Biology 102 Laboratory

USCSumter

Mark A. Roberts

Populations

1Estimating Population Size

When studying populations in the wild one crucial piece of information is often "how many individuals make up this population". Obviously, knowing the size of a population is critical to understanding many other aspects of a population's biology and life history; and is particularly important from a conservation management perspective.

But it is nearly always impossible to count every individual in a population. So, we must estimate the size of a population using one of numerous methods. The most widely employed is a simple "mark-recapture" method. In this technique, a certain number of individuals of a population are marked in some way (often with "tags") and then an effort is made to recapture them later on. At its most basic, you start by marking a certain number of individuals (M) out of all of the entire population (N). You release the marked individuals and wait for an adequate amount of time for them to redistribute themselves in the population. You assume that when you catch them you are catching random individuals, and that if you re-release them that they will then "re-shuffle" themselves among the population. When you try to catch individuals again, some portion out of all the individuals you catch (n) will be marked (m). If the organisms have re-sorted themselves and you are now randomly sampling them again, then the ratio of tagged to untagged in your sample should be the same as the ratio of tagged to untagged in the entire population. In other words:

N n
____ = ____
M m

So, if we catch and mark 20 individuals in a population (M=20) and then wait a week and attempt to catch individuals again and we collect 30 individuals total (n) and only 5 of them are marked (m) we now have this:

N 30
____ = ____
20 5

We can then solve for N:

N = (30/5) * 20

or

N = 120

Of course, basing our estimate on just one re-sampling event is a bad idea. There is likely to be a lot of variation between sampling events. So, what is normally done is to re-sample several times and then use the average in our previous calculation. So, our formula becomes:

N x̄n
____ = ____
M x̄m

You will be given a set of beads (or beans or some similar objects) in a bag. All of the items in the bag represent the population whose size you wish to estimate. To estimate them you must first capture and mark some of them. Reach into the bag and remove 30 beads. Mark those beads with a marker. Now, place the beads back in the bag and shake the bag thoroughly. Very thoroughly. This will represent your value, M. It is all of the individuals marked in the population.

Now we need to do the "recapture" part of mark-recapture. After making sure that your population is sufficiently reshuffled, reach back into the bag and remove 30 beads. Count and record how many are marked. Put them back into the bag and reshuffle them thoroughly. Do this 4 more times so that you have a total of 5 recapture events.

Using the formula above, estimate your population size. When you turn in your estimate, write down the letter code that is on the bottom of the bag so that your instructor knows which bag you had.

2Introduction To Population Genetics

2.1Mendelian Refresher

Population genetics is a field of study that deals with understanding populations by studying their genes. The genetic variation within and between populations has been an area of interest since the work of Theodosius Grygorovych Dobzhansky in the 1930s. However, molecular experiments really didn't gain traction until the 1960s (although they employed indirectly studying genes by examining differences in proteins). By the early 1990s researchers were routinely using variations in genetic material and a mathematical understanding of inheritance and evolution to gain insights into the otherwise difficult to study life histories of organisms. Today there are entire journals devoted to this field of study.

In this lab you will study the very basic ideas of hereditary transmission in populations. To understand this, we will need to refresh our memory about the Mendelian inheritance. Note that we will be assuming that the genes we are interested in will be inherited in a Mendelian fashion, but that is definitely not always the case. You will need to remember the definitions for the following terms: genotype, phenotype, chromosome, gene, locus, allele, homozygote and heterozygote. Your instructor will review them in class.

Imagine that there is population of squirrels that has three color morphs: grey, brown and red. Let's assume that that color trait is controlled by one gene. There are two alleles for this gene in our population: G and R. GG produced grey squirrels, RR produces red squirrels and RG or GR produces brown squirrels. Note that in most genetic studies of populations only a small portion of a gene is usually sequenced and examined (a particular locus).

Since these alleles are inherited in a Mendelian fashion we can easily predict what chance are for various potential offspring offspring of any given set of parents. For example, if a female GG and a male RR reproduce we know that all of the eggs will be haploid and contain one of the G alleles and all of the sperm will be haploid and contain an R allele. So, we know that to make a baby we have to combine a sperm and an egg. Therefore all potential fertilization events between these two individuals will result in an RG offspring.

What if two of these RG offspring were to reproduce? We can again determine what the offspring will be but this time its a tiny bit more complicated. So, to keep track of the potential combinations, we can use a graphical "trick" called a Punnett Square to help us understand this:

Possible Eggs
R / G
Possible / R / RR / GR
Sperm / G / RG / GG

By doing this we can see that 1 out of every 4 possible combinations will result in an RR offspring. Likewise, 1 out of every 4 combinations will result GG offspring. And 2 out of 4 will result in a heterozygote individual.

But this is telling us nothing about the population, its simply telling us what chance these two parents have of creating the various combinations. If they had only one little squirrelly offspring, what is the most likely color of its coat based on the above table? ______

1. Now make a Punnett Square for the following two parents: an RG male and an RR female. What is the probability of having a heterozygote offspring?

2.2Alleles in Populations

Population geneticists aren't particularly concerned with individual mating events. They are concerned with the patterns of inheritance for the entire population. For example, we might be interested in how many RR, GG and RG individuals there are in a population. Lets say that we have the following :

RR / RG / GG
Count / 37 / 19 / 98

We can use this information to make predictions about future generations as well as to learn some things about the current generation. The first step is to determine the frequency of the individual alleles in the population. To do this, simply multiply each of the counts of homozygous individuals by two since every individual has two copies of the allele. However, we still have to deal with the heterozygous individuals. 19 RG individuals have 19 R alleles and 19 G alleles. We need to add those to the number that we determined for each homozygote. In other words, the number of each allele can be determined by:

R = (#RR * 2) + #RG

G = (#GG * 2) + #RG

In our case that is:

R = (37 *2) + 19 = 93 R alleles

G = (98 * 2) + 19 = 215 G alleles

But this is still not frequency, its count. To turn this into frequency, divide the # of each allele by the total number of alleles (93 + 215 = 208).

p(R) = 93 / 308 = 0.30 ( 30% of all alleles in the population are "R")

p(G) = 215 / 308 = 0.70 ( 70% of all alleles in the population are "G")

1. Now determine the allele frequencies given the following:

RR / RG / GG
Count / 200 / 127 / 87

So, how does knowing the allele frequencies help us? If we know the allele frequencies, we know the likelihood of that population producing any of the possible genotypes. In other words, if we know that the current generation is p(R)= 0.30 and p(G) = .70, then we know that if the population is randomly mating that the probability of two R alleles coming together is simply the frequency of R in the population times the frequency of R in the population (0.30 * 0.30) = 0.09

2. If the population is randomly mating, determine the frequency of the other genotypes.

3. In front of you are paper bags with 30 red "alleles" (beans) and 70 grey alleles. Shake the bag well and then pull out two alleles to make a new individual. Do this 20 times. Are these frequencies similar to those determined mathematically in #2? Why do you think this is?

4. Lets assume you sample the next generation and found exactly what you calculated in #2 above. Given those data, what are the allele frequencies in the next generation? Are they different than in the first generation? What does this mean about the population?

2.3Hardy-Weinberg Equilibrium

Your instructor will now go over Hardy-Weinberg Equilibrium theory and why it is the most widely used idea in population level studies. You will also learn how to apply the Chi^2 statistic (that you used in lab previously) to determine if the population is in HWE or not.

2.3.1HWE Problem

A study made in 1958 in the mining town of Ashibetsu in Hoikkaido, Japan, revealed the following frequencies of MN blood-types (co-dominant) for married couples:

Genotype / Individuals
MM / 138
MN / 173
NN / 117
  1. Calculate frequencies of the M and N alleles.
  1. Calculate frequencies for all three genotypes (MM, MN and NN).
  1. Calculate expected number of individuals with the MM, MN, NN genotypes assuming HW assumptions apply.
  1. With this information, calculate a chi-square (2) statistic to test whether data differ significantly from expectations assuming HWE (for 1 d.f., 2 critical value is 3.841).
  1. Are the couples in this town in Hardy-Weinberg equilibrium with respect to MN blood type?