Tag Archives: evolution

My first Evolution meeting…

Austin (TX). June 17 2016. I get off the plain and the heat assails me. Is it different from the famous Mississippi heat?? Not sure, but I am still sweating like a ……………………. (fill the blank with whatever kind of metaphor you like to use in these kind of circumstances).

The shuttle takes us from Austin’s Airport to Durden Hall (2624 Whitis Ave.). It is actually a pretty sweet place, at least for me. My boss is already complaining that he would have preferred to go to the Hilton or whatever other Hotel…I am loving it.

We go looking for some food. We try this local Mex restaurant called El Patio. Puts out with our expectation. Cold “cerveza” and meal of decent size and flavor. We leave with a full belly and no complaints.

We take the shuttle downtown to the Austin conference center. This place is huge. Now I know what they mean when they say “Everything is bigger in Texas!!”. We register for the conference…

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I am super excited and scared at the same time…so many names…so many “big” names…and here I am, with my story about Iguanas (that I should be rehearsing before tomorrow!!!!). We go to the Keynote Opening Speech. Only then I realize how many people are actually there….

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Carl Zimmer is giving a talk. It is about his career as a scientific writer, and of course is somewhat celebratory to Stephen Jay Gould. Nothing fancy, but is still love it. He talks about Evolution, with an emphasis on us, Homo sapiens.

I use all my drink tickets on the first night….tomorrow things get serious…

Why is population structure important?

The date for my dissertation defense is approaching fast. A couple of months or so and I will be seating in front of my committee.

While reviewing the work I have been doing for the past 5 years I realized that intuitively simple things could be the toughest to explain to a committee of PhDs.

For example, in my dissertation I talk a lot about population structure in different species of endangered iguanas. The concept of population structure is intuitively very simple to grasp. That is why I never spent too much time in formalizing an answer to the potential question “Why is population structure important?” (and I am glad to know that I am not the only one who struggled with this, see here).

To anticipate any “debacle” during my defense I decided to write a short post on why I thing population structure is such an important concept, worthwhile to study and understand clearly. Here it goes.

Studying biological evolution is basically to study the processes of cumulative changes (morphological changes, genetic changes, behavior changes etc. etc.) happening in any group of  living beings. Biologists and researchers recognize that evolutionary cumulative changes are not uniformly distributed across all individuals within a species. Rather different processes will affect individuals accordingly to their spatial and/or temporal organization. Finding ways to describe the structure of individuals within species, then, becomes important to better understand what kind of changes (genetic drift rather than selection and such…) are going to play a role in shaping their evolution. Eventually, this information is not only used to better understand evolutionary processes, but also to inform conservation strategies and make meaningful predictions about the overall survival of populations.

As aforementioned, (and as I hopefully managed to explain) the concept of population structure is simple to grasp. A way more complicated endeavor is finding a clustering algorithm that could accurately represent shared evolutionary history among clustered individuals. Unfortunately, despite the many advancements and the many algorithms developed, finding a “one ring to rule them all” kind of deal is rather complicated if not impossible (very much like it is difficult to find a species definition that applies to all organisms). And I will try to address this issue in the next post.

Understanding Genetic Drift with the help of R.

A long standing debate among evolutionary biologists concerns the contribution of genetic drift to evolving populations. Fisher and Wright were the first scientists with different opinions on this topic. The former was in favor of selection as major engine of population evolution, while the latter argued that genetic drift could have a paramount effect, especially in small populations.

What is genetic drift? Genetic drift is the random loss of genetic variability within populations, generation after generation. By “random” I mean that it is impossible (or almost impossible) to predict the directionality of this process (i.e. whether an allele will increase or reduce in frequency). This, though, doesn’t prevent us to try and quantify the effect of genetic drift on allele frequency. As we shall see, the size-effect of genetic drift is strictly dependent on population size.

Lets assume that we have a very large population. Individuals have been genotyped for a di-allelic locus (A and a). Turns out that the frequency of A is p = 0.5 and the frequency of a is, hence,  1 – p. One generation goes by. How big of allele frequency change we expect to see in this new generation? Lets try to work this out, and always remind that we are only looking at genetic drift and not considering any other evolutionary mechanism like selection or the insurgence of new mutations.

A different way to ask the above question is: what is the probability of having the exact same allele frequency in the new generation if we sample 2N individuals? (two indicates that we are working with a diploid species.)

For example, if we extract 50000 gametes, we need exactly 25000 of them to be A in order to maintain p = 0.5. This is a classical binomial example in that we only have two possible outcomes (allele A and a), the probability of each outcome stays the same every time we extract a gamete (we allow replacement), and every gamete extraction is independent from the next one. So, what is the probability that extracting 50000 gametes we get exactly 25000 successes, i.e. 25000 times allele A?  In R is actually pretty easy. The following code will calculate the binomial probability of having exactly 25000 successes over 50000 trials and giving a probability of success of 0.5.


> dbinom(25000, 50000, 0.5)
[1] 0.00356823

Well. That probability is rather small. Would this change if we sample less individuals? We can try with ten, in which case we would need 5 A alleles to maintain p = 0.5


> dbinom(5, 10, 0.5)
[1] 0.2460938

According to the above data it seems that the smaller the number of individuals in the second generation, the higher the probability that we will have exactly the same allele frequency. This is only half the truth. That is, although the probability of maintaining p = 0.5  increases with a reduce number of individual, what changes is the variance around this frequency. Lets graph these results to have a better understanding of what I mean. Following is a little routine I wrote that will calculate a series of binomial probabilities and plots them against allele frequencies.


> k <- sort(c(2, 5, 10, 20, 50, 100, 500, 1000, 5000, 10000, 20000, 50000), decreasing = T)
> par(mfrow = c(3, 4))
> for (i in k) {
   y <- dbinom(0:i,i,0.5)
   x <- (seq(1,length(0:i)))/length(0:i)
   plot(x, y, xlim = c(0,1), col = "blue", ylab = "Probability", xlab = "Allele Frequency",
   main = paste("Probability Mass Function\n 0 < k <", i, ", p = 0.5"))
   abline(v = 0.5, lty = 2, lwd = 3,col = "red")
 }

The output is this nice collection of bell curves. From top left to bottom right we are varying sample sizes.

GeneticDrift_BinomialSampleSize
K denotes number of successes

These graphs should tell us two very important things. First, no matter how big the sample, there will always be a randomly associated change in allele frequency. Second, the magnitude of this change (the width of the bell curve) grows with smaller sample sizes.

So, this is why genetic drift is supposedly considered a much stronger evolutionary agent in small populations, where the fluctuations of allele frequency is going to be rather large and could bring alleles to fixation or lost in a small number of generations.

 

 

Read about the man to understand his science.

I recently start to read about the life of one of the most brilliant evolutionary biologist of the 20th century: John Burdon Sanderson Haldane, aka J.B.S. Haldane. Born in England in 1892, he died in 1964 in India. He was one of the scientists, together with Sir Ronald Fischer and Sewal Wright, who laid the foundations for the establishment of the field of Population Genetics, and dramatically contributed to the modern synthesis of Darwinian evolution.

Even more remarkable about the man is that he not only was a great scientist, mathematician and literate, but he also had an incredible and exciting life. Now, this is something that you generally wouldn’t expect or grasp from scientists that in most cases are depicted in those austere, rather “boring-looking” black and white pictures of their early life and career. And yet, J.B.S. Haldane was far from being a boring person. For one thing, he participated in World War I and he was put in charge of training new soldiers in the use of explosives. He himself wrote that one of the practice he used to teach the anatomy of a hand-grenade was to let “each pupil attach a detonator to a fuse with his teeth.” And in 9 months of teaching no accidents were reported at the school. Since fighting a war and instructing other soldiers on the use of weapons wasn’t quite enough, he actually finished to write his first paper while fighting in the trenches.

Long story short, J.B.S. Haldane was an incredible man and an incredible scientist, and the more I learn about his life, the more I appreciate his achievements in science. If you want to know more about his life I recommend the book “J.B.S. Haldane – The Life and Work of J.B.S. Haldane” by Ronald Clark, Bloombsbury Reader.