William Bateson in the context of "Mendelian genetics"

The modern synthesis was the early 20th-century synthesis of Charles Darwin's theory of evolution and Gregor Mendel's ideas on heredity into a joint mathematical framework. Julian Huxley coined the term in his 1942 book, Evolution: The Modern Synthesis. The synthesis combined the ideas of natural selection, Mendelian genetics, and population genetics. It also related the broad-scale macroevolution seen by palaeontologists to the small-scale microevolution of local populations.

The synthesis was defined differently by its founders, with Ernst Mayr in 1959, G. Ledyard Stebbins in 1966, and Theodosius Dobzhansky in 1974 offering differing basic postulates, though they all include natural selection, working on heritable variation supplied by mutation. Other major figures in the synthesis included E. B. Ford, Bernhard Rensch, Ivan Schmalhausen, and George Gaylord Simpson. An early event in the modern synthesis was R. A. Fisher's 1918 paper on mathematical population genetics, though William Bateson, and separately Udny Yule, had already started to show how Mendelian genetics could work in evolution in 1902.

Mendelian inheritance (also known as Mendelism) is a type of biological inheritance following the principles originally proposed by Gregor Mendel in 1865 and 1866, re-discovered in 1900 by Hugo de Vries and Carl Correns, and later popularized by William Bateson. Its defining characteristic is heavy association with a singular gene. The principles were initially controversial. When Mendel's theories were integrated with the Boveri–Sutton chromosome theory of inheritance by Thomas Hunt Morgan in 1915, they became the core of classical genetics. Ronald Fisher combined these ideas with the theory of natural selection in his 1930 book The Genetical Theory of Natural Selection, putting evolution onto a mathematical footing and forming the basis for population genetics within the modern evolutionary synthesis.

Particulate inheritance is a pattern of inheritance discovered by Mendelian genetics theorists, such as William Bateson, Ronald Fisher or Gregor Mendel himself, showing that phenotypic traits can be passed from generation to generation through "discrete particles" known as genes, which can keep their ability to be expressed while not always appearing in a descending generation.

Self-decoration camouflage is a method of camouflage in which animals or soldiers select materials, sometimes living, from the environment and attach these to themselves for concealment.

The method was described in 1889 by William Bateson, who observed Stenorhynchus decorator crabs. It was classified as "adventitious protection" by Edward Bagnall Poulton in 1890, and as "adventitious concealing coloration" or "adventitious resemblance" by Hugh Bamford Cott in 1940, who compared it to the way Australian aborigines stalked waterfowl, covering their faces with water lily leaves.

Mutationism is one of several alternatives to evolution by natural selection that have existed both before and after the publication of Charles Darwin's 1859 book On the Origin of Species. In the theory, mutation was the source of novelty, creating new forms and new species, potentially instantaneously, in sudden jumps. This was envisaged as driving evolution, which was thought to be limited by the supply of mutations.

Before Darwin, biologists commonly believed in saltationism, the possibility of large evolutionary jumps, including immediate speciation. For example, in 1822 Étienne Geoffroy Saint-Hilaire argued that species could be formed by sudden transformations, or what would later be called macromutation. Darwin opposed saltation, insisting on gradualism in evolution as geology's uniformitarianism. In 1864, Albert von Kölliker revived Geoffroy's theory. In 1901 the geneticist Hugo de Vries gave the name "mutation" to seemingly new forms that suddenly arose in his experiments on the evening primrose Oenothera lamarckiana. In the first decade of the 20th century, mutationism, or as de Vries named it mutationstheorie, became a rival to Darwinism supported for a while by geneticists including William Bateson, Thomas Hunt Morgan, and Reginald Punnett.