University of Wisconsin - Madison
Statistics as the bridge between ecological theory and ecological data
More and more, hypotheses generated from theoretical ecology are tested by fitting models to data. This contrasts the case a generation ago when patterns predicted from models were tested against data, yet the theoretical models themselves were not fit. Fitting a model to data is more rigorous, because it exposes the mechanisms underlying the behavior of the model to statistical testing. Thus, ecologists are taking advantage of the growing flexibility of statistical tools and the computing power to implement them. I will give examples of models fit to data to investigate the possibility of alternative states in ecological systems. Alternative states describe the case when a model can give different dynamics depending on the starting conditions, which occurs when there are multiple attracting states. For example, for a model with two stable point attractors, if the system starts at a high state it may stay there until a stochastic event shifts it to the alternative low state. Systems with alternative states are important in ecology, because they can lead to abrupt, unanticipated, and hard-to-manage shifts in ecosystems. They also present a change for statistical model fitting, because they produce complex time series.
Copula models for multivariate ecological count data
Current statistical methods used to analyse multivariate ecological data are generally unable to adequately model correlation structures among the variables. Variables consisting of counts of species abundances may be well-modelled individually (one variable at a time) using statistical distributions such as the Poisson (P), the negative binomial (NB), or their zero-inflated versions (ZIP, ZINB). However, in real community data, different variables have different degrees of overdispersion and/or zero-inflation, hence require different marginal distributions. Furthermore, the sheer number of variables (species) in communities precludes adequate estimation of their inter-correlations, and pair-wise Pearson correlations of the original variables are inappropriate to use when joint-absences should logically be ignored. In this talk, I will outline a general approach for modelling multivariate ecological count data using copulas – a greatly under-utilised tool in ecology that has big potential. I will describe useful approaches for identifying appropriate disparate marginal distributions and relevant associations to model among species. I will then show how resultant copula models can be exploited for estimation, ordination, inference, prediction and power in the analysis of ecological communities.
Challenges of modelling the spatial patterns of palaeo-community turn-over in response to ancient human expansion
African populations of Homo sapiens migrating out of Africa ~ 120,000 to 70,000 years ago preceded waves of animal extinctions across most of the globe from about 50,000 years ago. Thus, having a better understanding of regional migration pathways of pre-historical modern humans is an important precursor to being able to evaluate our impact on past species’ extinction dynamics and community turn-over. Despite a consensus on a general colonisation pattern that modern humans spread rapidly across Asia, reaching Southeast Asia by at least 45,000 years ago, and crossing into Sahul (Australia and Papua New Guinea) between 60,000 and 40,000 years ago, the regional colonisation paths taken after leaving Africa have been the subject of considerable debate. I will discuss the modelling challenges of combining disparate data types (archaeological, palaeontological, ancient DNA, environmental) to ascertain spatial patterns of species’ extinctions and community turn-over with respect to these putative human colonisation patterns. Using case studies from the Holarctic (humans, mammoths, bison) and Sahul (humans, diprotodontids, large macropodids), I will demonstrate how using coupled space-time models that combine the Verhulst population-dynamic model to geostatistical methods can be applied it to quality-rated versions of Homo sapiens archaeological datasets, and then validated using genetic and hydrological data collected independently. These approaches account simultaneously for the temporal bias in last and first occurrence estimates (Signor-Lipps effect) with the spatial uncertainty arising from non-random sampling. I will also present some preliminary human demographic transition models for the Sahul region constrained by the phenomenological patterns arising from geostatistical analyses. I will close with a discussion on how these models must evolve as new data come to light, with focus on the Sahul region from about 60,000 years ago.
Colorado State University
Modeling teleconnections: remote effects spatial process models
Teleconnection patterns reflect relationships between weather and other environmental phenomena that are distant. The El Nino-Southern Oscillation (ENSO) teleconnection pattern, where Pacific Ocean sea surface temperature affects global weather, is the most well-known example but teleconnections can impact other ecological processes such as animal migration. We propose a geostatistical model that uses covariates observed on a spatially remote domain to improve locally-driven models of a spatial process. The model accounts for local factors, like orographic effects and temperature, as well as more remote processes that create different patterns of dependence, like the El Nino-Southern Oscillation (ENSO) teleconnection. Many statistical methods can only account for spatial patterns in either local or remote processes. The proposed model simultaneously accounts for the effects of local and remote covariates. Our model draws on ideas from spatially varying coefficient models, spatial basis functions, and predictive processes to allow several interpretations of effects and to overcome modeling challenges for teleconnections. We adopt a hierarchical Bayesian framework for inference. We demonstrate the methodology by modeling the precipitation in Colorado and accounting for both local covariates and teleconnection effects with Pacific Ocean sea surface temperatures. We also discuss physical motivations and interpretations for our model.
Spatial data and Gaussian processes: A beautiful marriage
In the past twenty years analysis of spatial data has become increasingly model-based. Full specification of stochastic models for the spatial process being investigated enables full inference and uncertainty assessment regarding the process. Gaussian processes on subsets of R^2 have become a fundamental specification for such modeling, particularly in settings where prediction is a primary goal. Therefore, focusing on the point-referenced case, we elaborate the substantial range of spatial settings where Gaussian processes have enabled rich and flexible modeling.
We start with the basic geostatistical model, in hierarchical form, moving to generalized spatial regression models, multivariate process models, and spatially varying coefficient models. We will consider the use of Gaussian processes to handle skewed distributions as well as nonparametric distributional models and also the role of Gaussian processes in dimension reduction strategies to accommodate large datasets. Also, we will look at less standard contexts including spatial extremes, spatial directional data, and spatial quantile regression. Modeling details, model fitting, and examples will be provided.
Colorado State University
Nonstationary stochastic process models for animal trajectories
Advances in animal telemetry data collection techniques have served as a catalyst for the creation of statistical methodology for analyzing animal movement data. Such data and methodology have provided a wealth of information about animal space use and the investigation of individual-based animal-environment relationships. While the technology for data collection is improving dramatically over time, we are left with massive archives of historical animal telemetry data of varying quality. However, many contemporary statistical approaches for inferring movement behavior are designed for newer data that are very accurate and high-resolution. From a scientific perspective, the behaviors we are interested in learning about may be complicated, nonstationary, and constrained. Furthermore, telemetry data often contain substantial measurement error and can be nonelliptically distributed. I provide a brief overview of the history of statistical models for animal movement and present an accessible framework for accommodating the inherent nonstationary characteristics of Lagrangian movement processes and uncertainty associated with telemetry data.
University of Queensland
Adding versatility and complexity to simple fitness models; the importance of facilitation and higher-order interactions to accurately modelling individual fitness
Recently, there has been renewed interest in how species interactions contribute to coexistence dynamics and diversity maintenance. Despite a widespread appreciation that many types of interactions occur in natural communities, few models of coexistence or diversity maintenance account for complex species interactions, with most including information about direct competitive interactions alone. In this talk, I will explain the benefits of our exponential form of a classic individual fitness model. This new fitness model provides a tractable approach to modelling individual fitness while allowing for both facilitative and competitive direct interactions as well as non-additive higher-order interactions. First, I will compare our fitness model to more traditional individual fitness models. Second, I will explain higher-order interactions and how they can be included in fitness estimations using our model. Third, I will use two plant datasets, one on annual plants from SW Western Australia and a second on perennial plants from Tasmania, to illustrate the benefits of our model for improving fitness model accuracy and for identifying which types of interactions are important to fitness outcomes. In SW Western Australia, we find that the inclusion of even a subset of higher-order interactions improves the accuracy of fitness models, significantly. In Tasmania, we show that even when sufficient data for higher-order interactions are not available, our model has notable benefits by allowing facilitation to occur. We show that in these alpine communities up to 50% of direct interactions are facilitative, a reality ignored by traditional fitness models. In conclusion, we present a simple individual fitness model that greatly improves model fit above commonly used individual fitness models and that can be used with a wide range of coexistence and diversity models. We show that this model can be used with little or no additional field data and without major increases in computational power.
University of Canterbury
Dimensions of complexity in ecological communities
Interactions are a defining characteristic of every species' "milieu" since no individual organism exists without participating in some sort of ecologically relevant interaction during its lifetime. Indeed, interactions between species underpin community ecology to the extent that they have been described as "the architecture of biodiversity". Not only do interactions play this central role, but they also form the backbone of the idea that ecological communities are paradigmatic complex systems where the whole is greater than the sum of its parts. In this talk, I will draw from classic concepts in complexity theory to demonstrate that the exact opposite is often true. While doing so, I will draw on examples from predator-prey antagonistic networks, plant-pollinator mutualistic networks, and plant-plant competitive networks, all of which indicate that these are inherently "low-dimensional" systems. I will then highlight recent research that helps reconcile why low-dimensional systems often give the (false) impression that they are instead high dimensional. I will then conclude by explaining how the limits to ecological complexity are not a drawback but instead should guide future research in the area.
University of St Andrews
Counting something that’s almost gone: combined visual-acoustic abundance estimate of the vaquita
The vaquita is the world’s most endangered cetacean – now almost extinct due to bycatch in an illegal fishery in its native upper Gulf of California, Mexico. Reliable estimates of population size and trend are key to prompting conservation action; ironically these are harder to obtain as population size decreases. We describe a combined visual line transect and passive acoustic population survey that took place in autumn 2015. We focus on the analysis, which involved combining (1) a Bayesian line transect model of variation in detectability as a function of sighting conditions and variation in density over geographic space (using previous, as well as current survey data); (2) a simulation model of detectability under perfect sighting conditions; (3) a Bayesian model of spatial variation in acoustic detection rate. The resulting abundance estimate was 59 (95% CRI 22-145). Despite the complications, analysis was undertaken by an Expert Panel, using BUGS and R, in just a few days – illustrating the power of modern approaches to obtain useful estimates with relative ease. The abundance estimate, combined with separate acoustic monitoring that shows an ongoing precipitous decline, has prompted efforts to catch the last remaining vaquita and try to preserve the species in captivity.
formerly University of Auckland
Things my mother never told me about capture –recapture: A review of open population models
It is about 18 years since I was last involved with methods of estimating animal abundance. Since my 1982 book “The estimation of animal abundance and related parameters” is somewhat out of date, I decided a couple of years ago in a fit of madness to revisit the subject again and consider the possibility of writing a book on “Capture-recapture for open populations”. It has been a huge undertaking as I have been very surprised at how much the subject has been and is expanding in every direction, both mathematically and computationally. A lot of people are now doing both theoretical and practical research in the subject area. As I like a challenge I got hooked, and by the end of this year I hope to have a first draft available. In my talk I will endeavour to review in broad brush terms what I have found.