A NOTE ON STABILITY AND CONVERGENCE OF GENETIC SYSTEMS

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).

Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

Other than maintaining genome stability via DNA repair, homologous recombination plays an important role in diversifying the genome. In fact, the recombination of sequences forms the molecular basis of genomic evolution. Random and non-random permutations of genomic sequences create a library of new amalgamated sequences. These newly formed genomes can determine the fitness and survival of cells. In bacteria, homologous and non-homologous types of recombination lead to the evolution of new...

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....