Estimating thresholds in occupancy when species detection is imperfect

Abstract

Identification of thresholds (state changes over a narrow range of values) is of basic and applied ecological interest. However, current methods of estimating thresholds in occupancy ignore variation in the observation process and may lead to erroneous conclusions about ecological relationships or to the development of inappropriate conservation targets. We present a model to estimate a threshold in occupancy while accounting for imperfect species detection. The threshold relationship is described by a break-point (threshold) and the change in slope (threshold effect). Imperfect species detection is incorporated by jointly modeling species occurrence and species detection. We used WinBUGS to evaluate the model through simulation and to fit the model to avian occurrence data for three species from 212 sites with two replicate surveys in 2007-2008. To determine if accounting for imperfect detection changed the inference about thresholds in avian occupancy in relation to habitat structure, we compared our model to results from a commonly used threshold model (segmented logistic regression). We fit this model in both frequentist and Bayesian modes of inference. Results of the simulation study showed that 95% posterior intervals contained the true value of the parameter in approximately 95% of the simulations. As expected, the simulations indicated more precise threshold and parameter estimates as sample size increased. In the empirical study, we found evidence for threshold relationships for four species by covariate combinations when ignoring species detection. However, when we included variation from the observation process, threshold relationships were not supported in three of those four cases (95% posterior intervals included 0). In general, confidence intervals for the threshold effect were larger when we accounted for species nondetection than when we ignored nondetection. This model can be extended to investigate abundance thresholds as a function of ecological and anthropogenic factors, as well as multispecies hierarchical models.

Assessing Regional and Interspecific Variation in Threshold Responses of Forest Breeding Birds through Broad Scale Analyses

“…This warrants the advice put forward by many ecologists that threshold values cannot simply be transferred across regions [35] or interpreted as clear-cut targets for ecosystem management and conservation [74]. We also warn that 4) sample size (in our study number of atlas blocks) might have large effects on the outcome of threshold studies (see also [63]) and that this might be one factor driving differences between threshold studies. Finally, our results indicate that 5) thresholds in long-term persistence and extinction dynamics can be found across a wide range of habitat cover or area.…”

“…However, it remains an issue that needs to be addressed. We are aware, and have shown here, that sample size may be one potential reason for the difference in outcome in support for thresholds and in associated forest cover estimates [63]. Therefore, this is an additional factor that we have to take into account when we try to extrapolate from one study or species to the next or when we try to infer conservation and management targets based on studies of threshold responses.…”

“…One important factor in the comparison of thresholds in Vermont and those found in New York is the effect of sample size on our model outcome [63]. The sample size (number of atlas blocks) in Vermont is low (175) compared to New York (5074).…”

“…Sample size might have pronounced effects on the power to detect thresholds and the percentage of forest cover at which the thresholds are estimated [63] and could thus potentially explain (part of) differences in results the Vermont (N = 175 atlas blocks) and New York (N = 5074 atlas blocks) analyses. We investigated the effect of sample size by obtaining 5000 random subsets of 175 blocks from the entire New York data set and fitted a segmented regression and logistic regression to each of these subsets.…”

Regional variability in extinction thresholds for forest birds in the north‐eastern United States: an examination of potential drivers using long‐term breeding bird atlas datasets

“…Finally, the estimation of the thresholds may be influenced by methodological and statistical issues in threshold detection. Variability in species detection and survey efforts (Betts et al ., ; Zuckerberg & Porter, ; Jones et al ., ), the use of different sample sizes (van der Hoek et al ., ) and the use of various statistical approaches (Ficetola & Denoël, ) may make comparisons and generalizations across studies or study sites difficult.…”