Three links between Darwin and the above mentioned scholars are established historical facts that, nevertheless, need further evidence. It would be a fair thesis topic for a student at some history of science department, I guess.
But before presenting these facts and setting readers on a wild goose chase for fraud and plagiarism, I want to suggest a different historical context and frame of interpretation.
Historical frame of interpretation
Firstly, tracing the history of the idea of natural selection has frustrated many a historian, because it is a continuous flow of thoughts and words with almost insensible gradations. Ideas flow from abstruse philosophizing, lofty poetry, wild speculation, political agendas, rants of a madmen towards the momentous publication when everybody suddenly realised that now it was pure science. This does not only refute the myth that the idea of natural selection fell from heaven and precipitated in the brains of Darwin and Wallace. It also refutes the equally false myth that it fell from the sky and precipitated in Matthew's mind (or that of any other predecessor for that matter).
Secondly, Darwin almost had to be silent about his predecessors given that they were lofty poets abstruse philosophers, political agitators etc. If I may use an analogy, Darwin's position was not unlike that of an advocate of defense, who needed to fight free, against all odds, a culprit facing a sure death sentence. He must not associate his summing up to any of the shysters who have tried and failed before him lest it would damage his case. The reception of the Vestiges surely warned him of that danger.
Thirdly, they all pilfered like looters, according to our standards, including Matthew and Darwin. However, it was accepted practice back then, if you put on your own spin onto the received idea. For example, Charles Darwin turned natural selection from a principle conserving species (sensu Blyth) into one transforming them. He would therefore be allowed to brand it 'made by Darwin.' Likewise, Patrick Matthew turned the variation in trees from a fact used for ornamentation and utility (sensu Loudon) into a fact about a natural law and brand it 'made by Matthew.'
Back then, theories seem to have been accepted or rejected as wholes, that is, some false detail seems to have made a theory fair game for exploit. Times have changed and we, now, try to find references for every minor detail of a publication. It has already lead some scholars to deplore the poor style and bad reading through excessive referencing (e.g., here).
To apply our standards of referencing to Darwin or Wallace would simply be Whiggish. Those were gold rush days, back then, when land was simply taken, when slight modifications of any device were patented without specific citation of the predecessors being thus modified.*
Three facts of historical interest
Eiseley explains how Blyth used the concept of natural selection (though not the words) as a principle keeping species immutable, whereas Darwin turned it into the opposite. He admits that Darwin could hardly associate his work with the poetic ejaculations, philosophic speculations, or political rants of his predecessors without severely damaging the scientific standing of his work. Darwin was surely more able and willing to acknowledge predecessors in the third edition, after his case was won with the first. But he did not mention Blyth in his historical sketch. Darwin reduced Blyth to the role of taxonomist and field observer.
2. A link between Matthew (1831) and Loudon (1832. "Matthew Patrick On Naval Timber and Arboriculture with Critical Notes on Authors who have recently treated the Subject of Planting." Gardener’s Magazine. Vol. VIII. p.703). Matthew (1860) made it himself in his letter to Gardener's Chronicle.
It is clear that Loudon has not only read Matthew (1831), but also received his idea of natural selection and mentioned it explicitly as being concerned with the "origin of species and varieties."
Darwin, however, was on board the HMS Beagle when this review got published and will probably have missed it. May he not also have missed it after his return to England? There is no proof that Darwin has read Loudon's review, but that would be needed to establish the claim that Darwin must have read Matthew (1831). Later citations of Matthew by Loudon, as far as I have seen, do not mention the concept of natural selection or the origin of species, but only practical matters of pruning, planting and training trees.
3. A third fact is mentioned by Eisely (1979, 71), again. Namely the following passage in Darwin's essay of 1844 published only posthumously:
"In the case of forest trees raised in nurseries, which vary more than the same trees do in their aboriginal forests, the cause would seem to lie in their not having to struggle against other trees and weeds, which in their natural state doubtless would limit the conditions of their existence."While this is strikingly reminiscent of a similar passage in Matthew (1831, p. 308),
"Man's interference, by preventing this natural process of selection among plants, independent of the wider range of circumstances to which he introduces them, has increased the difference in varieties, particularly in the more domesticated kinds;"there is again no smoking gun showing that Darwin has gotten the inspiration for his statement from Matthew. In fact, Matthew may have gotten it from elsewhere and that may be the common, unacknowledged source of Matthew and Darwin. Matthew got his idea of variation in trees from others including Loudon (1806) and spin doctored it (see last post).
Matthew's combined two old ideas (natural selection + species transformation). The theory that the former could effect the latter did not fall from heaven. It was simply a contrarian theory of the orthodoxy of that time, namely that natural selection kept species fixed.
* See here for many examples of the engineering kind, with patents giving the most general and unspecific hint that the patent in question is a modification of animal traps of a similar kind, but not one specific citation of a previous patented or unpatented trap.