Tips on Problem Solving ≠ From Introduction to Genetics 8^th edition.

Ratios: a 1:2:1 (or 3:1) ratio indicates that one gene is involved (see Problem 3). A 9:3:3:1 ratio, or some modification of it, indicates that two genes are involved (see Problem 4). A testcross results in a 1:1 ratio if the organism being tested is heterozygous and a 1:0 ratio if it is homozygous (see Problem 2).

Pedigrees: normal parents have affected offspring in recessive disorders (see Problem 8). Normal parents have normal offspring and affected parents have affected and/or normal offspring in dominant disorders (see Problems 7). If phenotypically identical parents produce progeny with two phenotypes, the parents were both heterozygous (see Problems 27).

Probability: when dealing with two or more independently assorting genes, consider each gene separately (see Problem 48).

X‑linked or autosomal: if the male phenotype is different from the female phenotype, X linkage is involved for the allele carried by the female (see Problems 15, 27).

Inheritance patterns: there are only seven possible inheritance

patterns for a gene . Usually only numbers 1 ≠ 4 will be encountered:

1. Autosomal dominant

2. Autosomal recessive

3. X‑linked dominant

4. X-linked recessive

5. Autosomal with expression limited to one sex

6. Y‑linked

7. X‑ and Y‑linked (pseudoautosomal)

A Systematic Approach to Problem Solving

Now that you have struggled with a number of genetics problems, it may be worthwhile to make some generalizations about problem solving beyond what has been presented for each chapter so far.

The first task always is to determine exactly what information has been presented and what is being asked. Frequently, it is necessary to rewrite the problem or to symbolize the presented information in some way.

The second task is to formulate and test hypotheses. If the results generated by a hypothesis contradict some aspect of the problem, then the hypothesis is rejected. If the hypothesis generates data compatible with the problem, then it is retained.

A systematic approach is the only safe approach in working genetics problems. Shortcuts in thought processes usually lead to an incorrect answer. Consider the following two types of problems.

1. When analyzing pedigrees, there are usually only four possibilities (hypotheses) to be considered: autosomal dominant, autosomal recessive, X‑linked dominant, and X‑linked recessive. The criteria for each should be checked against the data. Additional factors that should be kept in mind are epistasis, penetrance, expressivity, age of onset, incorrect diagnosis in earlier generations, adultery, adoptions that are not mentioned, and inaccurate information in general. All these factors can be expected in real life, although few will be encountered in the problems presented here.

2. When studying matings, frequently the first task is to decide whether you are dealing with one gene, two genes, or more than two genes (hypotheses). The location of the gene or genes may or may not be important. If location is important, then there are two hypotheses: autosomal and X‑linked. If there are two or more genes, then you may have to decide on linkage relationships between them. There are two hypotheses: unlinked and linked.

If ratios are presented, then 1:2:1 (or some modification signaling dominance) indicates one gene, 9:3:3:1 (or some modification reflecting epistasis) indicates two genes, and 27:9:9:9:3:3:3:1 (or some modification signaling epistasis) indicates three genes. If ratios are presented that bear no relationship to the above, such as 35:35:15:15, then you are dealing with two linked genes (see Chapter 4 for a discussion of linkage).

If phenotypes rather than ratios are emphasized in the problem, then a cross of two mutants that results in wild type indicates the involvement of two genes rather than alleles of the same gene. Both mutants are recessive to wild type. A correlation of sex with phenotype indicates X linkage for the gene mutant in the female parent, while a lack of correlation indicates autosomal location.

If the problem involves X linkage, frequently the only way to solve it is to focus on the male progeny.

Once you determine the number of genes being followed and their location, the problem essentially solves itself if you make a systematic listing of genotype and phenotype.

Sometimes, the final portion of a problem will give additional information that requires you to adjust all the work that you have done up to that point. As an example, in Problem 64 of Chapter 6, crosses 1 ≠ 3 lead you to assume that you are working with one gene. In cross 4, data incompatible with this assumption are presented. Your initial assumption of one gene is correct for the information given in the first three crosses; it is not a mistake. Other than a lack of systematic thought, the greatest mistake that a student can make is to label a rejected hypothesis an error. This decreases self-confidence and increases anxiety, with the result that real mistakes will likely follow. The beginner needs to keep in mind that science progresses by the rejection of hypotheses. When a hypothesis is rejected, something concrete is known: the proposed hypothesis does not explain the results. An unrejected hypothesis may be right or it may be wrong, and there is no way to know without further experimentation.

A very generalized procedure for problem solving would look like this:

1. Determine what information is being presented and what is being asked.

2. Formulate all possible hypotheses.

3. Check the consequences of each hypothesis against the data (the given information).

Reject all hypotheses that are incompatible with the data.

Retain all hypotheses that are compatible with the data.

If no hypothesis is compatible with the data, return to step 1.