Quantitative Developments


Quantitative Developments - ARMI Papers & Reports

Papers & Reports ring species availability biases occupancy estimates in single-level occupancy models
Authors: Graziella V DiRenzo; David AW Miller; Evan H Campbell Grant
Outlet: Ecology
1. Most applications of single-level occupancy models do not differentiate between availability and detectability, even though species availability is rarely equal to one. The availability process includes elements of species movement, behavior, and phenology, and availability can be estimated using multi-scale occupancy models. However, for the practical application of multi-scale occupancy models, it can be unclear what a robust sampling design looks like and what the statistical properties of the multi-scale and single-level occupancy models are when availability is less than one.

2. Using simulations, we explore the following common questions asked by ecologists during the design phase of a field study: (Q1) what is a robust sampling design for the multi-scale occupancy model when there are a priori expectations of parameter estimates?, (Q2) what is a robust sampling design when we have no expectations of parameter estimates?, and (Q3) can a single-level occupancy model with a random effects term adequately absorb the extra heterogeneity produced when availability is less than one and provide reliable estimates of occupancy probability?.

3. Our results show that there is a tradeoff between the number of sites and surveys needed to achieve a specified level of acceptable error for occupancy estimates using the multi-scale occupancy model. We also document that when species availability is low (< https://0.40 on the probability scale), then single-level occupancy models severely underestimate occupancy by as much as https://0.40 on the probability scale, produce overly precise estimates, and provide poor parameter coverage. This pattern was observed when a random effects term was and was not included in the single-level occupancy model, suggesting that adding a random-effects term does not adequately absorb the extra heterogeneity produced by the availability process. In contrast, when species availability was high (> 0.60), single-level occupancy models performed similarly to the multi-scale occupancy model.

4. As a companion, we provide an RShiny app that allows users to further explore our results and determine optimal designs across different sampling scenarios https://gdirenzo.shinyapps.io/multi-scale-occ/. Our results suggest that unaccounted for availability can lead to underestimating species distributions using single-level occupancy models, which can have large implications on ecological inference and predictions for practitioners, such as those working at the front lines of invasion ecology, disease emergence, and species conservation.
Papers & Reports Staggered-entry analysis of breeding and occupancy dynamics of Arizona Toads from historically occupied habitats of New Mexico, USA
Authors: M J Forzley; Mason J Ryan; I M Latella; J T Giermakowski; Erin L Muths; Brent H Sigafus; Blake R Hossack
Outlet: Copeia
For species with variable phenology, it is often challenging to produce reliable estimates of population dynamics or changes in occupancy. The Arizona Toad (Anaxyrus microscaphus) is a southwestern USA endemic that has been petitioned for legal protection, but status assessments are limited by a lack of information on population trends. Also, timing and consistency of Arizona Toad breeding varies greatly, making it difficult to predict optimal survey times or effort required for detection. To help fill these information gaps, we conducted breeding season call surveys during 2013–2016 and 2019 at 86 historically occupied sites and 59 control sites across the species’ range in New Mexico. We estimated variation in mean dates of arrival and departure from breeding sites, changes in occupancy, and site-level extinction since 1959 with recently developed multi-season staggered-entry models, which relax the within-season closure assumption common to most occupancy models. Optimal timing of surveys in our study areas was approximately March 5 - March 30. Averaged across years, estimated probability of occupancy was https://0.58 (SE = 0.09) for historical sites and https://0.19 (SE = 0.08) for control sites. Occupancy increased from 2013 through 2019. Notably, even though observer error was trivial, annual detection probabilities varied from https://0.23 to https://0.75 and declined during the study; this means naïve occupancy values would have been misleading, indicating apparent declines in toad occupancy. Occupancy was lowest during the first year of the study, possibly due to changes in stream flows and conditions in many waterbodies following extended drought and recent wildfires. Although within-season closure was violated by variable calling phenology, simple multi-season models provided nearly identical estimates as staggered-entry models. Surprisingly, extinction probability was unrelated to the number of years since the first or last record at historically occupied sites. Collectively, our results suggest a lack of large, recent declines in occupancy by Arizona Toads in New Mexico, but we still lack population information from most of the species’ range.
Papers & Reports Accommodating the role of site memory in dynamic species distribution models using detection/non-detection data
Authors: Graziella V DiRenzo; A David; Blake R Hossack; Sigafus H Brent; P E Howell; Evan HC Grant; Erin L Muths
Outlet: Ecology xx:xxx-xxx
First-order dynamic occupancy models (FODOMs) are a class of state-space model in which the true state (occurrence) is observed imperfectly. An important assumption of FODOMs is that site dynamics only depend on the current state and that variations in dynamic processes are adequately captured with covariates or random effects. However, it is often difficult to measure the covariates that generate ecological data, which are often spatio-temporally correlated. Consequently, the non-independent error structure of correlated data causes underestimation of parameter uncertainty and poor ecological inference. Here, we extend the FODOM framework with a second-order Markov process to accommodate site memory when covariates are not available. Our modeling framework can be used to make reliable inference about site occupancy, colonization, extinction, turnover, and detection probabilities. We present a series of simulations to illustrate the data requirements and model performance. We then applied our modeling framework to 13 years of data from an amphibian community in southern Arizona, USA and find that site memory helps describe dynamic processes for most species. Our approach represents a valuable advance in obtaining inference on population dynamics, especially as they relate to metapopulations.
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