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Assessing the Effect of Density on Population Growth When Modeling Individual Encounter Data Simone Tenan, Giacomo Tavecchia, Daniel Oro, Roger Pradel

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Assessing the Effect of Density on Population Growth When Modeling Individual Encounter Data Simone Tenan, Giacomo Tavecchia, Daniel Oro, Roger Pradel View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Archive Ouverte en Sciences de l'Information et de la Communication Assessing the effect of density on population growth when modeling individual encounter data Simone Tenan, Giacomo Tavecchia, Daniel Oro, Roger Pradel To cite this version: Simone Tenan, Giacomo Tavecchia, Daniel Oro, Roger Pradel. Assessing the effect of density on population growth when modeling individual encounter data. Ecology, Ecological Society of America, 2019, 100 (3), pp.e02595. 10.1002/ecy.2595. hal-02104959 HAL Id: hal-02104959 https://hal.archives-ouvertes.fr/hal-02104959 Submitted on 19 Apr 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Statistical Reports Ecology, 100(3), 2019, e02595 © 2019 by the Ecological Society of America Assessing the effect of density on population growth when modeling individual encounter data 1,5 2 3 4 SIMONE TENAN, GIACOMO TAVECCHIA, DANIEL ORO, AND ROGER PRADEL 1MUSE - Science Museum, Vertebrate Zoology Section, Corso del Lavoro e della Scienza 3, Trento 38122 Italy 2Animal Ecology and Demography Group, IMEDEA (CSIC-UIB), Miquel Marques 21, Esporles, Mallorca 07190 Spain 3Blanes Centre for Advanced Studies, CEAB (CSIC), C/d’acces a la Cala St. Francesc 14, Blanes 17300 Spain 4CEFE UMR 5175, CNRS, Universite de Montpellier, Universite Paul-Valery Montpellier - EPHE, Montpellier Cedex 5 France Citation: Tenan, S., G. Tavecchia, D. Oro, and R. Pradel. 2019. Assessing the effect of density on population growth when modeling individual encounter data. Ecology 100(3):e02595. 10. 1002/ecy.2595 Abstract. The relative role of density-dependent and density-independent variation in vital rates and population size remains largely unsolved. Despite its importance to the theory and application of population ecology, and to conservation biology, quantifying the role and strength of density dependence is particularly challenging. We present a hierarchical formula- tion of the temporal symmetry approach, also known as the Pradel model, that permits estima- tion of the strength of density dependence from capture–mark–reencounter data. A measure of relative population size is built in the model and serves to detect density dependence directly on population growth rate. The model is also extended to account for temporal random vari- ability in demographic rates, allowing estimation of the temporal variance of population growth rate unexplained by density dependence. We thus present a model-based approach that enable to test and quantify the effect of density-dependent and density-independent factors affecting population fluctuations in a single modeling framework. More generally, we use this modeling framework along with simulated and empirical data to show the value of including density dependence when modeling individual encounter data without the need for auxiliary data. Key words: Audouin’s Gull; capture-recapture; Gibbs variable selection; open population estimation; population dynamics; Pradel model; rate of population change; temporal symmetry model. of density dependence is thus fundamental to the under- INTRODUCTION standing of processes that regulate temporal and spatial Because a population cannot grow indefinitely, it is variation in population size (Lack 1954, Ricker 1954, expected that density will eventually check population Andrewartha and Birch 1986). growth (Malthus 1798). At the opposite, low levels of It has always been challenging to demonstrate density density have also been found to sometimes limit popula- dependence in real populations. There are practical, the- tion growth (Allee et al. 1949). The first phenomenon oretical, and technical difficulties in tackling the prob- (negative density dependence) will result in population lem (Lebreton 2009). First, population size and hence fluctuations around the carrying capacity (Sibly and density is notoriously difficult to measure accurately; Hone 2002) while the second (positive density depen- second, density is only a proxy for interactions among dence) will precipitate population decline. It follows that individuals and is thus a noisy measure of what actually the way density regulates population dynamics influ- occurs; but probably the main obstacle is statistical: suc- ences persistence time of threatened populations as well cessive densities and changes in density are obviously as the sustainable harvest rate of exploited populations strongly related, a fact that must be acknowledged in (Lande et al. 2003). The study of the strength and form any model. Early attempts focused on fitting the theoret- ical logistic growth model (Verhulst 1838, Pearl and Manuscript received 25 May 2018; revised 6 November 2018; Reed 1920) but were inconclusive (Slobodkin 2001). accepted 3 December 2018. Corresponding Editor: Brett T. Among the extant approaches, retrospective studies ana- McClintock. 5 E-mail: [email protected] lyze variation of population growth rate over time by Article e02595; page 1 Article e02595; page 2 SIMONE TENAN ET AL. Ecology, Vol. 100, No. 3 focusing on the realized population growth rate between where the latter includes both local recruitment and two successive time steps as qi = Ni+1/Ni, where Ni is immigration, and estimated mortality includes perma- population size at time i. However, abundance estima- nent emigration. However, the Pradel model likelihood tion in open populations can be biased when the error in can be parameterized with population growth rate q as a the counts around the true population size (observation structural parameter, thus allowing to test biological error) is not accounted for, leading to spurious detection hypotheses directly on q. In addition, a Bayesian formu- of density dependence (Dennis et al. 2006, Freckleton lation of the Pradel model permits the hierarchical mod- et al. 2006, Lebreton 2009). State-space models is elling of the biological and sampling processes and another approach that can reduce bias in parameter esti- allows the extension of the original fixed time effects mates when population counts are the only data avail- structure to random time effects (Tenan et al. 2014b). able (Clark and Bjørnstad 2004), however separating At this point, density can be integrated in the model, observation variance from process variance is only possi- only as an external covariate. This is not very satisfac- ble when the observation error is relatively small (Knape tory as the changes in density and population growth 2008). In addition, negative autocorrelation between are obviously related and considering an external mea- successive estimators may lead to an overestimation of sure of density and the population growth rate parame- temporal variance of population growth rate (an overes- ters of the model as independent is obviously wrong. In timation of Ni biases qi low but biases qiÀ1 high). this paper we derive a measure of relative population Some methods, based on individual encounter histo- size directly from the CMR data, and use it to detect ries, are currently available to assess the impact of density density dependence within the same model. In this way, on demographic rates while accounting for imperfect we circumvent the statistical difficulty inherent in den- detection. Schofield and Barker (2008) and Schofield sity-dependent models of having the same quantity, et al. (2009) propose to study the effect of density on namely density, at the same time estimated and the dri- recruitment and survival. However, density dependence ver of its own changes. may be effected differently in different years. For instance, Here we propose a new Bayesian hierarchical formula- eports for a given density, it may entail a reduced survival in tion of the temporal symmetry approach that allows years of high fecundity whereas survival will remain high quantification of the effect of population size on in years of low fecundity. Methods that allow to study the population growth rate and, more generally, the study R effect of density directly on population growth rate are of density-dependent and density-independent (i.e., thus needed. The approach proposed by Schofield et al. environmental) factors that affect temporal variation of (2009) can be reparameterized so that recruitment rate is population growth rate. Such decomposition into deter- defined as the difference between population growth rate ministic and stochastic components is important to the and survival (Nichols 2016) thus allowing modeling in assessment of the effects of environmental change on terms of population growth rate. population dynamics. Integrated population models (IPMs; Besbeas et al. We illustrate the modeling approach with simulated 2002) allow estimation of the strength of density depen- data, to investigate the effectiveness of detecting density- dence not only on demographic rates but also on the dependent effects on population growth rate, and we derived population growth rate (Abadi et al. 2012). apply the approach to encounter histories of a long-lived However,
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