The maintenance of heritable variation through social competition

The paradoxical persistence of heritable variation for fitness-related traits is an evolutionary conundrum that remains a preeminent problem in evolutionary biology. Here we describe a simple mechanism in which social competition results in the evolutionary maintenance of heritable variation for fitness related traits. We demonstrate this mechanism using a genetic model with two primary assumptions: the expression of a trait depends upon success in social competition for limited resources; and competitive success of a genotype depends on the genotypes that it competes against. We find that such social competition generates heritable (additive) genetic variation for "competition-dependent" traits. This heritable variation is not eroded by continuous directional selection because, rather than leading to fixation of favored alleles, selection leads instead to allele frequency cycling due to the concerted coevolution of the social environment with the effects of alleles. Our results provide a mechanism for the maintenance of heritable variation in natural populations and suggest an area for research into the importance of competition in the genetic architecture of fitness related traits.     

The capture of heritable variation for genetic quality through social competition

In theory, females of many species choose mates based on traits that are indicators of male genetic quality. A fundamental question in evolutionary biology is why genetic variation for such indicator traits persists despite strong persistent selection imposed by female preference, which is known as the lek paradox. One potential solution to the lek paradox suggests that the traits that are targets of mate choice should evolve condition-dependent expression and that condition should have a large genetic variance. Condition is expected to exhibit high genetic variance because it is affected by a large number of physiological processes and hence, condition-dependent traits should 'capture' variation contributed by a large number of loci. We suggest that a potentially important cause of variation in condition is competition for limited resources. Here, we discuss a pair of models to analyze the evolutionary genetics of traits affected by success in social competition for resources. We show that competition can contribute to genetic variation of 'competition-dependent' traits that have fundamentally different evolutionary properties than other sources of variation. Competition dependence can make traits honest indicators of genetic quality by revealing the relative competitive ability of males, can provide a component of heritable variation that does not contribute to trait evolution, and can help maintain heritable variation under directional selection. Here we provide a general introduction to the concept of competition dependence and briefly introduce two models to demonstrate the potential evolutionary consequences of competition-dependent trait expression.     

Spreading of healthy mood in adolescent social networks

Depression is a major public health concern worldwide. There is evidence that social support and befriending influence mental health, and an improved understanding of the social processes that drive depression has the potential to bring significant public health benefits. We investigate transmission of mood on a social network of adolescents, allowing flexibility in our model by making no prior assumption as to whether it is low mood or healthy mood that spreads. Here, we show that while depression does not spread, healthy mood among friends is associated with significantly reduced risk of developing and increased chance of recovering from depression. We found that this spreading of healthy mood can be captured using a non-linear complex contagion model. Having sufficient friends with healthy mood can halve the probability of developing, or double the probability of recovering from, depression over a 6–12-month period on an adolescent social network. Our results suggest that promotion of friendship between adolescents can reduce both incidence and prevalence of depression.     

Spreading speed and linear determinacy for two-species competition models

 One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper [11]. Received: 7 August 2000 / Revised version: 5 January 2002 / Published online: 17 July 2002     

Spreading disease with transport-related infection

Transportation among regions is found as one of the main factors which affect the outbreak of diseases. It will change the disease dynamics and break infection out even if infectious diseases will go to extinction in each city without transport-related infection. In this paper, a mathematical model is proposed to demonstrate the dynamics of such disease propagation between two regions (or cities) due to the population dispersal and infection on transports. Further, our analysis shows that transport-related infection intensifies the disease spread if infectious diseases break out to cause an endemic situation in each region, in the sense that both the absolute and relative size of patients increase. This suggests that it is very essential to strengthen restrictions of passengers once we know infectious diseases appeared.     

Evolutionary dynamics through multispecies competition

Disruptive selection, emerging from frequency-dependent intraspecific competition can have very exciting evolutionary outcomes. One such outcome is the origin of new species through an evolutionary branching event. Literature on theoretical models investigating the emergence of disruptive selection is vast, with some investigating the sensitivity of the models on assumptions of the competition and carrying capacity functions’ shapes. What is seldom modeled is what happens once the population escapes its effect via increase phenotypic or genotypic variance. The expectation is mixed: disruptive selection could diminish and ultimately disappear or it could still exist leading to further speciation events through multiple evolutionary branching events. Here, we derive the conditions under which disruptive selection drives two subpopulations that originated at a branching point to other points in trait space where each subpopulation again experiences disruptive selection. We show that the general pattern for further branchings require that the competition function to be even narrower than what is required for the first evolutionary branching. However, we also show that the existence of disruptive selection in higher dimensional systems is also sensitive to the shapes of the functions used.     

Androgen response to social competition in a shoaling fish

Androgens respond to social challenges and this response has been interpreted as a way for males to adjust androgen-dependent behavior to social context. However, the androgen responsiveness to social challenges varies across species and a conceptual framework has been developed to explain this variation according to differences in the mating system and parental care type, which determines the regimen of challenges males are exposed to, and concomitantly the scope (defined as the difference between the physiological maximum and the baseline levels) of response to a social challenge. However, this framework has been focused on territorial species and no clear predictions have been made to gregarious species (e.g. shoaling fish), which although tolerating same-sex individuals may also exhibit intra-sexual competition. In this paper we extend the scope of this conceptual framework to shoaling fish by studying the endocrine response of zebrafish (Danio rerio) to social challenges. Male zebrafish exposed to real opponent agonistic interactions exhibited an increase in androgen levels (11-ketotestosterone both in Winners and Losers and testosterone in Losers). This response was absent in Mirror-fighters, that expressed similar levels of aggressive behavior to those of winners, suggesting that this response is not a mere reflex of heightened aggressive motivation. Cortisol levels were also measured and indicated an activation of the hypothalamic–pituitary–interrenal axis in Winners of real opponent fighters, but not Losers or in Mirror-fighters. These results confirm that gregarious species also exhibit an endocrine response to an acute social challenge.     

Reductional groupings in cold-treated onion roots

Summary In roots which had been kept for ten days at 5–6°C the observed frequency of metaphase and anaphase reductional groupings (R. G’s) was lower, that of prophase R. G’s higher, than in simultaneously fixed roots kept at 21–22°C. The frequency of R. G’s can undergo considerable changes independent of temperature. It appears highly likely that a process of somatic reduction may start from R. G’s but its successful conclusion would be, at least in onion, a very rare event. In the present material the probability of a mitosis becoming a R. G. that finally leads to a haploid cell with a complete genome is almost certainly less than 10⁻⁵ and more likely less than 10⁻⁶. Contribution from the Programme in Cytology, Department of Botany, University of Wisconsin, Madison, supported by grants to late Dr.C. Leonard Huskins from the American Cancer Society upon recommendation of the Committee on Growth of the National Research Council, from the Rockefeller Foundation and from the Research Committee of the Graduate School with funds supplied by the Wisconsin Alumni Research Foundation.     

Dynamics of a disinhibitory prefrontal microcircuit in controlling social competition

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Evolution of species trait through resource competition

To understand the evolution of diverse species, theoretical studies using a Lotka–Volterra type direct competition model had shown that concentrated distributions of species in continuous trait space often occurs. However, a more mechanistic approach is preferred because the competitive interaction of species usually occurs not directly but through competition for resource. We consider a chemostat-type model where species consume resource that are constantly supplied. Continuous traits in both consumer species and resource are incorporated. Consumers utilize resource whose trait values are similar with their own. We show that, even when resource-supply has a continuous distribution in trait space, a positive continuous distribution of consumer trait is impossible. Self-organized generation of distinct species occurs. We also prove global convergence to the evolutionarily stable distribution.     

The conditions for speciation through intraspecific competition

Abstract It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency‐dependent selection caused by a balance of intraspecific competition and frequency‐independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment sometimes none at all. In addition to the strength of frequency‐dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.     

Optimization of oncogene expression through intra-population competition

Although functional roles have been assigned to many genes, e.g. those involved in cell-cycle regulation, growth signaling, or cancer, considerably less is known about the quantitative relationship between gene expression levels and outcome. We devised an intra-population competition to study oncogene dosage. Cell populations were engineered to express a range of H-Ras oncogene levels. Cells with different levels of H-Ras then “competed” for an increased share of the total cell population. Using flow cytometry to track the population composition over time, we determined the relationship between the different H-Ras oncogene expression levels and the net proliferation rate. Under culture conditions in which wild-type Ras activation was suppressed, we found that increased and maximal net proliferation occurred when the H-Ras G12V oncogene was expressed at a level 1.2-fold that of wild-type Ras. As the H-Ras G12V expression levels increased above this optimal level, proliferation rates decreased. Our findings suggest that the tumor evolution process may optimize gene expression levels for maximal cell proliferation. In principle, engineered intra-population competitions can be used to determine proliferation rates associated with the level of any ectopically expressed gene. The approach also may be used to determine proliferation rates associated with different cell species in a heterogeneous population or to improve the proliferation rate of a cell line. We also envision that the tracking of intra-population competitions could be utilized to investigate the evolution of tumors in the body.     

Speciation through competition: a critical review

We examined causes of speciation in asexual populations in both sympatry and parapatry, providing an alternative explanation for the speciation patterns reported by Dieckmann and Doebeli (1999) and Doebeli and Dieckmann (2003). Both in sympatry and parapatry, they find that speciation occurs relatively easily. We reveal that in the sympatric clonal model, the equilibrium distribution is continuous and the disruptive selection driving evolution of discrete clusters is only transient. Hence, if discrete phenotypes are to remain stable in the sympatric sexual model, there should be some source of nontransient disruptive selection that will drive evolution of assortment. We analyze sexually reproducing populations using the Bulmer's infinitesimal model and show that cost-free assortment alone leads to speciation and disruptive selection only arises when the optimal distribution cannot be matched--in this example, because the phenotypic range is limited. In addition, Doebeli and Dieckmann's analyses assumed a high genetic variance and a high mutation rate. Thus, these theoretical models do not support the conclusion that sympatric speciation is a likely outcome of competition for resources. In their parapatric model (Doebeli and Dieckmann 2003), clustering into distinct phenotypes is driven by edge effects, rather than by frequency-dependent competition.     

Spreading disease: integro-differential equations old and new

We investigate an integro-differential equation for a disease spread by the dispersal of infectious individuals and compare this to Mollison's [Adv. Appl. Probab. 4 (1972) 233; D. Mollison, The rate of spatial propagation of simple epidemics, in: Proc. 6th Berkeley Symp. on Math. Statist. and Prob., vol. 3, University of California Press, Berkeley, 1972, p. 579; J. R. Statist. Soc. B 39 (3) (1977) 283] model of a disease spread by non-local contacts. For symmetric kernels with moment generating functions, spreading infectives leads to faster traveling waves for low rates of transmission, but to slower traveling waves for high rates of transmission. We approximate the shape of the traveling waves for the two models using both piecewise linearization and a regular-perturbation scheme.