Modeling Nonlinearity in Population Dynamics of Atlantic Salmon

Atlantic salmon Salmo salar (hereafter referred as salmon) are iteroparous, and are known for displaying variable life history tactics (e.g., variable schedules for smolting and maturation). The combination of iteroparity and variable life histories suggests distinct population cycles and demographic structures among different salmon stocks. Further, different salmon stocks experience differential temperatures, freshwater habitats, oceanographic conditions as well as harvesting operations. These factors likely affect salmon through different pathways (e.g., ecological and/or evolutionary effects) and at different scales. As a result, salmon population dynamics in response to such multifold forcing are likely complex, and potentially nonlinear. Most research to date has relied on correlation analyses to examine salmon population responses to a potential factor. However, these analyses do not provide insight on nonlinear patterns. We compiled time series data (range 20-37 yrs) of adult salmon abundance for 30 stocks throughout eastern coastal Canada, and examined degrees of nonlinearity in the salmon data using the nonlinear forecasting techniques, Simplex and S-map. Our analyses will identify the embedding dimensions and infer significance of the nonlinear signals within each stock time series. Furthermore, we will compare the nonlinear patterns both within- and among-stocks, evaluating cross-predictability (i.e., a time series’ forecasting power for another; measured by correlation coefficient between the predicted and observed values of the predicted time series) among different sea ages or size classes within a stock as well as among stocks in different geographic regions.