There is no best method for constructing size-transition matrices for size-structured models

Tuesday, February 18th at 2:00 PM (PST) in FSH 106

Lee Cronin-Fine and Andrè E. Punt

Stock assessment methods for many invertebrate stocks, including crab stocks in the Bering Sea and Aleutian Islands region of Alaska rely on size-structured population dynamics models. A key component of these models is the size-transition matrix, which specifies the probability of growing from one size-class to another after a certain period of time. Size-transition matrices can be defined using three parameters, the growth rate (k), the asymptotic height (L_∞), and the variability in the size increment. Most assessments assume that all individuals follow the same growth curve. Unfortunately, not accounting for individual variation in growth can result in biased estimates of growth parameters. It is also unrealistic to assume that every individual has the same k and L_∞. We developed a new method for constructing size-transition matrices that allows k and L_∞ to vary among individuals. We compared this technique to two other methods each with different assumptions about individual variation in growth. The first assumes all individuals follow the same growth curve. The second assumes individuals follow one of three growth curves through the “platoon” method. This method divides the population into separate platoons, each with their own growth curve and size transition matrix. My talk shall describe the methods and results from this research and provide suggestions on how best to model individual variation in growth in size structured models.