Modelling natural mortality with age in short-lived invertebrate populations: definition of a strategy of gnomonic time division

Abstract

Most highly fecund marine fish show a steep decline in natural death rate from egg to first maturity, after which the natural mortality rate remains constant, or may even increase with age for old animals. Relatively few investigations have quantified early life-history mortality vectors for short-lived invertebrate stocks, but this overall picture is also true here for species with planktonic life stages such as penaeid shrimps, and for squids. If M decreases rapidly with age, one logical approach to demographic analysis is by subdividing the lifespan into intervals which increase in duration in proportion to the age up to the start of each interval. This time subdivision strategy is referred to as `gnomonic’. Earlier work (Caddy, 1990) showed that if a reciprocal mortality function applies with age, the product of the instantaneous annual rate of natural mortality and interval duration should be roughly constant for gnomonic intervals. This working hypothesis is shown to produce similar results to the reciprocal function for Mt, but allows a simpler approach to generating realistic life history Mt vectors in the absence of direct estimates of M for stock assessment. Values of a constant probability of death, G = Mt Δt, were used to generate vectors of M-at-age for a gnomonic series of intervals from hatching up to the mean parental age. The value of G is found by iteration that results in 2 survivors from the mean population fecundity by 1 year of age, under the assumption of steady-state population replacement for an unexploited stock. The natural mortality rate in the final, longest interval was assumed to correspond to the ‘constant adult M’ value used in stock assessment. Two extremes of reproductive strategy were chosen by comparison with data from for annual species of cephalopods or penaeid shrimps: cephalopods such as Sepia sp. and Rossia sp., with few, large yolky eggs (and/or parental care), occupy one extreme, and are contrasted with high fecundity penaeid shrimps and at least some Illex squids.