Environmental effects on survival rates: robust regression, recovery planning and endangered Atlantic salmon

Describing how population-level survival rates are influenced by environmental change becomes necessary during recovery planning to identify threats that should be the focus for future remediation efforts. However, the ways in which data are analyzed have the potential to change our ecological understanding and thus subsequent recommendations for remedial actions to address threats. In regression, distributional assumptions underlying short time series of survival estimates cannot be investigated a priori and data likely contain points that do not follow the general trend (outliers) as well as contain additional variation relative to an assumed distribution (overdispersion). Using juvenile survival data from three endangered Atlantic salmon Salmo salar L. populations in response to hydrological variation, four distributions for the response were compared using lognormal and generalized linear models (GLM). The influence of outliers as well as overdispersion was investigated by comparing conclusions from robust regressions with these lognormal models and GLMs. The analyses strongly supported the use of a lognormal distribution for survival estimates (i.e., modeling the instantaneous rate of mortality as the response) and would have led to ambiguity in the identification of significant hydrological predictors as well as low overall confidence in the predicted relationships if only GLMs had been considered. However, using robust regression to evaluate the effect of additional variation and outliers in the data relative to regression assumptions resulted in a better understanding of relationships between hydrological variables and survival that could be used for population-specific recovery planning. This manuscript highlights how a systematic analysis that explicitly considers what monitoring data represent and where variation is likely to come from is required in order to draw meaningful conclusions when analyzing changes in survival relative to environmental variation to aid in recovery planning.