Mapping growth and mortality rates of crevice-dwelling organisms onto a perforated surface: The relevance of ‘cover’ to the carrying capacity of natural and artificial habitats

Abstract

A theoretical basis is suggested for examining habitat limitations of artificial surfaces for population enhancement of crevice-dwelling, or territorial organisms such as reef fish or lobsters, that takes into account known growth and mortality rates. This approach is compared with the crevice frequency at size in a ‘natural’ substrate, which, it is assumed, corresponds to fractal expectation. With naturally dissected surfaces, fractal expectation predicts that crevice availability declines with size, so that a ‘bottleneck’, limits the population of larger-sized individuals, but that natural mortality, or rate of loss of individuals displaced from crevices, will also decline with age. The paper considers a surface perforated with circular niches of a limited number of discrete radii, distributed at random over a surface, without overlap, and considers what is the size frequency of hole radii needed to complete the life history of an infaunal organism with a given mortality and growth schedule, and a constant occupancy rate. Determining a priori crevice frequency at size before constructing an artificial surface, and for a given packing density, distributing the crevices over it in two dimensions, is referred to as ‘mapping’ the growth and mortality rates onto the surface. Sample calculations are described either for continuous recruitment or where recruitment occurs as a ‘pulse’ during a specific season, and subsequent cohort growth obeys a common scheduling. It is shown that fractal surfaces limit the production of larger individuals unless migration intervenes, but are more suitable for recruitment enhancement. Using units with a limited size range of perforations is biologically inefficient, and depends on natural recruitment elsewhere for stock replenishment by migration. These calculations are relevant to the design of artificial surfaces, throw light on mechanisms limiting productivity of dissected surfaces, and point to effects of individual niche size on abundance at size of niche-limited organisms. The existence of nursery areas which can support large numbers of small individuals but few adults, and migratory stages in the life history of crevice-dwelling organisms, could be functions of the fractal nature of natural surfaces. An experimental field approach (a ‘niche sampler’) measuring occupancy at size of existing habitats is proposed that could be used prior to designing and installing artificial reefs in a given area to determine the optimal hole frequency at size.