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Hamel S, Yoccoz NG, Gaillard JM. Assessing variation in life-history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists. Biol Rev Camb Philos Soc 2016; 92:754-775. [PMID: 26932678 DOI: 10.1111/brv.12254] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2015] [Revised: 12/21/2015] [Accepted: 01/08/2016] [Indexed: 02/06/2023]
Abstract
Mixed models are now well-established methods in ecology and evolution because they allow accounting for and quantifying within- and between-individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi-modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life-history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life-history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long-term studies of large mammals to illustrate the potential of using mixture models for assessing within-population variation in life-history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life-history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.
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Affiliation(s)
- Sandra Hamel
- Faculty of Biosciences, Fisheries and Economics, Department of Arctic and Marine Biology, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Nigel G Yoccoz
- Faculty of Biosciences, Fisheries and Economics, Department of Arctic and Marine Biology, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Jean-Michel Gaillard
- CNRS, UMR 5558 'Biométrie et Biologie Evolutive', Université de Lyon, Université Lyon 1, F-69622, Villeurbanne, France
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Abstract
Modelling wildlife disease poses some unique challenges. Wildlife disease systems are data poor in comparison with human or livestock disease systems, and the impact of disease on population size is often the key question of interest. This review concentrates specifically on the application of dynamic models to evaluate and guide management strategies. Models have proved useful particularly in two areas. They have been widely used to evaluate vaccination strategies, both for protecting endangered species and for preventing spillover from wildlife to humans or livestock. They have also been extensively used to evaluate culling strategies, again both for diseases in species of conservation interest and to prevent spillover. In addition, models are important to evaluate the potential of parasites and pathogens as biological control agents. The review concludes by identifying some key research gaps, which are further development of models of macroparasites, deciding on appropriate levels of complexity, modelling genetic management and connecting models to data.
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Gimenez O, Buckland ST, Morgan BJT, Bez N, Bertrand S, Choquet R, Dray S, Etienne MP, Fewster R, Gosselin F, Mérigot B, Monestiez P, Morales JM, Mortier F, Munoz F, Ovaskainen O, Pavoine S, Pradel R, Schurr FM, Thomas L, Thuiller W, Trenkel V, de Valpine P, Rexstad E. Statistical ecology comes of age. Biol Lett 2015; 10:20140698. [PMID: 25540151 PMCID: PMC4298184 DOI: 10.1098/rsbl.2014.0698] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1–4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.
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Affiliation(s)
- Olivier Gimenez
- CEFE UMR 5175, CNRS, Université de Montpellier, Université Paul-Valéry Montpellier, EPHE, 1919 Route de Mende, 34293 Montpellier Cedex 5, France
| | - Stephen T Buckland
- Centre for Research into Ecological and Environmental Modelling, University of St Andrews, St Andrews KY16 9LZ, UK
| | - Byron J T Morgan
- School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK
| | | | | | - Rémi Choquet
- CEFE UMR 5175, CNRS, Université de Montpellier, Université Paul-Valéry Montpellier, EPHE, 1919 Route de Mende, 34293 Montpellier Cedex 5, France
| | - Stéphane Dray
- Université de Lyon, F-69000, Lyon; Université Lyon 1; CNRS, UMR5558, Laboratoire de 18 Biométrie et Biologie Evolutive, F-69622, Villeurbanne, France
| | | | - Rachel Fewster
- Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand
| | - Frédéric Gosselin
- Irstea, UR EFNO, Centre de Nogent-sur-Vernisson, 45290 Nogent-sur-Vernisson, France
| | | | | | - Juan M Morales
- Laboratorio Ecotono, CRUB, INIBIOMA-CONICET, Bariloche, Argentina
| | | | - François Munoz
- UM2, UMR AMAP, Bd de la Lironde, TA A-51/PS2, 34398 Montpellier Cedex 5, France
| | - Otso Ovaskainen
- Department of Biosciences, University of Helsinki, Helsinki, Finland
| | - Sandrine Pavoine
- UMR 7204 CNRS UPMC, Centre for Ecology and Conservation Sciences, Muséum National d'Histoire Naturelle, 55-61 rue Buffon, 75005 Paris, France Mathematical Ecology Research Group, Department of Zoology, University of Oxford, Oxford OX1 3PS, UK
| | - Roger Pradel
- CEFE UMR 5175, CNRS, Université de Montpellier, Université Paul-Valéry Montpellier, EPHE, 1919 Route de Mende, 34293 Montpellier Cedex 5, France
| | - Frank M Schurr
- Institute of Landscape and Plant Ecology, University of Hohenheim, 70593 Stuttgart, Germany
| | - Len Thomas
- Centre for Research into Ecological and Environmental Modelling, University of St Andrews, St Andrews KY16 9LZ, UK
| | - Wilfried Thuiller
- Laboratoire d'Ecologie Alpine, UMR CNRS 5553, Université Joseph Fourier, Grenoble I, BP 53, 38041 Grenoble Cedex 9, France
| | - Verena Trenkel
- Ifremer, Rue de l'île d'Yeu, BP 21105, 44311 Nantes Cedex 3, France
| | - Perry de Valpine
- Environmental Science, Policy and Management, University of California, Berkeley, CA 94720, USA
| | - Eric Rexstad
- Centre for Research into Ecological and Environmental Modelling, University of St Andrews, St Andrews KY16 9LZ, UK
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Heisey DM, Osnas EE, Cross PC, Joly DO, Langenberg JA, Miller MW. Rejoinder: sifting through model space. Ecology 2010. [DOI: 10.1890/10-0894.1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Affiliation(s)
- Dennis M. Heisey
- USGS, National Wildlife Health Center, Madison, Wisconsin 53711 USA
| | - Erik E. Osnas
- Department of Forest and Wildlife Ecology, University of Wisconsin, 1630 Linden Drive, Madison, Wisconsin 52706 USA
| | - Paul C. Cross
- USGS, Northern Rocky Mountain Science Center, Bozeman, Montana 59717 USA
| | - Damien O. Joly
- Global Health Programs, Wildlife Conservation Society, 1008 Beverly Drive, Nanaimo, British Columbia V9S 2S4 Canada
| | - Julia A. Langenberg
- Wisconsin Department of Natural Resources, 101 South Webster Street, Madison, Wisconsin 53703 USA
| | - Michael W. Miller
- Colorado Division of Wildlife, Wildlife Research Center, 317 West Prospect Road, Fort Collins, Colorado 80526-2097 USA
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