Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

Abstract

Summary1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5·1%. 4. Significant density regulation was present in 53·6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.

Likelihood ridges and multimodality in population growth rate models

“…Inferential statements about model parameters based on the posterior distribution of H, posterior predictive distributions of population states, and Bayesian model averaging all rely on the likelihood function to inform the model and subsequent predictions. Thus, because the ridge in the likelihood surface contains the best fitting model in realistic regions of parameter space, a strictly Bayesian approach would not be expected to improve the ambiguity about the ''true'' form of the pgr as a function of density, even after assigning zero mass to prior parameter distributions in regions describing implausible models (see also example studies by Ward [2006] and Saether et al [2007]). These cautions also apply to methods that utilize a Bayesian approach en rout to obtaining ML estimates (e.g., de Valpine 2004, Lele et al 2007).…”

“…Accounting for observation error in addition to process noise with real density time series can be informative (de Valpine and Hastings 2002, de Valpine and Hilborn 2005, Dennis et al 2006, Saether et al 2007, Lillegard et al 2008), and we accommodate this level of stochasticity using a statespace model (Eq. A.4) with an iid normal random variable e t with zero mean and standard deviation r o for observation error (see Appendix: sections A2 and A4).…”

Spring spotlight counts provide reliable indices to track changes in population size of mountain‐dwelling red deer Cervus elaphus

“…Il range altitudinale è piuttosto ampio, essendo generalmente disgiunti l'areale estivo (2.300 -3.200 m slm) e quello invernale (1.600 -2.800 m slm). Le precipitazioni nevose influenzano la dinamica di popolazione, la sopravvivenza invernale è infatti influenzata dalla quantità di neve caduta al suolo (Grøtan et al, 2008;Jacobson et al, 2004;Saether et al, 2007) e questa variabile sembra essere un fattore chiave in grado di limitare la crescita delle popolazioni. Per lo svernamento, è rilevante la disponibilità di versanti estesi esposti a sud e a sud-ovest e con pendenze medie (35-45°), dove la neve tende a sciogliersi più rapidamente (Grignolio et al, 2004).…”

Estimation of the parameters of fish stock dynamics from catch-at-age data and indices of abundance: can natural and fishing mortality be separated?

“…Our approach is based on obtaining information of the hidden population dynamical process, described by the state model, from an observation model (for a similar approach, see Clark (2005), Clark and Bjørnstad (2004), and Saether et al (2007)). The observations are connected to the population processes through models including error terms, allowing them to be uncertain.…”