Wallace made very few direct references to Matthew. His book “Darwinism” (1st Edn May 1889, 2nd Edn Aug 1889, 3rd Edn 1901) contains a short treatment of “The Early Transmutationists”, which contains references to Lamarck and Chambers, and later on to Geoffroy Saint Hilaire, Dean Herbert, Grant and Von Buch, but nothing on Matthew. His autobiography “My Life: a Record of Events and Opinions” (1905, Vol 1 and Vol 2), contains the now well-known account of how he arrived at his version of the evolutionary origin of species by natural selection, while bed-ridden between bouts of (probably) malarial fever in the Malay Archipelago, and which sets out his claim to have arrived at his ideas independently rather than as a result of reading Matthew’s book.
Wallace makes a brief reference to Matthew in the Preface to his collection of essays “Contributions to the Theory of Natural Selection” (1st Edn 1870, 2nd Edn 1871), over the question of where Wallace’s contribution should stand in relation to Darwin and others (p.iv):
It therefore happens, that, while some writers give me more credit than I deserve, others may very naturally class me with Dr. Wells and Mr. Patrick Matthew, who, as Mr. Darwin has shown in the historical sketch given in the 4th and 5th Editions of the “Origin of Species”, certainly propounded the fundamental principle of “natural selection” before himself, but who made no further use of that principle, and failed to see its wide and immensely important applications.
Wallace’s most interesting comments on Matthew are in relation to Samuel Butler’s “Evolution, Old and New” (1st Edn 1879, 2nd Edn 1882, 3rd Edn 1911). Butler believed that Darwin had no good answer to the question of how variation among organisms was engendered, and believed that previous writers, especially Buffon, Erasmus Darwin and Lamarck, had a clearer and better solution to this problem through the action of use-and-disuse inheritance of acquired characteristics (more details here). Butler saw Matthew’s view on this question as Lamarckian, and quoted extensively from “On Naval Timber and Arboriculture” to prove his point. The passages quoted are, apart from the omission of a single paragraph discussing spontaneous generation, the same as those presented by Matthew in his letter to the Gardeners’ Chronicle of 7 April 1860.
As Wallace recounts in his autobiography “My Life: a Record of Events and Opinions”, p.83, Butler sent Wallace copies of both “Life and Habit” and “Evolution, Old and New” in 1879, and Wallace wrote reviews of both of them in the journal Nature in the same year. Wallace also wrote a letter to Samuel Butler of 9 May 1879, in which he wrote the following regarding Butler’s treatment of Matthew in “Evolution, Old and New”:
To my mind, your quotations from Mr. Patrick Matthew are the most remarkable things in your whole book, because he appears to have completely anticipated the main ideas both of the ‘Origin of Species’ and of ‘Life and Habit.’
As promised in his letter to Butler, Wallace reviewed “Evolution, Old and New” in Nature, Vol 20 (issue of 12 June 1879), pp.141-4, and had these glowing words to say about his treatment of Matthew:
We come next to Mr. Patrick Matthew, who in 1831 put forth his views on the development theory in a work on arboriculture; and we think that most naturalists will be amazed at the range and accuracy of his system, and will give him the highest credit as the first to see the important principles of human and “natural selection,” conformity to conditions, and reversion to ancestral types; and also the unity of life, the varying degrees of individuality, and the continuity of ideas or habits forming an abiding memory, thus combining all the best essential features of the theories put forth by Lamarck, Darwin, and Mr. Butler himself. The following quotations illustrate Mr. Matthews’s views:– “As the field of existence is limited and preoccupied, it is only the hardier, more robust, better-suited-to-circumstance individuals who are able to struggle forward to maturity, these inhabiting only the situations to which they have superior adaptation and greater power of occupancy than any other kind; the weaker and less circumstance-suited being prematurely destroyed. This principle is in constant action; it regulates the colour, the figure, the capacities, and instincts; those individuals in each species whose colour and covering are best suited to concealment or protection from enemies, or defence from inclemencies or vicissitudes of climate, whose figure is best accommodated to health, strength, defence, and support; in such immense waste of primary and youthful life those only come forward to maturity from the strict ordeal by which nature tests their adaptation to her standard of perfection and fitness to continue their kind by reproduction.” He then goes on to show how this law tends to the production of almost uniform groups of individuals which we term species, and then adds: “This circumstance-adaptive law operating upon the slight but continued natural disposition to sport in the progeny, does not preclude the supposed influence which volition or sensation may have had over the configuration of the body.” This, he says, is a matter to be inquired into, as well as “its dependency upon the preceding links of the particular chain of life, variety being often merely types or approximations of former parentage; thence the variation of the family as well as of the individual must be embraced by our experiments.” These, and many other passages, show how fully and clearly Mr. Matthew apprehended the theory of natural selection, as well as the existence of more obscure laws of evolution, many years in advance of Mr. Darwin and myself, and in giving almost the whole of what Mr. Matthew has written on the subject Mr. Butler will have helped to call attention to one of the most original thinkers of the first half of the 19th century.
Later in the same review, Wallace also recognises that Matthew, like Darwin, used artificial selection as his motivation for deducing natural selection:
… there is this great advantage in using the term “natural selection,” that it keeps before the mind the striking analogy and almost identity between the action of man and of nature in modifying species, an identity that was never seen by any of the older writers, but which was first clearly apprehended by Mr. Patrick Matthew, and first fully worked out by Mr. Darwin himself.