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 N_t+1 = N_t + RN_t, in which N _t is the population densities at time t, N_t+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.