The role of molecular size in ligand efficiency

Ligand efficiency is a simple metric for assessing whether a ligand derives its potency from optimal fit with the protein target or simply by virtue of making many contacts. Comparison of protein-ligand binding affinities for over 8000 ligands with 28 protein targets shows conclusively that the average ligand binding affinities are not linear with molecular size. It is therefore important to scale ligand efficiencies by the size of the ligand, particularly where small ligands (e.g., fragments) are involved. We propose a simple 'fit quality' metric that removes this dependence.     

The evolution of body size in birds. II. The role of reproductive power

Given that body mass evolves non-randomly in birds, it is important to ask what factors might be responsible. One suggestion is that the rate at which individuals turn resources into offspring, termed reproductive power, might explain this non-randomness. This is because, in mammals, the body mass with the highest reproductive power is the most common (modal) one. Reproductive power was estimated for birds from data on energetic content of eggs and population productivity. According to the formulation of Brown et al. (1993), reproductive power is composed of two component processes: acquisition (acquiring resources and storing them in reproductive biomass) and conversion (converting reproductive biomass into offspring). As with mammals, estimates of reproductive power indicate that the most common body mass in birds is also the body mass that maximizes reproductive power. The relationship between reproductive power and diversity is different for species smaller than this modal body mass when compared to those that are larger. The relationship of body mass and reproductive power is different between birds and mammals in two ways: (1) the body mass that maximizes reproductive power is smaller in birds (33g) than in mammals (100g), and (2) mammals generate more reproductive power than an equivalent-sized bird. Reproductive power is determined primarily by acquisition in small birds and mammals, while it is determined by conversion in the largest birds and mammals. It is likely that reproductive power is closely tied to the evolution and diversification of body masses because it constrains the ways in which traits affecting fitness can evolve.     

The role of compensatory neutral mutations in molecular evolution

A pair of mutations at different loci (or sites) which are singly deleterious but restore normal fitness in combination may be called compensatory neutral mutations. Population dynamics concerning evolutionary substitutions of such mutants was developed by making use of the diffusion equation method. Based on this theory and, also, by the help of Monte Carlo simulation experiments, a remarkable phenomenon was disclosed that the double mutants can easily become fixed in the population by random drift under continued mutation pressure if the loci arc tightly linked, even when the single mutants are definitely deleterious. More specifically, I consider two loci with allelesA andA’ in the first locus, and allelesB andB’in the second locus, and assign relative fitnesses 1, 1-s’, 1-s’ and 1 respectively to the four gene combinationsAB, A’B, AB’ andA’B’, wheres’ is the selection coefficient against the single mutants (s’ > 0). Letv be the mutation rate per locus per generation and assume that mutation occurs irreversibly fromA toA’ at the first locus, and fromB toB’ at the second locus, whereA andB are wild type genes, andA’ andB’ are their mutant alleles. In a diploid population of effective size N _e (or a haploid population of 2N _e breeding individuals), it was shown that the average time (T) until joint fixation of the double mutant (A’B’) starting from the state in which the population consists exclusively of the wild type genes (AB) is not excessively long even for large 4N _e s’ values. In fact, assuming2N _e v = 1 we have -T = 54Ne for 4Nes’ = 400, and -T = 128Ne for 4N _e s’ = 1000. These values are not unrealistically long as compared with -T~ 5N _e obtained for 4N _e s’ = 0. The approximate analytical treatment has also been extended to estimate the effect of low rate crossing over in retarding fixation. The bearing of these findings on molecular evolution is discussed with special reference to coupled substitutions at interacting amino acid (or nucleotide) sites within a folded protein (orrna) molecule. It is concluded that compensatory neutral mutants may play an important role in molecular evolution.     

The evolution of harm--effect of sexual conflicts and population size

Conflicts of interest between mates can promote the evolution of male traits that reduce female fitness and that drive coevolution between the sexes. The rate of adaptation depends on the intensity of selection and its efficiency, which depends on drift and genetic variability. This leads to the largely untested prediction that coevolutionary adaptations such as those driven by sexual conflict should evolve faster in large populations. We tested this using the bruchid beetle Callosobruchus maculatus, a species where harm inflicted by males is well documented. Although most experimental evolution studies remove sexual conflict, we reintroduced it in populations in which it had been experimentally removed. Both population size and standing genetic variability were manipulated in a factorial experimental design. After 90 generations of relaxed conflict (monogamy), the reintroduction of sexual conflicts for 30 generations favored males that harmed females and females that were more resistant to the genital damage inflicted by males. Males evolved to become more harmful when population size was large rather than when initial genetic variation was enriched. Our study shows that sexual selection can create conditions in which males can benefit from harming females and that selection may tend to be more intense and effective in larger populations.     

Egg size evolution and energetic constraints on population dynamics.

We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.     

The role of population size, pleiotropy and fitness effects of mutations in the evolution of overlapping gene functions

Sheltered from deleterious mutations, genes with overlapping or partially redundant functions may be important sources of novel gene functions. While most partially redundant genes originated in gene duplications, it is much less clear why genes with overlapping functions have been retained, in some cases for hundreds of millions of years. A case in point is the many partially redundant genes in vertebrates, the result of ancient gene duplications in primitive chordates. Their persistence and ubiquity become surprising when it is considered that duplicate and original genes often diversify very rapidly, especially if the action of natural selection is involved. Are overlapping gene functions perhaps maintained because of their protective role against otherwise deleterious mutations? There are two principal objections against this hypothesis, which are the main subject of this article. First, because overlapping gene functions are maintained in populations by a slow process of "second order" selection, population sizes need to be very high for this process to be effective. It is shown that even in small populations, pleiotropic mutations that affect more than one of a gene''s functions simultaneously can slow the mutational decay of functional overlap after a gene duplication by orders of magnitude. Furthermore, brief and transient increases in population size may be sufficient to maintain functional overlap. The second objection regards the fact that most naturally occurring mutations may have much weaker fitness effects than the rather drastic "knock-out" mutations that lead to detection of partially redundant functions. Given weak fitness effects of most mutations, is selection for the buffering effect of functional overlap strong enough to compensate for the diversifying force exerted by mutations? It is shown that the extent of functional overlap maintained in a population is not only independent of the mutation rate, but also independent of the average fitness effects of mutation. These results are discussed with respect to experimental evidence on redundant genes in organismal development.     

The role of host population heterogeneity in the evolution of virulence

I examine here the effects of host heterogeneity in the growth of immune response on the evolution and co-evolution of virulence. The analysis is based on an extension of the 'nested model' by Gilchrist and Sasaki [Modeling host-parasite coevolution, J. Theor. Biol. 218 (2002), pp. 289-308]; the criteria for host and parasite evolution, in the paradigm of adaptive dynamics, for that model are derived in generality. Host heterogeneity is assumed to be fixed at birth according to a lognormal distribution or to the presence of two discrete types. In both cases, it is found that host heterogeneity determines a dramatic decrease in pathogen virulence, since pathogens will tune to the 'weakest' hosts. Finally we clarify how contrasting results present in the literature are due to different modelling assumptions.     

Population size and molecular evolution on islands

The nearly neutral theory predicts that the rate and pattern of molecular evolution will be influenced by effective population size (Ne), because in small populations more slightly deleterious mutations are expected to drift to fixation. This important prediction has not been widely empirically tested, largely because of the difficulty of comparing rates of molecular evolution in sufficient numbers of independent lineages which differ only in Ne. Island endemic species provide an ideal test of the effect of Ne on molecular evolution because species restricted to islands frequently have smaller Ne than closely related mainland species, and island endemics have arisen from mainland lineages many times in a wide range of taxa. We collated a dataset of 70 phylogenetically independent comparisons between island and mainland taxa, including vertebrates, invertebrates and plants, from 19 different island groups. The rate of molecular evolution in these lineages was estimated by maximum likelihood using two measures: overall substitution rate and the ratio of non-synonymous to synonymous substitution rates. We show that island lineages have significantly higher ratios of non-synonymous to synonymous substitution rates than mainland lineages, as predicted by the nearly neutral theory, although overall substitution rates do not differ significantly.     

The molecular evolution of trypanosomes.

The absence of a fossil record has meant that the evolution of protozoa has remained largely a matter for speculation. Recent advances in molecular biology and phylogenetic analysis, however, are allowing the 'history written in the genes' to be interpreted. Here, Jamie Stevens and Wendy Gibson review progress in reconstruction of trypanosome phylogeny based on molecular data from rRNA and protein-coding genes.     

Innovativeness, population size and cumulative cultural evolution

Henrich [Henrich, J., 2004. Demography and cultural evolution: how adaptive cultural processes can produce maladaptive losses—the Tasmanian case. Am. Antiquity 69, 197-214] proposed a model designed to show that larger population size facilitates cumulative cultural evolution toward higher skill levels. In this model, each newborn attempts to imitate the most highly skilled individual of the parental generation by directly-biased social learning, but the skill level he/she acquires deviates probabilistically from that of the exemplar (cultural parent). The probability that the skill level of the imitator exceeds that of the exemplar can be regarded as the innovation rate. After reformulating Henrich’s model rigorously, we introduce an overlapping-generations analog based on the Moran model and derive an approximate formula for the expected change per generation of the highest skill level in the population. For large population size, our overlapping-generations model predicts a much larger effect of population size than Henrich’s discrete-generations model. We then investigate by way of Monte Carlo simulations the case where each newborn chooses as his/her exemplar the most highly skilled individual from among a limited number of acquaintances. When the number of acquaintances is small relative to the population size, we find that a change in the innovation rate contributes more than a proportional change in population size to the cumulative cultural evolution of skill level.     

The role of the North Atlantic Oscillation in controlling U.K. butterfly population size and phenology

1. The North Atlantic Oscillation (NAO) exerts considerable control on U.K. weather. This study investigates the impact of the NAO on butterfly abundance and phenology using 34 years of data from the U.K. Butterfly Monitoring Scheme (UKBMS).2. The study uses a multi-species indicator to show that the NAO does not affect overall U.K. butterfly population size. However, the abundance of bivoltine butterfly species, which have longer flight seasons, were found to be more likely to respond positively to the NAO compared with univoltine species, which show little or a negative response.3. A positive winter NAO index is associated with warmer weather and earlier flight dates for Anthocharis cardamines (Lepidoptera: Pieridae), Melanargia galathea (Lepidoptera: Nymphalidae), Aphantopus hyperantus (Lepidoptera: Nymphalidae), Pyronia tithonus (Lepidoptera: Nymphalidae), Lasiommata megera (Lepidoptera: Nymphalidae) and Polyommatus icarus (Lepidoptera: Lycaenidae). In bivoltine species, the NAO affects the phenology of the first generation, the timing of which indirectly controls the timing of the second generation.4. The NAO influences the timing of U.K. butterfly flight seasons more strongly than it influences population size.     

Adaptive evolution and effective population size in wild house mice

Estimates of the proportion of amino acid substitutions that have been fixed by selection (α) vary widely among taxa, ranging from zero in humans to over 50% in Drosophila. This wide range may reflect differences in the efficacy of selection due to differences in the effective population size (N(e)). However, most comparisons have been made among distantly related organisms that differ not only in N(e) but also in many other aspects of their biology. Here, we estimate α in three closely related lineages of house mice that have a similar ecology but differ widely in N(e): Mus musculus musculus (N(e) ～ 25,000-120,000), M. m. domesticus (N(e) ～ 58,000-200,000), and M. m. castaneus (N(e) ～ 200,000-733,000). Mice were genotyped using a high-density single nucleotide polymorphism array, and the proportions of replacement and silent mutations within subspecies were compared with those fixed between each subspecies and an outgroup, Mus spretus. There was significant evidence of positive selection in M. m. castaneus, the lineage with the largest N(e), with α estimated to be approximately 40%. In contrast, estimates of α for M. m. domesticus (α = 13%) and for M. m. musculus (α = 12 %) were much smaller. Interestingly, the higher estimate of α for M. m. castaneus appears to reflect not only more adaptive fixations but also more effective purifying selection. These results support the hypothesis that differences in N(e) contribute to differences among species in the efficacy of selection.     

The evolution of endothermy: role for membranes and molecular activity

On the basis of the comparative approach and three models of metabolism (endothermic and ectothermic vertebrates, body mass, and mammalian development), we suggest that a few common cellular processes, linked either directly or indirectly to membranes, consume the majority of energy used by most organisms; that membranes act as pacemakers of metabolism through changes in lipid composition, altering membrane characteristics and the working environment of membrane proteins--specifically, that changes in the membrane environment similarly affect the molecular activities (specific rates of activity) of membrane-bound proteins; and that polyunsaturation of membranes increases whereas monounsaturation decreases the activity of membrane proteins. Experiments designed to test this theory using the sodium pump support this supposition. Potential mechanisms considered include fluidity, electrical fields, and related surface area requirements of lipids. In considering the evolution of endothermy in mammals, for example, if the first mammals were small, possibly nocturnal and active organisms, all these factors would favour increased polyunsaturation of membranes. Such changes (from monounsaturated to polyunsaturated membranes) would allow membranes to set the pace of metabolism in the evolution of endothermy.     

Species-specific size expansion and molecular evolution of the oleosins in angiosperms

Oleosins are hydrophobic plant proteins thought to be important for the formation of oil bodies, which supply energy for seed germination and subsequent seedling growth. To better understand the evolutionary history and diversity of the oleosin gene family in plants, especially angiosperms, we systematically investigated the molecular evolution of this family using eight representative angiosperm species. A total of 73 oleosin members were identified, with six members in each of four monocot species and a greater but variable number in the four eudicots. A phylogenetic analysis revealed that the angiosperm oleosin genes belonged to three monophyletic lineages. Species-specific gene duplications, caused mainly by segmental duplication, led to the great expansion of oleosin genes and occurred frequently in eudicots after the monocot–eudicot divergence. Functional divergence analyses indicate that significant amino acid site-specific selective constraints acted on the different clades of oleosins. Adaptive evolution analyses demonstrate that oleosin genes were subject to strong purifying selection after their species-specific duplications and that rapid evolution occurred with a high degree of evolutionary dynamics in the pollen-specific oleosin genes. In conclusion, this study serves as a foundation for genome-wide analyses of the oleosins. These findings provide insight into the function and evolution of this gene family in angiosperms and pave the way for studies in other plants.     

On the role of body size for life-history evolution

1. Body size is a central element in current theories of life-history evolution. Models for optimal age at maturity are based on the assumptions that there is a trade-off between development time and adult size and that larger size provides a reproductive advantage.
2. The results of large, replicated experiments with the water strider Gerris buenoi (Heteroptera: Gerridae) contradict both these assumptions. Individual rearings under field conditions showed that there is a negative, not a positive, correlation between development time and adult size. The physiological basis of growth, with stretch-induced moulting, may provide a partial explanation for this correlation.
3. This study examined a number of fitness components for their correlations with female size: lifetime fecundity, reproductive life span, average volume per egg, total volume of eggs laid, and the proportion of eggs hatched. None of these traits was correlated with female size.
4. The data on water striders suggest an alternative scenario for life-history evolution, in which size is not an adaptive trait, but evolves as a correlated response to selection on other traits. This expands the range of possible models, and opens life-history theory to the debate about adaptation and optimality.     

The role of target size in neuronal survival.

A loss of about half of the trochlear motor neurons occurs during the course of normal development in duck and quail embryos. The role of the size of the target muscle in controlling the number of surviving motor neurons was examined by making motor neurons innervate targets either larger or smaller in size than their normal target. In one experiment the smaller trochlear motor neuron pool of the quail embryo was forced to innervate the larger superior oblique muscle of the duck embryo. This was accomplished by grafting the midbrain of a quail embryo in the place of the midbrain of a duck embryo. Results indicated that no additional quail trochlear motor neurons were rescued in spite of a considerable increase in target size. In another experiment the larger trochlear motor neuron pool of the duck embryo was made to innervate the smaller superior oblique muscle of the quail embryo. This resulted in loss of some additional neurons; however, the number of surviving motor neurons was not proportionate to the reduction in target size. These experiments failed to provide support for the hypothesis that the size of the target muscle controls the number of surviving motor neurons. Although contact with target is necessary for survival of neurons, factors other than the number or size of target cells are involved in the control of motor neuron numbers during development.     

The role of finite population size and linkage in response to continued truncation selection

Summary In an attempt to analyse long-term response in finite dioecious populations, selection processes are simulated on a computer with situations of parental population size, linkages between loci, selection intensity, and heritability, specified in a 3⁴ factorial design. A diploid polygenic system of 40 loci on 4 chromosomes is considered for additive genes. Linkage levels are specified as free recombinations, adjacent loci 5 map units apart, and as clusters on chromosomes with a distance of only .5 units between adjacent loci. Parental populations of 8, 16, and 64, truncation selection of 1/2, 1/4, and 1/8 of the progeny each generation, and initial heritability of 1, 1/3, and 1/9 are simulated for various populations.For these populations, which are initially samples from a theoreticalHardy-Weinberg situation, it is shown that an initial linear phase of response, which may last for only 2 or 3 generations in some cases, depends on the intensity of selection alone. The effects and interactions of all the above factors on the curvilinearity of response in later generations are analysed. It appears that linkages between loci have a strong influence in reducing the rate of response and the total response. In the extreme cases of gene clusters in a parental population size of 8 with low heritability, truncation selection is relatively almost completely ineffective in causing change in the mean over generations. The effect of tight linkage is also exhibited in causing more reduction in genotypic variance than can be accounted for by corresponding response.The depressing effect of finiteness of population size on the rate of response and the total response appears to increase in geometric proportion with linkages between loci. The number of generations to fixation appears to be reduced in a similar manner. A strong interaction between population size and linkage is thereby found in various analyses. With parental populations as large as 64, linkage effects on response are negligible when recombinations between adjacent loci are .05 or more. In such situations there is a slower rate of response in later generations with linkage but the total response attained and the rate of fixation of inferior genes is about the same as for free recombinations. Increase in the intensity of selection appears to augment the effects of linkage in reducing the rate of response in later generations. This type of interaction is attributed to the accumulation of gametic disequilibria due to selection which are retained in the population over generations with linkage.

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Zusammenfassung In der Absicht, das Verhalten einer begrenzten diözischen Population über einen langen Zeitraum zu analysicren, wurden Selektionsvorgänge auf einem Computer simuliert. Hierbei wurden die Größe der Elterpopulation, die Koppelung zwischen den Loci, die Selektionsintensität und die Heritabilität in einem 3⁴-faktoriellen Versuch variiert. Es wird ein diploides polygenes System mit vierzig Loci auf vier Chromosomen mit additiver Genwirkung zugrunde gelegt. Für die Koppelungsbeziehungen werden freie Rekombination, ein Abstand von fünf Rekombinationseinheiten zwischen benachbarten Loci und die Bildung von Genclustern auf den Chromosomen mit jeweils nur 0,5Morgan-Einheiten Abstand zwischen benachbarten Loci angenommen. Es werden elterliche Populationen des Umfanges 8, 16 und 64, trunkierende (stutzende) Selektion mit einer Fraktion von 1/2, 1/4 und 1/8 der Nachkommen je Generation und eine ursprüngliche Heritabilität von 1, 1/3 und 1/9 für verschiedene Populationen simuliert.Für alle jene Populationen, die ursprünglich als Stichproben aus einer theoretischenHardy-Weinberg-Situation stammen, kann gezeigt werden, daß eine anfänglich lineare Phase der Reaktion, die in einigen Fällen nur über zwei bis drei Generationen anhält, allein von der Selektionsintensität abhängt. Die Wirkungen und Wechselwirkungen aller oben genannten Faktoren auf die Nichtlinearität der Reaktion in späteren Generationen wird untersucht. Es zeigt sich, daß Koppelung zwischen den Loci einen starken Einfluß auf die Reduktion der Reaktionsgeschwindigkeit und auf die Endreaktion ausübt. In dem extremen Fall der Gencluster in einer Ausgangspopulation des Umfanges 8 mit geringer Heritabilität ist die trunkierende Selektion hinsichtlich der Änderung des Mittels über Generationen hinweg praktisch völlig unwirksam. Die Wirkung enger Koppelung manifestiert sich außerdem in einer stärkeren Reduktion der genotypischen Varianz, als sie auf Grund der entsprechenden Reaktion erklärt werden kann. Der reduzierende Effekt der Begrenzung des Populationsumfanges auf die Reaktionsgeschwindigkeit und die Endreaktion erweist sich als geometrisch proportional zur Koppelung zwischen den Loci. Die Zahl der Generationen bis zur Fixierung wird in ähnlicher Weise reduziert. Hierbei wird eine starke Wechselwirkung zwischen der Populationsgröße und der Koppelung in den verschiedenen Untersuchungen beobachtet. Der Einfluß der Koppelung auf die Reaktion der Populationen kann vernachlässigt werden, wenn die elterliche Population den Umfang 64 hat und die Rekombination zwischen benachbarten Loci 0,05 übersteigt. In derartigen Situationen gibt es zwar eine langsamere Antwortrate in späteren Generationen mit Koppelung, jedoch ist die Endreaktion, die erreicht wird, und die Fixierungsrate überlegener Gene etwa die gleiche wie bei freier Spaltung. Eine Zunahme der Selektionsintensität scheint die Wirkung der Koppelung hinsichtlfch der Reduktion der Reaktionsgeschwindigkeit in späteren Generationen zu vergrößern. Dieser Typ der Wechselwirkung wird der Häufung gametischer Ungleichgewichte, die infolge der Selektion über Generationen in der Population erhalten werden, zugeschrieben.

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Journal Paper No. 5872, Iowa Agriculture and Home Economics Experiment Station, Ames, supported by National Science Foundation Grant 19218 and National Institute of Health Grant GM-13827.

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On leave fromWest Pakistan Agricultural University Lyallpur.

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Statistical Laboratory and Department of Animal Science, respectively.