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.     

Thermodynamical interpretation of an adaptive walk on a Mt. Fuji-type fitness landscape: Einstein relation-like formula holds in a stochastic evolution

We have theoretically studied the statistical properties of adaptive walks (or hill-climbing) on a Mt. Fuji-type fitness landscape in the multi-dimensional sequence space through mathematical analysis and computer simulation. The adaptive walk is characterized by the "mutation distance" d as the step-width of the walker and the "population size" N as the number of randomly generated d-fold point mutants to be screened. In addition to the fitness W, we introduced the following quantities analogous to thermodynamical concepts: "free fitness" G(W) is identical with W+T x S(W), where T is the "evolutionary temperature" T infinity square root of d/lnN and S(W) is the entropy as a function of W, and the "evolutionary force" X is identical with d(G(W)/T)/dW, that is caused by the mutation and selection pressure. It is known that a single adaptive walker rapidly climbs on the fitness landscape up to the stationary state where a "mutation-selection-random drift balance" is kept. In our interpretation, the walker tends to the maximal free fitness state, driven by the evolutionary force X. Our major findings are as follows: First, near the stationary point W*, the "climbing rate" J as the expected fitness change per generation is described by J approximately L x X with L approximately V/2, where V is the variance of fitness distribution on a local landscape. This simple relationship is analogous to the well-known Einstein relation in Brownian motion. Second, the "biological information gain" (DeltaG/T) through adaptive walk can be described by combining the Shannon's information gain (DeltaS) and the "fitness information gain" (DeltaW/T).     

Adaptive walks by the fittest among finite random mutants on a Mt. Fuji-type fitness landscape II. Effect of small non-additivity

We examined properties of adaptive walks by the fittest on “rough Mt. Fuji-type” fitness landscapes, which are modeled by superposing small uncorrelated random component on an additive fitness landscape. A single adaptive walk is carried out by repetition of the evolution cycle composed of (1) mutagenesis process that produces random d-fold point mutants of population size N and (2) selection process that picks out the fittest mutant among them. To comprehend trajectories of the walkers, the fitness landscape is mapped into a (x, y, z)-space, where x, y and z represent, respectively, normalized Hamming distance from the peak on the additive fitness landscape, scaled additive fitness and scaled non-additive fitness. Thus a single adaptive walk is expressed as the dynamics of a particle in this space. We drew the “hill-climbing” vector field, where each vector represents the most probable step for a walker in a single step. Almost all of the walkers are expected to move along streams of vectors existing on a particular surface that overlies the (x, y)-plane, toward the neighborhood of a characteristic point at which a mutation-selection-random drift balance is reached. We could theoretically predict this reachable point in the case of random sampling search strategy. Received: 1 March 2000 / Published online: 3 August 2000     

A model for the emergence of adaptive subsystems

We investigate the interaction of learning and evolution in a changing environment. A stable learning capability is regarded as an emergent adaptive system evolved by natural selection of genetic variants. We consider the evolution of an asexual population. Each genotype can have ‘fixed’ and ‘flexible’ alleles. The former express themselves as synaptic connections that remain unchanged during ontogeny and the latter as synapses that can be adjusted through a learning algorithm. Evolution is modelled using genetic algorithms and the changing environment is represented by two optimal synaptic patterns that alternate a fixed number of times during the ‘life’ of the individuals. The amplitude of the change is related to the Hamming distance between the two optimal patterns and the rate of change to the frequency with which both exchange roles. This model is an extension of that of Hinton and Nowlan in which the fitness is given by a probabilistic measure of the Hamming distance to the optimum. We find that two types of evolutionary pathways are possible depending upon how difficult (costly) it is to cope with the changes of the environment. In one case the population loses the learning ability, and the individuals inherit fixed synapses that are optimal in only one of the environmental states. In the other case a flexible subsystem emerges that allows the individuals to adapt to the changes of the environment. The model helps us to understand how an adaptive subsystem can emerge as the result of the tradeoff between the exploitation of a congenital structure and the exploration of the adaptive capabilities practised by learning.     

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.     

MHC-associated mating strategies and the importance of overall genetic diversity in an obligate pair-living primate

Mate choice is one of the most important evolutionary mechanisms. Females can improve their fitness by selectively mating with certain males. We studied possible genetic benefits in the obligate pair-living fat-tailed dwarf lemur (Cheirogaleus medius) which maintains life-long pair bonds but has an extremely high rate of extra-pair paternity. Possible mechanisms of female mate choice were investigated by analyzing overall genetic variability (neutral microsatellite marker) as well as a marker of adaptive significance (major histocompatibility complex, MHC-DRB exon 2). As in human medical studies, MHC-alleles were grouped to MHC-supertypes based on similarities in their functional important antigen binding sites. The study indicated that females preferred males both as social and as genetic fathers for their offspring having a higher number of MHC-alleles and MHC-supertypes, a lower overlap with female’s MHC-supertypes as well as a higher genome wide heterozygosity than randomly assigned males. Mutual relatedness had no influence on mate choice. Females engaged in extra-pair mating shared a significant higher number of MHC-supertypes with their social partner than faithful females. As no genetic differences between extra-pair young (EPY) and intra-pair young (IPY) were found, females might engage in extra-pair mating to ‘correct’ for genetic incompatibility. Thus, we found evidence that mate choice is predicted in the first place by the ‘good-genes-as-heterozygosity hypothesis’ whereas the occurrence of extra-pair matings supports the ‘dissassortative mating hypothesis’. To the best of our knowledge this study represents the first investigation of the potential roles of MHC-genes and overall genetic diversity in mate choice and extra-pair partner selection in a natural, free-living population of non-human primates.     

Multiple mating in the ant Cataglyphis cursor: testing the sperm limitation and the diploid male load hypotheses

Multiple mating (i.e., polyandry) by queens in social Hymenoptera is expected to weaken social cohesion since it lowers within-colony relatedness, and hence, indirect fitness benefits from kin selection. Yet, there are many species where queens mate multiply. Several hypotheses have been put forward to explain the evolution and maintenance of polyandry. Here,we investigated the ‘sperm limitation’ and the ‘diploid male load’ hypotheses in the ant Cataglyphis cursor. Genetic analyses of mother-offspring combinations showed that queens mate with up to 8 males, with an effective mating frequency of 3.79. Significant paternity skew (unequal contribution of the fathers) was detected in 1 out of 5 colonies. The amount of sperm stored in the spermatheca was not correlated with the queen mating frequency, and males carry on average enough sperm in their seminal vesicles to fill one queen’s spermatheca. Analyses of the nuclear DNA-content of males also revealed that all were haploid. These results suggest that the ‘sperm limitation’ and the ‘diploid male load’ hypotheses are unlikely to account for the queen mating frequency reported in this ant. In light of our results and the life-history traits of C. cursor, we discuss alternative hypotheses to account for the adaptive significance of multiple mating by queens in this species. Received 13 August 2008; revised 19 November 2008; accepted 21 November 2008.     

Reversed selection responses in small populations of the housefly (Musca domestica L.)

We compared the efficacy of artificial and natural selection processes in purging the genetic load of perpetually small populations. We subjected replicate lines of the housefly (Musca domestica L.), recently derived from the wild, to artificial selection for increased mating propensity (i.e., the proportion of male–female pairs initiating copulation within 30 min) in efforts to cull out the inbreeding depression effects of long-term small population size (as determined by a selection protocol for increased assortative mating). We also maintained parallel non-selection lines for assessing the spontaneous purge of genetic load due to inbreeding alone. We thus evaluated the fitness of artificially and ‘naturally’ purging populations held at census sizes of 40 individuals over the course of 18 generations. We found that the artificially selected lines had significant increases in mating propensity (up to 46% higher from the beginning of the protocol) followed by reversed selection responses back to the initial levels, resulting in non-significant heritabilities. Nevertheless, the ‘naturally’ selected lines had significantly lower fitness overall (a 28% reduction from the beginning of the protocol), although lower effective population sizes could have contributed to this effect. We conclude that artificial selection bolstered fitness, but only in the short-term, because the inadvertent fixation of extant genetic load later resulted in pleiotropic fitness declines. Still, the short-term advantage of the selection protocol likely contributed to the success of the speciation experiment since our recently-derived housefly populations are particularly vulnerable to inbreeding depression effects on mating behavior.     

Darwinian adaptation,population genetics and the streetcar theory of evolution

 This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context of n-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinism in n-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses – at unusual length for a mathematical journal – their fundamental role in our current understanding of evolution. Received 22 April 1994; received in revised form 10 July 1995     

Relative Fitness, Teleology, and the Adaptive Landscape

The metaphor of the adaptive landscape, introduced by Sewall Wright in 1932, has played, and continues to play, a central role in much evolutionary thought. I argue that the use of this metaphor is tied to a teleological view of the evolutionary process, in which natural selection directs evolution toward an improved future state. I argue further that the use of “relative fitnesses” standardized to an arbitrary value, which is closely connected with the metaphor of an adaptive landscape, produces a disconnect between the mean fitness of a population and any real property of that population. This allows for a vague and ill-defined improvement to occur under the influence of selection. Instead, I suggest that relative fitnesses should be standardized by the mean absolute fitness (expected population growth rate), so that they express the expected rate of increase in frequency, rather than number. Under this definition, the mean relative fitness of all populations is always 1.0, and never changes as long as the population continues to exist.     

History of the word photosynthesis and evolution of its definition

In 1893, Charles Barnes (1858–1910) proposed that the biological process for ‘synthesis of complex carbon compounds out of carbonic acid, in the presence of chlorophyll, under the influence of light’ should be designated as either ‘photosyntax’ or ‘photosynthesis.’ He preferred the word ‘photosyntax,’ but ‘photosynthesis’ came into common usage as the term of choice. Later discovery of anoxygenic photosynthetic bacteria and photophosphorylation necessitated redefinition of the term. This essay examines the history of changes in the meaning of photosynthesis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Darwin without borders? Looking at ‘generalised Darwinism’ through the prism of the ‘hourglass model’

This article critically analyzes the arguments of the ‘generalized Darwinism’ recently proposed for the analysis of social-economical systems. We argue that ‘generalized Darwinism’ is both restrictive and empty. It is restrictive because it excludes alternative (non-selectionist) evolutionary mechanisms such as orthogenesis, saltationism and mutationism without any examination of their suitability for modeling socio-economic processes and ignoring their important roles in the development of contemporary evolutionary theory. It is empty, because it reduces Darwinism to an abstract triple-principle scheme (variation, selection and inheritance) thus ignoring the actual structure of Darwinism as a complex and dynamic theoretical structure inseparable from a very detailed system of theoretical constraints. Arguing against ‘generalised Darwinism’ we present our vision of the history of evolutionary biology with the help of the ‘hourglass model’ reflecting the internal dynamic of competing theories of evolution.     

On the Spectrum of Prebiotic Chemical Systems

We reexamine Eigen’s paradox using the asymptotic limit theorems of information theory. Applying the homology between information source uncertainty and free energy density, under rate distortion constraints, the error catastrophe emerges as the lowest energy state for simple prebiotic systems without error correction. Invoking the usual compartmentalization – i.e., ‘vesicles’ – and using a Red Queen argument, suggests that information crosstalk between two or more properly interacting structures can initiate a coevolutionary dynamic having at least two quasi-stable states. The first is a low energy realm near the error threshold, and, depending on available energy, the second can approach zero error as a limit. A large deviations argument produces jet-like global transitions which, over sufficient time, may enable shifts between the many quasi-stable modes available to more complicated structures, ‘locking in’ to some subset of the various possible low error rate chemical systems, which become subject to development by selection and chance extinction. Energy availability, according to the model, is thus a powerful necessary condition for low error rate replication, suggesting that some fundamental prebiotic ecosystem transformation entrained reproductive fidelity. This work, then, supports speculation that our RNA/DNA world may indeed be only the chance result of a very broad prebiotic evolutionary phenomenon. Processes in vitro, or ex planeta, might have other outcomes.     

Adaptive evolutionary walks require neutral intermediates in RNA fitness landscapes

In RNA fitness landscapes with interconnected networks of neutral mutations, neutral precursor mutations can play an important role in facilitating the accessibility of epistatic adaptive mutant combinations. I use an exhaustively surveyed fitness landscape model based on short sequence RNA genotypes (and their secondary structure phenotypes) to calculate the minimum rate at which mutants initially appearing as neutral are incorporated into an adaptive evolutionary walk. I show first, that incorporating neutral mutations significantly increases the number of point mutations in a given evolutionary walk when compared to estimates from previous adaptive walk models. Second, that incorporating neutral mutants into such a walk significantly increases the final fitness encountered on that walk - indeed evolutionary walks including neutral steps often reach the global optimum in this model. Third, and perhaps most importantly, evolutionary paths of this kind are often extremely winding in their nature and have the potential to undergo multiple mutations at a given sequence position within a single walk; the potential of these winding paths to mislead phylogenetic reconstruction is briefly considered.     

An Evolutionary Scenario For The Origin Of Pentaradial Echinoderms—Implications From The Hydraulic Principles Of Form Determination

The early evolutionary history of echinoderms was reconstructed on the basis of structural-functional considerations and application of the quasi-engineering approach of ‘Konstruktions-Morphologie’. According to the presented evolutionary scenario, a bilaterally symmetrical ancestor, such as an enteropneust-like organism, became gradually modified into a pentaradial echinoderm by passing through an intermediate pterobranch-like stage. The arms of a pentaradial echinoderm are identified as hydraulic outgrowths from the central coelomic cavity of the bilateral ancestor which developed due to a shortening of the body in length but widening in the diameter. The resulting pentaradial symmetry is a consequence of mechanical laws that dictate minimal contact surface areas among hydraulic pneumatic entities. These developed in the coelomic cavity (metacoel) in the bilaterally symmetrical ancestor, when from the already U-shaped mesentery with the intestinal tract two additional U-shaped bows developed directly or subsequently. During the subsequent development tensile chords of the mesentery ‘sewed’ the gut with the body wall first in three and secondly in five ‘seams’. During the direct development five ‘seams’ between tensile chords and body wall developed straightly. These internal tensile chords subdivide the body coelom into five hydraulic subsystems (‘pneus’), which eventually arrange in a pentaradial pattern. The body could then enlarge only between the tensile chords, which means that five hydraulic bulges developed. These bulges initially supported the tentacles and finally each of them enclosed the tentacle until only the feather-like appendages of the tentacles projected over the surface. The tentacles with their feathers were transformedinto the ambulacral system, and the bulges become the arms. These morphological transformations were accompanied and partly determined by specific histological modifications, such as the development of mutable connective tissues and skeletal elements that fused to ossicles and provided shape stabilization in form of a calcareous skeleton in the body wall. The organism resulted was an ancestral echinoderm (‘Ur-Echinoderm’) with an enlarged metacoel, stabilized by hydraulic pressure working againsta capsule of mutable connective tissue, skeletal elements and longitudinal muscles. In regard to these reconstructions, the body structure of echinoderms can be understood as a hydraulic skeletal capsule.     

Construction of an integrated pepper map using RFLP,SSR, CAPS,AFLP, WRKY,rRAMP, and BAC end sequences

Map-based cloning to find genes of interest, markerassisted selection (MAS), and marker-assisted breeding (MAB) all require good genetic maps with high reproducible markers. For map construction as well as chromosome assignment, development of single copy PCR-based markers and map integration process are necessary. In this study, the 132 markers (57 STS from BAC-end sequences, 13 STS from RFLP, and 62 SSR) were newly developed as single copy type PCR-based markers. They were used together with 1830 markers previously developed in our lab to construct an integrated map with the Joinmap 3.0 program. This integrated map contained 169 SSR, 354 RFLP, 23 STS from BAC-end sequences, 6 STS from RFLP, 152 AFLP, 51 WRKY, and 99 rRAMP markers on 12 chromosomes. The integrated map contained four genetic maps of two interspecific (Capsicum annuum ‘TF68’ and C. chinense ‘Habanero’) and two intraspecific (C. annuum ‘CM334’ and C. annuum ‘Chilsungcho’) populations of peppers. This constructed integrated map consisted of 805 markers (map distance of 1858 cM) in interspecific populations and 745 markers (map distance of 1892 cM) in intraspecific populations. The used pepper STS were first developed from end sequences of BAC clones from Capsicum annuum ‘CM334’. This integrated map will provide useful information for construction of future pepper genetic maps and for assignment of linkage groups to pepper chromosomes.     

Molecular domestication – more than a sporadic episode in evolution

Transposable elements are short but complex pieces of DNA or RNA containing a streamlined minimal-genome with the capacity for its selfish replication in a foreign genomic environment. Cis-regulatory sections within the elements orchestrate tempo and mode of TE expression. Proteins encoded by TEs mainly direct their own propagation within the genome by recruitment of host-encoded factors. On the other hand, TE-encoded proteins harbor a very attractive repertoire of functional abilities for a cell. These proteins mediate excision, replication and integration of defined DNA fragments. Furthermore, some of these proteins are able to manipulate important host factors by altering their original function. Thus, if the host genome succeeds in domesticating such TE-encoded proteins by taming their ‘anarchistic behavior,’ such an event can be considered as an important evolutionary innovation for its own benefit. In fact, the domestication of TE-derived cis-regulatory modules and protein coding sections took place repeatedly in the course of genome evolution. We will present prominent cases that impressively demonstrate the beneficial impact of TEs on host biology over evolutionary time. Furthermore, we will propose that molecular domestication might be considered as a resumption of the same evolutionary process that drove the transition from ‘primitive genomes’ to ‘modern’ ones at the early dawn of life, that is, the adaptive integration of a short piece of autonomous DNA into a complex regulatory network. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sources for Imanishi Kinji’s views of sociality and evolutionary outcomes

Prior to the contribution of genetics or the modern evolutionary synthesis (MES) to natural selection theory, social ecologists searched for factors in addition to natural selection that could influence species change. The idea that sociality, not just biology, was important in determining evolutionary outcomes was prevalent in research in social ecology in the 1920s and 1930s. The influence of ‘tradition’ (or the transmission of learned behaviours between generations) and the view that animals are active in selecting their own environments, rather than passive organisms acted upon by chance, were given as much attention as natural selection theory in European ecology, while animal aggregation and cooperation studies were pursued in America. Imanishi Kinji’s personal library and his scientific notes and papers reveal that he was well aware of this literature and had been profoundly influenced by these earlier viewpoints prior to writing his view of nature in his first book, Seibutsu no Sekai (The World of Living Things, 1941). Evidence is presented to show that he developed his theories based partly on early western debates in social ecology while finding inspiration and a way to express his views in the writings of philosopher Nishida Kitarō and, perhaps, General J C Smuts. One of Imanishi’s lasting contributions is in the demonstrated results of over 40 years of subsequent ecological and ethological research by Imanishi and those trained by him that maintained the broader viewpoints on evolution that had been dropped from the western corpus of research by the 1950s. The current attempt to again get beyond natural selection theory is reflected in debates surrounding genetic and cultural evolution of cooperation, the biology of ‘traditions’ and the idea of ‘culture’ in animal societies. Imanishi Kinji is the Japanese name order, with family name first. Other Japanese names in the text are also written with family name first. A modified version of this paper appeared in Japanese in Seibutsu Kagaku, Vol. 57 No. 3, April 2006, pp 142–149.