^{**}=7/3ψ

# The unfolding of interactive selection

The evolution of interactive competition selects for large self-replicating cells with complex metabolic pathways

The initial dependence of mass specific metabolism on mass is selecting for small self-replicating cells. And the selection for increased net energy generates population growth and interactive competition (ι); with the latter creating a mass bias in net energy

ε (w_{i}/w)^{ψι} with ψι > 0

where the larger (w_{i}) than average (w) individuals monopolise (ψ) the resource to some degree.

This resource bias is increasing with the evolution of active interactive behaviour (increased ψ). And with the selection of an active resource handling that generates more net energy for population growth and a higher equilibrium abundance with increased interference competition (increased ι). On top of this we have the partial selection of the quality-quantity trade-off that is selecting for the β-dependent minimum mass (w_{β}^{*}) that is required to sustain the mass specific metabolism of the self-replicating cell. This partial selection of a minimum mass implies that the interactive competition in the population is being maintained at a selection maximum [ ι^{*}(w_{β}^{*}) ], where the minimum mass is generating maximum interference because of the inverse relationship [ λ ∝ 1 / w ] between population growth and mass.

The joint selection of mass -- where the dependence of mass specific metabolism on minimum mass, and the resource bias of the selected maximum interference are acting against the downward pull of the quality-quantity trade-off -- is

∂ r / ∂ ln w_{β,i}^{*}_{|wi=w} = ψ ι^{*} + β_{β}^{•} - 1

As long as the exponent of the maximum resource bias is smaller than one [ ψι^{*}<1 ], there is selection for a self-replicating cell with a β-dependent minimum mass. This mass is being maintained by a joint increase in net energy with mass, from the bias of interference competition and the dependence of metabolism on mass, that is balanced against the quality-quantity trade-off. And the mass is the minimum that is required to sustain a pre mass-rescaling mass specific metabolism that increases sub-linearly with mass with the following exponent

β_{β}^{•} = 1 - ψι^{*}

As this exponent is smaller than one it follows that these interacting self-replicating cells are larger, and with a more fully developed metabolism, than the minimum cells that evolve with no resource bias.