Single species population dynamic models are usually based on the consensus of the 20th century; that the population dynamic mechanism intrinsic to the species is Malthusian increase with superimposed density regulation. Although it is known that these density regulated models will not explain the widespread tendency for cyclic dynamics in natural species (Turchin, 1990; Witteman et al., 1990; Turchin and Taylor, 1992; Ginzburg and Taneyhill, 1994), the models have gained acceptance in part because they are based on very plausible mechanisms. The alternative models with delayed density regulation have never been generally accepted as adequate single species models despite of the fact that these models can explain the cyclic dynamics and the fact that delayed density dependence is documented in many species (e.g., Turchin, 1990; Turchin and Taylor, 1992; Berryman, 1996). The rejection of the delayed density regulated models is scientifically sound because the delayed density dependence of those models were given by assumption instead of being deduced from mechanisms that operate within the population.

In resent years a new class of single species population dynamic models have been developed (Ginzburg, 1980, 1998; Ginzburg and Taneyhill, 1994; Inchausti and Ginzburg, 1998; Witting, 1997, 2000b). These are the models of inertial dynamics that, at least in the version proposed by Witting, resemble traditional density regulated models with superimposed density dependent changes in the intrinsic life history. The inertia models might be compared with the older models of delayed density regulation in the sense that both models can explain the cyclic dynamics in many natural species, and that both models include delayed density dependence, although the delay in inertia models is restricted to one generation. But where the delayed density dependence is given by assumption in the delayed density regulated models, the delay in the inertia models arises from plausible mechanisms that operate within the population. A second difference is that the intrinsic growth rate is a parameter in delayed, as well as direct, density regulated models, while it is an initial condition in inertia models. And a third difference is that the density independent fundament of inertial dynamics is Fisher's (1930) fundamental theorem of natural selection (Witting, 2000a) instead of the Malthusian law of exponential increase (Malthus, 1798).

Malthusian Relativity has played an essential role in the deduction of inertial dynamics. It was shown theoretically that selection by density dependent competitive interactions can induce the changes in the intrinsic life history required for the inertia models to work (Witting, 1997, 2000b). These between-generation changes in the intrinsic life history have been observed in species with cyclic dynamics (e.g., Krebs and Myers, 1974; Stenseth, 1982; Stenseth and Ims, 1993), and they may arise either from genetic responses to selection and/or from plastic phenotypic responses, where inherited environmental effects and epigenetic inheritance systems respond to the intra-specific selection pressure. Maternal effect is one example of an epigenetic inheritance system, and this particular response is the basis for the inertia models developed by Ginzburg and Taneyhill (1994) , Ginzburg (1998) , and Inchausti and Ginzburg (1998) .

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