Evolution: Technically Random?

[Jekyll]

So we'd agree that the state of an organism at time t, denoted X_t, has a probability distribution?

Not to be an arse or anything but a constant distribution P(x=1)=1, P(x!=1)=0 is a probability distribution.
And this sort of distribution is what we're talking about with many species. They're so well settled in their evolutionary niche that they're not going to go anywhere without enviromental upheavel.

 

[BillHoyt]

Not to be an arse or anything but a constant distribution P(x=1)=1, P(x!=1)=0 is a probability distribution.
And this sort of distribution is what we're talking about with many species. They're so well settled in their evolutionary niche that they're not going to go anywhere without enviromental upheavel.

Jekyll, this is wrong. Theoretical population geneticist, John Gillespie calls the quest to explain the unbelievably high variability seen in populatons "The Great Obsession." Geneticists used to view this variability as the "genetic load," assuming it was bad and wrong, and that populations had not settled. But it is now quite clear, from the measurements that they settle into high-variability equilibria.

 

[Jekyll]

Jekyll, this is wrong. Theoretical population geneticist, John Gillespie calls the quest to explain the unbelievably high variability seen in populatons "The Great Obsession." Geneticists used to view this variability as the "genetic load," assuming it was bad and wrong, and that populations had not settled. But it is now quite clear, from the measurements that they settle into high-variability equilibria.

How does that make my post wrong?
I just see what you've discribed as the species spreading out to fill their niche.

There may be high levels of diversity within a species and individual fluctuations, but as taken as a whole the population isn't going anywhere.

The key concept which I keep coming back to is that of local entropy maximas.

Am I missing something here?

 

[BillHoyt]

How does that make my post wrong?
I just see what you've discribed as the species spreading out to fill their niche.

There may be high levels of diversity within a species and individual fluctuations, but as taken as a whole the population isn't going anywhere.

The key concept which I keep coming back to is that of local entropy maximas.

Am I missing something here?

We're discussin probability distributions of alleles. You asserted values of 0 or 1 as results of settling down into niches. Are you misunderstanding the discussion?

 

[Jekyll]

We're discussin probability distributions of alleles. You asserted values of 0 or 1 as results of settling down into niches. Are you misunderstanding the discussion?

Whilest I was talking about the probability of the [distribution of the alleles within the species] shifting.

No wonder we've got our wires crossed.

 

[BillHoyt]

Whilest I was talking about the probability of the [distribution of the alleles within the species] shifting.

No wonder we've got our wires crossed.

Okay, got it.

 

[T'ai Chi]

If it is the case that stochastic implies a combination of deterministic and random factors, then to say "evolution is random" is even more misleading, given that we could say "evolution is stochastic" and be more accurate.

It certainly can be that, and is in many applications such as time series for example, but "stochastic" doesn't imply that.

The definition of a stochastic process is:

A stochastic process {X(t), t in T} is a collection of random variables. That is, for each t in T, X(t) is a random variable. The index t is often interpreted as time and, as a result, we refer to X(t) as the state of the process at time t. For example, X(t) might equal the total number of customers that have entered a supermarket by time t;..."
(source: Introduction to Probability Models, Sheldon Ross)

The idea is that some variable like you describe above, a variable such that it has random and non-random terms, it is still a random variable because of the random terms.

From wikipedia

In the mathematics of probability, a stochastic process is a random function.
http://en.wikipedia.org/wiki/Stochastic_process

 

[lenny]

However, the statement "Evolution is random" would bring the wrath of a million biologists down on your head, and rightly so.

few mathematical biologists would so descend (and none of the small sampled polled).

Isn't there a confusion here between the map and the territory? Specifically between properties of our models and properties of the systems which we are modelling. models may have properties that cannot be meaningfully assigned to the "real" systems.

We can ask if our models are deterministic or stochastic. And we can answer this question by looking at the right hand side of the equations to see if there is a random number generator (or its continuous time equivalent). If there isn't one then the model is deterministic. if there is then the model is stochastic.

We cannot meaningfully address the question of whether or not reality is deterministic or stochastic. the question has no scientific/empirical handle by which to grasp it.

so to answer the question of whether or not a model of evolution is random or not, we have to be given a specification of the model.

while the question of whether or not "evolution itself" is random is ill-posed.

no?