Estimating steepness of the stock-recruitment relationship in Chilean fish stocks using meta-analysis

Steepness (h) is a fundamental metric in population dynamics because it defines the relationship between parental stock and offspring. h represents a direct measurement of resilience and is therefore crucial in the management of harvested populations. However, h represents one of the most difficult parameters to estimate, even for data-rich stocks. It is usually estimated using indirect methods based on meta-analysis. Existing meta-analyses use all available estimates of h from different sources of information (i.e., from outside or within the stock assessment model) and report non-significant relationships between h and other life history traits, even though several theoretical analyses suggest the contrary. We conducted a two-stage meta-analysis, firstly selecting suitable h estimates from stock assessment models for fish stocks worldwide. 42 estimates of h were collected and several life history attributes were used as explanatory variables within generalised linear models (GLMs). We found a significant relationship (p < 0.05) between h and the ratio between length at 50% maturity (L50) and asymptotic length (L∞). The second stage of our meta-analysis was to apply this relationship to 19 fish stocks harvested off Chile to estimate species-specific h and the associated uncertainty. We discuss the assumptions of the proposed meta-analysis, the reliability of the estimated uncertainties and outline the potential application in the assessment and management of fish resources in Chile.