S A Frank

Publications of S A Frank

• Natural selection. III. Selection versus transmission and the levels of selection.

  Authors: S A Frank

  Journal of evolutionary biology. 12/2011; 25(2):227-43.

  George Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In thisGeorge Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In this article, I extend Williams' approach to show that the ratio of selection bias to transmission bias provides a unifying framework for diverse biological problems. Specific examples include Haldane and Lande's mutation-selection balance, Eigen's error threshold and quasispecies, Van Valen's clade selection, Price's multilevel formulation of group selection, Szathmáry and Demeter's evolutionary origin of primitive cells, Levin and Bull's short-sighted evolution of HIV virulence, Frank's timescale analysis of microbial metabolism and Maynard Smith and Szathmáry's major transitions in evolution. The insights from these diverse applications lead to a deeper understanding of kin selection, group selection, multilevel evolutionary analysis and the philosophical problems of evolutionary units and individuality.

• Natural selection. II. Developmental variability and evolutionary rate.

  Authors: S A Frank

  Journal of evolutionary biology. 09/2011; 24(11):2310-20.

  In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories haveIn classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and learning enhance nonheritable phenotypic variation, which in turn can accelerate evolutionary response. In this paper, I show how developmental variability alters evolutionary dynamics by smoothing the landscape that relates genotype to fitness. In a fitness landscape with multiple peaks and valleys, developmental variability can smooth the landscape to provide a directly increasing path of fitness to the highest peak. Developmental variability also allows initial survival of a genotype in response to novel or extreme environmental challenge, providing an opportunity for subsequent adaptation. This initial survival advantage arises from the way in which developmental variability smooths and broadens the fitness landscape. Ultimately, the synergism between developmental processes and genetic variation sets evolutionary rate.

• Natural selection. I. Variable environments and uncertain returns on investment.

  Authors: S A Frank

  Journal of evolutionary biology. 09/2011; 24(11):2299-309.

  Many studies have analysed how variability in reproductive success affects fitness. However, each study tends to focus on a particular problem, leaving unclear the overall structure of variability inMany studies have analysed how variability in reproductive success affects fitness. However, each study tends to focus on a particular problem, leaving unclear the overall structure of variability in populations. This fractured conceptual framework often causes particular applications to be incomplete or improperly analysed. In this article, I present a concise introduction to the two key aspects of the theory. First, all measures of fitness ultimately arise from the relative comparison of the reproductive success of individuals or genotypes with the average reproductive success in the population. That relative measure creates a diminishing relation between reproductive success and fitness. Diminishing returns reduce fitness in proportion to variability in reproductive success. The relative measurement of success also induces a frequency dependence that favours rare types. Second, variability in populations has a hierarchical structure. Variable success in different traits of an individual affects that individual's variation in reproduction. Correlation between different individuals' reproduction affects variation in the aggregate success of particular alleles across the population. One must consider the hierarchical structure of variability in relation to different consequences of temporal, spatial and developmental variability. Although a complete analysis of variability has many separate parts, this simple framework allows one to see the structure of the whole and to place particular problems in their proper relation to the general theory. The biological understanding of relative success and the hierarchical structure of variability in populations may also contribute to a deeper economic theory of returns under uncertainty.

• A simple derivation and classification of common probability distributions based on information symmetry and measurement scale.

  Authors: S A Frank, E Smith

  Journal of evolutionary biology. 03/2011; 24(3):469-84.

  Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of theCommonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His approach was phenomenological: a differential equation that generated common distributions without any underlying conceptual basis for why common distributions have particular forms and what explains the familial relations. Pearson's system and its descendants remain the most popular systematic classification of probability distributions. Here, we unify the disparate forms of common distributions into a single system based on two meaningful and justifiable propositions. First, distributions follow maximum entropy subject to constraints, where maximum entropy is equivalent to minimum information. Second, different problems associate magnitude to information in different ways, an association we describe in terms of the relation between information invariance and measurement scale. Our framework relates the different continuous probability distributions through the variations in measurement scale that change each family of maximum entropy distributions into a distinct family. From our framework, future work in biology can consider the genesis of common patterns in a new and more general way. Particular biological processes set the relation between the information in observations and magnitude, the basis for information invariance, symmetry and measurement scale. The measurement scale, in turn, determines the most likely probability distributions and observed patterns associated with particular processes. This view presents a fundamentally derived alternative to the largely unproductive debates about neutrality in ecology and evolution.

• Measurement scale in maximum entropy models of species abundance.

  Authors: S A Frank

  Journal of evolutionary biology. 03/2011; 24(3):485-96.

  The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverseThe consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.

• A general model of the public goods dilemma.

  Authors: Steven A Frank

  Journal of evolutionary biology. 03/2010; 23(6):1245-50.

  An individually costly act that benefits all group members is a public good. Natural selection favours individual contribution to public good [corrected] only when some benefit to the individualAn individually costly act that benefits all group members is a public good. Natural selection favours individual contribution to public good [corrected] only when some benefit to the individual offsets the cost of contribution. Problems of sex ratio, parasite virulence, microbial metabolism, punishment of noncooperators, and nearly all aspects of sociality have been analysed as public goods shaped by kin and group selection. Here, I develop two general aspects of the public goods problem that have received relatively little attention. First, variation in individual resources favours selfish individuals to vary their allocation to public goods. Those individuals better endowed contribute their excess resources to public benefit, whereas those individuals with fewer resources contribute less to the public good. Thus, purely selfish behaviour causes individuals to stratify into upper classes that contribute greatly to public benefit and social cohesion and to lower classes that contribute little to the public good. Second, if group success absolutely requires production of the public good, then the pressure favouring production is relatively high. By contrast, if group success depends weakly on the public good, then the pressure favouring production is relatively weak. Stated in this way, it is obvious that the role of baseline success is important. However, discussions of public goods problems sometimes fail to emphasize this point sufficiently. The models here suggest simple tests for the roles of resource variation and baseline success. Given the widespread importance of public goods, better models and tests would greatly deepen our understanding of many processes in biology and sociality.

• The trade-off between rate and yield in the design of microbial metabolism.

  Authors: S A Frank

  Journal of evolutionary biology. 03/2010; 23(3):609-13.

  Extra energy devoted to resource acquisition speeds metabolic rate, but reduces the net yield of energy. In direct competition, microbial strains with high rates of resource acquisition oftenExtra energy devoted to resource acquisition speeds metabolic rate, but reduces the net yield of energy. In direct competition, microbial strains with high rates of resource acquisition often outcompete strains with slower resource acquisition but higher yield, reducing the net output of the group. Here, I use mathematical models to analyse the genetic and demographic factors that tip the balance toward either rate or yield. My models clarify the widely discussed roles of kin selection and the spatial structure of populations. I also emphasize the strong effect of two previously ignored factors: demographic aspects of colony survival and reproduction strongly shape the design of metabolic rate and efficiency, and competitive mutants within long-lived colonies favour rate over yield, degrading the efficiency of the population.

• Natural selection maximizes Fisher information.

  Authors: S A Frank

  Journal of evolutionary biology. 12/2008;

  Abstract In biology, information flows from the environment to the genome by the process of natural selection. However, it has not been clear precisely what sort of information metric properlyAbstract In biology, information flows from the environment to the genome by the process of natural selection. However, it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher information arises as the intrinsic metric of natural selection and evolutionary dynamics. Maximizing the amount of Fisher information about the environment captured by the population leads to Fisher's fundamental theorem of natural selection, the most profound statement about how natural selection influences evolutionary dynamics. I also show a relation between Fisher information and Shannon information (entropy) that may help to unify the correspondence between information and dynamics. Finally, I discuss possible connections between the fundamental role of Fisher information in statistics, biology and other fields of science.

• Mechanisms of pathogenesis and the evolution of parasite virulence.

  Authors: S A Frank, P Schmid-Hempel

  Journal of evolutionary biology. 04/2008; 21(2):396-404.

  When studying how much a parasite harms its host, evolutionary biologists turn to the evolutionary theory of virulence. That theory has been successful in predicting how parasite virulence evolves inWhen studying how much a parasite harms its host, evolutionary biologists turn to the evolutionary theory of virulence. That theory has been successful in predicting how parasite virulence evolves in response to changes in epidemiological conditions of parasite transmission or to perturbations induced by drug treatments. The evolutionary theory of virulence is, however, nearly silent about the expected differences in virulence between different species of parasite. Why, for example, is anthrax so virulent, whereas closely related bacterial species cause little harm? The evolutionary theory might address such comparisons by analysing differences in tradeoffs between parasite fitness components: transmission as a measure of parasite fecundity, clearance as a measure of parasite lifespan and virulence as another measure that delimits parasite survival within a host. However, even crude quantitative estimates of such tradeoffs remain beyond reach in all but the most controlled of experimental conditions. Here, we argue that the great recent advances in the molecular study of pathogenesis provide a way forward. In light of those mechanistic studies, we analyse the relative sensitivity of tradeoffs between components of parasite fitness. We argue that pathogenic mechanisms that manipulate host immunity or escape from host defences have particularly high sensitivity to parasite fitness and thus dominate as causes of parasite virulence. The high sensitivity of immunomodulation and immune escape arise because those mechanisms affect parasite survival within the host, the most sensitive of fitness components. In our view, relating the sensitivity of pathogenic mechanisms to fitness components will provide a way to build a much richer and more general theory of parasite virulence.

• Programmed Cell Death and Hybrid

  Authors: S. A. Frank, C. M. Barr

  12/2003;

  t way. Distinct polymorphic sets of mitochondrial and nuclear genes coexist, each set with mitochondrial destruction of pollen production and matching nuclear repression of mitochondrial action. Thet way. Distinct polymorphic sets of mitochondrial and nuclear genes coexist, each set with mitochondrial destruction of pollen production and matching nuclear repression of mitochondrial action. The matching mitochondrial and nuclear polymorphisms arise from the conflicting patterns of transmission between mitochondrial and nuclear genes (Frank 2000). Mitochondria typically transmit only through seeds and not through pollen. Matrilineally transmitted mitochondria increase their fitness by pollen abortion and enhanced seed production, whereas biparentally inherited nuclear genes favor a balance of pollen and seeds. The polymorphisms from this reproductive conflict are much like the matching polymorphisms of attack and defense that often occur in host-parasite systems. Morphological signs of tapetal deterioration have been observed in several male-sterile species. The maize mitochondrial gene T-urf13 expresses a protein that results in early tapetal degeneration soon after microspore me

• Genetic variation of polygenic characters and the evolution of genetic degeneracy.

  Authors: S A Frank

  Journal of evolutionary biology. 02/2003; 16(1):138-42.

  The classical model of mutation-selection balance for quantitative characters sums the effects of individual sites to determine overall character value. I develop an alternative version of thisThe classical model of mutation-selection balance for quantitative characters sums the effects of individual sites to determine overall character value. I develop an alternative version of this classical model in which character value depends on the averaging of the effects of the individual sites. In this new averaging model, the equilibrium patterns of variance in allelic effects and character values change with the number of sites that affect a character in a different way from the classical model of summing effects. Besides changing the patterns of variance, the averaging model favours the addition of loci to the control of character values, perhaps explaining in part the recent observation of widespread genetic degeneracy.

• Multiplicity of infection and the evolution of hybrid incompatibility in segmented viruses.

  Authors: S A Frank

  Heredity. 12/2001; 87(Pt 5):522-9.

  Some viral genomes are divided into segments. When multiple viruses infect a single cell, progeny form by reassorted mixtures of genomic segments. Hybrid incompatibilities arise when a progeny virusSome viral genomes are divided into segments. When multiple viruses infect a single cell, progeny form by reassorted mixtures of genomic segments. Hybrid incompatibilities arise when a progeny virus has incompatible segments from different parental viruses. Hybrid incompatibility has been observed in influenza and in the multiparticle plant virus Dianthovirus. Hybrid incompatibility provides an opportunity to study rates of viral evolution, divergence and speciation, and the extent of epistatic interactions among components of the viral genome. This paper presents mathematical and computer simulation models to study hybrid incompatibility between diverging strains. The models identify multiplicity of infection as a key factor. When many viral particles infect each host cell, the effective ploidy of the genetic system is high. High ploidy dilutes the contribution of each locus to the phenotype, weakening the selective intensity on each locus. Weaker selection on variant alleles allows the population to maintain greater genetic diversity and to be more easily perturbed by stochastic fluctuations. Greater diversity and stochastic fluctuations explore more widely the space of epistatic interactions, causing more frequent shifts among favoured combinations of alleles. Variable ploidy of viral genetics differs from standard Mendelian genetics.

• The probability of severe disease in zoonotic and commensal infections.

  Authors: S A Frank, J S Jeffrey

  Proceedings. Biological sciences / The Royal Society. 02/2001; 268(1462):53-60.

  Cross-species transfers of pathogens (zoonoses) cause some of the most virulent diseases, including anthrax, hantavirus and Q fever. Zoonotic infections occur when a pathogen moves from its reservoirCross-species transfers of pathogens (zoonoses) cause some of the most virulent diseases, including anthrax, hantavirus and Q fever. Zoonotic infections occur when a pathogen moves from its reservoir host species into a secondary host species. Similarly, commensal infections often have a primary reservoir location within their hosts' bodies from which they rarely cause disease symptoms, but commensals such as Neisseria meningitidis cause severe disease when they cross into a different body compartment from their normal location. Both zoonotic and commensal infections cause either mild symptoms or severe disease, but rarely intermediate symptoms. We develop a mathematical model for studying three factors that affect the probability of severe disease: the size of the inoculum, the route of inoculation and the frequency of naturally occurring infections that do not cause symptoms but do induce protective immunity (vaccinating inoculations). With a single route of infection, increasing pathogen density causes inoculations to develop more often into disease rather than asymptomatic vaccinations that provide protective immunity. With two routes of infection, it may happen that a lower density of a pathogen or of a particular antigenic variant leads to a relatively higher frequency of disease-inducing versus vaccinating inoculations. This reversal occurs when one route of infection tends to vaccinate against relatively common pathogens but less often vaccinates against relatively rare pathogens, whereas the other route of infection is susceptible to disease-inducing inoculation even at relatively low pathogen density.

• Within-host spatial dynamics of viruses and defective interfering particles.

  Authors: S A Frank

  Journal of theoretical biology. 10/2000; 206(2):279-90.

  Defective-interfering (DI) viruses arise spontaneously by deletion mutations. The shortened genomes of the DI particles cannot replicate unless they coinfect a cell with a wild-type virus. UponDefective-interfering (DI) viruses arise spontaneously by deletion mutations. The shortened genomes of the DI particles cannot replicate unless they coinfect a cell with a wild-type virus. Upon coinfection, the DI genome replicates more quickly and outcompetes the wild type. The coinfected cell produces mostly DI viruses. At the population level, the abundances of DI and wild-type viruses fluctuate dramatically under some conditions. In other cases, the DI viruses appear to mediate persistent infections with relatively low levels of host cell death. This moderation of viral damage has led some to suggest DI particles as therapeutic agents. Previous mathematical models have shown that either fluctuation or persistence can occur for plausible parameter values. I develop new mathematical models for the population dynamics of DI and wild-type viruses. My work extends the theory by developing specific predictions that can be tested in the laboratory. These predictions, if borne out by experiment, will explain the key processes that control the diversity of observed outcomes. The most interesting prediction concerns the rate at which killed host cells are replaced. A low rate of replacement causes powerful epidemics followed by a crash in viral abundance. As the rate of replacement increases, the frequency of oscillations increases in DI and wild-type viral abundances, but the severity (amplitude) of the fluctuations declines. At higher replacement rates for host cells, nearly all cells become infected by DI particles and a low level of fluctuating, wild-type viremia persists.

• Specific and non-specific defense against parasitic attack.

  Authors: S A Frank

  Journal of theoretical biology. 03/2000; 202(4):283-304.

  Specific defense protects against some parasite genotypes but not others, whereas non-specific defense is effective against all genotypes of a parasite. Some empirical studies observe hosts withSpecific defense protects against some parasite genotypes but not others, whereas non-specific defense is effective against all genotypes of a parasite. Some empirical studies observe hosts with variability only in non-specific defense, other studies find only specific defense. I analyse a model with combined specific and non-specific defense to determine the conditions that favor detectable variation in each form of defense. High variation in non-specific defense is often maintained when resistance increases in an accelerating way with investment, whereas low variation tends to occur when resistance increases at a decelerating rate with investment. Variation in specific defense rises as the parasite pays a higher cost to attack a broad host range (high cost of virulence), as the number of alternative specificities declines, and as the average level of non-specific defense increases. The last condition occurs because greater non-specific protection tends to stabilize the gene frequency dynamics of specific defense. Selection favors a negative association between costly components of specific and non-specific defense-hosts defended by one component are favored if they have reduced allocation to other costly components. A negative association confounds the measurement of costs of resistance. Individuals with specific defense may have reduced investment in costly non-specific defense. This leads to an apparent advantage of specifically defended hosts in the absence of parasites and a measured cost of resistance that is negative.

• A model for the sequential dominance of antigenic variants in African trypanosome infections.

  Authors: S A Frank

  Proceedings. Biological sciences / The Royal Society. 08/1999; 266(1426):1397-401.

  Trypanosoma brucei infects various domestic and wild mammals in equatorial Africa. The parasite's genome contains several hundred alternative and highly diverged surface antigens, of which only aTrypanosoma brucei infects various domestic and wild mammals in equatorial Africa. The parasite's genome contains several hundred alternative and highly diverged surface antigens, of which only a single one is expressed in any cell. Individual cells occasionally change expression of their surface antigen, allowing them to escape immune surveillance. These switches appear to occur in a partly random way, creating a diverse set of antigenic variants. In spite of this diversity, the parasitaemia develops as a series of outbreaks, each outbreak dominated by relatively few antigenic types. Host-specific immunity eventually clears the dominant antigenic types and a new outbreak follows from antigenic types that have apparently been present all along at low frequency. This pattern of sequential dominance by different antigenic types remains unexplained. I use a mathematical model of parasitaemia and host immunity to show that small variations in the rate at which each type switches to other types can explain the observations. My model shows that randomly chosen switch rates do not provide sufficiently ordered parasitaemias to match the observations. Instead, minor modifications of switch rates by natural selection are required to develop a sequence of ordered parasitaemias.

• Population and quantitative genetics of regulatory networks.

  Authors: S A Frank

  Journal of theoretical biology. 05/1999; 197(3):281-94.

  I evolved boolean regulatory networks in a computer simulation. I varied mutation, recombination, the size of the network, and the number of connections per node. I measured the performance ofI evolved boolean regulatory networks in a computer simulation. I varied mutation, recombination, the size of the network, and the number of connections per node. I measured the performance of networks and the heritability and epistasis of genetic effects. Networks of intermediate connectivity performed best. The distinction between metabolic and quantitative genetic additivity explained some of the variation in performance. Metabolic additivity describes the interaction between changes in a single network, whereas quantitative genetic additivity measures the consistency of phenotypic effect caused by gene substitution in randomly chosen members of the population. I analysed metabolic additivity by the distribution of epistatic effects of pairs of mutations in individual networks. I measured quantitative genetic additivity by heritability. Highly connected networks had greater metabolic additivity for perturbations to individual networks, but had lower additivity when measured by the average effect of a gene substitution (heritability). The lower heritability of highly connected nets appeared to reduce the effectiveness of recombination in searching evolutionary space.

• Inducible defence and the social evolution of herd immunity.

  Authors: S A Frank

  Proceedings. Biological sciences / The Royal Society. 11/1998; 265(1408):1911-3.

  Many organisms vary their level of investment in defensive characters. Protective traits may be induced upon exposure to predators or parasites. In a similar way, humans vaccinate in response toMany organisms vary their level of investment in defensive characters. Protective traits may be induced upon exposure to predators or parasites. In a similar way, humans vaccinate in response to threatening epidemics. When most group members defend themselves, epidemics die out quickly because parasites cannot spread. A high level of group (herd) immunity is therefore beneficial to the group. There is, however, a well-known divergence between the optimum degree of induction for selfish individuals and the level of induction that maximizes group benefit. I develop two optimality models for the frequency of induction. The first model shows that higher relatedness favours more induction and a smaller difference between selfish and cooperative optima. The second model assumes variation in the vigour of individuals and therefore differences in the relative cost for induction. The model predicts that strong individuals induce more easily than weak individuals. Small differences in vigour cause a large divergence in the optimal levels of induction for strong and weak individuals. The concept of genetic relatedness in an evolutionary model is analogous to correlated interests and correlated strategies in an economic model of human behaviour. The evolutionary models presented here therefore provide a basis for further study of human vaccination.

• Multivariate analysis of correlated selection and kin selection, with an ESS maximization method.

  Authors: S A Frank

  Journal of theoretical biology. 01/1998; 189(3):307-16.

  Kin selection coefficients are used in two distinct ways. First, these coefficients measure phenotypic correlations that affect the marginal costs and benefits of behaviors. For example, theKin selection coefficients are used in two distinct ways. First, these coefficients measure phenotypic correlations that affect the marginal costs and benefits of behaviors. For example, the phenotypic correlation in sex ratio produced by two females in an isolated patch influences the favoured sex ratio. Second, kin selection coefficients describe genotypic correlations that measure fidelity of transmission. For example, a female values daughters vs. nieces according to genotypic correlations. It is widely known that kin selection coefficients may be interpreted as phenotypic or genotypic correlations in different contexts. However, these different interpretations have never been fully separated, and their different role have not been clearly explained. I provide proofs of a generic analytical approach. The technique automatically separates phenotypic correlations among social partners from genotypic components of transmission. The result is a general method that can be derived from first principles and applied to multivariate problems in social evolution. I emphasize a simple, practical maximization method that can be used to calculate equilibrium conditions for complex social interactions.

• Models of symbiosis.

  Authors: S A Frank

  The American naturalist. 08/1997; 150 Suppl 1:S80-99.

  Abstract A tentative outline of concepts is proposed for the evolutionary genetics of symbiosis. There are three main topics. The first concerns the tension between the integrative and disruptiveAbstract A tentative outline of concepts is proposed for the evolutionary genetics of symbiosis. There are three main topics. The first concerns the tension between the integrative and disruptive forces of kin selection. Kin selection can be disruptive because competition among close relatives favors dispersal and a reduction in relatedness among neighbors. Kin selection acts independently within each species of a symbiotic community but has important consequences for the integration of the community into a cooperative unit. The second topic describes the evolution of beneficial, synergistic effects between species. The evolution of mutual effects depends on various correlations between species. Genetic correlations are analogous to linkage disequilibrium in standard Mendelian genetics. Correlations in reproductive success between symbiotic partners arise from codispersal and reproductive synchrony. The third topic concerns the evolution of asymmetrical symbioses in which one species can dominate its partner. Dominance may explain the evolution of uniparental inheritance among cytoplasmic symbionts and a peculiar form of germ-soma separation in the symbionts of insects.