Effects of size-dependent relative fecundity specifications in fishery stock assessments

A comprehensive understanding of reproductive biology is fundamental to the accurate assessment of a given stock's spawning potential relative to the unfished level. Such an understanding is particularly important given the growing recognition of size, age or weight dependent relative fecundity (Фrel, eggs per kg of female weight), or other maternal effects that may demonstrate a relatively greater contribution of specific demographic components of a population toward reproduction. However, size-specific data on Фrel, or other data on maternal effects on reproductive output, are not always available for many stock assessments because intensive efforts are required to collect such data. In the absence of data, the assumption of no size-specific Фrel relationship is typically made, which can lead to bias in estimating stock status and related management parameters. We examined effects of misspecifications of size-specific Фrel functions on estimated stock assessment parameters and related management quantities using two stocks as case studies and three sets of simulation models, chosen to represent wide ranges of life and fishing histories. The results showed that misspecification effects were relatively small when stocks were less depleted (e.g. 75% of virgin spawning output), but could lead to more substantive misspecifications in more depleted stocks with slower growth and lower mortality rates. For example, we found that stock was estimated to be as much as 20% less depleted if a strong size-specific Фrel exists in a population, but no size-specific Фrel is used in the model. This represents a non-trivial shift in the perception of status for most stocks. The results also showed that overestimating the strength of the size-specific Фrel function in stock assessment models led to smaller estimation errors in assessment outputs compared to underestimating the size-specific Фrel. The results are insightful with respect to the importance of gathering data on size-dependent Фrel and other aspects of reproductive ecology, as well as with respect to the nature of assumptions that are made with regards to reproductive ecology in data limited situations.