates neutral dynamics (the selection strength is alpha, so alpha = 0 is neutral) for a panmictic population of n individuals. The initial conditions are 50 species, mutation rate is dmu. The output is the file st1.dat, which is a list of abundance of species (of families) - the list is not sorted so if st1.dat contains the numbers 13,25,11 it implies that one species has abundance 13, another has 25, another has 11 and so on.
File List varY_lag.m (MD5: ac6cef05a4f087a2f14fc91ab62d0cd4) Description varY_lag.m is a matlab script that calculates the variance of Y over increasing timelags. The main output is the y_lag matrix of calculated variances, with columns denoting time lag and rows - size group. The code receives as output a very specific data structure: a STRUCT vector of sites, each site containing a STRUCT vector of species (+some metadata, i.e., all the lags and species at that site), each species having it's time series at this site. the time series is represented by a matrix with the first row denoting years and the second row denoting population size at that year. For example, sites(3).species(10).ts=[1970 1971; 10 15] means that at site3 for species 10, in 1970 there were 10 individuals and in 1971 there were 15. Some metadata are sites.all_lags (all available lags for this site) and sites.tot_abundance (which species are available at the site?). The grouping requires entering the minimum edges of each group. For example, if group_min = [1 31], the variance would be calculated separately for two groups, one with initial size 1-30, the other 30 and beyond.
File List abc.m (MD5: 00196d8d3afef5257cb3d380ef8e0f1d) Description abc.m is a matlab script that simulates the alpha-beta-gamma model we introduced in thearticle. It checks the normalized population variation, Y, as function of population size. The graph is linear.
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