The equations that are core to demographic ecology theory are represented by the logistic equation, which we introduce below and which reflects the central value given to balance or equilibrium in demographic ecology (as argued by Cooper 2001). Populations are perceived to be in a state of balance or equilibrium because they are seen to be regulated against excessive growth by density dependent processes-competition, predation, herbivory and the like. However, density dependence is written directly into the logistic equation virtually entirely in the form of intraspecific

ã Introduction ã Studying population dynamics ã The intrinsic rate of population

increase, r, and constraining exponential growth

ã The underlying assumptionsthe paradox of retaining the logistic

ã Structuring the ecological response process

ã Some methodological remarks ã Conclusion

competition, as described more fully in Section 3. The logistic equation has, however, also been expanded in various forms to incorporate other density dependent influences, interspecific competition and predation, each in their own general equation. The concepts embodied in the S-shaped logistic curve, and the equation itself, are evidently linked deeply and inextricably within the concepts and practice of demographic ecology, although the realism of the patterns and concepts, the relationship between them, and their extension to specific interpretations in ecology have been contested vigorously (e.g., Kingsland 1995). This point holds true even though different models are now frequently used to model population dynamics, including simulation and matrix models. An understanding of demographic ecology therefore needs an appreciation of the structure and workings of the logistic equation, as well as its deficiencies with regard to its central role in ecological theory and research.