Modern Evolution I:Population Genetics

 

I. Modern Evolution: Population Genetics

A. Overview

As a consequence of our modern understanding of heredity and genetics, we have learned quite a bit about variation AND evolution, and our model, a this point in the class is:

Sources of Variation                                                Agents of Change
MUTATION:
-New Genes:                                                           Natural Selection
     point mutation                                                    Mutation (polyploidy can make new species)  

RECOMBINATION:
- New Genes:
    exon shuffling
-New Genotypes:
    -crossing over
    - independent assortment

In the early 20th century, at the same time that T. H. Morgan was studying mutations and creating linkage maps, other biologists were considering the evolutionary implications of this new knowledge regarding genetic variation. They appreciated that individuals do not evolve - evolution is a process that occurs at the population level. For example, as a consequence of differential reproductive success among individuals in a population, the range of phenotypes and their relative frequencies in the population will change over time. Individuals are born, life, reproduce (maybe) and die. As a result of passing on their genes at different frequencies, the genetic structure of the population changes over time (evolution). Two biologists, G. Hardy and W. Weinberg, constructed a model to explain how the genetic structure of a population might change over time.

Their model begins by constructing an 'equilibrium' model - a model of what the gentic structure would look like, and how it would behave, if there was NO CHANGE over time. (We can liken this to a "stitstical null hypothesis of no effect"). Then, an actual population is compared to this model, so see whether the population is evolving or not.    

B. The Genetic Structure of a Population

Our first step is to describe the genetic structure of a population; we need to do this before we can model what it would do over time. The genetic structure of a population is defined by the gene array and the genotypic array. To understand what these are, some definitions are necessary: 

1. Definitions:

                - Evolution: a change in the genetic structure of a population
                - Population: a group of interbreeding organisms that share a common gene pool; spatiotemporally and genetically defined
                - Gene Pool:  sum total of alleles held by individuals in a population
                - Genetic structure: Gene array and Genotypic array
                - Gene/Allele Frequency: % of alleles at a locus of a particular type
                - Gene Array: % of all alleles at a locus: must sum to 1.
                - Genotypic Frequency: % of individuals with a particular genotype
                - Genotypic Array: % of all genotypes for loci considered; must = 1.          

2. Basic Computations - Determining the Genotypic and Gene Arrays:

The easiest way to understand what these definitions represent is to work a problem showing how they are computed.               

Consider the population shown to the right, in which there are 70 AA individuals, 80 heterozygotes, and 50 aa individuals. We can easily calculate the Genotypic Frequencies by dividing each of these values by the total number of individuals in the population. So, the Genotypic Frequency of AA = 70/200 = 0.35. If we account for all individuals in the population (and haven't made any careless math erros), then the three genotypic frequencies should sum to 1.0. The Genotypic Array would list all three genotypic frequencies: f(AA) = 0.35, f(Aa) = 0.40, f(aa) = 0.25. A Gene Frequency is the % of all genes in a population of a given type. This can be calculated two ways. First, let's do it the most obvious and direct way, by counting the alleles carried by each individual. So, there are 70 AA individuals. Each carries 2 'A' alleles, so collectively they are 'carrying' 140 'A' alleles. The 80 heterozygotes are each carrying 1 'A' allele. And of course, the 'aa' individuals aren't carrying any 'A' alleles. So, in total, there are 220 'A' alleles in the population. With 200 diploid individuals, there are a total of 400 alleles at this locus. So, the gene frequency of the 'A' gene = f(A) = 220/400 = 0.55. We can calculate the frequency of the 'a' alleles the same way. The 50 'aa' individuals are carrying 2 'a' alleles each, for a total of 100 'a' alleles. The 80 heterozygotes are each carrying an 'a' allele, and the 140 AA homozygotes aren't carrying any 'a' alleles. So, in total, there are 180 'a' alleles out of a total of 400, for a gene frequency f(a) = 180/400 = 0.45. The gene array presents all the gene frequencies, as: f(A) = 0.55, f(a) = 0.45.

There is a faster way to calculate the gen frequencies in a population than adding up the genes contributed by each genotype. Rather, you can use these handy formulae:

f(A) = f(AA) + f(Aa)/2

f(a) = f(aa) + f(Aa)/2

So, to calculate the frequency of a gene in a population, you add the frrequency of homozygotes for that allele with 1/2 the frequency of heterozygotes. In our example, this would be:

f(A) = 0.35 + 0.4/2 = 0.35 + 0.2 = 0.55

f(a) = 0.25 + 0.4/2 = 0.25 + 0.2 = 0.45

Wow... that's alot faster.

C. The Hardy-Weinberg Equilibrium Model

1. Goal:

The goal of the "Hardy-Weinberg Equilibrium Model" (HWE) is to describe what the genetic structure of the population would be if NO evolutionary change occurs. Working independently, Hardy and Weinberg realized that the gene frequencies in a population will NOT change - will remain in EQUILIBRIUM - if the following conditions are met:

- there is random mating

- no selection

- no mutation

- no migration

- and the population is infinitely large.

And, they realized that a population will reach an equilibrium in GENOTYPIC frequencies, too, after one generation of meeting these expectations (and for as long as it does so), a population will NOT EVOLVE. Let's see how they came by these conditions.

2. Example:

Consider the initial population, with a genotypic array as shown. The gene frequencies are:   

A = 0.4 + (0.4/2) = 0.6

a = 0.2 + (0.4/2) = 0.4                

Now, consider this gene pool in which 60% of the alleles are 'A' and 40% of the alleles are 'a' (as defined by the gene frequencies).

So, now we employ the HWE model. IF the population mates at random, then we can use the product rule to determine the probability of any two gametes coming together. The propability that and 'A' sperm fertilizes an 'A' egg = 0.6 x 0.6 = 0.36. And of course, this is the only way to produce an 'AA' zygote. So, the frequency of 'Aa' zygotes (the F1 offspring) produced by this population should be 0.36. Likewise, the probability that an 'a' sperm fertilizes an 'a' egg = 0.4 x 0.4 = 0.16. And again, this is the only way to make an 'aa' zygote, so the total frequency of 'aa' zygotes in the F1 will be 0.16. Now, there are two ways to make an 'Aa' zygote: an 'A' sperm can fertilize an 'a' egg (probability = 0.6 x 0.4 = 0.24), and an 'a' sperm can fertilize an 'A' egg (also with a probability of 0.4 x 0.6 = 0.24). So, the total frequency of Aa zygotes in the F1 will be 2 x 0.24 = 0.48. If we generalize, and let f(A) = p and f(a) = q, then the genotypic frequencies under HWE can be calculated as: f(AA) = p2, f(Aa) = 2pq, and f(aa) = q2.

Now, of course, these calculations will only be true IF the population mates at random. AND, they will only be true if there is no mutation. If 'A" alleles are mutating into 'a' alleles, then the gene frequencies will not be 0.6 and 0.4, and calculations based on these numbers will not be correct. So, we must assume NO MUTATION. Likewise, we can't have any migration; we can't have 1000 AA individuals migrate into our population, or that would change the gene frequencies, too; and our predictions based on frequencies of 0.6 and 0.4 would be incorrect. So, we must assume NO MIGRATION, too.

So, at this point we have zygotes at the frequencies shown in the "Genotypes, F1" row. In order for there to be no change in the genetic structure of the population, there must be NO SELECTION. In other words, all genotypes must have the same probability of survival and reproduction. Only then will they contribute gametes at frequencies of p = 0.6 and q = 0.4. (If there were selection, and if AA individuals were the only zygotes to survive to reproeuce, for instance, then the gene frequencies would change and our predictions based on frequencies of 0.6 and 0.4 would not be correct).

And finally, this model will only be explicitly true for populations that are infinitely large: because that is the only time when we can be garaunteed that predictions based on random chance will be exactly met. (Think about it this way... suppose I give you a coin that is absolutely perfectly balanced at the molecular level. It IS PERFECTLY BALANCED. And suppose I ask you, "how many times do you have to flip that coin to be ABSOLUTELY SURE of producing a 50:50 ratio of heads to tails? Well, if you only flip it four times, you know that, just by chance, you would often get 3 heads and a tail or 3 tails and a head. And even if you flip it 10,000 times, you might get 5001 heads and 4999 tails, even though the coin is perfectly balanced. To be absolutely garaunteed that the predictions of this probabilisitic model will be met exactly, you must flip the coin an infinite number of times. Obviously, this is a theoretical constraint because no population is infinitely large. But this is a theoretical model of no change, so we can employ theoretical expectations. The same is true of our 'expectation' of a perfectly balanced coin - this expectation will only be met, for sure, in an infinitely large sample. Yet we continually employ that expectation for a perfectly balanced coin.

So, that is why these assumptions exist. It is only when these are met that a population will not evolve. Wow. That should seem rather amazing. It is only when these assumptions are ALL met that a population WON'T change. If any of these assumptions is not met, a population's genetic structure WILL change... and that is evolution. So, from this analysis, we should expect populations to evolve - it is only under a rare combination of events (no, mutation, no selection, no migration, random mating, and an infinitiely large population) that evolution WON'T happen.

3. Utility                

- If no real populations can explicitly meet these assumptions, how can the model be useful?  For instance, no real population is infinitely large, so how can the model be useful?  We use it for COMPARISON.  This model describes what the genotypic frequencies should be IF the population was in equilibrium.  If the real genotypic frequencies are not close to these expectations, then the population is not in HWE.... it is evolving. And if a population is not in HWE, then the population must be violating one of the assumptions of the HWE model.  Think about that.  The HWE is only 'true' if the assumptions are being met.  If your real population differs from the model, then one of the assumptions must not apply to your real population.  This narrows your focus on WHY the real populations isn't behaving randomly... and it might identify WHY the population is evolving.... which is a biologically interesting question.                

- Again, the coin analogy applies.  No REAL coin is probably exactly perfectly balanced. But, if I give you a coin and ask you how balanced it is, you flip it a few times and compare its behavior to WHAT YOU WOULD EXPECT FROM A PERFECT COIN (50:50 RATIO). Even though a perfectly balanced coin does not exist, we can use this theoretical model as a benchmark, to compare the behavior of real coins.  Many real coins act in a manner that is consistent enough with the expectations from a perfectly balanced coin that we are willing to use them AS IF they were perfectly balanced.   The Hardy Weinberg Equilibrium Model is the same... it is a model of no change against which we can measure real populations. 

If HWE can be assumed, then the frequency of recessive diseases can be assumed to equal q2, and the frequency of carriers in the population can be estimated like this:

1) The frequency of hemachromatosis worldwide is 1/450. If we assume that hemochromatosis is caused by a recessive gene (q), and if we assume the population is in HWE with respect to this trait, then q2 = 1/450 = 0.002. So, we take the square-root of both sides to find q = 0.047. Well, if q = 0.047, and if p + q = 1, then p = 1 - 0.047 = 0.953.

2) If q = 0.047 and p = 0.953, then the frequency of heterozygous carriers = 2pq = 0.09. So, we estimate that 9% of the population are carriers.

Now, you might say, "but we just determined that HWE would be unusual; so why would we assume it is true for a given gene?" Well, a deleterious gene has already been largely weeded out of a population, so selection against the few alleles that are left is really weak. Indeed, this condition may not influence reproductive success, anyway (NO SELECTION). In addition, we don't select mates based on whether they have hemochromatosis (I bet you NEVER asked your date if they have hemochromatosis, for example!!), so we can assume there is RANDOM MATING in the population with respect to this trait. And although the human population is not infinite, it is really big (6.9 BILLION), so the effect of sampling error is probably very small. Mutation is very rare, so the effects of mutation are likely to be very small. And if we are making an estimate based on the whole human population, then there can be no 'migrants' coming in from somewhere else (Martians?). So, in some cases, we can reasonably assume a population might be in HWE for a given gene. Of course, we could be wrong... and we would test that prediction by sampling individuals in the population and determining the frequency of heterozygotes genetically. But at least we would have a working hypothesis.

D.  Deviations From HWE:

1. Mutation

Although large scale mutations like polyploidy can cause instantaneous speciation, what we are talking about here are substitution mutations that change one allele into another, or make a new allele.   Although such changes are very important sources of new variation, they do not change the genetic structure of a population very much at all, even when they occur: these mutations are rare, usually occurring at a rate of 1 x 10-4 to 1 x 10-6.

Consider a population with:
f(A) = p = 0.6
f(a) = q = 0.4
 Suppose 'a' mutates to 'A' at a realistic rate of: µ = 1 x 10-5 . How will this rate of mutation change gene frequencies? Not much: 'a' will decline by: qm = .4 x 0.00001 = 0.000004
'A' will increase by the same amount. So, the new gene frequencies will be: p1 = p + µq = .600004, and q1 = q - µq = q(1-µ) = .399996. So, mutation is a very important source of new alleles, but it doesn't change the gene frequencies in a population very much.

2. Migration

Consider a resident population in which p = 0.6 and q = 0.4. Suppose immigrants migrate into this population, bringing A and a alleles into the population at these frequencies: p =0.8 and q = 0.2. The effect of this influx will depend on the number of immigrants relative to the number of residents. 100 immigrants may not change the genetic structure of a population containing 1 million residents, but they could have a dramatic effect on a population of 100 residents. We measure this relative effect by quantifying the proportion of the total combined population that are immigrants. So, in our example, suppose so many immigrants move in that they represent 10% of the new, combined population.  We calculate new p as a weighted average based on fraction of immigrants and residents:                        

So, p1 = (0.6)(0.9) + (0.8)(0.1) = 0.54 + 0.08 = 0.62
residents contribute p at a rate of 0.6, and they represent 90% of the combined population.  Immigrants contribute p at a rate of 0.8, and they are 10% of the population.
q1 = (0.4)(0.9) + (0.2)(0.1) = 0.36 + 0.02 = 0.38, so we have done our math right because 0.62 + 0.38 = 1.0

There are two possible evolutionary effects. First, migration will make two populations similar to one another; particularly if the rate of immigration is high or the process is continuous over time. Migration can also introduce new alleles into a population, but again this effect will be correlated with the abundance of immigrants relative to the number of residents.  

3. Non-Random Mating:            

a. Positive Assortative Mating

There are many ways that non-random mating can occur. We will look at a couple. The first example is called "positive assortative mating". This is where mates 'sort' themselves with others of the same genotype. This can be thought of as "like mates with like". So, consider our old four o'clock plants with incomplete dominance. A population might contain red, pink, and white flowers. Suppose the red flowers open in morning, and are pollinated just by hummingbirds (that prefer red flowers). Suppose the white flowers open at night, and are pollinated by moths. And suppose the pink flowers open in the afternoon, and are pollinated by bees and butterflies. In this case, "like mates with like" for flower color (and time of opening). So, a plant with red flowers will only mate with another plant having the same genotype for (red) flower color. Now, it is IMPORTANT to realize that plants are only positively assorting for flower color and opening time in this case. One red flowering plant may be tall while the other is short; one may have hairy leaves while the other has smooth leaves. Indeed, the plants may be mating at random with respect to all other traits.

When AA individuals mate only with each other, all their offspring will be AA, as well. So, if 20% of the population is AA (intial genotypic frequency = 0.2), and if there is no difference in reproductive success (because we are only violating the assumption of random mating so there is no selection), then these parents will make 20% of the offspring and they will all be AA. The same goes for aa individuals only mating with other aa individuals - all their offspring are aa. However, when Aa heterozygotes only mate with one another, they produce AA, Aa, and aa offspring in a 1/4:1/2:1/4 ratio. If 60% of the population is heterozygous, then they will make 60% of the offspring... but these offspring won't all be heterozygous; only 1/2 - or 30% will be heterozygous. 15% will be AA and 15% will be aa. So, the total frequency of AA offspring in the F1 will be 35%; 20% had AA parents and 15% had Aa parents.

As a consequence of positive assortative mating, the frequency of heterozygotes will decline and the frequency of homozygotes will increase. Curiously, the gene frequencies won't change, so in the F1, f(A) = .35 + 0.30/2 = 0.5... just as it was in the orginal population (f(A) = 0.2 + 0.6/2 = 0.5). The genes are just being 'dealt' to offspring in a non-random manner, affecting the genotypic frequencies at this locus.

So, suppose we observed the F1 population in nature, and wanted to know if it was in HWE. We would calculate the gene frequencies (A = 0.5, a = 0.5), and then estimate what the frequencies of the genotypes would be IF the population was in HWE: p2 = 0.25, 2pq = 0.5, q2 = 0.25. We would compare our real population's genotypic array with this HWE expectation, and see that they are not the same. And we could see one thing more... we would see that the ACTUAL OBSERVED frequency of heterozygotes (0.30) is LESS THAN the expected frequency of heterozygotes under the HWE hypothesis (0.5). And we would see that the observed frequency of both homozygotes is greater than expected. Knowing that positive assortative mating can cause this pattern, we would have a working hypothesis regarding the agent of evolution at work in this population.

b. Inbreeding: Mating with a Relative

Inbreeding is mating with a relative. It is similar to positive assortative mating, except that the two mates are not just similar at one locus, but they are probably similar at MANY loci because they are related and got their genes from the same ancestors. Siblings share, on average, half their genes. Matings between siblings, then, will tend to reduce heterozygosity at MANY loci, not just one.

The most extreme example is "obligate self-fertilization". This is where a hermaphrodite ONLY mates with themselves. This is not asexual reproduction - they produce gametes by meiosis and get all the benefits of producing variable gametes that occurs in sexual reproduction; but they only fertilize their own gametes. This has a profound effect on the genetic structure of the population. Think about it: when an organism mates with themselves, they are mating with an organism that has the SAME genotype at EVERY locus. So, there will be a decrease in heterozygosity across the entire genome, with a 50% reduction in heterozygosity each generation. This is the most rapid loss possible. Siblings are only related, on average, by 50%, so the loss of heterozygosity will only occur 1/2 as fast.... but it will still occur at all loci across the genome.

Inbreeding often reduces reproductive success, because there is an increase in homozygosity - and this means that deleterious recessives are going to be expressed more frequently and exert their negative effects on the offspring. A deleterious allele may be rare in a population, but inbreeding will increase the probability that it occurs in the homozygous condition and is expressed. Because inbreeding can reduce the survivorship of offspring and thus reduce reproductive success of the parent, it is often selected against. Selection favors different strategies that reduce the likelihood of inbreeding, like "self-incompatibility" in some plants, like lions who push male cubs out of a pride when they mature (thus they don't breed with their sisters), or like humans who have a variety of cultural taboos against breeding with relatives.  However, inbreeding is also a mechanism for purging deleterious alleles from the population.  If a population can get through the first few generations in which homozygote recessive are produced and selected against, the net effect will be to eliminate these deleterious alleles from the population.  That can be a good thing in the long run.

4. Populations of Finite Size and Sampling Error/"Genetic Drift"
The genetic structure of a population can change from generation to generation just by chance - through a process statisticians call "sampling error" and geneticists call "genetic drift". Think about it this way: suppose we have a very large population in which p = 0.3 and q = 0.7, and the population is in HWE to start; so the f(AA) = 0.09, f(Aa) = 0.21, and f(aa) = 0.49. Now, suppose only 4 individuals mate, and suppose those four are just 'lucky' - they don't mate because they are better adapted in any way, they just got lucky. It is very unlikely that these four individuals will have the same genetic structure as the whole population; small samples are notoriously unrepresentative and variable. Indeed, all four may be 'aa', and the population will have changed dramatically, losing the 'A' allele. This is why, to have confidence in any observed pattern, you want a large sample. So, a population's genetic structure may change just due to chance.

There are two important patterns that result from this effect:

First, small samples will tend to differ more from the original population than large samples. Second, since the direction of this change is random, multiple small samples will tend to vary more from one another, on average, than multiple large samples. So, small populations will diverge more rapidly from one another, due to drift, than large populations.

There are two biological situations where these effects are particularly important. The first is called a "Founder Effect", where a small number of colonists establish a new population that is isolated from the original population. Because this population of "founders" is small, it is likely to differ dramatically from the original population.... and because it is small, it will also chance quickly just due to drift, as the simulations in lab showed.

The second important instance in which drift is important is called the "bottleneck effect". This is when a large population is reduced in size. Typically this reduction is caused by predation, a pathogen, or an environmental change. The survivors usually make it because of selection at certain loci. For instance, survivors of a pathogenic infection may be resistant to the pathogen. However, at other loci, the reduction in population size causes genetic change due to drift.

So, CHANCE can be an agent of evolutionary change.  CHANCE, especially in small populations, can cause changes in the genetic structure of a population. This is NOT selection - selection is "non-random reproductive success" - the organisms that breed are "better" than the others.  Here, in Genetic Drift, the breeders are just LUCKY, not better.  It is random change. And, as the computer modes demonstrate, populations will tend to become different genetically 'simply by chance', because these chance changes are unlikely to be the SAME changes, or in the same direction, from population to population. So, we can't STOP populations from evolving, really - they will all change over time, even just do to random sampling error, and they will tend to become different from other populations of the same species. Of course, if the populations are very large, these random patterns of divergence will be very slow.... but since no population is infintie in size, these random changes will necessarily occur over time.

5. Natural Selection

1. Fitness Components:

As you know, natural selection is "differential reproductive success" in a genetically variable population. We can measure lifetime reproductive success as the number of successfully reproductive offspring that a genotype produces, on average. This measureable quantity is called "fitness". There are three factors that can influence 'fitness', or reproductive success:

Now, it seems like natural selection would favor organisms that maximized all three components; and it would if that were possible. However, organisms can't maximize all three components because there are energetic constraints - organisms only have so much energy in their 'energy budget'. So, maximizing one component results in less energy that can be invested in the other two. In addition, there are contradictory selective pressures in the environment, such that a characteristic may increase fitness with respect to one variable but decrease it with respect to another variable. These are called 'trade-offs', and we will now examine these in more detail.                  

2. Constraints:

a. finite energy budgets and necessary trade-offs:

The most obvious constraint is ENERGY.  Every organism has a finite energy budget; it has harvested only so much energy from the environment that it can allocate to all of its activities.  There are three major expenses:

So, with limited energy, increasing one thing means that you must reduce costs in another area.  These patterns of energy allocation have direct effects on different fitness components.

Trade-Off #1: Survival vs. Immediate Reproduction: For example, ff an organism maximizes energy investment in growth and metabolism, then they will increase the probability that they survive. Why? Because being large tends to increase the probability of survival, if only because there are fewer things that can eat you. Likewise, large organisms are not as sensitive to changes in the environment. Simply because of their larger size (and smaller surface area/volume ratio), they don't lose heat, salt, water, or other materials to the environment as rapidly as small organisms. However, by investing in growth, this means that there is LESS energy to invest in immediate reproduction, meaning fewer offspring can be produced.  So, you CAN'T maximize all three components of selection at the same time; selection seeks the best compromise in a given environment, with particular biological potentials and constraints. Many organisms invest in growth when young, to develop as rapidly as possible through these early, vulnerable life-history stages.  They delay reproduction completely when they are young to maximize growth rate.  Then, after they are older and larger, they invest energy in reproduction (and growth rate SLOWS).  These organisms are "perennial" or "K" strategists - they are long-lived organisms.  Other organisms take a different strategy.  They reproduce early at the expense of growth.  They don't survive long as a consequence - they are "annual" or "r" strategists - species that live for less than a year but invest almost all their energy in immediate reproduction. These two examples are opposite sides of the same coin - they are both examples of this same trade-off between survival and immediate reproduction; organism can't maximize both at the same time, so they tend to maximize one or the other, or change their pattern of allocation through their life.

Trade Off #2: Offspring Number vs. Offspring Size/Survivorship: There are also trade-offs within the reproduction budget (the pink section in the budgets, above).  For the same "energetic cost", you can make lots of little offspring or a few big offspring. As we discussed above, small organisms have a lower probability of survival than large organisms, so you can make lots of small offspring that each have a small chance of surviving, or you can invest in fewer offspring and increase their chance of survival (by making them larger or by investments in parent care). Small organisms, like insects, can't really make a big offspring, so they exploit the other strategy and make lots of small offspring. Large organisms can really take advantage of this 'choice', and selection will favor different strategies in different large organisms.  Some organisms like mammals and birds tend to produce a few large offspring and invest significant amounts of energy in parental care, further increasing the probability that the offspring survive.  Large vertebrates without parental care, like many reptiles, produce more numerous smaller offspring and 'play the lottery' - increasing the chance that one offspring survives by producing more offspring.                  

b. Contradictory environmental pressures:                            

The environment is a complex place - there are pressures that might favor some structures, and other pressures acting AT THE SAME TIME that might select against that trait.  Selection can not maximize BOTH responses at the same time - so the solution will be a suboptimal compromise.  Consider leaf size.  Big leaves are GOOD for light absorption - they represent a larger solar panel that intercepts more light.  But big leaves are BAD for water loss - with a large SA/V ratio, water is lost rapidly from a large thin leaf.  So, the size of a leaf will be a compromise solution to these two pressures... a solution that maximizes neither function.  The 'adaptive compromise' size depends on the relative strengths of the contradictory pressures.  If the risk of water loss is low (like in a rainforest), then the leaf can be large.  If the risk of water loss is high (like in the desert)and there is strong sun, then the selective pressure to reduce leaf size is strong and leaves will be small or non-existent (cacti).

For these reasons, 'perfect' adaptations are impossible; there are biological costs to any adaptation (in terms of 'opportunity costs' - NOT being able to do something else as well),and in terms of the complex nature of the environment where selective pressures can be contradictory.

3. Modeling Selection:

a. Calculating relative fitness:

Consider the population to the right. Suppose a population has JUST mated, creating parental zygotes in the genotypic frequencies shown. Let's suppose that these zygotes, as a consequence of their genotypes at this locus, have different probabilities of surviving to reproductive age. But, to make things simple, lets assume that the other two components of fitness are equal across the genotypes. So, differences in FITNESS are only influenced by differences in the probability of survival to reproductive age. Suppose those survival probabilities are 0.8, 0.4, and 0.2, respectively (as shown).

These probabilities of survival are 'absolute' fitness values. Curiously, absolute fitness values are not very informative. What is important is relative reproductive success - reproductive success relative to the other genotypes in the population. Think about it this way... suppose I tell you that "I am thinking of an AA genotype that produces 1000 offspring a year. Do you think the f(A) will increase or decrease in the population as a consequence of selection?" Well, you might think, "wow, 1000 offspring is ALOT! Surely the f(A) will increase!" But this would be an incorrect assumption. You need to know what type of organism I am talking about, and how reproductively successful the other genotypes are in the population. If this organism is a salmon, then 1000 offspring might be more than other genotypes in the population. But if this organism is a clam, then the other genotypes might be producing 10's of thousands of offspring - and the F(A) will decline. So, the key to selection is differential reproductive success, which means reproductive success relative to other organisms in the population. We represent this as RELATIVE FITNESS, and calculate it by dividing all fitness values by the LARGEST (ie., most FIT) value. This means that one genotype will necessarily have a RELATIVE FITNESS = 1. In our case, above, we divide each fitness value by the greatest value (0.8), so the relative fitness values are "1, 0.5, and 0.25" for AA, Aa, and aa genotypes, respectively.

b. Modeling Selection:

Now let's see what effect this selection (in terms of differential survival) has on the genetic structure of the population. First, we multiply the initial genotypic array by the relative fitness values. For us, this describes the relative proportion of zygotes surviving to reproductive age. So, these are the same organisms - we don't have a new generation yet - it is just that the original zygotes have grown up and survived to adulthood at different rates. Since many organisms have died, these genotypic values no longer sum to 1. They sum to 0.49. If we want to know what the genotypic frequencies are in the population of surviving reproductive adults (and WE DO), then we must know what part of this new total is represented by each genotype. We calculate that by dividing each genotypic value by the total (0.49), producing the genotypic frequencies in this breeding population. These, of course, now sum to 1. From here, we are home free. we calculate the gene frequencies in this reproductive gene pool as:
F(A) = f(AA) = f(Aa)/2 = 0.575, and
f(a) = f(aa) + f(Aa)/2 = 0.425.
These sum to 1 so we've done the math correctly. Now, to produce the F1 zygotes, assume that all other conditions of HWE are met (we are only modelling the direct effect of selection, alone), so we assume that the organisms mate randomly and calculate the genotypic frequencies of zygotes in the F1 using the terms: p2, 2pq, and q2.

So, as the result of differential survival to reproductive age, A's and a's have not been transferred at the same rate. The intial frequency of these genes was f(A) = 0.4 and f(a) = 0.6. After one generation of differential reproductive success, the gene frequencies have changed dramatically; now the 'A' gene is more abundant.

4. Types of Selection

Selection can act in a number of ways in a population. Selection can favor one extreme phenotype over other phenotypes. This is called "directional selection", and the mean phenotype in the population (and the frequency of genes that influence the phenotype) should move in one direction. There is also "stabilizing" selection, in which an intermediate phenotype is most adaptive (think of sickle cell anemia in the tropics, where the heterozygote had the greatest probability of survival and reproduction). There is also "disruptive selection", in which both extremes are more adaptive than the intermediate type. Although this may seem unusual, it can be common for populations that exploit a complex environment. One phenotype might work well in one microenvironment within that habitat, the other extreme phenotype might work well in another specific microenvironment, but the intermediate might not do well in either. Consider the pollination example we used earlier for positive assortative mating. If there is a population of four o'clocks living in a habitat with no diurnal pollinating insects, then the pink flowers are selected against (don't reproduce) while the red and white flowers are selected for.

Darwin recognized another very important type of selection that he called "sexual selection". He realized that some traits in certain species might DECREASE the probability of survival, and yet might be adaptive. So, the long tail feathers in a peacock reduce survival: they hinder the bird from flying, and they also make it really easy for predators to see it. However, Darwin realized that these traits could still be adaptive if the cost of decreased survival was outweighed by the gain in reproduction while alive. So, Darwin appreciated the trade-offs that were possible in fitness components. Competition among members of one sex for access to the other is a type of sexual selection, too. When male bighorned sheep bash their heads and fight, they reduce their probability of survival because they can get hurt. However, winners increase their reproductive success so much that it compensates for the cost of battle in terms of relative fitness.

E. Summary:

The period from 1900-1940 was a very exciting and dynamic period in biology. With the rediscovery of Mendel's principles, it seemed that biology had become a truly mathematical, predictive science. The ability to predict patterns of heredity, and the transmission of 'mutant' genes through generations, had a profound impact on evolutionary biology, too. Many geneticists came to view mutation as the primary agent of evolutionary change - not just as a primary source of variation. They viewed Darwin's ideas of probabilistic Natural Selection as too weak to be responsible for the changes seen in the fossil record. However, supporters of Darwin like Ernst Mayr argued that random mutation could not explain the non-random adaptations that were so obvious and pervasive in the natural world. The models of Hardy and Weinberg, in the hands of new population geneticists like Theodosius Dobzhansky and Sewall Wright, were pivotal in resolving this dilemma. The resolution came in the Modern Synthetic Theory of Evolution, developed by these scientists and others in the 1930's and 1940's. As a consequence of the models you have just seen, biologists realized that mutations were too rare to explain the changes seen in natural populations over time. Rather, although mutation and recombination were important as a source of new genetic variation, natural selection and genetic drift were the primary agents that caused the genetic structure of population to change over time. And so, as of 1940, our model of evolution looked like this:

 


  Things to Know:

1.  What are the five assumptions of the Hardy-Weinberg Equilibrium Model?

2.  Consider the following population:

  AA Aa aa
Number of Individuals
60
20
20

3. If the HWE model does not describe any real population, how can it be useful?

1.  What are the five assumptions of the Hardy-Weinberg Equilibrium Model?

2.  Consider the following population:

  AA Aa aa
Number of Individuals
60
20
20

3. If the HWE model does not describe any real population, how can it be useful?

  Study Questions:

4. Consider a population with p = 0.8 and q = 0.2. If the mutation rate of A--> a = 4.0 x 10-6, what will the new gene frequencies be in the next generation?

5. Consider a population, p = 0.8 and q = 0.2. If migrants enter this population with p = 0.1 and q = 0.9, such that immigrants comprise 15% of the total population, what will the new gene frequencies be?

6. If the population below undergoes positive assortative mating, what will the genotype frequencies be in the next generation?

AA Aa aa
0.3 0.4 0.3

7.  Why is relative fitness more important than fitness?

8.  Consider the following population of zygotes:                                                     

AA              Aa              aa                

Genotypic Frequency     0.3             0.3             0.4                      

Prob. of survival       0.4             0.2             0.1

a. What are the initial gene frequencies?        

b. Is the population in HWE?        

c. What are the relative fitness values?        

d. What are the genotypic frequencies in the population of reproductive adults?        

e. What are the gene frequencies in the population of reproductive adults?        

f. If there is random mating, what will be the genotypic frequencies in the next generation?        

g. What agent of evolutionary change is at work?

9. Outline the modern synthetic theory of evolution.

10. List the three components of fitness, and explain two trade-offs that necessarily occur because of limited energy budgets.

11. Why can selection perfect an organism?  Describe in terms of contradictory selective pressures, and provide an example.

12. How can the decimation of a population by overhunting cause changes in a population due to both selection and drift?