This guest post is by Phillip Smith on his preprint Sex and Ageing: The Role of Sexual Recombination in Longevity
The two fold cost of sex is an old problem in the evolution of sex. Asexual organisms should out complete sexual organisms as they produce twice as many child bearing offspring as a sexual form. Some how sexual reproduction has pay for this twofold cost of sex.
Recombination has been shown in neutral network models to move the population toward the centre of genome space for protein models more efficiently than mutational load alone. This phenomenon of recombinational centring results in lower entropy and therefore greater robustness and stability. To investigate under which circumstances recombinational centring occurs we have to look at the relationship between genotype and phenotype. To do this we need some kind of machine that can simulate the complexity of a biology whilst being computation and conceptually simple enough to explore some of the parameter space of possible machines.
Biological entities must be some kind of complex machine. Machines can range in complexity from machines that do nothing (class I), through machines that oscillate (class II) to machines that are chaotic (class III). Somewhere on that continuum of machine types there are machines on the edge of chaos (class IV). For a cell to replicate a string (the genome) and a machine must interact to generate a new machine and a new string. In organism with sufficient genome length there is near zero probability that the parent and daughter cell have identical strings and machines. If the daughter cells string is incompatible with the machine then the cell will die.
Biology is an deeply nested system. Machines are made up of machines and the acceptability of a components state is dependent on the state of other machines within the nested hierarchy of the machine.
To capture the complexity of biology I developed these nested machines. They take a binary input string and use a machine to generate a smaller string representing the state of the machine at a higher level. The process is repeated at each stage until a single bit is left. If the bit is 1 then the string is accepted by the machine, else the string is rejected. To keep the parameter space small the wolfram elemental cellular automata ECA were used as the machines. The same machine was used for each level. There are 256 machines and they are known to have machines in all four wolfram classes. Rule 30 is a pseudo-random number generator for long strings (100) bits. Rule 110 is a turing complete machine capable of computation.
Movement of the population towards the centre of the genome space reduces mutational load this was shown to be very pronounced in the class IV machines whereas in the class III chaotic machines the opposite was observed, recombination increased mutational load. This shows that recombinational centring requires class IV machines to work, these are the same machines that are thought to me most similar to the complexity found in biology and the most likely to capable of computation.
Obviously the less entropy and individual starts with the longer they will be able to accumulate disorder and will be both more mutationally robust and robust to unpredicted environmental insult.
It is therefore reasonable that they should live longer. This was tested by simulating ageing on populations of differing machines at asexual and sexual equilibrium. Essential ageing was considered a random walk in genome space. The closer you start to the well connected centre the longer you will survive. Class IV machines saw the best increase in resistance to ageing.
For Rule 110 it was shown that this resistance to ageing was sufficient to compensate for the twofold cost of sex if the age of maturation was late enough in the lifespan as sexual forms had greater reproductive potential.
It is suggested that the increased resistance to ageing is sufficient to compensate for the twofold cost of sex in large complex organisms.