Darwinian aspects of molecular evolution at sublinear propagation rates

Mean fitness is non-decreasing in the symmetry sector of the frequency trajectory followed in competitive replication at sublinear propagation rates (parabolic time course). This sector contains the pairwise symmetric distribution of species frequencies and its neighboring states, and represents at least half the possible states of an evolving sublinear system. States in the non-symmetry sector produce a negative rate of change in mean fitness. The heterogeneous steady state attained in a finite sublinear system is destabilized by formation of a variant with above-threshold fitness. Evolution in the post-steady-state interval elevates the fitness threshold for coexistence. Contrary to the proposition that ‘parabolic growth invariably results in the survival of all competing species’, only species with sufficient fitness to avoid subthreshold fitness survive. An erratum to this article is available at .     

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in a evolution reactor,I

A theory for describing evolution as adaptive walks by a finite population with M walkers (M ≥ 1) on an anisotropic Mt. Fuji-type fitness landscape is presented, from a thermodynamical point of view. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrate that the behavior of these theoretical walkers is almost consistent with the thermodynamical schemes. The major conclusions are as follows: (1) an adaptive walk (=evolution) is driven by an evolutionary force in the direction in which free fitness increases; (2) the expectation of the climbing rate obeys an equation analogous to the Einstein relation in Brownian motion; (3) the standard deviation of the climbing rate is a quantity analogous to the mean thermal energy of a particle, kT (×constant). In addition, on the interpretation that the walkers climb the landscape by absorbing ‘fitness information’ from the surroundings, we succeeded in quantifying the fitness information and formulating a macroscopic scheme from an informational point of view.     

Rate of polymer formation and entropy production during competitive replication

Summary The rate of increase in the mean polymer formation rate constant during competitive replication byQ RNA variants (Kramer et al., 1974) has been shown to agree statistically with the variance in their formation rate constants. This result demonstrates that Fisher's fundamental theorem of natural selection (Fisher, 1930) can define time variations in the mean rate of synthesis for a heterogeneous population of replicating polymers. It was also revealed that RNA replication, far from equilibrium, accompanied a progressive decrease in the order of the entropy production derivative, with respect to time, that reached a maximum (with the next higher order being zero). Maximization of entropy at equilibrium, in compliance with the second law of thermodynamics, therefore appears as a natural extension of the earlier non-equilibrium pattern of entropy production within the system. The order of the zero-valued entropy production derivative was shown to be determined by the chemical affinity, and its rate of decrease was specified by the mean polymer formation rate constant.     

Hypermutation and stress adaptation in bacteria

Hypermutability is a phenotype characterized by a moderate to high elevation of spontaneous mutation rates and could result from DNA replication errors, defects in error correction mechanisms and many other causes. The elevated mutation rates are helpful to organisms to adapt to sudden and unforeseen threats to survival. At the same time hypermutability also leads to the generation of many deleterious mutations which offset its adaptive value and therefore disadvantageous. Nevertheless, it is very common in nature, especially among clinical isolates of pathogens. Hypermutability is inherited by indirect (second order) selection along with the beneficial mutations generated. At large population sizes and high mutation rates many cells in the population could concurrently acquire beneficial mutations of varying adaptive (fitness) values. These lineages compete with the ancestral cells and also among themselves for fixation. The one with the ‘fittest’ mutation gets fixed ultimately while the others are lost. This has been called ‘clonal interference’ which puts a speed limit on adaptation. The original clonal interference hypothesis has been modified recently. Nonheritable (transient) hypermtability conferring significant adaptive benefits also occur during stress response although its molecular basis remains controversial. The adaptive benefits of heritable hypermutability are discussed with emphasis on host–pathogen interactions.     

Selective advantage for sexual reproduction with random haploid fusion

This article develops a simplified set of models describing asexual and sexual replication in unicellular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be functional if it is equal to some master sequence σ₀, and non-functional otherwise. We review the previously studied case of selective mating, where it is assumed that only haploids with functional chromosomes can fuse, and also consider the case of random haploid fusion. When the cost for sex is small, as measured by the ratio of the characteristic haploid fusion time to the characteristic growth time, we find that sexual replication with random haploid fusion leads to a greater mean fitness for the population than a purely asexual strategy. However, independently of the cost for sex, we find that sexual replication with a selective mating strategy leads to a higher mean fitness than the random mating strategy. The results of this article are consistent with previous studies suggesting that sex is favored at intermediate mutation rates, for slowly replicating organisms, and at high population densities. Furthermore, the results of this article provide a basis for understanding sex as a stress response in unicellular organisms such as Saccharomyces cerevisiae (Baker’s yeast).     

Estimating seasonal density of blue sheep (<Emphasis Type="Italic">Pseudois nayaur</Emphasis>) in the Helan Mountain region using distance sampling methods

The monitoring of animal populations is necessary to conserve and manage the rare or harvest species and to understand the population change over several years. We used distance sampling methods to estimate seasonal density of blue sheep in a 2,740 km² area of Helan Mountain region by walking along 32 transect lines from winter 2003 to autumn 2005. In all, 367–780 blue sheep were observed in 91–143 groups in the surveys during the seasons. Observed mean group size ranged from 3.42 to 8.35 individuals; encounter rate, the number of groups detected per kilometre, varied from 0.19 to 0.30 during the seasons. A hazard rate key function with cosine series expansion and a half-normal key function with either cosine or simple polynomial series expansion were the best fitting models based on the lowest value of Akaike’s information criterion (AIC). Density estimates varied between 3.627 sheep per square kilometre in spring 2004 and 4.635 per square kilometre in summer 2005. There were no detectable differences in estimated density among seasons (P = 0.887). The estimated density of blue sheep was negatively correlated with the total number of deaths (P < 0.05), number of sub-adult males’ deaths (P < 0.05), number of sub-adult females’ deaths (P < 0.05), and number of male lambs’ deaths (P < 0.05). We concluded that distance sampling surveys should be used to monitor long-term population trends to provide the best quantitative estimates of blue sheep populations in the Helan Mountains region.     

From bad to good: Fitness reversals and the ascent of deleterious mutations

Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10⁻⁵ of all mutations).     

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor,II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371–1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing ‘effective’ quantities such as the effective mutation distance or the effective screening size.     

A comparative assessment of four methods for estimating ammonia emissions at microclimatic locations in a dairy building

Ammonia emissions were estimated at five microclimatic locations in a free stall dairy building using four different methods. Measurements were performed simultaneously with the different methods to enable comparison. In the first method, the rate of ammonia emission from manure was theoretically modeled utilizing Fick’s law and boundary layer theory. In the second method, recirculation flux-chamber technique was used to model ammonia emission from manure. In the third and fourth methods, respectively, carbon dioxide and methane balances were employed to calculate ammonia emission. The mean ammonia emissions measured from the five locations using the different methods ranged from 0.10 to 0.15 g m⁻² h⁻¹. The percentage of variation of ammonia emission from the different location ranged between 8 and 52% for the different methods. Recorded ammonia emission rates in the dairy building were from 0.04 to 0.25 g m⁻² h⁻¹. The percentage of variation in ammonia, carbon dioxide, methane, and manure properties in the building was 50%. Two-way statistical analysis of variance showed that there were no significant differences (p > 0.63) between the four different methods or between the measurements obtained at the five locations (p > 0.90).     

Testing competing measures of profitability for mobile resources

Optimal diet theory often fails to predict a forager’s diet choice when prey are mobile. Because they escape or defend themselves, mobile prey are likely to increase the forager’s handling time, thereby decreasing its fitness gain rate. Many animals have been shown to select their prey so as to maximize either their fitness gain or their fitness gain rate. However, no study has yet compared directly these two measures of profitability by generating testable predictions about the choice of the forager. Under laboratory conditions, we compared these two measures of profitability, using the aphid parasitoid Aphidius colemani and its host, Myzus persicae. Fitness gain was calculated for parasitoids developing in each host instar by measuring life-history traits such as developmental time, sex ratio and fecundity. Fitness gain rate was estimated by dividing fitness gain by handling time, the time required to subdue the host. Fourth instar aphids provided the best fitness gain to parasitoids, whereas second instar aphids were the most profitable in terms of fitness gain rate. Host choice tests showed that A. colemani females preferred second instar hosts, suggesting that their decision maximizes fitness gain rate over fitness gain. Our results indicate that fitness gain rate is a reliable predictor of animal’s choice for foragers exploiting resources that impose additional time cost due to their mobility. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Diploidy and the selective advantage for sexual reproduction in unicellular organisms

This article develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. The asexual and sexual life cycles are based on the asexual and sexual life cycles in Saccharomyces cerevisiae, Baker’s yeast, which normally reproduces by asexual budding, but switches to sexual reproduction when stressed. The mathematical models consider three reproduction pathways: (1) Asexual reproduction, (2) self-fertilization, and (3) sexual reproduction. We also consider two forms of genome organization. In the first case, we assume that the genome consists of two multi-gene chromosomes, whereas in the second case, we consider the opposite extreme and assume that each gene defines a separate chromosome, which we call the multi-chromosome genome. These two cases are considered to explore the role that recombination has on the mutation-selection balance and the selective advantage of the various reproduction strategies. We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as homologous recombination repair). As a result, we assume that the fitness of the organism only depends on the number of homologous gene pairs that contain at least one functional copy of a given gene. If the organism has at least one functional copy of every gene in the genome, we assume a fitness of 1. In general, if the organism has l homologous pairs that lack a functional copy of the given gene, then the fitness of the organism is κ _l . The κ _l are assumed to be monotonically decreasing, so that κ₀ = 1 > κ₁ > κ₂ > ⋯ > κ_∞ = 0. For nearly all of the reproduction strategies we consider, we find, in the limit of large N, that the mean fitness at mutation-selection balance is max{2 e^-m-1, 0} ,\hbox{max}\{2 e^{-\mu}-1, 0\} , where N is the number of genes in the haploid set of the genome, ε is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication, and μ = Nε. The only exception is the sexual reproduction pathway for the multi-chromosomed genome. Assuming a multiplicative fitness landscape where κ _l  = α ^l for α ∈ (0, 1), this strategy is found to have a mean fitness that exceeds the mean fitness of all the other strategies. Furthermore, while other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once μ exceeds ln2 ,\ln 2 , no such transition occurs in the sexual pathway. Indeed, in the limit as α → 1 for the multiplicative landscape, we can show that the mean fitness for the sexual pathway with the multi-chromosomed genome converges to e ^−2μ, which is always positive. We explicitly allow for mitotic recombination in this study, which, in contrast to previous studies using different models, does not have any advantage over other asexual reproduction strategies. The results of this article provide a basis for understanding the selective advantage of the specific meiotic pathway that is employed by sexually reproducing organisms. The results of this article also suggest an explanation for why unicellular organisms such as Saccharomyces cerevisiae (Baker’s yeast) switch to a sexual mode of reproduction when stressed. While the results of this article are based on modeling mutation-propagation in unicellular organisms, they nevertheless suggest that, in more complex organisms with significantly larger genomes, sex is necessary to prevent the loss of viability of a population due to genetic drift. Finally, and perhaps most importantly, the results of this article demonstrate a selective advantage for sexual reproduction with fewer and much less restrictive assumptions than those of previous studies.     

How much do army ants eat? On the prey intake of a neotropical top-predator

New World army ants (Ecitoninae) are nomadic group-predators that are widely thought to have a substantial impact on their prey. Nevertheless, quantitative data on prey intake by army ants is scarce and mostly limited to chance encounters. Here, I quantify the prey intake of the army ant Eciton hamatum at the contrasting scales of raid, colony (sum of simultaneous raids), and population. Like most army ants, E. hamatum conducts narrow ‘column raids’ and has a specialized diet of ant prey. I show that individual raids often had periods of no prey intake, and raid intake rates, calculated in g/min, differed significantly among colonies. Moreover, neither mean nor peak raid intake rates were correlated with colony size. Similarly, colony intake rates differed significantly among colonies, and mean colony intake rates were not correlated with colony size. However, mean colony intake rates were significantly higher than mean raid intake rates, and peak colony intake rate was correlated with colony size. Having multiple raids thus improves colony-level intake rates, and larger colonies can harvest more prey per unit time. Mean colony intake rate across colonies was 0.067 g/min dry weight and mean daily colony intake was calculated at 38.2 g. This intake is comparable to that of Eciton burchellii, which has a more generalized diet and conducts spectacular ‘swarm raids’ that are seen as having a greater impact on prey than column raids. Population size on Barro Colorado Island, Panama, was estimated to be 57 colonies, which extrapolates to a daily population intake of nearly 2 kg of prey dry weight, or 120 g/km². Broadly, these findings demonstrate that column raiding army ants experience considerable variation in prey intake for individual raids, but can still achieve notable impact at the larger scales of colony and population. Furthermore, they challenge the idea that swarm-raiding species necessarily have greater intake and thus impact on prey. Instead, I suggest that conducting multiple column raids may be a strategy that allows for comparable intake from a more specialized diet.     

Chromosome Interactions in DROSOPHILA MELANOGASTER. II. Total Fitness

In a large experiment, using nearly 200 population cages, we have measured the fitness of Drosophila melanogaster homozygous (1) for the second chromosome, (2) for the third chromosome, and (3) for both chromosomes. Twentyfour second chromosomes and 24 third chromosomes sampled from a natural population were tested. The mean fitness of the homozygous flies is 0.081 ± 0.014 for the second chromosome, 0.080 ± 0.017 for the third chromosome, and 0.079 ± 0.024 for both chromosomes simultaneously. Assuming that fitnesses are multiplicative (the additive fitness model makes no sense in the present case because of the large selection coefficients involved), the expected mean fitness of the homozygotes for both chromosomes is 0.0066; their observed fitness is more than ten times greater. Thus, it appears that synergistic interactions between loci are considerable; and that, consequently, the fitness function substantially departs from linearity. Two models are tentatively suggested for the fitness function: a "threshold" model and a "synergistic" model.—The experiments reported here confirm previous results showing that the concealed genetic load present in natural populations of Drosophila is sufficient to account for the selective maintenance of numerous polymorphisms (of the order of 1000).     

Further evaluation of physical fitness age versus physiological age in women

The present study was conducted to examine further whether adult women who are in a state of high physical fitness possess high physiological functions, and also to investigate whether those who exercise regularly are able to maintain a high quality of various physiological functions. The subjects of this study were 249 healthy Japanese adult women (aged 20–70 years). Of these subjects 30 had jogged or walked regularly for more than 3 years. The physiological ages (PA) and physical fitness ages (FA) of the individuals were estimated from 17 physiological function tests and 5 physical fitness tests, respectively, by principal components analyses. The results indicated that there was a significant correlation between PA and FA (r = 0.76, P < 0.01). To examine this relationship in more detail, the subjects were classified into three physical fitness groups (high, normal and low) based on the deviation from the regression line of FA. Comparison of the mean PA among three physical fitness groups revealed that the high physical fitness groups demonstrated a much lower PA (physiologically younger), while the low physical fitness groups showed a relatively higher PA (physiologically older) in spite of their equivalent chronological ages. From this series of studies, a new concept is proposed where different individuals have different peak physiological capacities, but that these capacities change with age at similar rates. It is suggested that interventions such as exercise and a proper diet for promoting health could increase peak functional capacity but have little effect on the rate of decline. Accepted: 3 March 1998     

Stationary mutant distributions and evolutionary optimization

Molecular evolution is modelled by erroneous replication of binary sequences. We show how the selection of two species of equal or almost equal selective value is influenced by its nearest neighbours in sequence space. In the case of perfect neutrality and sufficiently small error rates we find that the Hamming distance between the species determines selection. As the error rate increases the fitness parameters of neighbouring species become more and more important. In the case of almost neutral sequences we observe a critical replication accuracy at which a drastic change in the “quasispecies”, in the stationary mutant distribution occurs. Thus, in frequently mutating populations fitness turns out to be an ensemble property rather than an attribute of the individual. In addition we investigate the time dependence of the mean excess production as a function of initial conditions. Although it is optimized under most conditions, cases can be found which are characterized by decrease or non-monotonous change in mean excess productions.     

Enhancement of marennine production by blue light in the diatom <Emphasis Type="Italic">Haslea ostrearia</Emphasis>

The marine diatom Haslea ostrearia Simonsen produces a blue pigment, marennine, which is used for greening oysters. This microalga is cultured industrially indoors with artificial light. The influence of light quality on marennine production by cultures of H. ostrearia was investigated in the laboratory and at a semi-pilot scale (300 L tanks). In the first series of experiments in the laboratory, a clone of H. ostrearia was cultured under light of different colors (white, blue, green, yellow, and red) and at two irradiances (‘low’ and ‘high’, 20 and 100 μmol photons m⁻² s⁻¹, respectively). Compared to the white light controls, growth was increased in blue light at the ‘low’, but not at the ‘high’ irradiance, and marennine production at the end of the exponential phase was the highest in cells grown under blue light, regardless of the light quality or intensity during growth. Increased marennine production during growth was also observed, whichever color of light (blue or white) was used during the acclimation phase. In a second series of experiments, intraclonal differences were studied by comparing marennine production in seven clones differing with regard to their mean cell size. The total marennine expressed either per cell or per culture volume, was higher in blue light for all the clones. Complementary experiments carried out under semi-industrial conditions confirmed this effect of blue light, which could be relevant for the industrial, indoor production of marennine.     

Growth and physiology of a yeast cultivated in batch and continuous culture systems

Inoculum size has been found to affect significantly the maximum attainable specific growth rate during batch cultivation ofCandida utilis. Lower inoculum size resulted in an increased growth rate and relatively longer lag. The culture is found to be most active in the beginning of the exponential phase as regards its RNA synthesis rate. Batch data were used for predicting the conditions of the yeast population in single-stage continuous culture system. Predicted and the experimental values showed a reasonable agreement. In single-stage chemostat the physiology of the yeast was studied on the basis RNA, DNA and protein synthesis rates at various growth rates. The results indicate that the productivity of cells and the rate of synthesis of macromolecules is highest at the dilution rate values of 0.33 to 0.35 hr⁻¹. In order to attain so-called unrestricted conditions of growth a pluristage pluristream continuous system was employed. It is assumed that under such conditions the specific growth rate and the synthetic activity of yeasts may reach its maximum on a given medium. The results presented do not show such conditions of growth under the experimental conditions employed (D ₁=0.35 hr⁻¹ andD ₂=0.2 to 1.7 hr⁻¹) withCandida utilis cultivated on beet molasses medium. Second stage of a two-stage two-stream continuous system is constantly fed with the cells from the foregoing stage; this category of cells on entering the new conditions of the second stage is expected to show some adaptation period. Experiments are reported to this effect.     

A fitness function for optimal life history in relation to density effects,competition, predation and stability of the environment

A fitness function (function maximized under natural selection) is studied in a population model in which the growth of a population is suppressed by crowding, density-independent continuous mortality (by euryphagous predators) and periodic disturbances. The dynamics of the population density between occurrence of disturbance can be expressed as,dN/dt=(F(N/K)−D)N, whereN is the population density,K is the carrying capacity,D is the density-independent continuous mortality, andF is the growth regulation factor described as a function of crowding (N/K). The period of disturbance isS. The survival rate under disturbance isu. It is concluded that the fitness function is (approximately) a product of competitive ability (C), carrying capacity, and degree of saturation, and is given byCKF ⁻¹(D−(lnu)/S). The degree of saturation is the inverse function of regulation factor (F) at the death rate due to predators and disturbance. I assume a population in which density is regulated only through survival. In this case, a low survival rate at the critical age-group means a high value ofCKF ⁻¹(D−(lnu)/S). Therefore, the reciprocal of the density-dependent survival rate at critical age-group is a measure of the fitness function. Using this measure, I predict the optimal age (body size) at first reproduction of a species of salamander. I also found that fitness calculated from observed values ofl(x) andm(x) includes a tautology. When the concept of fitness function is compared with the ESS method, the latter is more flexible. However, there is a possibility that an ESS is at the minimum of fitness function.     

Land use/cover change and its drivers: a case in the watershed of Lake Kasumigaura, Japan

Land use/land cover (LULC) changes in the watershed (2,157 km²) of Lake Kasumigaura during 1979–1996 (Period-1: 1979–1990, Period-2: 1990–1996) were analyzed, and their socio-economic and biophysical drivers were compared using time-series, high-quality GIS datasets in order to examine the characteristics of a model forecasting the future LULC. The changes occurred over an area of more than 90 km² during the overall period at changing rates of 0.22% year⁻¹ in Period-1 and 0.25% year⁻¹ in Period-2. Forestland decreased most in both periods at changing rates of 0.45% year⁻¹ in Period-1 and 0.61% year⁻¹ in Period-2. However, predominant changing patterns differed, i.e., from forest to golf course in Period-1 and from forest to artificial field in Period-2. Particularly in Period-2, a significant LULC change was observed in an area of high population increase on the edge of an already high-population area. Relationships examined among LULC change, population, and rate of population change suggested that the urbanized area was highly resistant to LULC change, and that such change was less frequent in areas of population decline. Statistical analyses indicated that the most influential drivers for total LULC changes were population in Period-1 and distance from the Tokyo Station in Period-2. Since the change potentials differed between the periods, we could not assume a stationary process for the corresponding drivers. Somewhat low S values (indices for demonstrability) show that LULC changes in the watershed of Lake Kasumigaura occurred rather randomly, probably resulting in fragmentation of the landscape.