Mutation stochastic dependence

On the basis of the definition of mutation frequency given in equation (6), nonlinearities in frequency curves would be expected to arise only from the existence of multilesion mutation-induction processes. However, nonlinearities in mutation-frequency curves can arise if mutation and killing are not stochastically independent processes as assumed in Section 3 and in writing equation (6). We can generalize the formalism of Section 3 and 4 to allow for stochastic dependence of mutation and killing in the following way ... 

FIGURE 8. Effect of stochastic dependence of mutation and killing (6 1) superimposed on a basically linear response pattern Lk,Lm). Mutation-frequency curves calculated from equation (55) for mi = 10 and Ai = 0.1 (ergs/mm ) for various values of h. The curves for 6 > 1 lie below those for 6 < 1 merely because a single, fixed value of mi was used to calculate all curves. 

Stochastic dependence also produces shifts in the position and magnitude of the maximum mutant yield. The resulting yield curves have different shapes from (i.e., are not congruent with) those produced by nonlinearities in the basic mutation-induction process described by H ix) (cf. Figures 3 and 9). 

Two implementations of genomes, a binary and a decimal (figure 2), were compared to study the dependence on a DNA-like and chemist-like crossover and mutation. Further variables were population size, mutation rate and the crossover strategy. In order to eliminate the stochastic differences between different GA runs, each parameter set was used in 100 parallel runs and the averages and standard deviations for the various results were calculated and displayed on the following figures. All results were compared with a "random" screening method that was simulated by a repeated random selection of new products from the library. 

Figure 8. The activity of best reaction product found by the GA during the course of evolution depending on the stochastic mutation rate, crossover and generation size. The results are displayed as averages from 100 parallel runs for each GA parameter set and compared to random selection (20- and 80-random).

The PSO algorithm is based on a sociometric principle called gi,, which connects all the members of the swarm to one another (Kennedy and Eberhart, 2001). Each particle is affected by the very best performance of any member of the whole population. The key operators involved in evolutionary algorithm (EA) are recombination, mutation and selection however, PSO does not have a direct recombination operator (Kennedy and Eberhart, 2001). But, the stochastic acceleration of a particle towards its previous best position as well as towards the best particle of the swarm resembles the recombination in EA. In PSO, the information exchange takes place merely among the particle s own experience and the experience of the best particle in the swarm instead of being carried from fitness-dependent... 

If the relevant physical lesions are formed in direct proportion to dose, and if no dose-dependent processes are involved in the conversion of initial lesions to biological hits, then the hit function will be linear. More generally, H x) could be some more complex function that, nonetheless, can always be represented by an infinite power series in x with no constant term (since there can be no induced hits for zero dose). We denote the expected number of lethal and mutational hits at dose x by Hk x) and Hm(x), respectively. Thus, on the basis of single-event Poisson statistics, population homogeneity, and stochastic independence of mutation and killing, we can write... 

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