Anne Dambricourt Malassé • ADM DM #0 – ADM DM #1 – ADM DM #2 – ADM DM #3

I’ll keep the same here as for example #01, Specs in Isle, and *velo*, the gene determining Specs’ velocity, and the same *clonal* population at time T_{0}.

Let’s consider a particularity of gene *velo*. If two specific mutations are present on the same molecule, velo-d1 and velo-d2, they act synergistically and the velocity of the individual is V_{max}. velo-d1 and velo-d2 independently don’t affect the *velocity* trait, thus they aren’t selected, and they aren’t punctual mutations.

Say that this occurs at time T_{d1-d2}, and this is in a stage of Specs history that gives it a clear advantage, substantially increasing the movements of carrier Specs, this particular combination will spread rapidly in Specs population, as the carriers have plenty of time available for sex.

The history of Specs will be determined from the occurrence of this particular random event. It represents a *jump* in the evolution of the particular phenotypic trait, *velocity*.

A jump which amplitude will be inversely proportional to T_{d1/d2}-T_{0}.

If you observe the increase of velocity of the Specs and don’t know anything about their genetics, you may have the feeling that there is some Unknown Factor making them faster and faster. And that at time T_{d1/d2} another Unknown Factor changed the rules and produced the jump of the velocity’s increace. Then you have two solutions: considering some Mysterious Internal Blueprint due to Supernatural Causation being the cause of the *velocity’s* increase and some Mysterious Change of the Internal Blueprint at time T_{d1/d2}, or inventing genetics and understand how Specs evolved from Spec *SlowMotion* (those Specs present at T_{0}) to Spec *AsFastAsPossible* (those Specs living at time T_{s, including the velocity’s sudden increase at T}_{d1/d2}.

**And this is a third observation: Phenotypical traits may evolve in a directional way and by jumps, while mutations are still perfectly random.**

But a jump at V_{max} isn’t very probable. Let’s say that this is a smaller *jump*, an increase of x% of the initial velocity, V_{0}, and this particular event I’ll call a velo-jump from now on; the plot of velocity versus time (generations) will be something like that :

Concommitant to the velocity’s increase there is a drop of the selection pressure (they are correlated) and then the evolution of the phenotype will follow the same path as in example 1, reaching a plateau.

The coexistence of the two mutations in a single *velo* molecule is a random phenomenon. So it’s impossible to say « when » and « if » it will happen during the Specs history. I run a few simulations, and I had a very pleasant surprise; a velo-jump above V_{max}. I wasn’t expecting to talk here about the reversibility of the model, but here is what I got at the second run of the model:

There are two graphs in fig above. Both represent the same data, the one at the right isn’t versus time, but log(time), this is useful to see more clearly early events. The blue curve represent *velocity* and the red ones *selection pressure*. The genotype d1-d2 appears relatively late and the velocity gain set V_{s} above V_{max}. This phenotype isn’t privileged, as in the case where food’s density increased, I presented in example 1. So it will be progressively lost, either by reversion or by apparition of new mutations. I was glad to see that « happen », the model used for simulations seems to be *well constructed*.

**Reversibility is conserved.**

I gave it a few more runs and I overlaid a series of graphs to show alternative Specs histories:

There are three series presented here, a, b and c, corresponding to velo-jumps of 10, 20 and 40% of V_{0} respectively. For each series I show graphs with the x axis as time or log(time). The red arrows at « series c », points to a story where the d1-d2 genotype didn’t appeared. The duration of Specs history is normalized here. I’ll come back to this.

While V_{max} is reached for every run, which mean that the Specs will be optimized for their environment, the path, trough which this is achieved, is as random as the occurrence of the d1-d2 genotype; it may even not contain this particular event.

Now, why did I normalized the histories lengths? It’s only a matter of better visualisation. Let’s see at what generation d1-d2 appeared for a set of 1000 runs :

Quite random, ranging from 5 to 53777. To make it visible, without making a particular choice, the simplest way was to normalize the duration of the stories.

One may evaluate odds that d1-d2 appears during the Specs history; this is a simple probability calculation, predicting that d1-d2 *may* appear. If the probabilities are equal for both mutations, and **p** is the probability for each one, then the probability to get both simultaneously is **p _{d1-d2} = p^{2}**.

It doesn’t say

*when*.

On the other hand, you may evaluate what is the probability for d1-d2 to appear after n generation and that will be

**n * p**.

_{d1-d2}= n* p^{2}Randomness is preserved at the mutations level, and thus at the genotype level, the phenotype evolves directionally as long as it doesn’t exceed the optimal value (otherwise the direction change), and a particular genetic event may produce *jumps* of the phenotypic trait.

One couldn’t predict the history of the Specs otherwise then in terms of probabilities; the single predetermined element is V_{max}, and this is only to facilitate calculations, the *real* value being a function of the Specs physiology and foods density.

The probability to have two identical histories (runs of the simulations) is low. Some cases are present (difficult to see on the graph, but there are 42 repetitions! Now, that the genotype d1-d2 occurs at generation **g** twice (or more) that doesn’t mean that the paths where identical!

Technorati tags: Anne Dambricourt, Jean Staune, Intelligent Design, Darwinism, genotype, phenotype

## ADM-DM-03

Posted in ADM-DM, comments, Darwin, reactions on février 6, 2006| 1 Comment »

Anne Dambricourt Malassé • ADM DM #0 – ADM DM #1 – ADM DM #2 – ADM DM #3

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 sameclonalpopulation at time T_{0}.Let’s consider now three particular mutations of

velogene: 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 p_{1/2/3}= p^{3}. An event less probable then the double mutant d1-d2, p_{1/2}= p^{2}.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

fixedas it represents an advantage for the carriers and thus the probability to obtain the triple mutant will increase to p_{1•2/3}= p !The step from the initial genotype/phenotype (T

_{0}) to the d1-d2 ones (T_{s}) 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 ofvelocity(red arrow) is du to the effect of d1-d2-d3. The phenotype will reverse as a higher then the optimalvelocityisn’t selected, and the optimalvelocitywill be reached.Let’s summarize:

_{0}all Specs share the same genotype and present the same phenotype._{0}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 ofvelowill be transmitted to descendants. Foods density on Isle determine the V_{max}, which is the speed of movement of Specs, making meals so sort that they don’t interfere with sexual activity.observationperiod a single gene is able to mutate,velo, which is the only one modulatingvelocity, which is the phenotypic trait describing Specs maximal speed; variations on genotype produce equivalent variations on phenotype, directly.velothree are remarkable, d1, d2, and d3. The probability to observe these three mutations is equal and expressed byp, 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:

velocity, under selection pressure which is related to the actual Specs characteristics and the optimal value ofvelocity. The selection factor is a combination of Specs characteristics,velocityand available food resources density. Inversely proportional tovelocity, it is difficulty observable when the population reach a meanvelocityvalue equal to the optimal. The directionality of evolution of the phenotypic trait is reversible; if the population reach a meanvelocityvalue higher then V_{max}, it will tend to decrease, stabilizing around V_{max}.The probability to obtain d1-d2-d3 is p

_{1/2/3}= p^{3}before the apparition of genotype d1-d2,

the probability to obtain d1-d2 is p

_{1/2}= p^{2}, andthe probability to obtain d1-d2-d3 becomes p

_{1•2/3}= p after the apparition of genotype d1-d2.Thus, p

_{1•2/3}> p_{1/2}> p_{1/2/3}, 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 ofvelocity).velocityis respected, at the phenotype level.velocityis respected, at the phenotype level.velocityis respected, even at the phenotype level.The model is darwinian, theobservationssimilar 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 situhybridization, to validate and dispose of a spatial repartition overview. And this for bothHomo sapiensand a closely related species, which genome is known, sayPan troglodytes.If that fails, then something else may be considered.

Technorati tags: Anne Dambricourt, Jean Staune, Intelligent Design, Darwinism, genotype, phenotype

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