other environmental factors which, we can for now, assume to be constant in this approximated model. The differential equation is now: This can be rewritten as: where r = b-d and K = (b-d)/(a+c). The biological significance of K becomes apparent when stabilities of the equilibria of the system are considered. The constant K is the carrying capacity of the population. The equilibria of the system are N = 0 and N = K. If the system is linearized, it can be seen that N = 0 is an unstable equilibrium while K is a stable equilibrium. Structured population growth Another assumption of the exponential growth model is that all individuals within a population are identical and have the same probabilities of surviving and of reproducing. This is not a valid assumption for species with complex life histories. The exponential growth model can be modified to account for this, by tracking the number of individuals in different age classes (e.g. one-, two-, and three-year-olds) or different stage classes (juveniles, sub-adults, and adults) separately, and allowing individuals in each group to have their own survival and reproduction rates. The general form of this model is where Nt is a vector of the number of individuals in each class at time t and L is a matrix that contains the survival probability and fecundity for each class. The matrix L is referred to as the Leslie matrix for age-structured models, and as the Lefkovitch matrix for stage-structured models. If parameter values in L are estimated from demographic data on a specific population, a structured model can then be used to predict whether this population is expected to grow or decline in the long-term, and what the expected age distribution within the population will be. This has been done for a number of species including loggerhead sea turtles and right whales. Community ecology An ecological community is a group of trophically similar, sympatric species that actually or potentially compete in a local area for the same or similar resources. Interactions between these species form the first steps in analyzing more complex dynamics of ecosystems. These interactions shape the distribution and dynamics of species. Of these interactions, predation is one of the most widespread population activities. Taken in its most general sense, predation comprises predator–prey, host–pathogen, and host–parasitoid interactions. Predator–prey interaction Predator–prey interactions exhibit natural oscillations in the populations of both predator and the