The theory of evolution is perceived by many people, particularly but not only in the United States, as a controversial theory not yet fully demonstrated. Yet, that living organisms, including humans, have evolved from ancestors who were very different from them is beyond reasonable doubt, confirmed by at least as much evidence as any other widely accepted scientific theory. I argue that Darwin’s contribution to science goes much beyond the theory of evolution in itself. The theory of natural selection explains the adaptations of organisms, their ‘design’. The ‘Copernican Revolution’ brought the phenomena of the physical universe into the realm of science: explanations by natural causes that can be tested by observation and experiment. However, the scientific revolution that occurred in the 16th and 17th centuries had left the living world out of scientific explanations, because organisms seemingly show that they are ‘designed,’ and thus call for an intentional designer. It was Darwin’s greatest contribution to science, to demonstrate that the adaptations of organisms, their apparent ‘design’, can be explained by natural processes governed by natural laws. At that point, science came into maturity, because all natural phenomena in the universe, living as well as nonliving, could be investigated scientifically, and explained as matter in motion governed by natural laws.

The empirical study of speciation has brought us closer to unlocking the origins of life’s vast diversity. By examining recently formed species, a number of general patterns, or rules, become apparent. Among fixed differences between species, sexual genes and traits are one of the most rapidly evolving and novel functional classes, and premating isolation often develops earlier than postmating isolation. Among interspecific hybrids, sterility evolves faster than inviability, the X-chromosome has a greater effect on incompatibilities than autosomes, and hybrid dysfunction affects the heterogametic sex more frequently than the homogametic sex (Haldane’s rule). Haldane’s rule, in particular, has played a major role in reviving interest in the genetics of speciation. However, the large genetic and reproductive differences between taxa and the multi-factorial nature of each rule have made it difficult to ascribe general mechanisms. Here, we review the extensive progress made since Darwin on understanding the origin of species. We revisit the rules of speciation, regarding them as landmarks as species evolve through time. We contrast these ‘rules’ of speciation to ‘mechanisms’ of speciation representing primary causal factors ranging across various levels of organization—from genic to chromosomal to organismal. To explain the rules, we propose a new ‘hierarchical faster-sex’ theory: the rapid evolution of sex and reproduction-related (SRR) genes (faster-SRR evolution), in combination with the preferential involvement of the X-chromosome (hemizygous X-effects) and sexually selected male traits (faster-male evolution). This unified theory explains a comprehensive set of speciation rules at both the prezyotic and postzygotic levels and also serves as a cohesive alternative to dominance, composite, and recent genomic conflict interpretations of Haldane’s rule.

The analysis of evolutionary models requires an appropriate definition for fitness. In this paper, I review such definitions in relation to the five major dimensions by which models may be described, namely

1. finite versus infinite (or very large) population size,

2. type of environment (constant, fixed length, temporally stochastic, temporally predictable, spatially stochastic, spatially predictable and social environment),

3. density-independent or density-dependent,

4. inherent population dynamics (equilibrium, cyclical and chaotic), and

5. frequency-dependent or independent.

In simple models, the Malthusian parameter ‘𝑟’ or the net reproductive rate $R_0$ may be satisfactory, but once density-dependence or complex population dynamics is introduced the invasion exponent should be used. Defining fitness in a social environment or when there is frequency-dependence requires special consideration.

Although molecular methods, such as QTL mapping, have revealed a number of loci with large effects, it is still likely that the bulk of quantitative variability is due to multiple factors, each with small effect. Typically, these have a large additive component. Conventional wisdom argues that selection, natural or artificial, uses up additive variance and thus depletes its supply. Over time, the variance should be reduced, and at equilibrium be near zero. This is especially expected for fitness and traits highly correlated with it. Yet, populations typically have a great deal of additive variance, and do not seem to run out of genetic variability even after many generations of directional selection. Long-term selection experiments show that populations continue to retain seemingly undiminished additive variance despite large changes in the mean value. I propose that there are several reasons for this.

1. The environment is continually changing so that what was formerly most fit no longer is.

2. There is an input of genetic variance from mutation, and sometimes from migration.

3. As intermediate-frequency alleles increase in frequency towards one, producing less variance (as $p \to 1$, $p(1 - p) \to 0$), others that were originally near zero become more common and increase the variance. Thus, a roughly constant variance is maintained.

4. There is always selection for fitness and for characters closely related to it.

To the extent that the trait is heritable, later generations inherit a disproportionate number of genes acting additively on the trait, thus increasing genetic variance. For these reasons a selected population retains its ability to evolve. Of course, genes with large effect are also important. Conspicuous examples are the small number of loci that changed teosinte to maize, and major phylogenetic changes in the animal kingdom. The relative importance of these along with duplications, chromosome rearrangements, horizontal transmission and polyploidy is yet to be determined. It is likely that only a case-by-case analysis will provide the answers. Despite the difficulties that complex interactions cause for evolution in Mendelian populations, such populations nevertheless evolve very well. Long-lasting species must have evolved mechanisms for coping with such problems. Since such difficulties do not arise in asexual populations, a comparison of epistatic patterns in closely related sexual and asexual species might provide some important insights.

A fundamental assumption of models for the maintenance of genetic variation by environmental heterogeneity is that selection favours different genotypes in different environments. Here, I use a method for measuring total fitness of chromosomal heterozygotes in Drosophila melanogaster to assess genotype–environment interaction for fitness across two ecologically relevant environments, medium with and without added ethanol. Two-third chromosomes are compared, one from a population selected for ethanol tolerance, and the other from a control population. The results show strong crossing of reaction norms for outbred, total fitness, with the chromosome from the ethanol-adapted population increasing fitness on ethanol-supplemented food, but decreasing fitness on regular food, relative to the chromosome from the control population. Although I did not map the fitness effects below the chromosome level, the method could be adapted for quantitative trait locus mapping, to determine whether a substantial proportion of fitness variation is contributed by loci at which different alleles are favoured in different environments.

In the late 19th century, the evolutionary approach to the problem of ageing was initiated by August Weismann, who argued that natural selection was more important for ageing than any physiological mechanism. In the mid-twentieth century, J. B. S. Haldane, P. B. Medawar and G. C. Williams informally argued that the force of natural selection falls with adult age. In 1966, W. D. Hamilton published formal equations that showed mathematically that two ‘forces of natural selection’ do indeed decline with age, though his analysis was not genetically explicit. Brian Charlesworth then developed the required mathematical population genetics for the evolution of ageing in the 1970’s. In the 1980’s, experiments using Drosophila showed that the rate of ageing evolves as predicted by Hamilton’s ‘forces of natural selection’. The discovery of the cessation of ageing late in life in the 1990’s was followed by its explanation in terms of evolutionary theory based on Hamilton’s forces. Recently, it has been shown that the cessation of ageing can also be manipulated experimentally using Hamilton’s ‘forces of natural selection’. Despite the success of evolutionary research on ageing, mainstream gerontological research has largely ignored both this work and the opportunity that it provides for effective intervention in ageing.

Genetic variability of quantitative traits was investigated in aMoroccan population of Drosophila melanogaster, with an isofemale line design. Results were compared with data previously obtained from French populations. Although the environmental and thermal conditions are very different in France and Morocco, only two significant differences were observed: a shorter wing and a lighter abdomen pigmentation in Morocco. It is, therefore, concluded that Moroccan D. melanogaster are quite typical temperate flies, belonging to the Palaearctic region, and very different from the ancestral Afrotropical populations. Almost all traits were genetically variable, as shown by significant intraclass correlations among lines. Genetic correlations were highly significant among three size-related traits, while much lower between size and bristle numbers. Fluctuating asymmetry was greater for abdominal bristles than for sternopleural bristles. Sex dimorphism, analysed as a female/male ratio, was identical in French and Moroccan populations. Examination of the thorax length/thorax width ratio showed that the thorax is more elongated in females. Sexual dimorphism of wing length was significantly more correlated to thorax width than to thorax length. The results illustrate the value of measuring numerous quantitative traits on the same flies for characterizing the genetic architecture of a natural population. In several cases, and especially for genetic correlations, some interesting suggestions could be made, which should be confirmed, or invalidated, by more extensive investigations.

Intralocus sexual conflict occurs when males and females experience sex-specific selection on a shared genome. With several notable exceptions, intralocus sexual conflict has been investigated in constant environments to which the study organisms have had an opportunity to adapt. However, a change in the environment can result in differential or even opposing selection pressures on males and females, creating sexual conflict. We used experimental evolution to explore the interaction between intralocus sexual conflict, sexual dimorphism and environmental variation in Drosophila melanogaster. Six populations were selected for adult desiccation resistance (D), with six matched control populations maintained in parallel (C). After 46 generations, the D populations had increased in survival time under arid conditions by 68% and in body weight by 20% compared to the C populations. The increase in size was the result of both extended development and faster growth rate of D juveniles. Adaptation to the stress came at a cost in terms of preadult viability and female fecundity. Because males are innately less tolerant of desiccation stress, very few D males survived desiccation-selection; while potentially a windfall for survivors, these conditions mean that most males’ fitness was determined posthumously. We conjectured that selection for early maturation and mating in males was in conflict with selection for survival and later reproduction in females. Consistent with this prediction, the sexes showed different patterns of age-specific desiccation resistance and resource acquisition, and there was a trend towards increasingly female-biased sexual size dimorphism. However, levels of desiccation resistance were unaffected, with D males and females increasing in parallel. Either there is a strong positive genetic correlation between the sexes that limits independent evolution of desiccation resistance, or fitness pay-offs from the strategy of riding out the stress bout are great enough to sustain concordant selection on the two sexes. We discuss the forces that mould fitness in males under a regimen where trade-offs between survival and reproduction may be considerable.

The earlier mean adult emergence between males and females, protandry, has been well studied mathematically and in comparative studies. However, quantitative and evolutionary genetic research on protandry is scarce. The butterfly, Bicyclus anynana exhibits protandry and here we selected for each of the different combinations of male and female development time in this species, thus including direct selection on protandry (i.e., FAST, fast males and fast females; SLOW, slow males and slow females; FMSF, fast males and slow females; and SMFF, slow males and fast females). After eight generations of selection there was no significant response for increased or decreased protandry, whereas selection for increased or decreased development time in both sexes (FAST or SLOW) was successful. Continued selection (> 30 generations) for decreased or increased protandry showed a significant difference between the FMSF_C and SMFF_C lines (subscript c for continued selection), which was of the same magnitude as the nonsignificant difference observed between the FMSF and SMFF lines at generation eight. This indicated that the initial selection was successful, but that the difference between the lines did not increase with continued selection. Our results also indicate that the genetic covariance across sexes for development time is near unity. Interestingly, lines selected for decreased protandry (SMFF) had lower egg-to-adult survival, and broods from these lines had lower rates of egg hatching. This suggests that interactions with fertility might constrain certain directions of change in patterns of protandry. Moreover, selection yielded a change in the ratio of male to female development time for slow lines, suggesting that some amount of sex-specific genetic variance for development time is still present in this population. The FMSF_C line showed the largest effect of selection on protandry, mainly through an effect on female developmental time. Lastly, our results show that temperature has an effect on the amount of protandry in the selected lines. These results are discussed in relation to the ecology of this species and the evolution of protandry.

Environmental stress has been suggested to be a major evolutionary force, both through inducing strong selection and because of its direct impact on developmental buffering processes that alter the evolvability of organisms. In particular, temperature has attracted much attention because of its importance as an ecological feature and the relative ease with which it can be experimentally manipulated in the lab. Evolution Canyon, Lower Nahal Oren, Israel, is a well studied natural site where ecological parameters are suspected to drive evolutionary differentiation. In this study, using Drosophila melanogaster isofemale lines derived from wild flies collected on both slopes of the canyon, we investigated the effect of developmental temperature upon the different components of phenotypic variation of a complex trait: the wing. Combining geometric and traditional morphometrics, we find only limited evidence for a differentiation among slopes. Investigating simultaneously phenotypic plasticity, genetic variation among isofemale lines, variation among individuals and fluctuating asymmetry, we could not identify a consistent effect of the stressful conditions encountered on the south facing slope. The prevailing structuring effect is that of the experimentally manipulated temperature which clearly influences wing mean size and shape. Variability, in contrast, is not consistently affected by temperature. Finally, we investigated the specific relationship between individual variation and fluctuating asymmetry. Using metric multi-dimensional scaling we show that the related patterns of wing shape variation are not identical, supporting the view that the underlying developmental processes are to a certain extent different.

The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those biologists who believe on theoretical grounds that there is no sense of fitness that can usefully be said to be optimized. The current paper’s main objective is to provide a careful mathematical introduction to the project, and it also reflects on the project’s scope and limitations. The central argument is the proof of close ties between the mathematics of motion, as embodied in the Price equation, and the mathematics of optimization, as represented by optimization programmes. To make these links, a general and abstract model linking genotype, phenotype and number of successful gametes is assumed. The project has begun with simple dynamic models and simple linking models, and its progress will involve more realistic versions of them. The versions given here are fully mathematically rigorous, but elementary enough to serve as an introduction.