Genotypes and

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We have seen that the genome provides a highly elaborate code, largely based on its nucleotide sequence. We have also seen how the code works, how it evolves, and the indirect nature of the relationship between the code and phenotypes in an organism. In Chapter 3, we explained why having a genetic theory of evolution does not automatically provide a satisfactory phenogenetic theory, that is, a theory that explains the evolution of phenotypes. Here, we will try to give a sense of what is known about the internal connections between the genome and phenotypes. How are genes used, and how precise is the "code"? Does it actually code for phenotypes? In what senses can we read the organism from its code? How do we determine these relationships?

Phenogenetic relationships are the product of nature's single de facto criterion, that of the screen of evolutionary survival. Science looks at these relationships through different filters, however. In addition to wanting to understand evolution, we may wish to understand the genetic basis of disease or develop better agricultural products. These are not necessarily "natural" measures of a trait relative to its evolutionary origins. We may or may not be able to use our chosen filters to infer how phenogenetic relationships evolved, but we have been able to further our understanding of the relationship of the genetic code to phenotype.

THE RELATIONSHIP BETWEEN GENOTYPES AND PHENOTYPES A number of important aspects of the relationship between genotypes and pheno-types relate to both the biology of the relationship and the problems we face in trying to identify and understand the underlying genes (Weiss 2003c). Some of these relationships are shown in Figure 5-1. The terms and components shown in this figure are those commonly used in the study of human disease, where we try to infer genetic causation. However, the same issues apply to traits studied in nature or experimentally (after all, humans are studied in nature). The difference is that in experiments we can control some of the variables better or more explicitly. However, the overall idea is to identify genes associated in some way (mechanistically or in terms of variation) with a trait of interest to us.

Genetics and the Logic of Evolution, by Kenneth M. Weiss and Anne V. Buchanan. ISBN 0-471-23805-8 Copyright © 2004 John Wiley & Sons, Inc.

Figure 5-1. Gene mapping and Genotype-Phenotype relationships. G designates a gene that is assumed to have major effect on the phenotype, Ph. Other factors are also involved as indicated. To find the chromosomal location, or to "map," G, we rely on a sufficient predictive power from Ph to G, as well as a statistical association between nearby genetic markers and Ph (see text). After (Weiss and Terwilliger 2000).

Figure 5-1. Gene mapping and Genotype-Phenotype relationships. G designates a gene that is assumed to have major effect on the phenotype, Ph. Other factors are also involved as indicated. To find the chromosomal location, or to "map," G, we rely on a sufficient predictive power from Ph to G, as well as a statistical association between nearby genetic markers and Ph (see text). After (Weiss and Terwilliger 2000).

The primary relationship of interest is shown in the vertical arrow between the phenotype Ph that we actually identify or measure and some important genotype G that we wish to find. Associated with this are many other genes (the two ovals on the right) that contribute individually, in small interacting sets, or as a "polygenic" aggregate of unspecified numbers of individually small contributions.

Environmental factors—known or unknown—contribute in various ways. We often model them as an aggregate with some tractable behavior, which can be separated into various subaggregates: the effects of factors shared by siblings or other specified sets of relatives, factors unique to the individual, and cultural factors shared by the whole population.

We can refer to the number of genes, their interaction, and perhaps frequency relationships of their alleles in a population or species as the genetic architecture of a trait. An important point to make right away is that the genetic architecture is not inherent in the genome. Genes do a lot, but not everything, and the same allele or gene may do different things in different individuals, even within the same species; this is another way of expressing the many-to-many G-Ph relationship discussed in Chapter 3.

Penetrance Concepts for Alleles and Genotypes

The effects of genes on an organism can be assessed in many ways, although typically we are interested in some particular trait, such as the level of expression of a specific protein like insulin, or in more indirect genetic traits, such as wool quality, blood pressure, or flower morphology. We can ask the two genetic questions: (1) what is the mechanism of action of the genes? and (2) how is variation in the genes related to variation in the trait? Much of this book will concern the former question, but our interest at present is in questions of the second type. We can define the probability that a particular phenotype will be found in an individual with a particular genotype as the penetrance of that genotype.

For qualitative traits (ones with a discrete number of possible states, like presence/absence or the number of petals on a flower), the penetrance is the probability that a specified state will be found in an individual with the specified genotype. For quantitative traits, like blood pressure, which can take on an infinite number of possible values across some range, the penetrance of a genotype (sometimes called the expressivity) is the probability of a given value of the trait in bearers of the genotype. Actually, this is more properly referred to as a probability density, but since the probability of any exact trait value—like being 2.000001 meters tall—is zero, in practice we divide the possible values into intervals of a certain width, such as being 1.95 to 1.99 meters, 2.00 to 2.04 meters, etc.

Penetrance is inherently a statistical concept that is tied to a particular sample. Only in the limit (extremes) is a trait never or always observed (penetrance equal to 0 or 1, respectively). The extent to which this statistical nature is due to observational error and finite samples or to inherent chance factors in the actual G-Ph relationship is a major question with no single (or simple) answer, and clearly varies from situation to situation. The penetrance distributions provide the spectrum of genetic effects on the phenotype, at least relative to the alleles and genotypes being considered.

Gregor Mendel dealt with selected traits in crosses of hybrid pea plant strains. He deliberately chose traits and strains in which each parent strain was qualitatively different, meaning there were only two causal factors, one in each parent (one with strong and the other with weak effects). Only decades later was the nature of the factors, alleles at an individual gene, understood. Because of the simple situation he studied, Mendel got the general principles of genetic inheritance right. In fact, much of the 20th century, the century of genetics, was spent working out the details of the theory and designing experiments to understand genes in which there were basically only two alleles, or at least relatively simple relationships like Mendel's. In natural populations, or experimental organisms, the standard way of viewing things is to think of one state as more common and new states that arise as usually harmful; thus the alleles came to be called normal, or "wild type," and "mutant." These terms are still with us, although they somewhat misportray the situation outside the laboratory, where things are more variable and more complicated. Mendel might not have been able to reach the conclusions he did, if he had had to work with wild peas (Weiss 2002b).

For complex traits, like weight, stature, or blood pressure, the possible role of genes could until rather recently only be estimated crudely and indirectly. Relationships in trait values could be observed among individuals in specifically structured samples, such as sets of parents and offspring, controlled crosses among inbred strains, twins, or parents and offspring raised under conditions of artificial selection. This observed relationship was compared with the expected relationship that would arise under theoretical assumptions about how genes would affect the trait if they contributed quantitatively to it in aggregate. The genetic effects of many individu ally unidentified genes could be considered in aggregate, for example, as if the alleles contributed additively to the trait. In experimental situations, selection could be done by the investigator to follow the changes in the nature and amount of variation over many generations and then could be related to the model of underlying aggregate effects.

As long as one was satisfied to study effects and not specific genes—which was all that was possible for most of the 20th century anyway—this largely empirical approach to genetics was an effective way to study quantitative traits. Essentially, the underlying assumption, was that the many genes were individually inherited like Mendel's pea genes, and that the alleles at each gene, although not identifiable, were related to the trait in the same kind of way. Artificial selection, either on the farm or in the laboratory, is more deliberate and systematic than selection in nature, but it does mirror the natural way that selection works on phenotypes in whole organisms.

Advances in genetic technology in the past quarter of the 20th century made it possible to identify genes directly and thus to identify their alleles and assess the association of their observable variation with traits of interest. It is now fairly straightforward to do this for simple traits, in which genotypes have high pene-trance—that is, are directly associated with the measured phenotype. However, we have also learned how favorably artificial Mendel's experiments were. In general, there are multiple alleles at a typical locus in natural populations (including Mendel's traits in wild peas).

For a diploid species, multiple alleles means many possible genotypes. A locus with m alleles has m(m + l)/2 possible genotypes. For example, 2 alleles can form 3 genotypes (AA, Aa, and aa), 3 alleles 6 (AA, Aa, aa, Aa, aa, and aa), and 100 alleles can produce 5,050 different genotypes. Unlike Mendel's and many experimental situations, natural alleles are not equally frequent. Based on Hardy-Weinberg proportions, the genotypes will have comparable variation in frequency. If the three allele frequencies at a locus are 0.7, 0.2, and 0.1, the six genotypes will have frequencies 0.49,0.28, 0.04,0.14, 0.04, and 0.01.

Many possible genotypes are too rare to be found in a given population, and many may never be found at all (for example, if an allele has a frequency of 0.001— not unusual for a rare allele—then its homozygote will have a frequency of 0.000001, or one per 1,000,000 people). In addition, not all alleles that exist at a locus in a species will necessarily exist in any given population, and rare alleles usually will be found to be geographically localized near the area where the mutation that generated them originally occurred. Thus, not all possible genotypes, and hence pheno-types, will occur to be screened by evolution, certainly not in every population of the species. In addition, unlike Mendel's situation, even at a single locus, there is often a quantitative relationship between genotype and phenotype rather than a simple mendelian penetrance probability. An allele that is potentially favorable only in some genotypes may never get the chance to shine.

As we discussed in Chapter 3, new alleles arise as mutations mainly unique at the DNA level, at least in terms of the variants in their nearby chromosomal background. Because of the effects of genetic drift, migration, and natural selection, the distribution and even the identity of many alleles will vary among populations, and the penetrance may be affected by variation at other loci (often referred to as the genetic "background" relative to the gene(s) in question).

This complex of variation is consistent with the ability of experimental breeding systems, as found in agriculture and model systems like Drosophila, to respond to selection in the laboratory and also provides the fuel for natural selection to act on almost any trait. However, the amount of variation also generally means a relatively loose or nondeterministic relationship between genotypes and phenotypes. Over time, the variation can accumulate and change, especially between populations as they diverge into separate species or for other reasons cease to exchange mates.

One implication of quantitative genetic models, which is routinely confirmed by studies that look at the genes involved in complex traits, is that there is extensive phenogenetic equivalence, resulting in different genes in different individuals or populations being associated with the same phenotype (e.g., blood pressure). This provides fuel for phenogenetic drift. When we address the question as to how various biological traits are produced genetically, it may be that the answer differs among species even when they have shared the same trait since they shared a common ancestor.

How We Know: Mapping and Inference Issues

The elusive and statistical nature of penetrance relationships and the potential allelic and genotypic complexity even of individual loci in nature should be kept in mind when we think about genetic causation. This is especially so when a trait of interest is many steps removed from the direct action of a specific gene product. The safest, and most general way to conceive of the role of genes in life is to assume a priori that any gene or system of genes that we may wish to consider may be associated in some way with any phenotype. If natural selection can't effectively screen on genotypes via a given phenotype, we can't expect to predict the genotype from the phenotype (Weiss and Buchanan 2003).

When we attempt to or identify genes associated with a particular trait, for each genotype in the system, G, we can express penetrance as the probability, Pr(Ph|G) that some phenotype, Ph, will be found. Of course, a system of genes may empirically be found not to be related to the phenotype; the evidence would be that the penetrance functions were identical (that is, to statistical accuracy) for all genotypes under consideration. The red and green visual pigment (opsin) genes, for example, have to do with color vision, but all genotypes in those genes probably are associated with identical distributions of body weight or insulin levels. However, we have many times been surprised at the degree of pleiotropy in natural organisms, a major problem in contemporary biology. Apolipoprotein E was originally studied for its lipid-transporting effects, but it turns out to have important neurological function; its alleles may even be related to the ability to recover from childhood head trauma, it is associated with Alzheimer's disease, and it seems to be involved in the embry-ological development of the brain.

These issues are important in both a "forward" causal and a "reverse" inferential sense. In the forward sense, they relate to the way in which individual genes affect traits. This reflects the biology of an individual and the products of evolution. In particular, we generally use a model that has genes "causing" traits, following the downward G ^ Ph path in Figure 5-1, based on the role of genes as protein codes. To evaluate the effects or associations of genotypes with phenotypes, we should be careful to consider the range of environments in which a genotype might find itself, including the background genotypes. This is impossible, actually, because we have no way to know that range except approximately. But it is an important point of caution (Schlichting and Pigliucci 1998).

The "reverse" approach is also important; this has to do with how we infer the role of genes, or identify genes, associated with a trait we wish to understand, using natural variation to map the chromosomal location of genes that affect the trait. What we would like to do is to go from Ph directly to G, but that requires that we first map, or find the gene in its chromosomal location.

To map a gene, we try to take an indirect route through the correlation arrow to genetic markers in Figure 5-1. These are variable sites all along the genome, each with known chromosomal location. We genotype these markers in all sampled individuals. If the model (the main causation we hypothesize) is reasonably close to being true (in the sample we decided to collect), then at markers chromosomally near to G there may be alleles in LD with causal alleles at G. If so, then when we find such a marker allele in an individual we are also likely to find a causal allele at G in the same individual. That is, we find association between the marker and the phe-notype Ph; because we know the location of the marker, we now know chromoso-mally where to look for G.

There can be many a slip twixt Ph and G in this situation, ranging from statistical sampling variation, to our choice of sample, to our actual causal guess. Biologists often assume something about the forward sense, how genotypes predict phenotypes, but then use it in the reverse sense, assuming how phenotypes predict genotypes; too often, that "something" is highly oversimplified. The challenge of genetic inference is a subject beyond the scope of this book and dealt with in many places (Millikan 2002; Sham 1997; Weiss and Buchanan 2003; Weiss and Terwilliger 2000). However, it is appropriate to make a few comments here because this concept affects how we will interpret the evidence that exists for traits that we will consider.

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