Still more spawner-recruitment curves: the hockey stick and its generalizations

Estimation of maximum reproductive rate using spawner-recruitment models involves extrapolating survival for very low spawner abundance. Existing spawner-recruitment curves often lead to biologically unreasonable extrapo- lations or are unable to model nondecreasing spawner-recruitment data adequately. One alternative is a piecewise linear spawner-recruitment model known as the hockey stick. We compare the fit of the Beverton-Holt with the hockey stick for 246 spawner-recruitment data sets. We show that the Beverton-Holt usually estimates a larger carrying capacity of recruits and a larger maximum reproductive rate than the hockey stick. We propose two families of generalizations of the hockey stick, one with a simple interpretation and one that is more complex but smoother. These generalized hockey sticks are more biologically plausible, less subject to numerical difficulties, and of greater utility in metaanalytic models than the hockey stick. Resume : Pour estimer le taux maximum de reproduction au moyen de modeles geniteurs-recrutement, on doit extra- poler le taux de survie avec une tres faible abondance de geniteurs. Les courbes existantes reliant le nombre de geni - teurs et le recrutement donnent souvent lieu a des extrapolations biologiquement incorrectes ou ne permettent pas de modeliser adequatement les donnees geniteurs-recrutement non decroissantes. Face a ces difficultes, on peut avoir re - cours a un modele geniteurs-recrutement lineaire par morceaux appele modele en bâton de hockey. Nous comparons l'ajustement du modele de Beverton-Holt a celui de ce nouveau modele pour 246 ensembles de donnees geniteurs- recrutement. Nous montrons que le modele de Beverton-Holt donne habituellement une plus grande capacite de charge de recrues et un taux maximum de reproduction plus eleve que le modele en bâton de hockey. Nous proposons deux familles de generalisations du modele en bâton de hockey, l'une avec une interpretation simple et l'autre avec une in- terpretation plus complexe mais plus lisse. Ces modeles en bâton de hockey generalises sont biologiquement plus plau- sibles, moins sensibles aux difficultes numeriques, et plus utiles dans les modeles meta-analytiques que le modele en bâton de hockey. (Traduit par la Redaction) Barrowman and Myers 676

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