We expect a green world because the population dynamic equilibria are determined by competitive interaction fix-points.
The population dynamic equilibrium of selection-regulated dynamics is the competitive interaction fix-point of population dynamic feed-back selection. This implies that the densities of populations are no longer determined by famine from intense competition for depleted resources, as proposed by Malthus in 1798 and elaborated by density-regulation theory (Verhulst, 1838; Pearl and Reed, 1920; Lotka, 1925). The densities of natural populations are instead selected by the density-frequency-dependent gradient (ψ ι) in the access to resources across the individuals in populations.
At the strict evolutionary equilibrium [ ψι** = 1 ] all the individuals in a population reproduce and survive at the same optimal rates with no population dynamic growth. The competitively superior individuals obtain more resources than the competitively inferior, but they do also invest more resources in each offspring with the end result being that both variants have about similar rates of survival and reproduction (Witting, 1997, 2021).
For species that are selected at the evolutionary steady state with an exponentially increasing body mass (Witting 1997, 2020), the resource gradient is somewhat larger [ ψι** = (4
The evolutionary fixation of the intra-specific resource gradients at ψι** = 1 and ψι** = (4
A more complex prediction follows from the density dependent connection between the home range and the optimal foraging solution that satisfies the resource distribution constraints [ ψι** = 1 or ψι** = (4
This selection-based population dynamic equilibrium is not only part of the allometric solution for life history and ecological traits like mass, metabolism, abundance, and home range. It is actually the key that determines the allometric correlations, bacause it is the selected invariant density regulation
f = fe fι fs = fe(Nwβ) fι(NVH(d-1)/d) fs(βH1/d/V) ∝ w0
that determines the exponents of the body mass allometries (Witting, 1995, 2017a). Damuth's (1981, 1987) -3/4 power decline in abundance with mass follows as an essential prediction for species with predominantly two-dimensional interactive behaviour. The corresponding exponent for three-dimensional interaction is -5/6 (see e.g. the Metabolism and Mass section on mrLife.org).
The allometry for abundance tends to vary with the scale of observation (Nee et al., 1991) following expected variation in the distribution of resources across species (Witting, 2021). The exponents are usually around -0.75 across terrestrial species (Damuth, 1981, 1987; Peters, 1983; Nee et al., 1991) on scales where effects from inter-specific interactions are negligible (as assumed in the allometric deduction). The exponent has also been found to decline from -0.79 to -0.86 across species with two and three dimensional behaviour (Pawar et al.,2012); in close agreement with the predicted change from -0.75 to -0.83 (Witting, 1995, 2017).
On selection-regulated population dynamics in birds and mammals
The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals
Inevitable evolution: back to
Evolutionary dynamics of exploited populations selected by density dependent competitive interactions
Two contrasting interpretations of Fisher's fundamental theorem of natural selection
Interference competition set limits to the fundamental theorem of natural selection
A general theory of evolution. By means of selection by density dependent competitive interactions.
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