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 M_t, but allows a simpler approach to generating realistic life history M_t vectors in the absence of direct estimates of M for stock assessment. Values of a constant probability of death, G = M_t Δ_t, 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.

The first category has a low fecundity (130–150 eggs, and a K-selected reproductive strategy). Values of ‘adult M’ of the order of 1.0–1.3 are predicted for the last 60–80% of the annual life span. The high fecundity category (200 000 eggs or more) are opportunistic spawners such as many penaeids and some oceanic squids, and follow an r-selected reproductive strategy. An instantaneous value for pre-spawning M of the order of 2.8–3.4 is predicted for the same period mentioned above. Neither range of values falls outside those in the literature, for which a brief summary is presented.

An important research question relates to the order of magnitude of post-hatching mortality under population stability: it is suggested that irrespective of the specific model used for changes in M with age, this falls rapidly from an initial rate of some 50–75% per day for short-lived, high fecundity species in the 2 days following hatching, unless adult M values are much higher than above, and of the order of 25–40% for the low fecundity organisms over the same initial interval.