Morning

• Spent the morning writing up a short pre-proposal for a project I’d like to be involved in. Hoping this will become a full grant proposal in the near future. The prep-proposal follows:

Using multiple phylogenetic and compositional diversity metrics to predict endemism across Australia

It is increasingly recognized that phylogenetic diversity metrics contain important information about communities of organisms above and beyond that contained in species richness estimates (Cavender-Bares et al. 2009). The full power of phylogenetic diversity metrics (PD hereafter), has not been realized, however, because of a reliance on null model analysis to infer processes. The main issues with this approach are the following:

1. Null models hold other diversity metrics, such as species richness, constant, even though these may also contain important complementary information about processes.

2. Null model analysis can only reject a null model, it cannot measure support for one or another alternate hypotheses. This is particularly a problem when a single PD metric is not sufficient to distinguish between multiple potential processes underlying a pattern. This has been the source of recent criticism of the PD approach to inferring processes (e.g. Mayfield and Levine (2010)).

We propose to solve both these problems using an approach that uses multiple diversity metrics simultaneously, which can greatly reduce the possible processes responsible for a pattern (Stegen and Hurlbert 2011), and that measures the relative fit of multiple assembly hypotheses to occurrence data. We then propose to use this framework to make useful predictions about Australian Flora and Fauna, in particular the spatial distribution and phylogenetic placement of potential endemics in areas which are currently understudied.

Statistical Framework

The framework that makes this type of analysis possible is based on an emerging field of statistical inference known as “likelihood-free” methods. These methods allow the fitting to data of any model from which it is possible to generate simulated output (Hartig et al. 2011). Approximate Bayesian Computation (ABC) and synthetic likelihood (Wood 2010) are two examples of this framework. In short, these methods work by calculating a set of multiple ‘summary’ statistics (an example would be an auto-regressive coefficient at multiple lags for time-series data) for simulated and observed data-sets, and then finding the simulation parameters which produce summary statistics that most closely match the observed summary statistics. There appears to be an intriguing connection between diversity metrics — which ecologists routinely use to summarize the structure of occurrence data and to informally infer processes — and summary statistics — which summarize the structure of any data, and can be used to infer a model, formally. In other words, this provides a unifying mathematical formalism with strong theoretical support to what ecologists already do in a less structured way.

The Data

We propose to use likelihood-free statistical methods to fit process-based models to occurrence data of Australian organisms, drawn from the Atlas of Living Australia. At first, we will concentrate on fitting relatively simple models which contain environmental filtering by climate variables, as well as species interactions (e.g. competition), allowing both to be partly determined by the observed species’ phylogeny. We will use a host of different diversity metrics, including both alpha and beta versions of PD across a large spatial extent as summary statistics. Besides validating these methods as an effective way to understand the potential processes underlying complex patterns of biodiversity, a major impact of this work will be on deriving predictions from these model once they are fit to data.

Predictions in a likelihood-free framework: Turning a weakness into a strength

One potential disadvantage of likelihood-free methods comes when we wish to make predictions about unknown communities from models fit to known communities. Because we fit the model using summary statistics rather than the raw data, predictions can only be made about the summary statistics. In this case, we could only make predictions directly from the model about diversity metrics in unknown regions, and not about the individual species whose occurrence data were used to calculate the diversity metrics. However, we suggest that this potential weakness could be turned into a great strength. In traditional Species Distribution Models (SDMs) that predict species distributions in unknown areas, it is only possible for them to predict the presence or absence of species that were observed in the known areas. A major problem with this is that they cannot predict the presence or absence of any species which is not currently known in the region under observation. However, there are likely many potential endemic species across Australia, that may not yet occur in any useful occurrence database.

This is where likelihood-free method’s apparent weakness could be their strength. Because we are not trying to model specific species data, but rather are trying to model ‘emergent’ or ‘collective’ properties of the system, our predictions will not be tied to any particular permutation of species. Besides the interesting insights that can be drawn simply from making predictions about these types of properties, work at CSIRO has already shown that it is possible to find configurations of species, both known and hypothetical, which best match a particular set of diversity metrics (Mokany et al. 2011). And because our model will explicitly incorporate phylogeny from the beginning, it will be possibly to determine the phylogenetic placement of hypothetical unobserved species, which will best match predicted patterns of phylogenetic diversity across a landscape. This opens the possibility of predicting where currently unknown species are most likely to be found, as well as the most likely parts of a phylogeny they will come from.

References

Cavender-Bares, Jeannine, K.H. Kozak, P.V.A. Fine, and S.W. Kembel. 2009. “The Merging of Community Ecology and Phylogenetic Biology.” Ecology Letters 12 (7): 693–715. http://www3.interscience.wiley.com/journal/122388144/abstract.

Hartig, Florian, Justin M Calabrese, Björn Reineking, Thorsten Wiegand, and Andreas Huth. 2011. “Statistical Inference for Stochastic Simulation Models–Theory and Application.” Ecology Letters 14 (8): 816–827. doi:10.1111/j.1461-0248.2011.01640.x.

Mayfield, Margaret M, and Jonathan M Levine. 2010. “Opposing Effects of Competitive Exclusion on the Phylogenetic Structure of Communities.” Ecology Letters 13 (9) (September): 1085–93. doi:10.1111/j.1461-0248.2010.01509.x. http://www.ncbi.nlm.nih.gov/pubmed/20576030.

Mokany, Karel, Thomas D Harwood, Jacob McC Overton, Gary M Barker, and Simon Ferrier. 2011. “Combining α - and β -Diversity Models to Fill Gaps in Our Knowledge of Biodiversity.” Ecology Letters 14 (10) (October): 1043–51. doi:10.1111/j.1461-0248.2011.01675.x. http://www.ncbi.nlm.nih.gov/pubmed/21812884.

Stegen, James C., and Allen H. Hurlbert. 2011. “Inferring Ecological Processes from Taxonomic, Phylogenetic and Functional Trait β-Diversity.” PLoS ONE 6 (6).

Wood, Simon N. 2010. “Statistical Inference for Noisy Nonlinear Ecological Dynamic Systems.” Nature 466 (7310): 1102–1104.

Afternoon

• Updated Ralf package with basic functionality for my #AFD and #LDA-metagenomics projects.

• Started figuring out how to push .Rmd knitr documents to package gh-pages branch so they will be rendered at http://rdinnager.github.io/<project.name>/<Rmd.name> (example: http://rdinnager.github.io/LDA-metagenomics/assumption_test) ala @cboettig. Doing this so that I can use .svg plots which I think are superior to most other formats. See this post by @cboettig for my inspiration.