Age-structured population assessment models

Intro ASA (age-structured assessment) models permit reconstruction of the population dynamics Provide estimates of mortality rates and population abundance ASA is the primary method used for providing management advice

Advantages Can be applied without knowledge of: Fishing effort Catchability Gear selectivity Do not rely on FD CPUE as an IOA (a common problem with earlier assessment models) Hyper depletion patterns bias Availability of “aged catch” data, starting in the 1960’s has lead to widespread use. Rise of “microcomputing” Moore’s Law

Historical roots Derzhavin (1922) first to apply data describing age structure of a population to catch statistics in order to calculate the contribution of each cohort to each years’ total catch Derived from Baranov (1918) Catch (in numbers) is a function of initial population abundance, fishing, and natural mortality M. 𝐶= 𝐹 𝐹+𝑀 1− 𝑒 −(𝐹+𝑀) 𝑁 0

Question: Consider a population of 1,200 age-0 fish. 30% lost to natural mortality, 40% lost to fishing mortality. Fishing occurs on ages 2 to 6. Create a table with columns: Year, Abundance (F = 0), Abundance (F = realized F), Catch 𝐶= 𝐹 𝐹+𝑀 1− 𝑒 −(𝐹+𝑀) 𝑁 0

Historical roots In an age-structured population, the population size of a cohort as it enters the exploitable phase can be approximated by summing the catches removed from the cohort during the years it contributes to the fishery. Summing catch provides an estimate of the population must have been alive in order to generated the observed catches. Use mean age composition of the catch data from many years.

Historical roots Derzhavin (1922) analysis provides the minimum estimate of the total population Ignores M Use of mean estimate does not allow understanding of annual trends Provides a minimum estimate of total population size

Historical roots Beverton (1954) and Beverton and Holt (1957) proposed age- structured models that emphasized the estimation of M Formulations allow population reconstruction. Terminal F problem – reconstructions are very sensitive to the ‘terminal’ F value. Unfortunately, this is the exact information needed by fisheries managers…. Pope’s (1972) resolution – change exponential decay with a step function – computationally much simpler.

Seperability assumption Standard feature of ASA Fishing mortality is the product of age- and year- specific coefficient. Therefore, any one year fishing mortality can be described by two factors: F (full) Differential effect of the annual exploitation pattern on various age groups of the stock “separability of fishing mortality into year and age components” 𝐹 𝑎,𝑦 = 𝑆 𝑎 𝑓 𝑦

ASA data sources Catch-at-age Total catch Observed from catch-at-length Use length-at-age conversion Total catch Determine age composition of catch Effort data Stratified by gear type Integrated analysis… Incorporate many, many data sources “tuned”