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The swamping argument is an objection against Darwinism made by Fleeming Jenkin. He asserted that an accidentally-appearing profitable variety cannot be preserved by natural selection in the population, but should be 'swamped' with ordinary traits. Population genetics helped to overcome this logical difficulty.
Jenkin’s article was published anonymously in the North British Review in June 1867. It took Darwin a year and a half to discover that the author was Fleeming Jenkin, Regius Professor of Engineering at the University of Edinburgh. The critical article was most valuable to Darwin. In 1869 he wrote to Alfred Russel Wallace: "Fleming Jenkyn’s arguments have convinced me". Darwin's son Francis said that Jenkin’s critique was the most valuable ever made on his father's views. Jenkin’s article was a critique intended to be based entirely on science, unlike most other critiques which were based on religion. Jenkin humorously said in his article "we are asked to believe", suggesting he opposed the theory because it was too much like a religion.
In his article Jenkin stated that organisms could obtain adaptations through natural selection, but would never gain whole new organs for smell, hearing or sight if they had never possessed them. Jenkin further asserted that once selective pressure was removed, the population would revert to its original condition. He then introduced the 'swamping argument' to deny the possibility that an occasional monstrous individual, a saltation, could supply an escape from this state of affairs and give rise to a permanent adaptation. Jenkin made a mathematical calculation for his argument
…the advantage, whatever it may be, is utterly outbalanced by numerical inferiority. A million creatures are born; ten thousand survive to produce offspring. One of the million has twice as good a chance as any other of surviving; but the chances are fifty to one against the gifted individuals being one of the hundred survivors. No doubt, the chances are twice as great against any one other individual, but this does not prevent their being enormously in favour of some average individual. However slight the advantage may be if it is shared by half the individuals produced, it will probably be present in at least fifty-one of the survivors, and in a larger proportion of their offspring; but the chances are against the preservation of any one ‘sport’ in a numerous tribe…