RufusAtticus

Not at all. This is especially relevant when you consider non-independent events.

Consider a sequence of numbers draw from Poisson Distributions, such that X(t+1) ~ Poisson[ K \ X(t)] for some constant K. It is a random sequence, but it is not trendless. There are lots of examples in nature of random processes that are not trendless. Take for example electron clouds in an atom.

wade-w

What exactly do you mean by "trend"? Perhaps we are talking past each other.

KC

Agreed. If we consider mutation, one cannot say that there is an equal probability for a nucleotide substition to occur at every point along the chromosome. It depends on the biochemical and thermodynamic state within the cell, and even the physical structure of the nucleic acid itself (and probably a host of other factors as well). We do know that we do not observe mutations occurring in a mathematically random sense, but they do appear as Dobzhansky once remarked, in an adaptively ambiguous way. That is, they arise regardless of whether they are useful or harmful to an individual.That is what is meant by biologists when they say mutations are random with regard to fitness.

Cheers,

KC

[ December 12, 2002: Message edited by: KC ]</p>

abe smith

If there is/were true randomness ("Whutevuh DAT is."- Saint Thomas "Fats" Waller.), then one effect of it wd be that sometimes one's prayers, wishes , nutty thoughts DO receive POSITIVE answers. Someone in a lab did this to pigeons, and Pavloved them to display some really weird behavioural patterns, perhaps similar to the patterns of people who make novenas and pray to graven images & to relics.... = seeing/ imposing patterns where none are.
Hence It Is Easy To See that *randomness* can effectively bugger-up the Scientific Method. Dja know...

faded_Glory

If this is correct, the corollary is that the resulting increase or decrease in fitness resulting from a mutation is independent of the location where it occurs. This may be correct, but does not seem intuitive to me. I am much of a laymen in molecular genetics, so I may be way off, but if certain parts of the genome will be more critical to an organism's fitness than others, something seems amiss here.

fG

KC

No. A mutation can occur anywhere in the genome, and if it happens to disable a critical function, then it will be lethal. The point here is, the fact it is lethal has no apparent influence on whether or not it occurs.

Cheers,

KC

Principia

Is there a study that shows varying mutation rates as a function of genome location? Ugh too lazy to do a Pubmed search today.

KC

I was thinking specifically of hot spots, which James Watson talks about in The Molecular Biology of the Gene.

I dont have my copy here at work, but I think he talked about a higher frequency of mutations in the T4 phage where certain sequences were present.

Mutagens often require specific circumstances, so their actions cannot be considered random. Here is a nice discussion on
<a href="http://www.bact.wisc.edu/MicrotextBook/BactGenetics/mutasummary.html" target="_blank">mutagenesis</a>

Cheers,

KC

[ December 12, 2002: Message edited by: KC ]

[ December 12, 2002: Message edited by: KC ]</p>

RufusAtticus

Of course we're talking past one another, since you are the first person I've ever discussed "trends" with. I realized last week the distinction between a process that is statistically random in the sense that the outcomes are not deterministic and random in the sense that it lacks any trends.

Testing for trends can often be more or less wheather there is internal correlation in the sequence. Take the following example. In ecology, testing if a population shows density dependence is often done by measuring the correlation between the population size, N(T), and the growth rate, [r(t) = N(t+1)/N(t)]. If the correlation is approximately zero (or not significant) then it is often concluded that there are is no trend.

Biologists often explain how evolution is not random because of selection. However, we also say that evolution is not deterministic because it is random. Is there a confict here? Not at all because both sentances are using "random" differently and rarely do they ever have to appear together to cause immediate confusion.

Evolution is a random process, but selection ensures that the process has trends, such that those that survive have offspring that survive. Thus we get adaptations.

Clutch

I think that what's motivating wade's claim is that we wouldn't count something as a trend, strictu dictu, unless it defied our prior expectations given the assumption of randomness. E.g., since we expect that a truly random long series of coin tosses will produce some sustained strings of consecutive heads and consecutive tails, we don't call those trends when we see them.

So that makes randomness trendless by definition, if that's what was meant.

Or maybe I'm missing it.