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Prediction of Biodiversity - Richness and Evenness

submitted by Piers Dunstan

Figure 1: A characterisation of predictions of fish and invertebrate communities from Western Australia created by identifying unique combinations of species richness and community evenness from Rank Abundance Distributions.

Patterns in biodiversity can be illustrated by variation in the number of species (richness) and whether these species are evenly distributed or dominated by a minority (evenness). Combining these two properties of biodiversity leads to the identification of uncommon communities that are deserving of greater protection. In this application we use a statistically rigorous analysis of species ranks combined with physical samples to predict patterns in biodiversity through the physical space. This extends our information from known biological samples to the broader environment, with measured uncertainty.

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Scientific Background

Rank Abundance Distributions (RADs) are a ubiquitous distribution found in all biological samples where species abundances are counted. They are an ordering of all species in the sample from the most abundant to the least abundant. RADs are excellent metrics of community structure. The utility of predictions from RADs stems from three properties. First, they are a pattern that can be generated from any sample of an assemblage, irrespective of the actual sampling methods. Second, RADs are not dependent on species' identities and assemblages containing widely disparate species can be compared, allowing analysis over ecologically diverse areas. Third, rare species are explicitly included in this the formation of a RAD. This last property is attractive as most methods for dealing with multispecies assemblages either discard rare species or transform the data until rare and abundant species can be dealt with in a statistical context. RADs are a reordering of the data found in Species Abundance Distributions (McGill et al. 2007)

The shape of the RAD is a representation of the allocation of resources within a sample of a community. Communities where species partition relatively evenly will have relatively similar abundances while species that dominate resource use will likewise dominate the community.

Most metrics of biodiversity can be calculated from RAD's (eg Shannon or Simpson diversity). However, we derive just three that come naturally from the distribution, total abundance, species richness and community evenness.

How the EBSA was identified

We have developed a method of predicting Rank Abundance Distributions from physical covariates (Foster and Dunstan 2009, Dunstan and Foster (in review)). We decompose the RAD into three components that can each be predicted separately, total abundance, species richness and relative abundance. Statistical models can be constructed for each of the components and a measure of community evenness can be derived from the relative abundances of the predictions. Appropriate measures of uncertainty can be calculated from the asymptotic distributions of the fitted models.

Predictions of derived metrics total abundance, species richness and community evenness can be mapped into physical space. Predictions of the means and standard errors of each of the components can be calculated. We have created a R package to perform model fitting, diagnostics and prediction with a similar interface to the standard GLM/GAM functions in R. This is freely available to any appropriately skilled researcher.

This is not an EBSA for a particular region but a method of evaluating an area based on the EBSA biodiversity criterion. By predicting RAD's using physical covariates, unique combinations of total abundance, species richness and community evenness can be identified. Examining the bivariate density of richness and evenness spatially allows maps to be generated that identify the spatial position and extent of these regions. Not all combinations of richness and evenness will be equally common, and particularly rare combinations may require additional management. 

 

Sources of Data

RADs can be calculated and used to help evaluate the ecological or biological significance of an area from any appropriate data set. The method requires counts for each species in a sample and accurate taxonomic identification so that species can be identified. To fit the models, physical covariates are needed at the location the sample was taken from. Predictions can then be made from the fitted models using covariates in new locations.
The maps presented show the characterisation of communities for benthic fish and invertebrates in the continental shelf and slope adjacent to Western Australia from 21oS to 36oS. Models were parameterised with oceanographic data from the CSIRO atlas of regional seas (http://www.marine.csiro.au/~dunn/cars2006). 

Models can be developed for any region with appropriate biological data and covariates. It is not necessary for covariates to be measurements of physical processes, biologically derived covariates may be used (eg Organic Carbon). The only requirement is that biological covariates are collocated for model fitting and that the same covariates are available where predictions are being made.

 

Important Considerations

While RADs have been an acknowledged pattern in all sampled systems, understanding of their genesis and the ability to predict the distributions has been absent. Here we have used a statistical method to analyse and predict RADs to form measures of biodiversity for a wide range of habitats. The ability to combine and predict attributes of RADs into areas where sampling has not occurred will enhance both the management and understanding of the systems.
The predicted patterns complement current understanding of the processes structuring deep sea benthic communities (Levin 2001). Our predictions show that processes acting at medium to large scales (e.g. temperature, salinity and oxygen concentrations) affect the structure of benthic assemblages. Even though depth and latitude are useful surrogates to describe the patterns predicted here, they are not the covariates that structure most of the predictions. Rather it is other covariates such as temperature, salinity and oxygen that are important. This suggests that a simple interpretation using only depth and latitude would have missed important patterns that have emerged from our analysis. A deeper understanding of the patterns of biodiversity is obtained using a wide range of covariates that covers the range of environmental habitats.

 

Figure2

Figure 2: Predicted patterns of species richness for invertebrates on the Western Australian shelf and slope. Predicted mean richness (a) and coefficient of variation (b) are shown.



Figure 3

Figure 3: Predicted patterns of evenness for invertebrates on the Western Australian shelf and slope. Predicted mean evenness (a) and coefficient of variation (b) are shown. Evenness varied from very even communities at 0 (shaded blue) to very uneven communities at -1.4 (shaded red)

 


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