Lab 2 -- Sources of Phenotypic Variation
Darwin identified three necessary and sufficient conditions for natural selection: (1) individuals within populations must vary in traits; (2) variation in traits must be associated with differences in survivorship and reproduction; and (3) the variation in the traits must be heritable, i.e., parents and offspring must resemble each other in these traits. We now know that heritable differences among individuals are due to differences in the information passed from parents to offspring via molecules of DNA. However, it is important not to forget that the features of organisms result from developmental processes that are influenced by environmental conditions as well as genes. It is perhaps most accurate to describe a phenotype (the physical expression of a trait) as a product of the interaction between a set of genes and an environment. Thus if we observe a population of variable individuals, it is not immediately obvious how much of this variation is due to variation in genes among individuals versus variation in the environments these individuals experienced during development. As Darwins third condition suggests, the ability of natural selection to cause evolutionary change depends on the extent to which phenotypic variation is due to genetic variation among individuals.
The fact that phenotypic variation can have both genetic and environmental sources generates two complications for biologists in understanding evolutionary change. First, not all phenotypic change over generations is evolutionary. For example, human height has increased dramatically in developed countries over the last 100 years, not because taller individuals have higher survivorship and reproductive opportunities, but because childhood nutrition has improved in these countries. Should levels of nutrition decline, average height of populations would decrease. Second, consistent differences between individuals in survivorship and reproduction may not lead to phenotypic change over generations. For example, many of you performed a nutrition experiment in BIO 135 in which you varied levels of fertilizer and noted the growth responses of Brassica plants. Lets say that you decide to become an entrepreneur and start the Better BrassicaÔ Seed Co. You collect the seeds from the largest plants in your fertilizer experiment in an attempt to select for larger and larger Brassica plants, but not having had BIO 136 yet, you do not realize that the differences in your original population were not heritable. They were primarily (or perhaps completely) due to environmental effects associated with different levels of fertilizer.
Because of these complications, biologists need to be able to quantify the contribution of genes and environment to variation among individuals, to assess the potential for traits to respond to selection. The proportion of phenotypic variation in some trait that is due to genetic differences among individuals is called heritability, a statistic that can range continuously from 0 (in which case genetic differences do not contribute to phenotypic variation) to 1 (in which case genetic differences account for all of the phenotypic variation among individuals).
Measuring heritability -- Evolutionary biologists, breeders, and statisticians have developed techniques to quantify the sources of phenotypic variation among individuals. This field is known as quantitative genetics, since most of the traits of interest vary continuously --rather than discretely -- and may thus be measured on a quantitative scale.
In this exercise, you'll use a simple method for estimating heritability, which is to (1) replicate genotypes (i.e., make multiple copies of each of several genotypes), (2) raise individuals in a common environment, and (3) measure how much individuals of the SAME genotype vary (which estimates the contribution of environmental differences to phenotype variation) compared to the differences BETWEEN genotypes (which estimates genetic contributions to phenotypic variation). This method is easiest for organisms that reproduce asexually ("cloning") most or all of the time, because it is easy to replicate genotypes in such organisms. Somewhat more complicated experimental designs are necessary for organisms that reproduce solely by sexual means, which, of course, have genetically variable offspring.
The statistical measure used to describe how much a group varies in a trait is called the variance, which is equal to the average of the squared deviations from the mean of the group, or
where X1 is the first measurement, X2 the second, etc., is the mean value of the group, and N the total number of measurements.
[Note: The above equation calculates the variance (s 2) for an entire population. If you are estimating the variance based on a sample of the population (s2), replace N with (N-1) in the denominator of the above equation.] You may also recognize that the square root of the variance is equal to the standard deviation (s or s), a statistic you should be familiar with from BIO 135.
Quantitative geneticists use the variance rather than the standard deviation to describe variability because variances are additive. This means that for a population of individuals divided into groups, the total variance will be equal to the between-group variance plus the (average) within-group variance. The ability to partition the total variance into within- and between-group components can be very useful. If the groups are genetically identical individuals (clones), then the within-group variance is a measure of the effect of environmental variation and between-group variance a measure of the role of genotypic differences on phenotypic variation. The following example illustrates the property of additivity of variances.
Imagine that you've raised five clones each of three genotypes of goldenrod under the same conditions and measured their heights (in cm). The raw data are:
Genotype 1 Genotype 2 Genotype 3
------------- -------------- --------------
14 12 11
14 12 12
15 11 13
16 10 14
16 10 15
Mean 15 11 13
Variance 0.8 0.8 2
[Heres the variance calculated for genotype 1:
If we consider all the clones of all the genotypes as our population, the mean is 13 and the variance is 3.87. (Do these yourself to make sure you understand the calculations) The latter quantity is referred to as the total phenotypic variance (s P2).
The property of additivity means that the total phenotypic variance of the population should be equal to the sum of the within-genotype and between-genotype variances:
(1) The average within-genotype, or environmental, variance (s E2) is
s E2 = = 1.2
[Note: This calculation only works when you have equal sample sizes for each genotype!].
(2) The between-genotype variance (s G2) is just the variance of the genotype means or
s G2 = = 2.67
where 13 is the mean of genotype means (i.e., the mean of 15, 11 and 13).
(3) The total phenotypic variance (s P2) should be equal to the sum of these two components
s P2 = s E2 + s G2 = 1.2 + 2.67 = 3.87
All thats left to do now is to calculate the heritability, denoted by the symbol h2, which is the proportion of the variance that is due to genetic differences among individuals:
[Special Note: The measure of heritability we have calculated here is often called heritability in the broad sense or degree of genetic determination. If you move on to advanced courses in evolution, you'll learn that the ability of selection to act on phenotypic variation and produce evolutionary change actually depends on a portion of the genetic variance called the additive genetic variance (s A2). The ratio s A2/s P2 is called heritability in the narrow sense. How much of the genetic variance is additive depends on the importance of dominance, gene interactions and
gene-environment interactions. For this course, however, you neednt concern yourself with this distinction (unless you want to!).]
You and your partner will be assigned a species in which to measure the heritabilities of several traits. As you calculate these heritabilities, you are identifying whether populations contain the raw material necessary for evolutionary change via natural selection. Other things being equal, the potential rate of evolutionary change in a trait is proportional to its heritability.
Solidago gigantea ("Late goldenrod") and Solidago altissima ("Tall goldenrod")
Many flowering plants, in addition to reproducing sexually via seeds, also reproduce asexually via underground stems called rhizomes. Each rhizome is capable of sending up many shoots the following spring, which grow and flower in summer. This reproductive habit facilitates the estimation of heritabilities, as rhizomes can be unearthed in the fall, cut into pieces, and propagated in the greenhouse (i.e., cloned). Species in the genus Solidago (goldenrod) reproduce this way. For your heritability study, you may be assigned to one of the above Solidago species.
During November, your instructors excavated rhizomes from several genotypes of each species from the meadow between the lab and Perry Pond at CERA. The rhizomes rested in moistened vermiculite at 4° C until early January, when we cut them into 1.0 g pieces and placed them in a moist vermiculite/perlite mixture to induce sprouting in the greenhouse. On January 21, we trimmed all but one shoot from each rhizome and transplanted them to pots containing ProMixÔ potting medium. We used a random number table to position pots randomly on the greenhouse bench. High-pressure sodium vapor lamps supplemented light and simulated a 12:12 photoperiod.
During the first week (week 0), measure the following traits for each individual plant:
Then calculate heritabilities for these four traits.
Two weeks later (week 2), measure
The rates of change in height and leaf number between week 2 and week 0 represent two new traits (height growth rate and leaf production rate). Calculate heritabilities for the three traits listed above and for height growth rate and leaf production rate. (Notice that the same feature measured on two different dates is treated as two separate traits.)
Many fungi are wood decomposers, and their fruiting bodies (e.g. mushrooms) can be found growing on logs or branches on the forest floor. Most fruiting bodies are ephemeral, lasting only a few days while environmental conditions (moisture and temperature) are appropriate for spore dispersal. (Mushrooms are analogous to flowers in that they produce dispersal propagules (spores versus seeds). The fruiting bodies of Schizophyllum commune, however, are capable of folding up and withstanding periods of seasonal desiccation, and reviving and re-opening when moistened. Mushrooms of this species can thus form in early spring and continue to produce and disseminate spores during moist periods throughout the summer and fall. Spores form over the entire surface of the gills, on the underside of the fruiting body. Hence, the larger the surface area of the fruiting body, the greater the volume of spores produced.
Schizophyllum commune has a world-wide distribution, and can decompose many different types of wood including oak and pine, at temperatures ranging from 12 - 35 C. The mycelium penetrates wet wood, using cellulose and lignin from plant cell walls as a carbon source.
It is relatively easy to obtain living material of Schizophyllum for laboratory studies by placing a small piece of a fruiting body on nutrient media in a petri dish. These cultures grow luxuriously at 20-25 C, forming a colony of mycelium which grows outward from the point of inoculation, using the rich supply of nutrients in the complex malt media. Schizophyllum cultures will even form fruiting bodies in the petri dish, although the environmental conditions (in the petri dish) required for fruiting depends on the genotype. Some genotypes will fruit soon after inoculation on to the media, whereas others produce an extensive mycelium before fruiting. Clones of genotypes are easily made on new media and maintained at cold temperatures for long-term storage.
Five genotypes of Schizophyllum commune were collected from a forest in Vermont and maintained in this manner. These genotypes were collected from the same site, but from different substrates, over a period of three years. Four days before this lab, 5 clones of each of the 5 genotypes were inoculated on to nutrient media and grown at 23 C.
During the first week (week 0), measure the following traits for each clone:
Calculate heritabilities for these four traits.
Two weeks later (week 2), measure:
Calculate heritabilities for these six traits.
Writing your paper -- Here are some questions to consider as you analyze your data and write your papers:
What is the best way to illustrate the variation within and between genotypes?
Introduction and Discussion
Do different traits (including the same features measured on different dates) have very different heritabilities? Why might this be? Do traits vary in their potential for evolution by natural selection?
If you performed the same experiment outside in a garden plot, would you be likely to calculate identical estimates for heritabilities? Why or why not?
Would you expect heritabilities in nature to be higher or lower than you measured in the greenhouse (or that you might measure in a garden)? Why?