The development of Darwin's thought is traced from the uncritical acceptance of the theories of Independent Creation and Fixity of Species by his peers, through progressive dissatisfaction with the ability of these theories to account for the actual distribution of species in the natural world; and the formulation of his theory of Evolution through Natural Selection based on an analogy of the workings of nature, with the workings of the great English animal and plant breeders of the late 18th and early 19th centuries.

Fisher's theorem of natural selection implies that the population genetic variance of quasi-neutral traits should be mostly additive. In the case of fitness component traits, however, that variance would be characterised by a substantial contribution from non-additive loci. In parallel, Robertson's theorem states that selection will change the population mean of a trait proportionally to the magnitude of the genetic correlation between that trait and fitness, which should be weak for quasi-neutral traits or strong for the mean fitness components. Drosophila data from inbreeding and artificial selection experiments are discussed within that theoretical framework. In addition, the process of regeneration by mutation of the genetic variance of a quasi-neutral trait (abdominal bristle number) in a Drosophila population initially homozygous at all loci has been analysed. After 485 generations of mutation accumulation, the levels of additive variance found in this population closely approached those commonly observed in laboratory populations. Furthermore, these values, together with previously reported estimates for natural populations, could be jointly explained by a model assuming weak causal stabilising selection.

The observation of animal and plant breeding greatly influenced Darwin's thought. During the maturation of his theory of evolution, he realised that anthropogenic selection was the driving force shaping domestic animal phenotypes to meet human needs. A concept that was transferred to natural species after the reading of Malthus’ book on the struggle for existence. After the definition of his theory, Darwin continuously searched in domestic plant and animals confirmation of his hypotheses on the transmission of traits and evolution of species. He also observed that some morphological and physiological traits were shared among unrelated domestic animal species but were absent in the wild ancestors. The Russian scientist Dmitri Belyaev proved that these traits emerged as a consequence of domestication by recording their appearance in silver fox selected for tame behaviour, an experiment that is ongoing since about 50 years. Nowadays, genomic technologies allow scientists to explore the molecular basis of these traits and to reconstruct the evolutionary history of domestic animals. The availability of high-density single nucleotide polymorphisms panels permits the detection of signatures left by natural and artificial selection along the genome of domestic animals. The analysis of genomic and mitochondrial DNA contributes substantial information for the identification of sites of primary domestication, Neolithic routes of world colonisation and later voyages linked to human migration events. The understanding of all changes occurring following domestication and anthropogenic selection may help in understanding natural selection and molecular evolution occurring in all living organisms.

The Darwin theory of evolution by natural selection is based on three principles: (a) variation; (b) inheritance; and (c) natural selection. Here, I take these principles as an excuse to review some topics related to the future research prospects in Animal Breeding. With respect to the first principle I describe two forms of variation different from mutation that are becoming increasingly important: variation in copy number and microRNAs. With respect to the second principle I comment on the possible relevance of non-mendelian inheritance, the so-called epigenetic effects, of which the genomic imprinting is the best characterized in domestic species. Regarding selection principle I emphasize the importance of selection for social traits and how this could contribute to both productivity and animal welfare. Finally, I analyse the impact of molecular biology in Animal Breeding, the achievements and limitations of quantitative trait locus and classical marker-assisted selection and the future of genomic selection.