Sigmoidal growth curves

In addition, curves of the type shown in Figure 5.8a and b may be used to suggest the pattern by which a population might increase from an initially very small size (e.g. when a species colonizes a previously unoccupied area). This is illustrated in Figure 5.8c. Imagine a small population, well below the carrying capacity of its environment (point A). Because the population is small, it increases in size only slightly during one time interval, and only reaches point B. Now, however, being larger, it increases in size more rapidly during the next time interval (to point C), and even more during the next (to point D). This process continues until the population passes beyond the peak of its net recruitment curve (Figure 5.8b). Thereafter, the population increases in size less and less with each time interval until the population reaches its

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peak recruitment occurs at intermediate densities

Figure 5.10 Some dome-shaped net-recruitment curves. (a) Six-month old brown trout, Salmo trutta, in Black Brows Beck, UK, between 1967 and 1989. (After Myers, 2001; following Elliott, 1994.) (b) The relationship between crop growth rate of subterranean clover, Trifolium subterraneum, and leaf area index at various intensities of radiation (kJ cm-2 day-1). (After Black, 1963.) (c) 'Blackwater' herring, Clupea harengus, from the Thames estuary between 1962 and 1997. (After Fox, 2001.) (d) Estimates for the stock of Antarctic fin whales. (After Allen, 1972.)

Figure 5.11 Real examples of S-shaped population increase. (a) The bacterium Lactobacillus sakei (measured as grams of 'cell dry mass' (CDM) per liter) grown in nutrient broth. (After Leroy & de Vuyst, 2001.) (b) The population of wildebeest Connochaetes taurinus, of the Serengeti region of Tanzania and Kenya seems to be leveling off after rising from a low density caused by the disease rinderpest. (After Sinclair & Norton-Griffiths, 1982; Deshmukh, 1986.) (c) The population of shoots of the annual Juncus gerardi in a salt marsh habitat on the west coast of France. (After Bouzille et al., 1997.)

Figure 5.11 Real examples of S-shaped population increase. (a) The bacterium Lactobacillus sakei (measured as grams of 'cell dry mass' (CDM) per liter) grown in nutrient broth. (After Leroy & de Vuyst, 2001.) (b) The population of wildebeest Connochaetes taurinus, of the Serengeti region of Tanzania and Kenya seems to be leveling off after rising from a low density caused by the disease rinderpest. (After Sinclair & Norton-Griffiths, 1982; Deshmukh, 1986.) (c) The population of shoots of the annual Juncus gerardi in a salt marsh habitat on the west coast of France. (After Bouzille et al., 1997.)

carrying capacity (K) and ceases completely to increase in size. The population might therefore be expected to follow an S-shaped or 'sigmoidal' curve as it rises from a low density to its carrying capacity. This is a consequence of the hump in its recruitment rate curve, which is itself a consequence of intraspecific competition.

Of course, Figure 5.8c, like the rest of Figure 5.8, is a gross simplification. It assumes, apart from anything else, that changes in population size are affected only by intraspecific competition. Nevertheless, something akin to sigmoidal population growth can be perceived in many natural and experimental situations (Figure 5.11).

Intraspecific competition will be obvious in certain cases (such as overgrowth competition between sessile organisms on a rocky shore), but this will not be true of every population examined. Individuals are also affected by predators, parasites and prey, competitors from other species, and the many facets of their physical and chemical environment. Any of these may outweigh or obscure the effects of intraspecific competition; or the effect of these other factors at one stage may reduce the density to well below the carrying capacity for all subsequent stages. Nevertheless, intraspecific competition probably affects most populations at least sometimes during at least one stage of their life cycle.

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