Accounting for sampling error when inferring population synchrony from time-series data: a Bayesian state-space modelling approach with applications.
BACKGROUND
Data collected to inform time variations in natural population size are tainted by sampling error. Ignoring sampling error in population dynamics models induces bias in parameter estimators, e.g., density-dependence. In particular, when sampling errors are independent among populations, the classical estimator of the synchrony strength (zero-lag correlation) is biased downward. However, this bias is rarely taken into account in synchrony studies although it may lead to overemphasizing the role of intrinsic factors (e.g., dispersal) with respect to extrinsic factors (the Moran effect) in generating population synchrony as well as to underestimating the extinction risk of a metapopulation.


RESULTS
The aim of this paper was first to illustrate the extent of the bias that can be encountered in empirical studies when sampling error is neglected. Second, we presented a space-state modelling approach that explicitly accounts for sampling error when quantifying population synchrony. Third, we exemplify our approach with datasets for which sampling variance (i) has been previously estimated, and (ii) has to be jointly estimated with population synchrony. Finally, we compared our results to those of a standard approach neglecting sampling variance. We showed that ignoring sampling variance can mask a synchrony pattern whatever its true value and that the common practice of averaging few replicates of population size estimates poorly performed at decreasing the bias of the classical estimator of the synchrony strength.


CONCLUSIONS
The state-space model used in this study provides a flexible way of accurately quantifying the strength of synchrony patterns from most population size data encountered in field studies, including over-dispersed count data. We provided a user-friendly R-program and a tutorial example to encourage further studies aiming at quantifying the strength of population synchrony to account for uncertainty in population size estimates.
Office National de la Chasse et de la Faune Sauvage, Direction des Études et de la Recherche, Le Perray-en-Yvelines, France ; Université de Lyon, Lyon, Université Lyon 1, CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.
Hugues
H
Santin-Janin
UMR Biology of Aquatic Organims and Ecosystems, MNHN-IRD-CNRS-UPMC, Muséum National d'Histoire Naturelle, Paris, France.
Bernard
B
Hugueny
Office National de la Chasse et de la Faune Sauvage, Direction des Études et de la Recherche, Le Perray-en-Yvelines, France.
Philippe
P
Aubry
Université de Lyon, Lyon, Université Lyon 1, CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.
David
D
Fouchet
Centre d'Ecologie Fonctionnelle et Evolutive, CNRS, UMR 5175, Montpellier, France.
Olivier
O
Gimenez
Université de Lyon, Lyon, Université Lyon 1, CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.
Dominique
D
Pontier
D001499:Bayes Theorem; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics; D012107:Research Design; D015983:Selection Bias; D035501:Uncertainty