The idea that diversity is a combination of species richness and abundance distribution evenness is a bedrock concept in ecology. Researchers often either measure evenness with stand-alone indices or compute Hill numbers like Shannon's H and Simpson's D, which balance richness and evenness to various degrees. But evenness is an operationally problematic abstraction, not a thing out in the world. Evenness and Hill numbers in real-world data are highly sensitive to the abundance of dominant species, imprecise, variable among nearby communities, and a weak indicator of latitudinal trends. They are inconsistently related to the shape parameters of key underlying distributions, and they vary highly in simulation even when these distributions do not vary in their shape or scale. Ecologists would benefit by instead determining which real distributions fit which theoretical models and using the shape and scale parameters of those models to understand community structure.

Coverage-based rarefaction (CBR) is a high-profile tool for assessing biodiversity that provides relative species richness estimates. It leverages the Good-Turing index u to interpolate expected richness given a specified level of frequency distribution coverage. In contrast to alternatives such as the Shannon and Simpson indices, CBR’s main appeal is providing values in units of species. CBR is tested against a series of other biodiversity measures. Data are both simulated and empirical, in the latter case drawn from an eclectic global database of terrestrial organisms. First, species counts are simulated under three underlying abundance distributions: the compound exponential-geometric series (CEGS), Poisson log normal, and discretised Weibull. CBR and five other diversity estimators are then computed. Second, diversity estimates are computed for species inventories and then recomputed after excluding the single most common species in each one. Third, randomly selected pairs of inventories are either (1) analysed separately with richness estimates summed, or (2) combined and only then analysed. On average, fitting CEGS in simulation consistently returns an accurate and precise estimate of richness. CBR yields little signal. CEGS returns much the same values regardless of whether empirical data sets include or exclude dominants and regardless of whether they are combined or analysed separately. CBR often overestimates by a large margin when dominants are excluded and underestimates by a large margin when data are combined. CBR does not respond predictably to variation in species richness and cannot reconstruct it when the data have strong internal structure. CBR’s usefulness as a biodiversity indicator is unclear.

Previous methods of estimating species richness from ecological inventories are problematic. Many assume that underlying abundances are entirely even (e.g., the Chao 1 index). Any such estimator will provide a lower bound only, so it will be systematically wrong. In principle, more realistic estimates might be yielded by fitting each given species inventory to a substantive theoretical abundance distribution. But which one? Globally dispersed ecological data representing trees and terrestrial animals are fit here with a stripped-down equation that combines two of the most basic distributions in statistics. This compound exponential-geometric series (CEGS) model has high predictive power: when assorted models are fitted to the individual species inventories and the resulting shapes are projected onto the counts for ecologically similar data sets, CEGS yields better predictions than any of its rivals. This is true regardless of whether matches are based on taxonomic similarity and overall sample size or on similar patterns in the highest counts. Meanwhile, estimating richness, degrading the data, and recomputing richness shows that the method yields precise and accurate values. By unifying the problems of estimating richness and modelling species counts, CEGS explains key patterns in nature in an intuitive and elegant way.

The analysis of macroecological patterns has necessitated the use of large, composite datasets recording local-scale species occurrences distributed across the globe. These datasets, however, have various spatial and temporal biases. They have rarely been compared to data collected in the field across large spatial gradients. In this paper we use two datasets built from online repositories plus a standardised field collection to reconstruct macroecological patterns for marine bivalves along the eastern coastline of Australia – spanning over 20° of latitude. We test the strength of the latitudinal diversity gradient using four diversity measures and identify a biogeographical boundary. The field collection demonstrates a strong latitudinal gradient, but mixed support was found in the composite datasets. Worse, adding observation-based records to the composite dataset obscured the latitudinal gradient. The biogeographic boundary was consistently found, and the location mirrored two previously published bioregionalisations. Although broad patterns seen in the field can be uncovered from composite macroecological datasets, care both in dataset construction and choice of methods is needed to ensure robust results.

Species abundance distributions, meaning counts of individuals apportioned among species, are fundamental patterns in ecology. Numerous distribution models have been proposed, and most suffer from poor fit to data, complex formulation, excessive parameterisation, or unrealistic modelling of processes. I discuss three that meet all the basic criteria, are easily distinguished, and stem from simple and distinct population dynamics. The log series can be produced by assuming taxonomically and temporally fixed turnover rates. A model derived from scaled odds ratios assumes highly variable dynamics, and one derived from exponential variates assumes taxonomically variable but temporally fixed rates. Mathematical derivations are elementary. Maximum likelihood fits to published empirical data suggest that the two new distributions are more common in nature. Saturated models are rarely better. Ecological communities may be assembled by processes that are easily discerned, instead of being as mysterious as many have thought.

A document by Benjamin Carter. Click on the document to view its contents.

Latitudinal diversity gradients are among the most studied macroecological phenomena. However, they tend to be described using large composite datasets that often show taxonomic and geographic sampling bias. Here we describe a latitudinal gradient in marine bivalves along the eastern coastline of Australia, spanning 2,667km of coastline and 20° of latitude. We utilise a large, structured field dataset (5,552 individuals) in conjunction with a routine macroecological dataset downloaded from the Ocean Biogeographic Information System (OBIS - 36,226 specimens). Diversity is estimated using a series of analytical methods to account for undersampling, and biogeographic gradients in taxonomic composition are quantified and compared to existing biogeographical schemes. A strong latitudinal gradient is present in both datasets. However, the strength of the gradient depends on the dataset and analytical method used. The inclusion of observational data in the macroecological dataset obscures any latitudinal pattern. The documented biogeographic gradients are consistent with global and regional reconstructions. However, we find evidence for a strong transition zone between two clusters. Although latitudinal gradients inferred from large macroecological datasets such as OBIS can match those inferred from field data, care should be taken when curating downloaded data as small changes in protocol can generate very different results. By contrast, even modest regional field datasets can readily reconstruct latitudinal patterns.

Calculating spatial ranges of species and individuals is a crucial problem throughout ecology. However, sample size biases can be strong, and defining range boundaries can be difficult. These hurdles can be overcome by calculating areas without calculating boundaries. The first step is to algorithmically define a graph that connects the spatial points where observations have been made. The routine generates a small number of short edges that form a pattern resembling a mosaic. The edge lengths are summed, squared, divided by the edge count, and multiplied by a known constant to obtain a total area estimate for the shape. This non-parametric mosaic area method can work with irregular outlines and clumped point distributions. It is more accurate than convex hull, kernel density, and hypervolume estimation according to simulation analyses. Mosaic area calculations can be used in areas ranging all the way from conservation biology to morphometrics.