Abstract
Abstract. The carrying capacity K is the equilibrium population density of a species that an area can support while adequately meeting the needs of every individual. Although widely used in ecology, it has yet to be applied rigorously to living foraminifera. K is readily determined from time-series of population densities. Given that Nt+1 = Nt + RNt, in which Nt is the population densities at time t, Nt+1 is the density at a subsequent time t+1 and R is the per capita rate of change in population density, then linear regression gives Rt = Rm − sNt, in which Rt is the per capita rate of increase at time t, the constant Rm is the maximum possible individual rate of increase, and the negative slope s represents the strength of intraspecific interactions. Setting Rt = 0, so that Nt = K and Rm – sK = 0, gives K = Rm/s, which is applicable in aseasonal environments. There are two carrying capacities in seasonal environments, depending on whether the season is favourable (Kmax) or unfavourable (Kmin). Values of Kmax and Kmin are estimated for Nonion depressulus in the Exe estuary, UK (25 monthly samples), Quinqueloculina spp. in the Indian River Lagoon, USA (60 monthly samples) and Haynesina germanica in Cowpen Marsh, UK (25 fortnightly samples). The most precise estimate was for H. germanica, but it was unclear if this was due to the high rate of sampling or the large number of replicates used to erect this time-series.
Highlights
AlgebrAIc bAckground to cAlculAtIng cArryIng cApAcIty K from A tIme-SerIeS Aseasonal environments A population is a group of conspecific individuals that exist together in time and space (Levin et al, 2009)
Murray (1967) concluded that the annual production of benthonic foraminifera is a product of four main factors: the initial size of the standing crop, the proportion of individuals that reproduce, the frequency of reproduction and the number of surviving new individuals resulting from each reproductive phase
It follows that a given population of Nonion depressulus population densities (Nt) at time t will at a later time t+1 have changed to a population Nt+1 as follows: Nt+1 = Nt + B - D + I - E
Summary
The longest continual time-series for N. depressulus exceeding the median population density consisted of six samples for which linear regression of Rt+1 against Nt returned Rt = 1.336 – 0.004Nt (r2 = 0.659), which indicates Kmax of 334 N. depressulus per 90 ml. Haynesina germanica in cowpen marsh foraminiferal Zone II Of the 25 samples in this time-series, the longest subseries with lower than the median population density of 528 specimens per 130 ml of sediment contained five samples only table 2. Intercept Rm and slope s from linear regression Rt = Rm - sNt and estimated minimum (Kmin) and maximum (Kmax) carrying capacities for timesubseries for selected foraminifera in seasonal environments: (a) Nonion depressulus in Exe Estuary; (b) Quinqueloculina spp. in indian River lagoon, Florida, USA (Kmin 1–4 = four subseries of four samples each); (c) Haynesina germanica in lower Cowpen Marsh, UK, with Kmax calculated at lags of Nt+1 and Nt+3
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