Power to detect trends in abundance within a distance sampling framework

Abstract

Ensuring that inferences from biological monitoring are reliable requires a level of sampling effort that is commensurate with programmatic objectives and reflects attributes of target populations. Consensus guidelines have emerged to guide allocation of sampling effort for programmes designed to detect trends in occupancy but not for abundance, despite its prevalence as a target parameter. We evaluated the influence of population attributes (density, availability, detection probability and magnitude of trend) and sampling design features (number of sites, number of repeat surveys, and survey-year interval) on a Bayesian analogue of statistical power to detect declines in abundance estimated using distance sampling methods. For a range of values common to terrestrial vertebrates, we simulated spatially and temporally replicated populations from which we generated survey data. We then analysed each dataset with a hierarchical open-population model that allowed for temporary emigration to estimate power for periods of 5-20 years. For a given amount of sampling effort, power to detect trends was highest when effort was allocated to maximizing the number of sites by decreasing the number of repeat surveys within a year and increasing the interval between survey years. For example, to have an 80% chance of detecting a 3% annual decline required 40% longer when 67 sites were surveyed three times per year compared to 600 sites surveyed once every three years despite both allocations requiring 4,000 surveys over 20 years. Notably, these patterns were independent of density or detectability of the target species, which contrasts with occupancy studies where optimal allocation shifts from surveying more sites to more repeat surveys when detectability is low or occupancy is high. Synthesis and applications. Our findings provide guidance for allocating resources efficiently for distance sampling studies focused on terrestrial vertebrates. By comparing the approximate density and detectability of target populations to those we considered, monitoring programmes can balance the amount of survey effort allocated to sites, surveys per site, and annual revisits to help ensure sufficient power to meet objectives effectively and efficiently. These decisions are increasingly important as budgets for conservation decrease and consequences of inaction continue to increase.