I’ll keep the same here as for parts ADM-DM-01 and ADM-DM-02, Specs in Isle, velo, the gene determining Specs’ velocity, and the same clonal population at time T0.
Let’s consider now three particular mutations of velo gene: velo-d1, velo-d2, which are the same as in ADM-DM-02, and velo-d3.
The genotype d1-d2 is always at the origin of a velo-jump of x%; the genotype d1-d2-d3 produce a velo-jump of n*x%, where n>1. Genotypes d1-d3 and d2-d3 are neutral for velocity.
For equal probabilities of occurrence of the three mutations, p, the probability to observe the triple mutant d1-d2-d3 is p1/2/3 = p3. An event less probable then the double mutant d1-d2, p1/2 = p2.
Statistically the double mutant d1-d2 appears before the triple mutant d1-d2-d3. And the double mutant is necessary to observe a phenotypic impact from the mutation d3.
Once the double mutant d1-d2 present in Specs population it will be fixed as it represents an advantage for the carriers and thus the probability to obtain the triple mutant will increase to p1•2/3 = p !
The step from the initial genotype/phenotype (T0) to the d1-d2 ones (Ts) is expected to be longer then the step from d1-d2 to d1-d2-d3, statistically mean.
The following figure illustrates six runs of the model, with x%, the velo-jump du to d1-d2, equal to 25%, and n = 2, so the velo-jump associated with d1-d2-d3 is of 50%.
Only the mean velocity of the Specs population is represented. There is a story line where d1-d2 wasn’t observed. The rectangular ROI highlights the two velo-jumps. The circular ROI highlights overflows, where the velocity is above the optimal one, and show that the model is still reversible.
Let’s take a look at a particular line story:
Arrows point to the apparition of d1-d2 and d1-d2-d3 and the corresponding velo-jumps. And in this particular example the time lapsed between the wild type and the double mutant is longer then the time lapsed between the double and the triple mutants. This graph represents what one expect to observe as a statistical result.
The graph below was obtained with x% = 25% and n = 2, just for better visualization of the velo-jumps.
We have here a typical situation of overflow. The pic of velocity (red arrow) is du to the effect of d1-d2-d3. The phenotype will reverse as a higher then the optimal velocity isn’t selected, and the optimal velocity will be reached.
- A population of Specs, a species with three main activities: sleep, food and sex; duration of sleep is constant so Specs existence may be considered as part alimentation and part sexual activity.
- At the beginning of the stories lines T0 all Specs share the same genotype and present the same phenotype.
- At the T0 Specs aren’t perfectly adapted to their environment. There is a selection pressure favoring those able to move faster and thus feed in shorter times; those dispose of larger periods for sexual activity and their genetic variants of velo will be transmitted to descendants. Foods density on Isle determine the Vmax, which is the speed of movement of Specs, making meals so sort that they don’t interfere with sexual activity.
- During the observation period a single gene is able to mutate, velo, which is the only one modulating velocity, which is the phenotypic trait describing Specs maximal speed; variations on genotype produce equivalent variations on phenotype, directly.
- From the many variants of velo three are remarkable, d1, d2, and d3. The probability to observe these three mutations is equal and expressed by p, which satisfy to the condition 0velocity, what I called a velo-jump. The same is for genotype d1-d2-d3, which have a more important effect. Genotypes d1-d3 and d2-d3 don’t produce a velo-jump.
What could we get from such a simple model:
- Directional evolution of the phenotypic trait velocity, under selection pressure which is related to the actual Specs characteristics and the optimal value of velocity. The selection factor is a combination of Specs characteristics, velocity and available food resources density. Inversely proportional to velocity, it is difficulty observable when the population reach a mean velocity value equal to the optimal. The directionality of evolution of the phenotypic trait is reversible; if the population reach a mean velocity value higher then Vmax, it will tend to decrease, stabilizing around Vmax.
- Sudden increases of the value of the phenotypic trait, velo-jumps, are possible, when d1-d2 and d1-d2-d3 genotypes are produced by random mutations. If one can evaluate the probability to see those genotypes, it’s impossible to predict when they will occur. It is also impossible to predict the time laps between d1-d2 and d1-d2-d3, but one can calculate probabilities:
The probability to obtain d1-d2-d3 is p1/2/3 = p3
before the apparition of genotype d1-d2,
the probability to obtain d1-d2 is p1/2 = p2, and
the probability to obtain d1-d2-d3 becomes p1•2/3 = p after the apparition of genotype d1-d2.
Thus, p1•2/3 > p1/2 > p1/2/3, which means that the more probable path is to get d1-d2 first, then after a relatively short period d1-d2-d3 (which may be considered as an acceleration of the evolution of velocity).
- Directionality of evolution of velocity is respected, at the phenotype level.
- Discontinuity of evolution of velocity is respected, at the phenotype level.
- Reversibility of evolution of velocity is respected, even at the phenotype level.
- Randomness, as builded in the model, is respected, at the genetic level.
- The selection factor is a combination of physiological and environmental characteristics, inversely proportional to the phenotypic trait, and it would be quite difficult to determine once the optimal value reached or by fossils examination.
The model is darwinian, the observations similar to those reported by ADM.
Maybe she could spend some time considering this option before the evocation of Unknown Factors, Internal Plans or any thing else.
To do so, it is necessary to dispose of molecular (genetic) data. A first step would be the determination of genes expressed during the cranium build at the sphenoid region; gene arrays to determine which ones then in situ hybridization, to validate and dispose of a spatial repartition overview. And this for both Homo sapiens and a closely related species, which genome is known, say Pan troglodytes.
If that fails, then something else may be considered.