Evolutionary graph theory has grown to be an area of intense study. Despitethe amount of interest in the field, it seems to have grown separate from othersubfields of population genetics and evolution. In the current work I introducethe concept of Fisher's (1930) reproductive value into the study of evolutionon graphs. Reproductive value is a measure of the expected genetic contributionof an individual to a distant future generation. In a heterogeneousgraph-structured population, differences in the number of connections amongindividuals translates into differences in the expected number of offspring,even if all individuals have the same fecundity. These differences areaccounted for by reproductive value. The introduction of reproductive valuepermits the calculation of the fixation probability of a mutant in a neutralevolutionary process in any graph-structured population for either the moranbirth-death or death-birth process.
We derive formulas to compute mean number of worms in a newly Helminthinfected population before secondary infections are started (population isclosed). We have proved the two types of growth functions arise in this processas measurable functions.
Sexual reproduction in Nature requires two sexes, which raises the questionwhy the reproductive scheme did not evolve to have three or more sexes. Here weconstruct a constrained optimization model based on the communication theory toanalyze trade-offs among reproductive schemes with arbitrary number of sexes.More sexes on one hand lead to higher reproductive diversity, but on the otherhand incur greater cost in time and energy for reproductive success. Our modelshows that the two-sexes reproduction scheme maximizes the recombinationentropy-to-cost ratio, and hence is the optimal solution to the problem.
At the end of the first larval stage, the C elegans larva chooses between twodevelopmental pathways, an L2 committed to reproductive development and an L2d,which has the option of undergoing reproductive development or entering thedauer diapause. I develop a quantitative model of this choice usingmathematical tools developed for pricing financial options. The model predictsthat the optimal decision must take into account not only the expectedpotential for reproductive growth, but also the uncertainty in that expectedpotential. Because the L2d has more flexibility than the L2, it is favored inunpredictable environments. I estimate that the ability to take uncertaintyinto account may increase reproductive value by as much as 5%, and discusspossible experimental tests for this ability.
Many human males produce dysfunctional sperm. Various plants frequently abortpollen. Hybrid matings often produce sterile males. Widespread male sterilityis puzzling. Natural selection prunes reproductive failure. Puzzling failureimplies something that we do not understand about how organisms are designed.Solving the puzzle reveals the hidden processes of design.
Cultural transmission of reproductive success states that successful men havemore children and pass this greater fecundity to their offspring. Balaresqueand colleagues found high frequency haplotypes in a Central Asian Y chromosomedataset, which they attribute to cultural transmission of reproductive successby prominent historical men, including Genghis Khan. Using coalescentsimulation, we show that these high frequency haplotypes are expected simply bychance. Hence, an explanation invoking cultural transmission of reproductivesuccess is statistically unnecessary.
My analysis uses methods developed for data mining microarray experiments,adapted for ageing research. Methods bridge knowledge of statistical mechanicswith data mining methods developed in statistical mathematics. Analyses canreveal how the transcriptional regulation of genes might coincide, therebyimplicating proteins as parts of networks acting together towards a commonbiological function. Such experiments are most useful for complex biologicaltraits that result from the presumed functioning of several molecular pathways.Ageing is one such biological phenomenon that apparently incorporates numerousmolecular mechanisms underlying environmental stimulus sensing, metabolicregulation, stress responses, reproductive signalling, hibernation, andtranscriptional regulation.
Sexual reproductive behavior has a necessary social coordination component aswilling and capable partners must both be in the right place at the right time.It has recently been demonstrated that many social organizations that supportsexual reproduction can evolve in the absence of social coordination betweenagents (e.g. herding, assortative mating, and natal philopatry). In this paperwe explore these results by including social transfer mechanisms to our agentsand contrasting their reproductive behavior with a control group without socialtransfer mechanisms. We conclude that similar behaviors emerge in our sociallearning agents as those that emerged in the non-social learning agents. Sociallearners were more inclined towards natal philopatry. Social learners alsoevolved a culture of eusociality including reproductive division of labor.
We model a general, hierarchically organized tissue by a multi compartmentapproach, allowing any number of mutations within a cell. We derive closedsolutions for the deterministic clonal dynamics and the reproductive capacityof single clones. Our results hold for the average dynamics in a hierarchicaltissue characterized by an arbitrary combination of proliferation parameters.
Many studies have analyzed how variability in reproductive success affectsfitness. However, each study tends to focus on a particular problem, leavingunclear the overall structure of variability in populations. This fracturedconceptual framework often causes particular applications to be incomplete orimproperly analyzed. In this paper, I present a concise introduction to the twokey aspects of the theory. First, all measures of fitness ultimately arise fromthe relative comparison of the reproductive success of individuals or genotypeswith the average reproductive success in the population. That relative measurecreates a diminishing relation between reproductive success and fitness.Diminishing returns reduce fitness in proportion to variability in reproductivesuccess. The relative measurement of success also induces a frequencydependence that favors rare types. Second, variability in populations has ahierarchical structure. Variable success in different traits of an individualaffects that individual's variation in reproduction. Correlation betweendifferent individuals' reproduction affects variation in the aggregate successof particular alleles across the population. One must consider the hierarchicalstructure of variability in relation to different consequences of temporal,spatial, and developmental variability. Although a complete analysis ofvariability has many separate parts, this simple framework allows one to seethe structure of the whole and to place particular problems in their properrelation to the general theory. The biological understanding of relativesuccess and the hierarchical structure of variability in populations may alsocontribute to a deeper economic theory of returns under uncertainty.