Effects of environmental variables on invasive amphibian activity: using model selection on quantiles for counts

Abstract

Citation: Muller, B. J., B.S. Cade, and L. Schwarzkopf. 2018. Effects of environmental variables on invasive amphibian activity: using model selection on quantiles for counts. Ecosphere 9(1):e02067. 10. 1002/ecs2.2067 Abstract. Many different factors influence animal activity. Often, the value of an environmental variable may influence significantly the upper or lower tails of the activity distribution. For describing relationships with heterogeneous boundaries, quantile regressions predict a quantile of the conditional distribution of the dependent variable. A quantile count model extends linear quantile regression methods to discrete response variables, and is useful if activity is quantified by trapping, where there may be many tied (equal) values in the activity distribution, over a small range of discrete values. Additionally, different environmental variables in combination may have synergistic or antagonistic effects on activity, so examining their effects together, in a modeling framework, is a useful approach. Thus, model selection on quantile counts can be used to determine the relative importance of different variables in determining activity, across the entire distribution of capture results. We conducted model selection on quantile count models to describe the factors affecting activity (numbers of captures) of cane toads (Rhinella marina) in response to several environmental variables (humidity, temperature, rainfall, wind speed, and moon luminosity) over eleven months of trapping. Environmental effects on activity are understudied in this pest animal. In the dry season, model selection on quantile count models suggested that rainfall positively affected activity, especially near the lower tails of the activity distribution. In the wet season, wind speed limited activity near the maximum of the distribution, while minimum activity increased with minimum temperature. This statistical methodology allowed us to explore, in depth, how environmental factors influenced activity across the entire distribution, and is applicable to any survey or trapping regime, in which environmental variables affect activity.

Impacts of artificial light on food intake in invasive toads

“…Cage traps using ultraviolet light as a lure, which attracts invertebrates, capture toads 46 . Our results suggest that trapping may be more effective during darker lunar phases (corroborated by 47 ), and in urban areas shaded from ALAN, or in peri-urban and rural areas. Considering the spatio-temporal pattern of the impact of ALAN may contribute to better management of invasive amphibians, especially if lights are used to attract insect food.…”

Quantile regression estimates of animal population trends

“…One could obtain repeated random realizations (say R = 1,000) of population sizes from the binomial model for probability of detection, estimate the selected quantile regressions for each, and then average over R estimates to obtain quantile estimates of changes in population size that incorporate the detection probability model. Averaging of quantile regression estimates from repeated random jittering of counts has been previously employed successfully for extending conventional quantile regression to discrete responses (Machado and Santos Silva 2005, Cade and Dong 2008, Muller et al 2018 The first-, second-, and third-quartile estimates provide a flexible approach for obtaining an interval of estimates for common density-dependent and density-independent models of population growth based on population size transitions without assuming any parametric distributional form. Any of the typical extensions of the linear model made by using generalized additive models or splines to deal with nonlinearities are possible with quantile regression.…”

“…One could obtain repeated random realizations (say R = 1,000) of population sizes from the binomial model for probability of detection, estimate the selected quantile regressions for each, and then average over R estimates to obtain quantile estimates of changes in population size that incorporate the detection probability model. Averaging of quantile regression estimates from repeated random jittering of counts has been previously employed successfully for extending conventional quantile regression to discrete responses (Machado and Santos Silva 2005, Cade and Dong 2008, Muller et al 2018). Again, estimated detection probabilities will affect trend model relationships over time only if they differ across years.…”

“…We used a unit‐exponential weighted bootstrapping approach (Bose and Chatterjee 2003, Tarr 2012) that is appropriate for heterogeneous quantile regression models to obtain standard errors and confidence intervals of parameter estimates. We selected among alternative growth models using small sample‐size adjusted Akaike's Information Criterion (AIC c ) in R package MuMIn (Bartón 2020), appropriate for quantile regression assuming a working likelihood for an asymmetric double‐exponential distribution (Cade et al 2005, Muller et al 2018). All R statistical code is provided in Supporting Information.…”

The relationships between toad behaviour, antipredator defences, and spatial and sexual variation in predation pressure

“…In both trials, only one individual was recorded at a time. To remove the effect that temperature may have on amphibian activity ( Muller, Cade & Schwarzkopf, 2018 ) and locomotion ( Preest & Pough, 2003 ), the room was at approximately 19 °C at all times. Light conditions were standardized, as the only light source during all trials was a 60 W white light bulb 2.5 m high at the centre of the container where the toad was performing the trial in question (see below).…”