FIGURE 3-1 Population processes, including density-independent and density-dependent controls.
Population size can be reduced by predation, and predator abundance is affected by prey abundance. Population growth can also be affected by dispersal, immigration and emigration, and management factors, such as removal of animals from the range and contraception. This chapter examines the changes in population processes of free-ranging equids due to density-dependent, density-independent, predation, and management factors.
It is a general principle of ecology that populations do not continue to grow indefinitely, but the mechanisms of reduction in growth as densities increase are not always well understood (Flux, 2001). Mechanisms may include competition for resources among members of the same species at high densities (Ginzburg, 1986; Berryman, 2003), complex social behaviors (Wynne-Edwards, 1965), and combinations of physiological responses to social cues (Wolff, 1997).
Density dependence can be seen most easily by examining the S-shaped curve of population size changing over time described by the logistic equation
dN/dt = rN([K – N]/K),
where dN/dt is the instantaneous rate of change in N, N is the size of the population (number of individuals), r is the intrinsic rate of natural increase, and K is the carrying capacity, that is, the maximum population size that the environment can support as affected by resource abundance. The discrete form of the equation defines the population increment over an interval of time, such as a year, and is expressed as
Nt+1 = Nt + R(Nt[K – Nt]/K),
where Nt +1 is the population size in the next year or generation, Nt is the population size in the current year or generation, R is the maximum rate of increase per year or generation, and K is the carrying capacity. The annual or generational increment can be defined as
ΔN = Nt +1 – Nt.