Bias-corrected Pearson estimating functions for Taylor's power law applied to benthic macrofauna data (original) (raw)
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The lack of a common statistical approach describing the distribution and dispersion pattern of marine benthic animals has often hampered the comparability among studies. The purpose of this study is therefore to apply an alternative approach, Taylor's power law, to data on spatial and temporal distribution of 9 dominating benthic invertebrate species from two study areas, the estuaries Odense Fjord and Roskilde Fjord, Denmark. The slope (b) obtained from the power relationship of sample variance (s 2 ) versus mean (μ) appears to be species-specific and independent of location and time. It ranges from a low of~1 for large-bodied (> 1 mg AFDW) species (e.g. Marenzelleria viridis, Nereis diversicolor) to a high of 1.6-1.9 for small-bodied (b1 mg AFDW) species (e.g. Pygospio elegans and Tubificoides benedii). Accordingly, b is apparently a valuable species-specific dispersion index based on biological factors such as behavior and intraspecific interactions. Thus, at the examined spatial scale, the more intense intraspecific interactions (e.g. territoriality) cause less aggregated distribution patterns among large-than small-bodied invertebrates. The species-specific interactions seem sufficiently strong to override environmental influences (e.g. water depth and sediment type). The strong linear relationship between the slope b and intercept log(a) from the power relationship is remarkably similar for all surveys providing a common slope of −1.63 with the present sampling approach. We suggest that this relationship is an inherent characteristic of Taylor's power law, and that b as a dispersion index may be biased by e.g. sampling errors when this relationship is weak. The correlation strength between b and log(a) could therefore be envisioned as a data quality check.
Canadian Journal of Fisheries and Aquatic Sciences, 2016
Taylor’s power law (TPL) describes the variance of population abundance as a power-law function of the mean abundance for a single or a group of species. Using consistently sampled long-term (1958–2001) multimesh capture data of Lake Kariba in Africa, we showed that TPL robustly described the relationship between the temporal mean and the temporal variance of the captured fish assemblage abundance (regardless of species), separately when abundance was measured by numbers of individuals and by aggregate weight. The strong correlation between the mean of abundance and the variance of abundance was not altered after adding other abiotic or biotic variables into the TPL model. We analytically connected the parameters of TPL when abundance was measured separately by the aggregate weight and by the aggregate number, using a weight–number scaling relationship. We utilized TPL to find the number of samples required for fixed-precision sampling and compared the number of samples when samplin...
On fitting power laws to ecological data
2007
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find the parameters in the distribution, which can give highly misleading results. The potential pitfalls that can occur when using these methods are pointed out, and a step-by-step guide to fitting power-law distributions and assessing their goodness-of-fit is offered.
Estimation of Taylor's Power Law parameters a and b for tidal marsh macrobenthic species
In the Cananeia region of southeastern Brazil, Spartina alteniflora marshes colonize tidal flats fringing mangrove woodlands displaying a zonation typical of monocultures. The pattern observed can be explained by the combined effects of organism resistance to emersion and physical dependence on the plants as habitat. In this context, it is interesting to quantify the aggregation index for the dominant species associated with the salt marsh. A tool which enables us to do it is Taylor´s power law which combines the mean and the variance distributions of species in a known area. Ten random samples were taken monthly by a 20 cm diameter corer (0.03 m2) at a depth of 10 cm, from the lower and upper marshes, from August, 1988, to January, 1989. The five most representative species of the system were elected for further analysis, and for each of these Taylor´s power law parameters were calculated. Epifaunal species present aggregation indexes approaching randomness. The aggregation indexes...
Comparing estimators of animal abundance: a simulation study
Riassunto. L'obiettivo del lavoro consiste nel confrontare differenti stimatori della densità di una popolazione animale basati sul campionamento per transetti. L'attenzione è focalizzata sul "point transect" ed il confronto degli stimatori è effettuato sulla base di simulazioni delle distribuzioni associate alle funzioni di avvistamento seminormale ed esponenziale negativa, che rappresentano due situazioni ben distinte. Infatti, la seconda, a differenza della prima, non soddisfa all'usuale condizione di stazionarietà (corrispondente all'annullarsi della derivata nell'origine) ed è caratterizzata da una rapida riduzione della probabilità di avvistamento degli animali all'aumentare della loro distanza dai punti di osservazione. Gli stimatori considerati sono: gli stimatori a varianza uniformemente minima tra i corretti (UMVU) per i due modelli parametrici suddetti; gli stimatori di massima verosimiglianza (ML) per due modelli proposti da Buckland et ...
Strengthening statistical usage in marine ecology
Journal of Experimental Marine Biology and Ecology, 2012
Although within their own disciplines, the statistical, social science, medical, and terrestrial ecology literatures are replete with accounts of the widespread misapplication and misuse of statistical testing and interpretation, awareness of these issues is weak among marine scientists who are not statisticians, but whose work is nonetheless situated within the expanse of marine ecology. Moreover, the major recent developments in statistical approaches in these fields are, as yet, poorly-represented in the marine ecological literature. We present a non-technical review of (1) the most fundamental, yet pervasive, problems concerning classical statistics, with suggestions for improved practice, (2) alternate, often more appropriate and intuitive, approaches to statistical design and interpretation, and (3) the crucial roles of reviewers, and especially of editors and editorial boards. It is hoped that increasing the awareness of these issues will strengthen statistical usage in marine ecology.
African Journal of Marine Science, 2014
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance estimates. Regardless of the method used to obtain point estimates, a method is needed for variance estimation. A bootstrap technique is introduced for the evaluation of uncertainty in such models, taking into account inherent spatial and temporal correlations in the data sets thus avoiding many model-specification issues, which are commonly transferred as assumptions from a likelihood estimation procedure into Hessian-based variance estimation procedures. The technique is demonstrated on a real data set and used to look for estimation bias and the effects of different aggregation levels in population dynamics models.
How many sites? Methods to assist design decisions when collecting multivariate data in ecology
2022
1. Sample size estimation through power analysis is a fundamental tool in planning an ecological study, yet there are currently no well-established procedures for when multivariate abundances are to be collected. A power analysis procedure would need to address three challenges: designing a parsimonious simulation model that captures key community data properties; measuring effect size in a realistic yet interpretable fashion; and ensuring computational feasibility when simulation is used both for power estimation and significance testing. 2. Here we propose a power analysis procedure that addresses these three challenges by: using for simulation a Gaussian copula model with factor analytical structure, fitted to pilot data; assuming a common effect size across all taxa, but applied in different directions according to expert opinion (to "increaser", "decreaser" or "no effect" taxa); using a critical value approach to estimate power, which reduces computation time by a factor of 500 with little loss of accuracy. 3. The procedure is demonstrated on pilot data from fish assemblages in a restoration study, where it was found that the planned study design would only be capable of detecting relatively large effects (change in abundance by a factor of 1.5 or more). 4. The methods outlined in this paper are available in accompanying R software (the ecopower package), which allows researchers with pilot data to answer a wide range of design questions to assist them in planning their studies.