A Hierarchical Model to Estimate Fish Abundance in Alpine Streams by using Removal Sampling Data from Multiple Locations

Abstract

International audienceThe author compares 12 hierarchical models in the aim of estimating the abundance of fish in alpine streams by using removal sampling data collected at multiple locations. The most expanded model accounts for (i) variability of the abundance among locations, (ii) variability of the catchability among locations, and (iii) residual variability of the catchability among fish. Eleven model reductions are considered depending which variability is included in the model. The more restrictive model considers none of the aforementioned variabilities. Computations of the latter model can be achieved by using the algorithm presented by Carle and Strub (Biometrics 1978, 34, 621-630). Maximum a posteriori and interval estimates of the parameters as well as the Akaike and the Bayesian information criterions of model fit are computed by using samples simulated by a Markov chain Monte Carlo method. The models are compared by using a trout (Salmo trutta fario) parr (01) removal sampling data set collected at three locations in the Pyre'ne'es mountain range (Haute-Garonne, France) in July 2006. Results suggest that, in this case study, variability of the catchability is not significant, either among fish or locations. Variability of the abundance among locations is significant. 95% interval estimates of the abundances at the three locations are [0.15, 0.24], [0.26, 0.36], and [0.45, 0.58] parrs per m2. Such differences are likely the consequence of habitat variability

A hierarchical model to estimate the abundance and biomass of salmonids by using removal sampling and biometric data from multiple locations

“…dom spatial variability of the abundance, random spatial variability of the catchability, and residual variability of the catchability with fish. By using an index of complexity of fit, Laplanche (2010) suggested that a reduction with no variability of the catchability (among stream sections and residual) should be preferred. We have attained similar conclusions (a h = a, b h = b, and 1/h = 0).…”

“…This model has been popular among fish ecologists since the work of Carle and Strub (1978) who presented an algorithm to efficently compute a maximum likelihood estimate of the abundance. This approach actually provides inaccurate estimates of fish abundance (Riley and Fausch 1992;Peterson et al 2004;Laplanche 2010). The main source of inaccuracy is unaccounted variability of the catchability or of the abundance.…”

“…Several authors have therefore presented more advanced hierarchical models to estimate fish abundance from removal sampling data. Such models consider variability of the catchability between stream sections (Wyatt 2002(Wyatt , 2003, residual among fish (Dorazio et al 2005;Mäntyniemi et al 2005;Laplanche 2010), and variability of the abundance between stream sections (Wyatt 2002(Wyatt , 2003Dorazio et al 2008).…”

A length‐based hierarchical model of brown trout (Salmo trutta fario) growth and production

“…The trend is to construct such statistical models within a Bayesian framework (Congdon, 2006). Recent hierarchical Bayesian models (HBMs) relate abundance to environmental covariates (Rivot et al, 2008;Ebersole et al, 2009), include heterogeneity of the catchability (Ma¨ntyniemi et al, 2005;Do-razio et al, 2005;Ruiz and Laplanche, 2010), and can handle multiple sampling stream sections (Wyatt, 2002;Webster et al, 2008;Laplanche, 2010). The reason of popularity of HBMs over the last decade is their ability to handle complex relationships (multi-level, non-linear, mixed-effect) between variables with heterogeneous sources (relationships, data, priors) of knowledge.…”

Extending removal and distance-removal models for abundance estimation by modeling detections in continuous time

“…An alternative to removal sampling is to record complete detection records (all detections for every individual) instead of just the first (Alldredge et al, 2007a); however, this may not be feasible in studies like MNFB where many species are observed simultaneously Versions of time-varying models have been described for trap-based removal sampling and continuous-time capture-recapture. Time variation has been modeled through a non-constant hazard function (Schnute, 1983;Hwang and Chao, 2002), a randomly varying detection probability across trapping sessions (Wang and Loneragan, 1996), and constant detection probabilities that vary randomly from individual to individual (Mäntyniemi et al, 2005;Laplanche, 2010). Most of these approaches resulted marginally in a decreasing (nonpeaked) detection function over time.…”