Justin D. Yeakel | Search USGS

USGS2016

Characterizing species interactions to understand press perturbations: What is the community matrix?

The community matrix is among ecology's most important mathematical abstractions, formally encapsulating the interconnected network of effects that species have on one another's populations. Despite its importance, the term `community matrix' has been applied to matrices having differing interpretations. This has hindered the application of theory for understanding community structure and perturbation responses, particularly in the contexts of ecosystem-based management and conservation. Here we clarify the correspondence and distinctions between the Interaction matrix, the Alpha matrix and the Jacobian matrix, terms which are frequently used interchangeably and have numerous synonyms, including the term Community matrix. We illustrate how these matrices correspond to different ways of characterizing interaction strengths, how they permit insights regarding different types of press perturbations of species growth rates or abundances, and how these are related by a simple scaling relationship. Connections to additional interaction strength characterizations encapsulated by the Beta matrix, the Gamma matrix, and the Removal matrix are also discussed. Our synthesis highlights the empirical challenges that remain in using these mathematical tools to understand actual communities.

Ecology, Evolution, and Systematics↗

USGS2012

Tools for quantifying isotopic niche space and dietary variation at the individual and population level.

Ecologists are increasingly using stable isotope analysis to inform questions about variation in resource and habitat use from the individual to community level. In this study we investigate data sets from 2 California sea otter ( Enhydra lutris nereis ) populations to illustrate the advantages and potential pitfalls of applying various statistical and quantitative approaches to isotopic data. We have subdivided these tools, or metrics, into 3 categories: IsoSpace metrics, stable isotope mixing models, and DietSpace metrics. IsoSpace metrics are used to quantify the spatial attributes of isotopic data that are typically presented in bivariate (e.g., δ 13 C versus δ 15 N) 2-dimensional space. We review IsoSpace metrics currently in use and present a technique by which uncertainty can be included to calculate the convex hull area of consumers or prey, or both. We then apply a Bayesian-based mixing model to quantify the proportion of potential dietary sources to the diet of each sea otter population and compare this to observational foraging data. Finally, we assess individual dietary specialization by comparing a previously published technique, variance components analysis, to 2 novel DietSpace metrics that are based on mixing model output. As the use of stable isotope analysis in ecology continues to grow, the field will need a set of quantitative tools for assessing isotopic variance at the individual to community level. Along with recent advances in Bayesian-based mixing models, we hope that the IsoSpace and DietSpace metrics described here will provide another set of interpretive tools for ecologists.

Journal of Mammalogy↗