| Abstract: | Whatever popular the slogan of nonlinear ecological interactions has been in theory, practical ecology professes the projection matrix paradigm, which is essentially linear, i.e., the linear matrix model paradigm for discrete-structured population dynamics. The dominant eigenvalue lamda1, of the projection matrix L is considered as a growth potential of the population. It provides for a quantitative measure of the fitness at which the species is adapted to the given environment, the measure being adequate and accurate, given the data of"identified individuals" type. The case of"identified individuals with unknown parents" bears uncertainty in the status-specific reproduction rates, which eliminates in a unique way (for a broad class of structures and life cycle graphs) by maximizing lamda1(L) under the constraints ensuing from the data and knowledge of species biology. The paradigm of linearity gives way to nonlinear models when modeled are species interactions, such as competition for shared resources, and where the outcome of interaction depends on the population structure of the competitors. This circumstance dictates a need for the synthesis of two paradigms, which is achieved in nonlinear matrix operators as models of interaction between the species whose populations are discrete-structured. |
