Learning from long time series of harvest and population data - Swedish insights for European goose management

Temporal trends (finite growth rates) based on breeding season counts along the fixed routes, were analysed using TRIM (Trends & Indices for Monitoring data, v.3.53, Pannekoek and van Strien 2004www.ebcc.info/trim.html), taking into account that not all routes were done every year. The statistical model in TRIM builds on Poisson log-linear regression, estimating site and time (year) effects on species abundance (counts) as well as an overall linear trend (log-scale). The basic TRIM model is: expected count = year + site, where both year and site are fixed effects. Effects are estimated using maximum likelihood and generalized estimating equations, the latter to handle potential overdispersion and serial (auto) correlation. For autumn counts and harvest estimates, the finite rate of increase was calculated according to Caughley & Sinclair (1994). To identify possible changes in trends, we performed a breakpoint analysis using the package strucchange for all three species and all three indices (Kleiber et al. 2002). Breakpoint analysis is based on piecewise linear models and it identifies the time of significant shifts in trends (Zeileis et al. 2002). Coherence in timing of changes (breaks) between times series as well as differences in slopes of regression lines before and after breakpoints were used as basis to discuss plausible mechanisms and causality behind shifts in trends. To analyse the effect of harvest on the population growth rate, we need to relate harvest level to population size. By assuming that our indices provide relative numbers over time we calculated an annual (1977–2018) ‘relative harvest rate’ by dividing the harvest estimate (hunting year t) by the autumn count (year t). In a second step, relative harvest rate (year t) was related to the exponential rate of increase (Caughley and Sinclair 1994, Steidl et al. 1997) based on the autumn count data from year t to year t+1, by using linear regression. If harvest affect the population growth rate, we expect a negative relationship between the relative harvest rate (year t) and the exponential rate of increase (year t+1). All tests were performed using R 3.3.3. (R core team 2013).