Adaptation and the cost of complexity

Abstract.— Adaptation is characterized by the movement of a population toward a many-character optimum, movement that results in an increase in fitness. Here I calculate the rate at which fitness increases during adaptation and describe the curve giving fitness versus time as a population approaches an optimum in Fisher's model of adaptation. The results identify several factors affecting the speed of adaptation. One of the most important is organismal complexity—complex organisms adapt more slowly than simple ones when using mutations of the same phenotypic size. Thus, as Fisher foresaw, organisms pay a kind of cost of complexity. However, the magnitude of this cost is considerably larger than Fisher's analysis suggested. Indeed the rate of adaptation declines at least as fast as n^-1 , where n is the number of independent characters or dimensions comprising an organism. The present results also suggest that one can define an effective number of dimensions characterizing an adapting species.     

On an extension of R.A. Fisher's result on the dynamics of the reproductive value

A classical result by Fisher concerning reproductive value dynamics is extended to the case of varying vital rates with a constant cohort Lotka's r. Based on the demographic potential approach, a generalization of the concept of reproductive value is introduced, which exhibits exponential dynamics both in the classical case of constant vital rates and in a wider class of populations. The generalized reproductive value introduced in this paper fits the classical interpretation by Fisher as a discounted sum of future births in the general class of models addressed here. Our results show when Fisher's classical results may be used as good approximations. They could also be of importance for estimating the fitness of biological populations, aggregate population modeling, and studying the long-term consequences of varying vital rates.     

Adaptation in sexuals vs. asexuals: clonal interference and the Fisher-Muller model

Fisher and Muller's theory that recombination speeds adaptation by eliminating competition among beneficial mutations has proved a popular explanation for the advantage of sex. Recent theoretical studies have attempted to quantify the speed of adaptation under the Fisher-Muller model, partly in an attempt to understand the role of "clonal interference" in microbial experimental evolution. We reexamine adaptation in sexuals vs. asexuals, using a model of DNA sequence evolution. In this model, a modest number of sites can mutate to beneficial alleles and the fitness effects of these mutations are unequal. We study (1) transition probabilities to different beneficial mutations; (2) waiting times to the first and the last substitutions of beneficial mutations; and (3) trajectories of mean fitness through time. We find that some of these statistics are surprisingly similar between sexuals and asexuals. These results highlight the importance of the choice of substitution model in assessing the Fisher-Muller advantage of sex.     

Harnessing recombination to speed adaptive evolution in Escherichia coli

Evolutionary engineering typically involves asexual propagation of a strain to improve a desired phenotype. However, asexual populations suffer from extensive clonal interference, a phenomenon where distinct lineages of beneficial clones compete and are often lost from the population given sufficient time. Improved adaptive mutants can likely be generated by genetic exchange between lineages, thereby reducing clonal interference. We present a system that allows continuous in situ recombination by using an Esherichia coli F-based conjugation system lacking surface exclusion. Evolution experiments revealed that Hfr-mediated recombination significantly speeds adaptation in certain circumstances. These results show that our system is stable, effective, and suitable for use in evolutionary engineering applications.     

Stochastic thermodynamic limit on E. coli adaptation by information geometric approach

Biological systems process information under noisy environment. Sensory adaptation model of E. coli is suitable for investigation because of its simplicity. To understand the adaptation processing quantitatively, stochastic thermodynamic approach has been attempted. Information processing can be assumed as state transition of a system that consists of signal transduction molecules using thermodynamic approach, and efficiency can be measured as thermodynamic cost. Recently, using information geometry and stochastic thermodynamics, a relationship between speed of the transition and the thermodynamic cost has been investigated for a chemical reaction model. Here, we introduce this approach to sensory adaptation model of E. coli, and examined a relationship between adaptation speed and the thermodynamic cost, and efficiency of the adaptation speed. For increasing external noise level in stimulation, the efficiency decreased, but the efficiency was highly robust to external stimulation strength. Moreover, we demonstrated that there is the best noise to achieve the adaptation in the aspect of thermodynamic efficiency. Our quantification method provides a framework to understand the adaptation speed and the thermodynamic cost for various biological systems.     

Single-crossover recombination and ancestral recombination trees

We consider the Wright–Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the $N \rightarrow \infty $ limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help of a decomposition of the trees into subtrees, we calculate the probabilities of the topologies of the ancestral trees. At the same time, these probabilities lead to a semi-explicit solution of the deterministic single-crossover equation. The latter is a discrete-time dynamical system that emerges from the Wright–Fisher model via a law of large numbers and has been waiting for a solution for many decades.     

Co‐adaptation impacts the robustness of predator–prey dynamics against perturbations

Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.     

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated (“pulled”) waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.     

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. In classic work, Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher–Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects. We solve the deterministic, infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. This result is argued to hold for any nonzero value of the rate of recombination. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number L of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to L in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with L genomic segments.     

The fundamental theorem of natural selection

R. A. Fisher's Fundamental Theorem of Natural Selection states that the rate of increase in the mean fitness of a population ascribable to gene-frequency changes is exactly equal to the additive genetic variance in fitness. It has been widely misunderstood, though clarification has gradually come about particularly through the work of G. R. Price, W. J. Ewens, and S. Lessard. Building on their interpretations we here explain the approach adopted by Fisher (1941), devising a figure as an aid to understanding this important paper.     

Are Anomalous Invasion Speeds Robust to Demographic Stochasticity?

Two important issues for conservation are the range expansion of species as a result of climate change and the invasion of exotic species. Being able to predict the rate at which species spread is key for successful management. In deterministic models, the invasion speed of a polymorphic population can be faster than that of any of the component phenotypes, and these “anomalous” invasion speeds persist even when the mutation rate between phenotypes is vanishingly small. Here we investigate whether the same phenomenon is observed in a model with demographic stochasticity. The model that we use is discrete in time and space and we carry out numerical simulations to determine the invasion speed of a population that has two morphs which differ in their dispersal abilities. We find that anomalous speeds are observed in the stochastic model, but only when the carrying capacity of the population is large or the mutation rate between morphs is high enough. These results suggest that only species with large population sizes, such as many insect species, may be able to invade faster if they are polymorphic than if there is only a single morph present in the population.     

Field measurements of wind speed and reconfiguration in Arundo donax (Poaceae) with estimates of drag forces

The giant reed (Arundo donax) is well known as a species that can withstand high wind loads without mechanical damage. To examine wind impact, profiles of vertical wind speeds in the plant's natural habitat (southern France) were measured at the edge and within a stand in the main wind direction. Wind speed was recorded simultaneously at five heights. For 75 measurements of within-canopy wind speed profiles, the attenuation coefficient was 4.4 ± 0.5, a value typical for plant stands with very dense canopies. Video recordings proved that A. donax becomes streamlined with increasing wind speed, reducing the projected surface area of leaves and stem. The total projected surface area is a function of wind speed and can be characterized by a second-order polynomial regression curve. For small wind velocities up to 1 m/s, the calculated drag force is proportional to the square of the wind speed. However, when A. donax plants are subjected to higher wind speeds (1.5-10 m/s), the drag force becomes directly proportional to the wind speed. Streamlining is a potentially important adaptation for withstanding high wind loads, especially for individual plants and plants at the edge of stands, whereas in dense stands streamlining probably plays a minor role.     

Estimating downwind concentrations of viable airborne microorganisms in dynamic atmospheric conditions

A Gaussian plume model has been modified to include an airborne microbial survival term that is a best-fit function of laboratory experimental data of weather variables. The model has been included in an algorithm using microbial source strength and local hourly mean weather data to drive the model through a summer- and winter-day cycle. For illustrative purposes, a composite airborne "virus" (developed using actual characteristics from two viruses) was used to show how wind speed could have a major modulating effect on near-source viable concentrations. For example, at high wind speeds such as those occurring during the day, or with short travel times, near-source locations experience high viable concentrations because the microorganisms have not had time to become inactivated. As the travel time increases, because of slow wind speed or longer distances, die-off modulation by sunshine, relative humidity, temperature, etc., potentially becomes increasingly predominant.     

Estimating downwind concentrations of viable airborne microorganisms in dynamic atmospheric conditions.

A Gaussian plume model has been modified to include an airborne microbial survival term that is a best-fit function of laboratory experimental data of weather variables. The model has been included in an algorithm using microbial source strength and local hourly mean weather data to drive the model through a summer- and winter-day cycle. For illustrative purposes, a composite airborne "virus" (developed using actual characteristics from two viruses) was used to show how wind speed could have a major modulating effect on near-source viable concentrations. For example, at high wind speeds such as those occurring during the day, or with short travel times, near-source locations experience high viable concentrations because the microorganisms have not had time to become inactivated. As the travel time increases, because of slow wind speed or longer distances, die-off modulation by sunshine, relative humidity, temperature, etc., potentially becomes increasingly predominant.     

The rate of fitness-valley crossing in sexual populations

Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneficial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a "fitness valley" to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest fitness valley, in which an adaptation requires one mutation at each of two loci to provide a fitness benefit. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We find that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when the recombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valley-crossing time by up to several orders of magnitude relative to that in an asexual population.     

Population genetics and sociobiology: conflicting views of evolution

This article explores the tension between the population genetics and sociobiological approaches to the study of evolution. Whereas population geneticists, like Stanford's Marc Feldman, insist that the genetic complexities of organisms cannot be overlooked, sociobiologists (many of whom now prefer to call themselves "behavioral ecologists") rely on optimization models that are based on the simplest possible genetics.These optimization approaches have their roots in the classical result known as the fundamental theorem of natural selection, formulated by R. A. Fisher in 1930. From the start there was great uncertainty over the proper interpretation of Fisher's theorem, which became confused with Sewall Wright's immensely influential adaptive landscape concept. In the 1960s, a new generation of mathematical biologists proved that Fisher's theorem did not hold when fitness depended on more than one locus. Similar reasoning was used to attack W. D. Hamilton's inclusive fitness theory. A new theory, known as the theory of long-term evolution, attempts to reconcile the rigorous population genetics approach with the long-standing sociobiological view that natural selection acts to increase the fitness of organisms.     

Towards structural genomics of RNA: rapid NMR resonance assignment and simultaneous RNA tertiary structure determination using residual dipolar couplings

We report a new residual dipolar couplings (RDCs) based NMR procedure for rapidly determining RNA tertiary structure demonstrated on a uniformly (15)N/(13)C-labeled 27 nt variant of the trans-activation response element (TAR) RNA from HIV-I. In this procedure, the time-consuming nuclear Overhauser enhancement (NOE)-based sequential assignment step is replaced by a fully automated RDC-based assignment strategy. This approach involves examination of all allowed sequence-specific resonance assignment permutations for best-fit agreement between measured RDCs and coordinates for sub-structures in a target RNA. Using idealized A-form geometries to model Watson-Crick helices and coordinates from a previous X-ray structure to model a hairpin loop in TAR, the best-fit RDC assignment solutions are determined very rapidly (相似文献