Incorporating Collateral Data in Conservation Biology

Abstract

Conservation biologists often need to set ecological modeling assumptions or estimate parameters from sparse data. In some cases this problem can be addressed by incorporating data from closely related species or from the same species at different sites (i.e., collateral data). Currently no structured methods exist for incorporating such information. An analogous problem in Actuarial science is to set premium rates in situations with little direct data on claim frequency or size. The rates are estimated using actuarial credibility theory, which incorporates collateral data with the direct data. actuarial credibility theory combined with the actuarial control cycle financial management process also provides an adaptive mechanism for updating assumptions. This theory may have some utility for ecologists wanting to incorporate collateral data in an adaptive management framework, a companion to approaches such as Bayesian updating. We describe the historical development of actuarial credibility theory from early ad hoc methods to empirical Bayes approaches. We explore some of the theory's strengths, such as relative simple formulae for incorporation collateral data, and we explore some of the theory's weaknesses, such as the use of the best linear approximation to the Bayes estimate. We illustrate potential applications of the theory using an example on the mortality rate of the Powerful Owl ( Ninox strenua). Incorporando Datos Colaterales a la Biología de la ConservaciónResumen: A menudo, los biólogos de la conservación necesitan hacer supuestos en los modelos ecológicos o estimar parámetros a partir de datos dispersos. En algunos casos se pueden encarar estos problemas incorporando datos de especies cercanamente relacionadas o de la misma especie en sitios diferentes (es decir, datos colaterales). Actualmente no existen métodos para incorporar dicha información. Un problema análogo en la ciencia Actuarial es fijar tasas superiores en situaciones con pocos datos directos sobre frecuencia o tamaño de reclamaciones. Las tasas son estimadas utilizando la teoría actuarial de credibilidad, que incorpora datos colaterales a los datos directos. La teoría actuarial de credibilidad, combinada con el ciclo de control actuarial del proceso de administración financiera también proporciona un mecanismo adaptativo para actualizar supuestos. Esta teoría puede tener utilidad para ecólogos que quieren incorporar datos colaterales en un marco de manejo adaptativo, un acompañante de métodos como actualización Bayesiana. Describimos el desarrollo histórico de la teoría actuarial de credibilidad desde los primeros métodos ad hoc hasta métodos Bayes empíricos. Exploramos algunas de las fortalezas de la teoría, como las fórmulas simples para la incorporación de datos colaterales, y exploramos algunas de sus debilidades, como el uso de la mejor aproximación lineal a la estimación Bayes. Ilustramos las aplicaciones potenciales de la teoría utilizando como ejemplo la tasa de mortalidad de Ninox strenua.

Profiting from prior information in Bayesian analyses of ecological data

“…Bayesian statistics can evaluate such probabilistic predictions, making them particularly useful in ecology where predictions can rarely be made with complete certainty. Linacre et al . (2004) advocated using actuarial methods to include prior information in risk assessments for conservation biology.…”

Conservation biology for suites of species: Demographic modeling for Pacific island kingfishers

“…The deterministic model presented here should be viewed as a plastic and foundational model that can be enhanced as additional data become available. Enhancements to the generalized model might be implemented within an adaptive management framework, through a flexible Bayesian approach (Frigessi et al, 2005) or through other methods of incorporating data from multiple sources and of varying reliability (Linacre et al, 2004). The generalized population matrix also provides a foundation for localized models directed toward managing single species in specific situations, which might incorporate collateral data, local environmental variation, stochastic environmental events (Lande, 1993), and population-specific demographic parameters (Dugger et al, 2004;LaHaye et al, 2004;Mazerolle et al, 2005).…”

“…Conservation biologists have long embraced the use of information from surrogate populations for managing endangered species (Bednarz, 1987;Sydeman, 1989;Legge, 2000;Linacre et al, 2004;Bar-David et al, 2005;Doak et al, 2005). Surrogates can be necessitated by a lack of knowledge about the particular population of interest, combined with time and resource constraints that prevent thorough investigations.…”

Importance of correlations among matrix entries in stochastic models in relation to number of transition matrices

“…The fact that a small number of observations leads to more extreme correlations is relatively poorly known in conservation biology, where the lack of sufficient demographic data is a common problem. To overcome this problem, data from other populations or related species are often used in simulations (Freedman et al 2003, Linacre et al 2003). Dependence of correlations on the number of matrices has two important implications for stochastic simulations.…”