sledgehammer
Posts: 533
Joined: Sep. 2008
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I haven't run the program, but perusing the description of the algorithm, it seem to me that this section that describes how fitness is assigned is the part that determines the ultimate behavior of the model. They clearly have built in an asymmetry in the fitness of beneficial vs deleterious mutations, and their justifications of the asymmetry smell fishy to me, but IANAB. (bolding mine)
| Quote | To provide users of Mendel even more flexibility in specifying the fitness effect distribution, we have chosen to use a
form of the Weibull function [12] that is a generalization of the more usual exponential function. Our function, expressed
by eq. (3.1), maps a random number x, drawn from a set of uniformly distributed random numbers, to a fitness effect d(x)
for a given random mutation.
d(x) = (dsf) exp(?ax^gamma), 0 < x < 1. (3.1)
Here (dsf) is the scale factor which is equal to the extreme value which d(x) assumes when x = 0. We allow this scale
factor to have two separate values, one for deleterious mutations and the other for favorable ones. These scale factors are meaningful relative to the initial fitness value assumed for the population before we introduce new mutations. In Mendel we assume this initial fitness value to be 1.0. For deleterious mutations, since lethal mutations exist, we choose dsf del = ?1. For favorable mutations, we allow the user to specify the (positive) scale factor dsf fav. Normally, this would be a small value (e.g., 0.01 to 0.1), since it is only in very special situations that a single beneficial mutation would
have a very large effect.
The parameters a and gamma, both positive real numbers, determine the shape of the fitness effect distribution. We applythe same values of a and gamma to both favorable and deleterious mutations. The parameter a determines the minimum absolute values for d(x), realized when x = 1. We choose to make the minimum absolute value of d(x) the inverse of the haploid genome size G (measured in number of nucleotides) by choosing a = loge(G). For example, for the human genome, G = 3 × 109, which means that for the case of deleterious mutations, d(1) = ?1/G = ?3 × 10?10. For large genomes,
this minimum value is essentially 0. For organisms with smaller genomes such as yeast, which has a value for G on
the order of 107, the minimum absolute effect is larger. This is consistent with the expectation that each nucleotide in a smaller genome on average plays a greater relative role in the organism’s fitness.
The second parameter gamma, can be viewed as ontrolling the fraction of mutations that have a large absolute fitness
effect. Instead of specifying gamma directly, we select two quantities that are more intuitive and together define gamma. The first is theta, a threshold value that defines a “high-impact mutation”. The second is q, the fraction of mutations that exceed this threshold in their effect. For example, a user can first define a high-impact mutation as one that results in 10% or more change in fitness (theta = 0.1) relative to the scale factor and then specify that 0.001 of all mutations (q = 0.001) be in this category. Inside the code the value of is computed that satisfies these requirements. We reiterate that Mendel uses the same value for gamma, and thus the same values for theta and q, for both favorable and deleterious mutations. Figure 3.1 shows the effect of the parameter q on the shape of the distribution of fitness effect. Note that for each of the cases displayed the large majority of mutations are nearly neutral, that is, they have very small effects. Since a utation’s effect on fitness can be measured experimentally only if it is sufficiently large, our strategy for parameterizing the fitness effect distribution in terms of high-impact situtations provides a means for the Mendel user to relate the numerical model input more directly to available data regarding the actual measurable frequencies of mutations in a given biological context. |
Part of the justification for asymmetry is that some mutations are lethal, meaning that individual has zero probability of reproducing. OK, but the maximum fitness benefit of a beneficial mutation is "a very small number like 0.001", which is then subject to "heritability factor", typically 0.2, and other probabilities that severely limit its ability to propagate.
To make matters worse, for some unjustified reason, the same distribution for beneficial and deleterious is used, after severely skewing the results with the above.
Again, IANOB, but it seems to me that a single beneficial mutation can, in many situations like disease resistance, blonde hair, big boobs, etc, virtually guarantee mating success, just like a deleterious mutation can be reproductively lethal.
I can see easily how the skewed treatment of beneficial vs deleterious mutations could virtually guarantee "genetic entropy", as evidenced by monotonically decreasing population fitness caused by accumulation of deleterious mutational load.
ETA source. link is above
Sanford, J., Baumgardner, J., Gibson, P., Brewer, W., & ReMine, W.
(2007a). Mendel’s Accountant: A biologically realistic forward-time population genetics program. Scalable Computing: Practice and Experience 8(2), 147–165.
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The majority of the stupid is invincible and guaranteed for all time. The terror of their tyranny is alleviated by their lack of consistency. -A. Einstein (H/T, JAD)
If evolution is true, you could not know that it's true because your brain is nothing but chemicals. ?Think about that. -K. Hovind
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