Malthusian Relativityι**=7/3ψ
Population dynamics - the evolutionary extension

Selection-delayed dynamics

The delay of natural selection explains population dynamic cycles

Selection-delayed dynamics predict the cyclic dynamics that is widespread in natural populations. This is illustrated in Fig. 1, where the dynamics of the larch budmoth in the Upper Engadine valley is shown together with a projection of a selection-delayed model.

Fig. 1 The curve is a projection of a selection-delayed model with discrete generations and the diamonds the yearly densities of the lack budmoth in the Upper Engadine valley from 1950 to 1985. Data from Baltensweiler and Fischlin (1988); figure from Witting (2000).

The predicted number of generations per cycle period is compared with the periods for forest insects in the left plot of Fig. 2. When observed as a function of mass, the predicted period in physical time will increase to the 1/4, or 1/6, power of mass, because of the predicted body mass allometry for generation time. This increase is known as the Calder allometry (Calder, 1983), and it is shown for mammals and birds in the middle plot in Fig. 2.

Fig. 2 Left: The period of the population cycles in generations against the response parameter (γ) of selection-delayed cycles. The curve is defined by the population dynamic equations, and the numbered diamonds represent the following species: (1) spruce budworm, (2) southern pine beetle, (3) douglas-fir tussock moth, (4) larch budmoth, (5) fall webworm, (6) nun moth, (7) pine looper moth, (8) larch cone fly, and (9) wasp. Spp. Middle: The period of population cycles against body mass for terrestrial homoiotherms on double logarithmic scale, with the line being the regression line. Right: The dynamics in the density (N, solid curve) and body mass (w, dashed curve) of a Daphnia population against time. From Witting (1997, 2000).

The similarity between the theoretically predicted and the observed population cycles does not necessarily imply that the dynamics of natural species are generated by selection-delayed dynamics. But when tested against density regulated growth and predator-prey dynamics, selection-delayed dynamics was the only sufficient mechanism to explain the long-term dynamics of baleen whales (Witting, 2013).

Other direct evidence on the causal mechanisms include observations on the presence versus absence of associated cycles in life history parameters like body mass. These cycles are only predicted by selection-delayed dynamics and they operate against the expectations of density regulation, in the sense that the largest body masses are predicted in the late peak phase of a cycle, where body masses should be smallest if controlled by density regulation.

The life history cycles that are predicted by selection-delayed dynamics are widespread in natural populations: Cycles in competitive quality occur in side-blotched lizard with selection-delayed dynamics (Sinervo et al., 2000), and the abundance cycle in the Daphnia experiments of Murdoch and McCauley (1985) had an associated cycle in body mass, with the larger Daphnia occurring mainly during the late peak phase of the cycle (Fig. 2, right). In fact, such body mass cycles appear to be the rule, rather than the exception, in species with cyclic population dynamics. They are widespread in voles and lemmings with cyclic dynamics (e.g., Chitty, 1952; Hansson, 1969; Krebs and Myers, 1974; Mihok et al., 1985; Stenseth and Ims; Norrdahl and Korpimäki, 2002; Lambin et al., 2006), and they have been observed in snowshoe hare (Hodges et al, 1999) and cyclic forest insects (Myers, 1990; Simchuk et al., 1999). Quite generally, it is observed that voles and lemmings are small, non-aggressive, and that they have a high reproductive rate when the abundance is low and increasing. When the abundance is high and declining, they are instead aggressive, and 20 to 30 percent larger with a delayed and low reproductive rate.


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