Estimating marine survival of Atlantic salmon using an inverse matrix approach

The marine phase of anadromous Atlantic salmon (Salmo salar) is the least known yet one of the most crucial with regards to population persistence. Recently, declines in many salmon populations in eastern Canada have been attributed to changes in the conditions at sea, thus reducing their survival. However, marine survival estimates are difficult to obtain given that many individuals spend multiple winters in the ocean before returning to freshwater to spawn; therefore, multiple parameters need to be estimated. We develop a model that uses an age-structured projection matrix which, coupled with yearly smolt and return abundance estimates, allows us to resample a distribution of matrices weighted by how close the resulting return estimates match the simulated returns, using a sample-importance-resampling algorithm. We test this model by simulating a simple time series of salmon abundances, and generate six different scenarios of varying salmon life histories where we simulate data for one-sea-winter (1SW)-dominated and non-1SW dominated populations, as well as scenarios where the proportion returning as 1SW is stable or highly variable. We find that our model provides reasonable estimates of marine survival for the first year at sea (S(1)), but highly uncertain estimates of proportion returning as 1SW (P(r)) and survival in the second year at sea (S(2)). Our exploration of variable scenarios suggests the model is able to detect temporal trends in S(1) for populations that have a considerable 1SW component in the returns; the ability of the model to detect trends in S(1) diminishes as the proportion of two-sea-winter fish increases. Variability in the annual proportion of fish returning as 1SW does not seem to impact model accuracy. Our approach provides an instructive stepping-stone towards a model that can be applied to empirical abundance estimates of Atlantic salmon, and anadromous fishes in general, and therefore improve our knowledge of the marine phase of their life cycles as well as examining spatial and temporal trends in their variability.