Counting with confidence: estimating the uncertainty associated with measures of avian abundance and productivity from the Goose & Swan Monitoring Programme (GSMP) (original) (raw)

2021

The long-term monitoring of wildlife populations provides critical data used to inform conservation policy and action. Within the UK, the Goose & Swan Monitoring Programme (GSMP) and affiliated schemes monitor the abundance (i.e. population size) and breeding success of native, migratory species of geese and swans through co-ordinated winter counts and age assessments at key sites. Typically, GSMP reports definitive annual estimates of the total population size based on the numbers of individuals counted, and the breeding success of the population based on the relative numbers of adults and juveniles (i.e. individuals born during the previous breeding season) in the surveyed population. However, to date there have been no attempts to estimate the uncertainty associated with these estimates of abundance or breeding success produced by GSMP. A widely-used approach to quantifying uncertainty associated with an estimate is to calculate a confidence interval, which indicates the likely range in which the mean estimate would be found if the sampling exercise was repeated. More specifically, if the same population was surveyed on multiple occasions and the 95% confidence intervals were estimated for each occasion, the resulting confidence intervals would contain the true population parameter in approximately 95% of the cases. To date, the estimation of confidence intervals for GSMP data has proven difficult, as for many of the monitored populations only a single survey of each site can be undertaken each winter, and the deployment of additional survey effort to repeat the surveys (which could be used to estimate the variance between surveys) is not practical. Even where multiple surveys are currently undertaken, the use of a consistent approach to the estimation of confidence intervals would facilitate meaningful comparisons among different populations. Approaches that would allow the estimation of comparable confidence intervals for all of the populations would therefore be beneficial. In this report, we compare two methods of estimating confidence intervals for the breeding success or abundance produced by GSMP. These two methods were (i) simple analytical expressions (based on binomial and Poisson distributions), and (ii) alternative approaches based on simulation (bootstrap resampling or Monte Carlo simulations). Both methods could be used for the data that have been routinely collected by GSMP and affiliated schemes. Comparison of the confidence intervals produced indicated broad similarity between the two methods, for juvenile proportion and abundance estimates. Indeed, the confidence intervals estimated by the two methods for the proportions of juveniles within populations were identical in 7 of the 12 populations considered, given the precision with which such estimates have been typically reported (i.e. a percentage given to one decimal place or a proportion given to three decimal places), with only minor deviations of ≤0.009 in the remaining 5 populations. Similarly, for annual estimates of total abundance, in all populations we found close matches between the size of the confidence intervals derived by Poisson tests and simulation. The mean difference between the sizes of the 95% CI values produced by the two methods did not exceed 7 individuals for any of the populations considered. As expected, smaller 95% confidence intervals for the proportion of juveniles within a population were found where greater numbers of birds were aged, indicating a trade-off between sampling effort and uncertainty. Moreover, samples containing higher proportions of juveniles had larger confidence intervals for a given total number of aged birds; hence, for populations with higher breeding success greater sample sizes would be required to achieve more precise confidence intervals. For abundance, the absolute size of the confidence interval increased with population size (i.e. higher population sizes have larger confidence intervals). However, when confidence intervals were expressed as a percentage of the population size, their size decreased as total abundance increased. Based on the findings in our report, we make a series of recommendations for the future development of GSMP and affiliated monitoring schemes. In particular, we recommend the use of binomial and Poisson 95% confidence intervals for age assessment and abundance data, respectively. These analytical methods can be implemented rapidly and require little prior knowledge of statistics or programming to implement. Furthermore, we recommend that consideration should be given to the trade-off between sampling effort and the size of confidence intervals, based on the information presented in this report, in order to optimise the deployment of survey effort as part of GSMP.