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Age-structured models (continued)

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

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Age-structured models (continued)

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

  2. 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)

  3. 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.

  4. Recruitment

  5. Spawner Biomass

  6. Catch Series

  7. Fishing Mortality

  8. 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.

  9. 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).

  10. 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:

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

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

  13. 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.

  14. 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?

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