m.r.Life ι**=7/3ψ

Population abundance

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** = (4d - 1) / (2d - 1) ], and so is the population abundance and frequency of competitive encounters. This generates an intra-specific reproductive rate that increases in approximate proportion with body mass, as observed in many species (e.g., Peters 1983; Reiss 1989; Kingsolver and Pfennig 2004).

The evolutionary fixation of the intra-specific resource gradients at ψι** = 1 and ψι** = (4d - 1) / (2d - 1) by the attractors of the competitive interaction fix-points are the top-down constraints of natural selection. Yet these gradients are mechanistically determined by the bottom-up processes of the density-frequency-dependent competitive interactions among the individuals. This implies that a large part of the variation in population densities can be explained by the density dependent variation in the behavioural interactions that determines the resource gradient. The intuitive prediction, that population densities increase with an increased availability of resources, follow from a redistribution where more individuals are needed to generate the necessary steepness [ ψι** = 1 or ψι** = (4d - 1) / (2d - 1) ] in the distribution of resources across the individuals.

Allometric abundance

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** = (4d - 1) / (2d - 1) ] at the evolutionarily determined population dynamic equilibrium. This selection optimises the home range to minimise the overall regulation [ fι fs ] of the counteracting forces of interference competition (fι) and local resource exploitation (fs). On top of this there is population dynamic feed-back selection for the level of interference competition that matches the level of the competitive interaction fix-points (Fig. 1).

Fig. 1 The optimal home range is selected to minimise the joint regulation by interference competition and local resource exploitation (green arrows), and the population dynamic feed-back selects the population density where the level of interference that is generated by individuals in optimal home ranges matches the level of the competitive interaction fix-point, as determined by the selection attractor on body mass (red arrows). From Witting (2017b).

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).

Download publications

bioRxiv 2021.11.27.470201 (2021)Download

On selection-regulated population dynamics in birds and mammals

Theoretical Population Biology 117:23-42 (2017)Download

The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals

Biological Reviews 83:259-294 (2008)Download

Inevitable evolution: back to The Origin and beyond the 20th Century paradigm of contingent evolution by historical natural selection

Ecological Modelling 157:51-68 (2002)Download

Evolutionary dynamics of exploited populations selected by density dependent competitive interactions

Comments on Theoretical Biology 7:1-10 (2002)Download

Two contrasting interpretations of Fisher's fundamental theorem of natural selection

Acta Biotheoretica 48:107-120 (2000)Download

Interference competition set limits to the fundamental theorem of natural selection

Peregrine Publisher, Aarhus (1997)Download

A general theory of evolution. By means of selection by density dependent competitive interactions.


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