Competitive interaction fix-points

Fig. 1 The competitive interaction fix-points, given 2D interactions for the evolutionary steady state.

Many life history characters are used in interactive competition, and we need to understand the natural selection of interference competition in order to explain the evolution of these traits.

The evolution of interference competition starts from the absence of a resource bias

ψι^** = 0

in replicating molecules and the smallest self-replicating cells with an internal metabolism. As these self-replicating cells are selected to have the minimum mass that is required for their mass specific metabolism (Witting, 2017), their net energy is selected into replication and they have a maximum equilibrium abundance with maximum interference (ι^*). Yet, in the absence of interactive behaviour, we expect the cost gradient (ψ) and the resource bias (ψι^*) to be essentially zero, even with some interference in the population.

With the gradual evolution of interactive behaviour and a cost gradient above zero, we get the evolutionary unfolding of a resource bias

0 < ψι^** < 1

that is predicted to increase from zero to one with the evolution of larger self-replicating cells (Witting, 2017). These cells are also selected to have the minimum masses that are required by their metabolic pathways, and the interference competition and resource bias are thus at the possible maximum given the net energy of the self-replicating cells.

With the complete unfolding of population dynamic feed-back selection, the maximum resource bias is increasing above unity. This interactive competition is selecting net energy into a mass that increases above the minimum that is required by the metabolic pathways of the organisms. And this allows for the evolution of multicellularity, and the selection of a competitive interaction fix-point with a resource bias of unity

ψι^** = 1

The increased net energy of the larger individuals is then out-balancing the quality-quantity trade-off, making relative fitness independent of mass.

The equilibrium fix-point of a multicellular animal is defined by a sufficiently high and evolutionary stable net energy. Given unconstrained selection we expect species at the competitive interaction fix-point of an evolutionary steady state

ψι^** = (4d - 1) / (2d - 1)

where d is the spatial dimensionality of the intra-specific interactions (Witting, 1997, 2003, 2008). This resource bias is ψι^** = 3 for 1D interactions, ψι^** = 7 / 3 for 2D, and ψι^** = 11 / 5 for 3D. The net energy and body mass at the evolutionary steady state is selected to increase exponentially on the per generation time scale of natural selection.

A final attractor can arise from an absolute, or temporal, upper limit on mass (Witting, 1997, 2003, 2008). The increased net energy from the evolutionary increase in resource assimilation is then no longer selected into mass. It is instead selected into increased reproduction, and this generates a population abundance and interaction level that increase towards infinity

ψι^** → ∞

These transitions in the evolution of the interference competition in the population are generating selection for an increased organisation of the life history.

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References

• Witting, L. 1997. A general theory of evolution. By means of selection by density dependent competitive interactions. Peregrine Publisher, Århus, 330 pp, URL https://mrLife.org.
• Witting, L. 2003. Major life-history transitions by deterministic directional natural selection. Journal of Theoretical Biology 225:389--406, https://doi.org/10.1016/S0022--5193(03)00274--1.
• Witting, L. 2008. Inevitable evolution: back to The Origin and beyond the 20th Century paradigm of contingent evolution by historical natural selection. Biological Reviews 83:259--294, https://doi.org/10.1111/j.1469--185X.2008.00043.x.
• Witting, L. 2017. 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.