OIKOS 113: 132Á/138, 2006 Estimation of local extinction rates when species detectability covaries with extinction probability: is it a problem? Stephanie Jenouvrier and Thierry Boulinier Jenouvrier, S. and Boulinier, T. 2006. Estimation of local extinction rates when species detectability covaries with extinction probability: is it a problem? Á/ Oikos 113: 132Á/ 138. Estimating the rate of change of the composition of communities is of direct interest to address many fundamental and applied questions in ecology. One methodological problem is that it is hard to detect all the species present in a community. Nichols et al. presented an estimator of the local extinction rate that takes into account species probability of detection, but little information is available on its performance. However, they predicted that if a covariance between species detection probability and local extinction rate exists in a community, the estimator of local extinction rate complement would be positively biased. Here, we show, using simulations over a wide range of parameters that the estimator performs reasonably well. The bias induced by biological factors appears relatively weak. The most important factor enhancing the performance (bias and precision) of the local extinction rate complement estimator is sampling effort. Interestingly, a potentially important biological bias, such as the covariance effect, improves the estimation for small sampling efforts, without inducing a supplementary overestimation when these sampling efforts are high. In the field, all species are rarely detectable so we recommend the use of such estimators that take into account heterogeneity in species detection probability when estimating vital rates responsible for community changes. S. Jenouvrier, Centre d’Etudes Biologiques de Chize´, Centre National de la Recherche Scientifique, FR-79360 Villiers en Bois, France ([email protected]). Á/ T. Boulinier, Centre d’Ecologie Fonctionnelle et Evolutive, CNRS Á/ UMR 5175, Montpellier, France. Estimating the rate of change of the composition of be differ according to the particular situations. Higher communities is of direct interest to address many apparent local extinction rates could be due to a fundamental questions in ecology (Rosenzweig and confounding effect of the relative species detection Clark 1994, Doherty et al. 2003a), but also in relation probabilities, which could be linked to their local to more applied questions linked with the conservation abundance (Doherty et al. 2003b, Alpizar-Jara et al. of biodiversity (Heywood 1995, Yoccoz et al. 2001). One 2004). For instance, in the case of animal communities in methodological problem is that it is hard to detect all the landscapes that are more or less fragmented, results may species present in a community at a given location and be biased if animal species are more or less likely to be time period, and thus it is necessary to account for that detected in landscapes with different levels of fragmenta- when one wants to infer rates of change in communities tion. (Nichols et al. 1998a, Gu and Swihart 2004). This is Estimators of species richness that take into account especially the case if such estimates are used to compare species probability of detection have been available to the dynamics of communities in contrasting situations ecologists for a long time (Burnham and Overton 1979, (e.g. habitats), as the probability of detecting species may reviewed by Bunge and Fitzpatrick 1993, Colwell and Accepted 9 September 2005 Copyright # OIKOS 2006 ISSN 0030-1299 132 OIKOS 113:1 (2006) Coddington 1994, Nichols and Conroy 1996, Boulinier predicted that if such a covariance between detection et al. 1998, Gotelli and Colwell 2001). Recently, interest probability and local extinction rate exists in a commu- has intensified in the development and evaluation of nity, the species more likely to be detected during the estimators to measure turnover of species assemblages, primary sampling session may be the highly detectable and Chao et al. (2005) proposed for instance a method ones, so that the LERC would thus be positively biased. to estimate similarity between communities taking into Indeed, if species are more detectable because they are account unseen shared species. Nichols et al. (1998a) more abundant, they will obviously have more chance of proposed estimators for parameters of the rates of being present and identified during the second primary change of communities, and in particular local extinc- session than species not yet detected. This can lead to an tion and turnover rates. Their approach is based on an overestimation of both the numbers of shared species analogy with work at the population level (Williams between two sampling sessions (i and j) and the LERC et al. 2002), and relies on the robust design of Pollock (fij). (1982), which enables estimation of parameters of Alpizar-Jara et al. (2004) provided strong empirical populations when there are heterogeneous probabilities evidence that local extinction probability covaries nega- of detection of individuals. With this approach, the tively with species detection probability and probably estimate of the local extinction rate complement (LERC, abundance of individuals within species. They also or (fij) in a demographic context) between two primary suggested an ad hoc weighted estimator to try to reduce Ri bias in the extinction probability estimator. The differ- sampling period i and j is: fˆ Mˆ =R ; where R is the ij j i i ence between the original estimator and the new number of species observed at the primary sampling weighted estimator was much smaller than they ex- ˆ Ri period i, and Mj is the estimated number of these pected, suggesting that the bias associated with the species still present at the primary sampling period j original estimators is not large. However, their empirical (Nichols et al. 1998a). Secondary sampling periods and simulation work was based on the North American within the second primary sampling period enable the Breeding Bird Survey, and they highlighted that analyses use of a ‘‘closed community’’ estimator (by analogy to a of different kinds of community-level data will likely ‘‘closed population’’, Williams et al. 2002) to estimate merit additional simulations tailored to other sampling the number of species detected the previous period situations. Ri Here, we investigate, using simulations over a wide (/Mˆ ): This estimator can be chosen from among a j range of parameters, the bias induced by the relationship series of estimators that rely on different hypotheses between detection probability and local extinction prob- regarding the way species detection probability may ability. The bias appears to be relatively small, and we vary, e.g. among species or time period/occasion (Otis show that the most important factor affecting the et al. 1978). Practically, the use of the jackknife performance (bias and precision) of the local extinction estimator of species richness developed to account for rate complement estimator is the sampling effort. Inter- heterogeneity in the probability of detecting species estingly, the estimator of the LERC performs actually (Burnham and Overton 1978, 1979, Boulinier et al. slightly better when there is a positive covariance 1998, Nichols et al. 1998a, 1998b) to compute the between the probability of species to be detected and estimators of rates of change has been suggested and their probability to ‘‘survive’’. Such estimators of can be implemented using an internet based program extinction and turnover rates based on captureÁ/recap- (Hines et al. 1999, COMDYN). ture modelling are thus of much practical value for One potential problem with the estimator of the local analysing data to study the dynamics of biodiversity extinction rate is that it is based on a ratio involving a when species detection probabilities cannot be assumed sub-sample of the community that may have specific to equal one. characteristics, one important characteristic being that they have been detected at the first primary sampling period. Nichols et al. (1998a) did not present any study of the performance of their estimator but stressed that, Simulation approach as the estimator of the local extinction rate was condi- tioned on the species that had been detected at the first In order to study the performance of the estimator, we primary sampling session, it could be biased towards simulated (1) a virtual community undergoing temporal lower values if species that are the most detected are also change in composition and (2) a sampling of that the most abundant, and thus possibly the most likely not community under a robust design (Williams et al. to go extinct due to environmental and/or demographic 2002). We simulated a community of N species, in which stochasticity. Indeed, the local extinction rate should species could go extinct between two primary sampling depend on the number of individuals as a result of sessions (PSS). Within each PSS, the community is demographic or environmental stochasticity (Gilpin and considered closed and we could set the number of Soule´ 1986, Kinney 1997). Nichols et al. (1998a) thus secondary sampling occasions. The overall probability OIKOS 113:1 (2006) 133 of detection over a PSS will depend on both the average occasion, (3) intrinsic features of the community, i.e. species detection probability at each occasion, p, and the the number of species, the heterogeneity in their detec- number of secondary sampling occasions (Nichols et al. tion probability, and the covariance effect between 1998a). With the sets of parameters we used for each species detection probability and extinction probability. combination of number of occasions and probability of To study the covariance effect between species detection detection at each occasion, the probability of detection probabilities and extinction probabilities, we set a low at the scale of a PSS varied between 20% and 100% (e.g. local extinction rate for the highly detectable group of 5 occasions and p/0.05 leads to a pPSS / 22.6%; 20 species and a high local extinction rate for the less occasions and p/0.30 leads to pPSS /99.9%).