Malthusian Relativityι**=7/3ψ
The natural selection of lifeforms

From viruses to mammals

When the selection on metabolism, mass, allometries and life histories are considered together, we find that the gradual unfolding of the population dynamic feed-back is selecting for well-known lifeforms; from viruses over prokaryotes and single celled protozoa to the multicellular animal with sexual, co-operative or eusocial reproduction.

Virus - the replicating molecules

Viruses are like replicating molecules with no net energy. Their “life-form” with asexual replication, no internal metabolism, no cell, and practically no mass is the most likely origin for the evolution of living organisms with cells and internal metabolism.

Once arisen, replicating molecules with no intrinsic metabolism evolves by a special type of selection where replication is driven directly by an external source of energy; let it be from the metabolism of a host, or from the random encounters between molecules in an abiotic environment.

The molecular replicator and its special selection can also evolve as the selection attractor of a low-energy self-replicator with an internal metabolism. This is the case when the maximum exponent [ ββ,0 = max(ββ) ] for the dependence of mass specific metabolism on mass [ β ∝ wβββ ] is smaller than one [ ββ,0 < 1 ]. It is then impossible to enhance the replication rate by an increase in mass specific metabolism. This is because the extra net energy that is generated by an increase in metabolism with mass is smaller than the extra energy that is required by the larger mass of the offspring. These replicators may instead increase their replication by a mass that evolves towards zero, with the side effect that they are shutting down their metabolic processes.

Prokaryotes - the minimum self-replicating cell

A minimum self-replicating cell, with internal metabolism and asexual reproduction, can be selected from replicating molecules by the dependence of mass specific metabolism on mass [ β ∝ wβββ ]. This is the case when the maximum exponent is larger than one [ ββ,0 = max(ββ) > 1 ]. The increase in net energy by an initial increase in metabolism with mass is then larger than the extra energy that is required by the extra mass of the offspring. Metabolism and mass are then selected to an equilibrium where the exponent for the pre-mass dependence of mass specific metabolism on mass is unity [ ββ**=1 ].

These minimum self-replicating cells will have an incomplete metabolism because the ββ exponent is larger than zero, and they are selected exclusively by the dependence of mass specific metabolism on the entire mass of the cell. They are the smallest single celled organisms, and they are selected to have the minimum mass that is required by the self-replicating cell with the given metabolism and heritable code. Given ecological interactions in three spatial dimensions, these self-replicators evolve a mass specific metabolism that increases to the 5/6 power of mass; in agreement with data from prokaryotes.

Protozoa - the interacting self-replicating cell

Having a 5/6 exponent for an increase in mass specific metabolism with mass, the selection attractors of the minimum self-replicators have incomplete metabolic pathways. But somewhat larger cells with more fully developed metabolic pathways are selected from the minimum self-replicator by a gradual unfolding of an interactive competition that generates a bias in the distribution of resource over mass.

This mass bias (ψι*) in the net assimilated energy is selecting for a larger cell with more developed metabolic pathways and a somewhat smaller dependence of mass specific metabolism on mass. Mass, however, is still being selected as the minimum that is required for the cell, metabolism and heritable code. And with the cell being selected as the metabolic compartment, the selection for minimum mass is selecting for a single-celled self-replicator.

These interacting single-celled self-replicators are selected by a gradual unfolding of a yet incomplete population dynamic feed-back selection; an unfolding that generates a resource bias exponent that increases from zero to one [ 0 < ψι* → 1 ]. This generates selection for an increase in mass with an associated decline from 5/6 to -1/6 in the allometric exponent for mass specific metabolism (given 3D interactions); a decline that is observed in single-celled eukaryotes like protozoa.

Multicellular animals - the sexual reproducer

The population dynamic feed-back is fully developed when the maximum exponent for the resource bias of interactive competition evolves beyond unity [ ψι* > 1 ]. This marks a transition where interactive competition is selecting mass beyond the threshold where the metabolic pathways are fully developed; making mass specific metabolism functionally independent of mass.

An increase in net energy is then selected into mass by an interactive competition that is selected to a mass invariant balance where the positive selection of mass from the resource bias of interactive competition is balanced against the negative selection of the quality-quantity trade-off. And with mass being selected beyond the required minimum for the metabolism of the cell, there is selection for a multitude of metabolic cells that specialise and cooperate to enhance the behavioural and physiological functionality of the individual.

When these multicellular animals adapt to a multitude of niches it follows that their energetic differences will be invariant of metabolism [ ββ=0 ]. This creates a life history that evolves by mass-rescaling, with ± 1/4 exponents across species with interactive behaviour in two spatial dimensions, and ± 1/6 exponent for three dimensional interactions; as observed quite commonly in major taxa of multicellular animals.

The selection attractor with stable net energy is the competitive interaction fix-point with a resource bias exponent of unity [ ψι**=1 ]. This interference is selecting for other interacting traits that include a senescing soma, and sexual reproduction between a male and female with diploid genomes.

Cooperative families - the unconstrained group

Where the optimal reproducing unit is the male-female pair in high-energy organisms with equilibrium masses, it contains one or two extra interacting individuals in species with unconstrained selection and exponentially increasing masses at evolutionary steady states. Should these extra interactors be offspring workers or sexually reproducing males?

With the interactive quality of the male being transferred by sexual reproduction to potential offspring workers, there is a diminishing return in the interactive quality that can be gained by increasing the number of males that participate in sexual reproduction. The result is selection for co-operative families, where the extra interactors are sexually produced offspring workers that evolve at the cost of unknown forms of sexual reproduction with several males per female.

Eusocial reproduction - the mass constrained colony

The main energetic buffer of competitive quality can shift from mass to the number of individuals in the reproducing unit if there is an absolute or temporal upper evolutionary limit to the mass of an individual. An increase in net energy is then selected into increased population growth, resulting in increased interactive competition, and selection for eusocially reproducing units where the sexually reproducing pair forms a colony with a plenitude of sexually produced offspring workers.

The offspring workers and underlying ploidy level of the genome at the evolutionary equilibrium will depend on the role of the sexual male for the colony. If the male is needed only to transfer his genome to the offspring, the two-fold cost of the male is selecting for a male-haploid female-diploid genome and a worker caste of pure females; as seen in eusocial hymenoptera like ant and bees. If instead the male has an ecological role and forms a permanent pair with the sexual female, there is selection for a diploid genome, and female and male workers; as seen in eusocial termites.

Macro evolution across major taxa

We have now seen that the correlated evolution between mass specific metabolism and mass is changing across the tree of life; from the absence of metabolism in replicating molecules like virus, over a positive 5/6 exponent in minimum self-replicators like prokaryotes, and a change in the exponent from 5/6 to -1/6 in interacting self-replicators like protozoa, to negative 1/4 and 1/6 exponents in multicellular animals, dependent upon the spatial dimensionality of the interactive behaviour.

At the macro evolutionary scale from prokaryotes to birds, the maximal mass specific metabolism in each taxa seems to be selected to an upper limit. This coincides with a mass-rescaling on the macro evolutionary scale that is balanced by pre-mass selection on metabolism, with the overall correlation being a mass specific metabolism that is invariant of mass.

Sessile organisms - the permanent interactor

Malthusian Relativity is developed mainly for mobile organisms where the interactive encounters between individuals are transient. Any interaction between sessile organisms is instead a permanent competition between neighbouring individuals for inflowing resources, and this is generating constant interference with selection of size whenever the density of individuals is sufficiently high.

This competition is also constraining the interacting unit to a single individual, with the absence of a cooperating interaction that can outbalance the two-fold cost of the male and the two-fold cost of meiosis. This selects for hermaphrodites that avoid the two-fold cost of the male and the two-fold cost of meiosis.