Event Type:

Mathematical Biology Seminar

Date/Time:

Thursday, May 15, 2014 - 05:00

Location:

KIDD 278

Guest Speaker:

Grant Thompson

Institution:

NOAA

Abstract:

Abstract: Management of commercially exploited marine fish stocks is typically based on mathematical models of those stocks. The practice of “stock assessment” consists of fitting these models to data and, given a set of management objectives, deriving management implications therefrom. The structure of these models is usually based on the types of data available. Data typically come from two sources: the fishery itself, and fishery-independent “surveys” of the stock. The most common configurations of data availability are often classified as follows:

·

Data-poor: time series of total catch from the fishery

·

Data-moderate: same as data-poor, plus a time series of relative stock biomass from a fishery-independent survey

·

Data-rich: same as data-moderate, plus a time series of age composition of the catch and a time series of age composition of the survey index

The data-poor case will not be considered here, as it is generally considered inadequate for development of stock assessment models. The data-moderate and data-rich cases both present challenges to the practice of stock assessment. In the data-moderate case, stock assessment has typically followed one of two paths: either fit a mathematical model so simplistic as to strain credibility, or adopt simple “rules of thumb” involving some strong assumptions. In the data-rich case, stock assessment has typically involved fitting age-structured mathematical models with several dozen or hundreds of estimated parameters, but which also typically require using simple “rules of thumb” for setting one to several of the hardest-to-estimate parameters. The mathematical models used in the data-rich case are typically designed to represent identifiable biological mechanisms such as growth, recruitment, migration, and mortality.

This presentation will describe a new assessment model (SEVAR) that avoids the difficulties encountered by conventional data-moderate and data-rich approaches. The information requirements for SEVAR fall into the data-moderate category. The ratio of total catch to relative biomass is used as the measure of exploitation. After some rescaling, the state variables in the SEVAR model consist of true relative biomass and true exploitation rate, which are stacked in a vector. The transition equation is linear and autoregressive with normal error, and the observation equation is also linear and normal. For a model with *p* time lags, 4(*p*+1) parameters need to be estimated. The choice of *p* can be based on an information-theoretic criterion (e.g., AIC, BIC, etc.) or cross-validation. After rearranging some terms, the SEVAR model can be cast as a Kalman filter (even when *p*>1), meaning that the state variables are integrated out automatically, thereby improving accuracy of parameter estimates. The parameters that are typically the hardest to estimate in data-rich models do not even appear in the SEVAR approach, because: 1) no attempt is made to model identifiable biological mechanisms (at least not explicitly); and 2) exploitation is defined with relative biomass (not absolute biomass) as the denominator, so that projecting the harvest for some future year (given an exploitation rate) involves projection of relative biomass only.