Jerry Coyne sez that natural selection is deterministic and non-random. However a simple reading of the definitions says natural selection is stochastic:
A mathematical representation in which every variable alters according to a mathematical formula, and not to random fluctuations.
It is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of initial conditions.
For instance a deterministic model can be applied to describe the predator-prey systems wherein the prey shows an age-specific vulnerability to predation.
detereministic: Referring to events that have no random or probabilistic aspects but proceed in a fixed predictable fashion.
Stochastic (from the Greek στόχος for aim or guess) is an adjective that refers to systems whose behavior is intrinsically non-deterministic, sporadic and categorically not intermittent. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E. Nelson, any kind of time development (be it deterministic or essentially probabilistic) which is analyzable in terms of probability deserves the name of stochastic process.
As for natural selection:
“Natural selection is the result of differences in survival and reproduction among individuals of a population that vary in one or more heritable traits.” Page 11 “Biology: Concepts and Applications” Starr fifth edition
“Natural selection is the simple result of variation, differential reproduction, and heredity—it is mindless and mechanistic.” UBerkley
“Natural selection is the blind watchmaker, blind because it does not see ahead, does not plan consequences, has no purpose in view.” Dawkins in “The Blind Watchmaker”?
“Natural selection is therefore a result of three processes, as first described by Darwin:
which together result in non-random, unequal survival and reproduction of individuals, which results in changes in the phenotypes present in populations of organisms over time.”- Allen McNeill prof. introductory biology and evolution at Cornell University
OK so it is a result of three processes- ie an output.
What drives the output? The inputs.
The variation is said to be random, ie genetic accidents/ mistakes.
With sexually reproducing organisms it is still a crap-shoot as to what gets inherited. For example if a male gets a beneficial variation to his Y chromosome but sires all daughters, that beneficial variation gets lost no matter how many offspring he has.
Fecundity/ differential reproduction- Don't know until it happens.
Can't tell what variation will occur. Can't tell if any of the offspring will inherit even the most beneficial variation and the only way to determine differential reproduction is follow the individuals for their entire reproducing age.
Then there can be competing "beneficial" variations.
In the end it all boils down to whatever survives to reproduce, survives to reproduce
But anyway- all of the variables of natural selection are either entirely stochastic (variation) or have a stochastic element. Therefor, by definition, natural selection is stochastic. Or at the very least natural selection cannot be deterministic.
Sorry Jerry, you lose... (again)