Scott D. Foster

Model-based thinking for community ecology

In this paper, a case is made for the use of model-based approaches for the analysis of community data. This involves the direct specification of a statistical model for the observed multivariate data. Recent advances in statistical modelling mean that it is now possible to build models that are appropriate for the data which address key ecological questions in a statistically coherent manner. Key advantages of this approach include interpretability, flexibility, and efficiency, which we explain in detail and illustrate by example. The steps in a model-based approach to analysis are outlined, with an emphasis on key features arising in a multivariate context. A key distinction in the model-based approach is the emphasis on diagnostic checking to ensure that the model provides reasonable agreement with the observed data. Two examples are presented that illustrate how the model-based approach can provide insights into ecological problems not previously available. In the first example, we test for a treatment effect in a study where different sites had different sampling intensities, which was handled by adding an offset term to the model. In the second example, we incorporate trait information into a model for ordinal response in order to identify the main reasons why species differ in their environmental response.

Model‐based approaches to unconstrained ordination

Summary Unconstrained ordination is commonly used in ecology to visualize multivariate data, in particular, to visualize the main trends between different sites in terms of their species composition or relative abundance. Methods of unconstrained ordination currently used, such as non-metric multidimensional scaling, are algorithm-based techniques developed and implemented without directly accommodating the statistical properties of the data at hand. Failure to account for these key data properties can lead to misleading results. A model-based approach to unconstrained ordination can address this issue, and in this study, two types of models for ordination are proposed based on finite mixture models and latent variable models. Each method is capable of handling different data types and different forms of species response to latent gradients. Further strengths of the models are demonstrated via example and simulation. Advantages of model-based approaches to ordination include the following: residual analysis tools for checking assumptions to ensure the fitted model is appropriate for the data; model selection tools to choose the most appropriate model for ordination; methods for formal statistical inference to draw conclusions from the ordination; and improved efficiency, that is model-based ordination better recovers true relationships between sites, when used appropriately.

The analysis of biodiversity using rank abundance distributions.

Biodiversity is an important topic of ecological research. A common form of data collected to investigate patterns of biodiversity is the number of individuals of each species at a series of locations. These data contain information on the number of individuals (abundance), the number of species (richness), and the relative proportion of each species within the sampled assemblage (evenness). If there are enough sampled locations across an environmental gradient then the data should contain information on how these three attributes of biodiversity change over gradients. We show that the rank abundance distribution (RAD) representation of the data provides a convenient method for quantifying these three attributes constituting biodiversity. We present a statistical framework for modeling RADs and allow their multivariate distribution to vary according to environmental gradients. The method relies on three models: a negative binomial model, a truncated negative binomial model, and a novel model based on a modified Dirichlet-multinomial that allows for a particular type of heterogeneity observed in RAD data. The method is motivated by, and applied to, a large-scale marine survey off the coast of Western Australia, Australia. It provides a rich description of biodiversity and how it changes with environmental conditions.

A climate of uncertainty: accounting for error in climate variables for species distribution models

Summary Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings – for example under climate change scenarios. We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation–extrapolation. We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues. We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables. The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions.

A Poisson-Gamma model for analysis of ecological non-negative continuous data

The statistical analysis of continuous data that is non-negative is a common task in quantitative ecology. An example, and our motivation, is the weight of a given fish species in a fish trawl. The analysis task is complicated by the occurrence of exactly zero observations. It makes many statistical methods for continuous data inappropriate. In this paper we propose a model that extends a Tweedie generalised linear model. The proposed model exploits the fact that a Tweedie distribution is equivalent to the distribution obtained by summing a Poisson number of gamma random variables. In the proposed model, both the number of gamma variates, and their average size, are modelled separately. The model has a composite link and has a flexible mean-variance relationship that can vary with covariates. We illustrate the model, and compare it to other models, using data from a fish trawl survey in south-east Australia.

Evidence of discrete yellowfin tuna (Thunnus albacares) populations demands rethink of management for this globally important resource.

Tropical tuna fisheries are central to food security and economic development of many regions of the world. Contemporary population assessment and management generally assume these fisheries exploit a single mixed spawning population, within ocean basins. To date population genetics has lacked the required power to conclusively test this assumption. Here we demonstrate heterogeneous population structure among yellowfin tuna sampled at three locations across the Pacific Ocean (western, central, and eastern) via analysis of double digest restriction-site associated DNA using Next Generation Sequencing technology. The differences among locations are such that individuals sampled from one of the three regions examined can be assigned with close to 100% accuracy demonstrating the power of this approach for providing practical markers for fishery independent verification of catch provenance in a way not achieved by previous techniques. Given these results, an extended pan-tropical survey of yellowfin tuna using this approach will not only help combat the largest threat to sustainable fisheries (i.e. illegal, unreported, and unregulated fishing) but will also provide a basis to transform current monitoring, assessment, and management approaches for this globally significant species.

To mix or not to mix: comparing the predictive performance of mixture models vs. separate species distribution models

Species distribution models (SDMs) are an important tool for studying the patterns of species across environmental and geographic space. For community data, a common approach involves fitting an SDM to each species separately, although the large number of models makes interpretation difficult and fails to exploit any similarities between individual species responses. A recently proposed alternative that can potentially overcome these difficulties is species archetype models (SAMs), a model-based approach that clusters species based on their environmental response. In this paper, we compare the predictive performance of SAMs against separate SDMs using a number of multi-species data sets. Results show that SAMs improve model accuracy and discriminatory capacity compared to separate SDMs. This is achieved by borrowing strength from common species having higher information content. Moreover, the improvement increases as the species become rarer.

Twenty years of high-resolution sea surface temperature imagery around Australia: inter-annual and annual variability.

The physical climate defines a significant portion of the habitats in which biological communities and species reside. It is important to quantify these environmental conditions, and how they have changed, as this will inform future efforts to study many natural systems. In this article, we present the results of a statistical summary of the variability in sea surface temperature (SST) time-series data for the waters surrounding Australia, from 1993 to 2013. We partition variation in the SST series into annual trends, inter-annual trends, and a number of components of random variation. We utilise satellite data and validate the statistical summary from these data to summaries of data from long-term monitoring stations and from the global drifter program. The spatially dense results, available as maps from the Australian Oceanographic Data Networks data portal (http://www.cmar.csiro.au/geonetwork/srv/en/metadata.show?id=51805), show clear trends that associate with oceanographic features. Noteworthy oceanographic features include: average warming was greatest off southern West Australia and off eastern Tasmania, where the warming was around 0.6°C per decade for a twenty year study period, and insubstantial warming in areas dominated by the East Australian Current, but this area did exhibit high levels of inter-annual variability (long-term trend increases and decreases but does not increase on average). The results of the analyses can be directly incorporated into (biogeographic) models that explain variation in biological data where both biological and environmental data are on a fine scale.

Tuning Parameter Selection for the Adaptive Lasso Using ERIC

The adaptive Lasso is a commonly applied penalty for variable selection in regression modeling. Like all penalties though, its performance depends critically on the choice of the tuning parameter. One method for choosing the tuning parameter is via information criteria, such as those based on AIC and BIC. However, these criteria were developed for use with unpenalized maximum likelihood estimators, and it is not clear that they take into account the effects of penalization. In this article, we propose the extended regularized information criterion (ERIC) for choosing the tuning parameter in adaptive Lasso regression. ERIC extends the BIC to account for the effect of applying the adaptive Lasso on the bias-variance tradeoff. This leads to a criterion whose penalty for model complexity is itself a function of the tuning parameter. We show the tuning parameter chosen by ERIC is selection consistent when the number of variables grows with sample size, and that this consistency holds in a wider range of contexts compared to using BIC to choose the tuning parameter. Simulation show that ERIC can significantly outperform BIC and other information criteria proposed (for choosing the tuning parameter) in selecting the true model. For ultra high-dimensional data (p > n), we consider a two-stage approach combining sure independence screening with adaptive Lasso regression using ERIC, which is selection consistent and performs strongly in simulation. Supplementary materials for this article are available online.

Choosing between strategies for designing surveys: autonomous underwater vehicles

Autonomous underwater vehicles (AUV), which collect images of marine habitats, are now an established sampling tool. The use of AUVs is becoming more widespread as they offer a non-destructive method to survey substantial spatial areas. The design of AUV surveys has historically been based on expert knowledge andAUVspecific considerations, such as reducing geolocation error. The expert knowledge encompasses intuition, previous surveying experiences and holistic knowledge of the study region. 2. We investigate the statistical aspects to AUV survey design for estimation of percentage cover of key benthic biota. We investigate the presence of spatial autocorrelation in AUV data using model-based geostatistics and examine the effect of autocorrelation on survey design by examining different design strategies – methods for placing AUV transects. The design strategies are assessed by inspecting the expected bias and the expected standard deviation ofmodel predictions, where the model depends on the choice of design. 3. The AUV data exhibited a wide range of autocorrelation, from non-existent to substantial. The design strategies varied in their statistical performance and nearly all strategies had shortcomings. Design strategies that were consistently poor performers had (i) transects placed in parallel in a single spatial dimension and (ii) made no attempt to spread out the transects in space. The superior design types had more transect-to-transect separation (but not toomuch) and effectively spanned important covariates. 4. The results give guidelines to researchers designing AUV surveys for biological mapping and for monitoring. In particular, we demonstrate that any spatial design should seek spatial balance, such as would be introduced by a systematic or stratified component within a randomized design. Knowledge of the system under study should be incorporated and, if possible, should be done so in a formalmanner that is objective and repeatable.