Determining carrying capacity from foraminiferal time-series

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 = N-t + RNt, in which N-t 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 R-t = R-m - sN(t), in which R-t is the per capita rate of increase at time t, the constant R-m is the maximum possible individual rate of increase, and the negative slope s represents the strength of intraspecific interactions. Setting R-t = 0, so that N-t = K and R-m - sK = 0, gives K = R-m/s, which is applicable in aseasonal environments. There are two carrying capacities in seasonal environments, depending on whether the season is favourable (K-max) or unfavourable (K-min). Values of K-max and K-min 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. J. Micropalaeontol. 31(2): 111-119, july 2012.