MODELING, SIMULATION AND APPLICATION OF BACTERIAL TRANSDUCTION IN GENETIC ALGORITHMS

At present, all methods in Evolutionary Computation are bioinspired by the fundamental principles of neo-Darwinism, as well as by a vertical gene transfer. Virus transduction is one of the key mechanisms of horizontal gene propagation in microorganisms (e.g. bacteria). In the present paper, we model and simulate a transduction operator, exploring the possible role and usefulness of transduction in a genetic algorithm. The genetic algorithm including transduction has been named PETRI (abbreviation of Promoting Evolution Through Reiterated Infection). Our results showed how PETRI approaches higher fitness values as transduction probability comes close to 100%. The conclusion is that transduction improves the performance of a genetic algorithm, assuming a population divided among several sub-populations or 'bacterial colonies'.


Transduction operator
In the genetic algorithm, the donors, Petri dish and bacterium, are selected by applying one of the following criteria. Let p D be the donor Petri dish representing the sub-population from which to select the donor bacterium.
The selection of the donor Petri dish is based upon one of the following criteria: a) Random selection (method r).-In this case a Petri dish p D is chosen at random from a uniform distribution according to the range [1, P]. b) Maximum fitness (method max).-Given P Petri dishes, the Petri dish p D with maximum fitness is selected. Thus, if i f is the fitness value of the ith donor Petri dish, then we select     Horizontal gene transfer (HGT) mechanisms in bacteria. Conjugation is a mechanism of HGT within population, whereas transduction is an HGT mechanism between populations.
Transduction experiment. The figure shows transduction from donor Petri dish (p D ) and bacterium (b D ) to recipient Petri dish (p R ) and bacterium (b R ). In the figure, P is the total number of Petri dishes (or sub-populations), N is the number of bacteria (or population size) per Petri dish and re the number of experimental replicates.
Multiple bacterial colonies (or Petri dishes) are communicated via bacteriophages, cycling through generations searching for an optimum solution during G generations.
AM radio receiver experiment with transduction transferring chromosome segments. Note how this kind of simulation experiment is an example of specialized transduction, where only three possible chromosome segments can be transferred by bacteriophages (for explanation see [Perales-Gravan and Lahoz-Beltra, 2008]).
Bacterial conjugation operator. Once a pair of chromosomes i and j (or bacteria, D=donor, R=recipient) are selected from the same population (or Petri dish), the gene transfer occurs from a random point ie on the donor chromosome i (O=chromosome origin). Since transfer of the donor chromosome is almost never complete, then the length of the strand (a copy) transferred to the recipient cell R is simulated with the Monte Carlo method, assuming DNA lengths exponentially distributed with a parameter α (conjugation parameter). Finally, the transferred strand experiences crossover, resulting a recombinant chromosome j in bacterium R.
AM radio receiver experiment:

Statistical analysis
The simulation experiments performance was evaluated as follows [Lahoz-Beltra and Perales-Gravan, 2010]. In first place, we obtained the average fitness of each Petri dish at the last generation G. Considering that P is the total number of Petri dishes and re the number of experimental replicates, then the total number of simulation trials was equal to P. re. Subsequently, a Multiple Box-and-Whisker Plot [Tukey, 1977] was obtained with the average fitness values, considering that each plot represents an experimental protocol with P. re values. Note that we used a Notched Box-and-Whisker Plot. In this plot, a confidence interval for the median is provided by a notch surrounding the median. The endpoints of the notches are located at the median 1. Furthermore, since the length of the box representing the interquartile range is a measure of variability, given two experimental protocols, that protocol with the longest box will be the protocol driving the population to reach a higher number of optimum solutions [Perales-Gravan and Lahoz-Beltra, 2008].
Only in experiment 3 did we calculate the mean of the average fitness values, but now taking into account the Petri dish class. Thus, we obtained MAF values for the donor Petri dishes (MAFD), the recipient Petri dishes (MAFR) and for the dishes that were neither recipients nor donors (MAF D R ): where D is the number of donor Petri dishes and R the number of recipient Petri dishes.
Note that in all the optimization problems (thus, the simulation experiments) D=R, D and R being equal to 1. Therefore, we selected only one donor and recipient Petri dish per generation.