Exploring MaxEnt based species-area relationship predictions [Research Summary]

This is a guest post by Dan McGlinn, a weecology postdoc (@DanMcGlinn on Twitter). It is a Research Summary of: McGlinn, D.J., X. Xiao, and E.P. White. 2013. An empirical evaluation of four variants of a universal species–area relationship. PeerJ 1:e212 http://dx.doi.org/10.7717/peerj.212. These posts are intended to help communicate our research to folks who might not have the time, energy, expertise, or inclination to read the full paper, but who are interested in a <1000 general language summary.

It is well established in ecology that if the area of a sample is increased you will in general see an increase in the number species observed.  There are a lot of different reasons why larger areas harbor more species: larger areas contain more individuals, habitats, and environmental variation, and they are likely to cross more barriers to dispersal – all things that promote more species to be able to exist together in an area. We typically observe relatively smooth and simple looking increases in species number with area. This observation has mystified ecologists: How can a pattern that should be influenced by many different and biologically idiosyncratic processes appear so similar across scales, taxonomic groups, and ecological systems?

Recently a theory was proposed (Harte et al. 2008, Harte et al. 2009) which suggests that detailed knowledge of the complex processes that influence the increase in species number may not be necessary to accurately predict the pattern. The theory proposes that ecological systems tend to simply be in their most likely configuration. Specifically, the theory suggests that if we have information on the total number of species and individuals in an area then we can predict the number of species in smaller portions of that area.

Published work on this new theory suggests that it has potential for accurately predicting how species number changes with area; however, it has not been appreciated that there are actually four different ways that the theory can be operationalized to make a prediction.  We were interested to learn

  1. Can the theory accurately predict how species number changes with area across many different ecological systems, and
  2. Do the different versions of the theory consistently perform better than others

To answer these questions we needed data. We searched online and made requests to our colleagues for datasets that documented the spatial configuration of ecological communities.  We were able to pull together a collection of 16 plant community datasets. The communities spanned a wide range of systems including hyper-diverse, old-growth tropical forests, a disturbance prone tropical forest, temperate oak-hickory and pine forests, a Mediterranean mixed-evergreen forest, a low diversity oak woodland, and a serpentine grassland.

Fig 1. A) Results from one of the datasets, the open circles display the observed data and the lines are the four different versions of the theory we examined.  B) A comparison of the observed and predicted number of species across all areas and communities we examined for one of the versions of the theory.

Across the different communities we found that the theory was generally quite accurate at predicting the number of species (Fig 1 above), and that one of the versions of the theory was typically better than the others in terms of the accuracy of its predictions and the quantity of information it required to make predictions. There were a couple of noteworthy exceptions in our results. The low diversity oak woodland and the serpentine grassland both displayed unusual patterns of change in richness. The species in the serpentine grassland were more spatially clustered than was typically observed in the other communities and thus better described by the versions of the theory that predicted stronger clustering. Abundance in the oak woodland was primarily distributed across two species whereas the other 5 species where only observed once or twice. This unusual pattern of abundance resulted in a rather unique S-shaped relationship between the number of species and area and required inputting the observed species abundances to accurately model the pattern.

The two key findings from our study were

  1. The theory provides a practical tool for accurately predicting the number of species in sub-samples of a given site using only information on the total number of species and individuals in that entire area.
  2. The different versions of the theory do make different predictions and one appears to be superior

Of course there are still a lot of interesting questions to address.  One question we are interested in is whether or not we can predict the inputs of the theory (total number of species and individuals for a community) using a statistical model and then plug those predictions into the theory to generate accurate fine-scaled predictions.  This kind of application would be important for conservation applications because it would allow scientists to estimate the spatial pattern of rarity and diversity in the community without having to sample it directly. We are also interested in future development of the theory that provides predictions for the number of species at areas that are larger (rather than smaller) than the reference point which may have greater applicability to conservation work.

The accuracy of the theory also has the potential to help us understand the role of specific biological processes in shaping the relationship between species number and area.  Because the theory didn’t include any explicit biological processes, our findings suggest that specific processes may only influence the observed relationship indirectly through the total number of species and individuals. Our results do not suggest that biological processes are not shaping the relationship but only that their influence may be rather indirect.  This may be welcome news to practitioners who rely on the relationship between species number and area to devise reserve designs and predict the effects of habitat loss on diversity.

If you want to learn more you can read the full paper (it’s open access!) or check out the code underlying the analysis (it’s open source and includes instructions for replicating the analysis!).


Harte, J., A. B. Smith, and D. Storch. 2009. Biodiversity scales from plots to biomes with a universal species-area curve. Ecology Letters 12:789–797.

Harte, J., T. Zillio, E. Conlisk, and A. B. Smith. 2008. Maximum entropy and the state-variable approach to macroecology. Ecology 89:2700–2711.

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