458 Age-structured models (continued) Fish 458, Lecture 5

458 Building Age-Structured Models Age-structured models are constructed by selecting specific hypotheses for each key population dynamic process: Growth, fecundity, natural mortality, exploitation, recruitment These process can be time-invariant, stochastic, density-dependent or depensatory. They can be linked via forcing functions (e.g. environmental variability)

458 Typical outputs of an Age-structured Model (northern cod) Abundance of various age-classes (typically the offspring). Trends in key population components: Spawner biomass Exploitable biomass Trends in fishing mortality Usually averaged over a number of age- classes.

458 Recruitment

458 Spawner Biomass

458 Catch Series

458 Fishing Mortality

458 Continuous Fishing - I Many models assume that fishing and natural mortality occur continuously throughout the year. For a single year class: M is the instantaneous rate of natural mortality, and F is the instantaneous rate of fishing mortality.

458 Continuous Fishing - II The catch from a cohort over a year is given by: Note that assuming that fishing occurs continuously throughout the year is seldom very different from assuming that it occurs instantaneously in the middle of the year (the first-order Taylor series approximation).

458 Building an age-structured model-II Build a model of a harvested seal population. The sex ratio at birth is 50:50. The survival rate in the absence of harvest is the same for females and males younger than 12 (when they achieve harem bull status). Pups and harem bulls are harvested. The survival rate for pups is related to water temperature according to the equation:

458 The model (females) 50% of pups are females Pup harvest and first-year survival Plus-group dynamics Pups are females multiplied by the age- specific pregnancy rate

458 The model (males) 50% of pups are males Pup harvest and first-year survival Plus-group dynamics (bull catches; high M for harem bulls)

458 More Model Structure-I This seal model is based on the population of Cape fur seals off Namibia. How would you extend it to account for: a harvest of females; a split of the pup harvest between males and females which differs from 50:50; a relationship between the survival rate of females and an environmental variable; and density-dependence on pup survival or pregnancy rate.

458 More Model Structure-II This model makes many assumptions - which ones do you consider to be the least realistic? Can you identify the state variables, forcing functions and parameters?