m.r.Life ι**=7/3ψ

Multicellular animals - the sexual reproducer

A fully developed population dynamic feed-back selection selects for multicellular animals with sexual reproduction

Feed-back selection, mass and multicellularity: Protozoa can evolve into larger multicellular animals by a population dynamic feed-back selection that is fully developed (Witting, 2017b).

When the exponent of the maximal resource bias from interactive competition is evolving beyond unity [ ψι* > 1 ], there is selection for a mass that evolves beyond the threshold where the metabolic pathways are fully developed. Mass specific metabolism is then functionally independent of mass, and mass is selected entirely by the intra-specific competitive interactions between individuals.

This marks a transition where the interference in the population is determined by the selection attractor on mass. With stable net energy, the resource bias exponent is selected to unity, and this defines mass invariant interference competition [ ψι** = 1 , => ι** = 1 / ψ, Fig. 1 right ]. The positive selection of mass from the resource bias of interference is then outbalancing the negative selection of the quality-quantity trade-off.

With a mass that evolves beyond the minimum that is required by the mass specific metabolism of the organism, there is no longer active selection for a single celled self-replicator. A multicellular animal is instead expected by the selection of a multitude of metabolic cells that specialise and cooperate to enhance the behavioural and physiological functionality of the individual.

Fig. 1 Left: Body mass (w) allometry for the lifespan (T) of 195 species of terrestrial mammals (open circles) where the exponent is 0.25 ±0.04, and 40 species of pelagic mammals (solid circles) where the exponent is 0.16 ±0.02 [ From Witting (1997) with data from Nowak (1991) ]. Right: An illustration of the fully developed feed-back selection that predicts a 2D lifespan exponent of 1/4 (0.25), and a 3D exponent of 1/6 (≈ 0.17). The interactive selection on mass is now fully developed, and given stable net energy the selection attractor on mass is determining the level of interference [ ι** = 1 / ψ ] from a selected resource bias exponent of unity [ ψι** = 1 ]. The dot on each circle is the selected female, and the square the selected male, that form the sexually reproducing pair of the reproducing unit.

Allometries: When a taxonomic group of multicellular animals evolve by species that adapt to a multitude of niches, their energetic differences will be invariant of metabolism [ ββ=0 ]; reflecting instead the variation in the handling, densities and energetic contents of the underlying resources. This inter-specific variation in net energy is selected into inter-specific body mass variation by the intra-specific feed-back selection. The result is life histories that diversify by a mass-rescaling selection that generates Kleiber scaling with ± 1/4 exponents across species with 2D interactions, and ± 1/6 exponent for 3D interactions (Witting, 1995, 2017a); as illustrated for mammals in Fig. 1, left.

Life history: The predicted allometric exponents, that define the evolutionary correlation of the life history with mass, are listed in Table 1.

With a resource bias exponent from interactive competition that is selected to unity by the selection attractor on mass, there is interactive selection for a reproducing unit where a male and female individual are using sexual reproduction to share the genome in the offspring equally among them (Witting, 1997, 2002).

The resource bias implies also that energy that could be used to maintain the tissue of the individual to obtain potential immortality, is predicted to be invested better in interactive competition (Witting, 1997). This is generating the expected evolution of a senescing soma.

With a resource bias of interference that is selected as an invariant attractor, the potential for population dynamic growth is selected to be invariant on the time-scale of the organism [ λ = p R = w0 ]. This implies a lifetime reproduction [ R = 1/p ] that is selected as the inverse of the probability to survive to reproduce (p).

Table 1 The predicted allometric exponents for multicellular animals. Net energy (ε), mass specific metabolism (β), survival (p), home-range (H), lifetime reproduction (R), population density (N), rate of population increase (r), and time periods like lifespan (τ). For details see Witting (1995, 1997, 2017a).

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  • Witting, L. 2017a. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42, https://dx.doi.org/10.1016/j.tpb.2017.08.005.
  • Witting, L. 2017b. The natural selection of metabolism and mass selects lifeforms from viruses to multicellular animals. Ecology and Evolution 7:9098--9118, https://dx.doi.org/10.1002/ece3.3432.