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Although Mendel's principle of independent assortment states that alleles of different genes will segregate independently into gametes, in reality, this is not always the case. Sometimes, alleles of certain genes are inherited together, and they do not appear to undergo independent assortment at all. Indeed, shortly after Mendel's discoveries about inheritance patterns became widely known, numerous researchers began to notice exceptions to his principles. For example, they realized that some crosses contradicted Mendel's principle of independent assortment, because these crosses produced organisms with certain phenotypes far more frequently than traditional Mendelian genetics predicted. Based on these findings, these scientists hypothesized that certain alleles of one gene were somehow coupled with certain alleles of another gene; however, they were not sure how this could occur. This phenomenon is now known as genetic linkage, and it generally describes an inheritance pattern in which two genes located in close proximity to each other on the same chromosome have a biased association between their alleles. This, in turn, causes these alleles to be inherited together instead of assorting independently. Genetic linkage is a violation of the Mendelian principle of independent assortment.
Independent assortment in test crosses
To understand linkage, we must first compare it to an example of independent assortment of parental gametes. The best way to generate such an example is through a dihybrid test cross, which considers two different genes during a cross between two heterozygote parents. Mendel's principle of independent assortment predicts that the alleles of the two genes will be independently distributed into gametes. Thus, according to Mendel's principles, a dihybrid cross between two heterozygous fruit flies with brown bodies and red eyes (BbEe X BbEe) should yield offspring with nine possible genotypes (BBEE, BBEe, BBee, BbEE, BbEe, Bbee, bbEE, bbEe, and bbee) and four possible phenotypes (brown body with red eyes, brown body with brown eyes, black body with red eyes, and black body with brown eyes) (Figure 1, left). In this case, the ratio of phenotypes observed among the offspring is 9 (brown body, red eyes): 3 (brown body, brown eyes): 3 (black body, red eyes): 1 (black body, brown eyes) (Figure 1, right). This 9:3:3:1 phenotypic ratio is the classic Mendelian ratio for a dihybrid cross in which the alleles of two different genes assort independently into gametes.
In another example of Mendel's independent assortment principle, a test cross between a heterozygous BbEe fly and a homozygous bbee fly will yield offspring with only four possible genotypes (BbEe, Bbee, bbEe, and bbee) and four possible phenotypes (brown body with red eyes, brown body with brown eyes, black body with red eyes, and black body with brown eyes), as shown in Figure 2. Thus, in this case, the ratio of phenotypes observed among the offspring will be 1 (brown body, red eyes): 1 (brown body, brown eyes): 1 (black body, red eyes): 1 (black body, brown eyes).
Exceptions to independent assortment
In nature, some fruit fly traits like those described above assort independently, whereas others do not. As an example, consider the relationship between fruit fly body color and wing length. Here, the gene for wing length is represented by two alleles, V and v; the V allele codes for long wings, which is the dominant phenotype, and the v allele codes for short, misshapen wings (called vestigial wings), which is the recessive phenotype (Figure 3).
What is the reason for this 5:1:1:5 non-Mendelian phenotypic ratio? It turns out that the body color and wing length genes are linked, which means they are located very close to each other on the same chromosome. The consequence of this is that these gene alleles are much less likely to segregate independently into gametes. In addition, if two genes are linked in this way, then gametes are more likely to contain specific allele combinations. In this example, those combinations of alleles are BV and bv. As such, the heterozygous parent produces more BV and bv gametes than Bv and bV gametes. (Recall that the homozygous parent can only produce bv gametes.) This is why, when the BbVv fly is crossed with the bbvv fly, the resulting offspring are more likely to have BbVv and bbvv genotypes than Bbvv and bbVv genotypes, and the observed phenotypic ratio is 5:1:1:5. In fact, because the alleles do not assort independently into gametes during meiosis, Punnett squares like the ones shown in Figures 2 and 3 cannot be used to accurately predict inheritance patterns for crosses involving linked genes. To return to the fruit fly example, linkage means that the BbVv parent is more likely to produce gametes that match those contributed by its own parents: BV and bv. Therefore, offspring with parental genotypes (BbVv and bbvv) are more common than offspring with non-parental, or recombinant, genotypes (Bbvv and bbVv) after the test cross. This means the parental genotypes and their corresponding phenotypes are observed five times more often than the recombinant genotypes and their corresponding phenotypes.
Summary
What is the lesson to be learned from the body color-wing length example? In short, whenever two genes are linked because of their location on a chromosome, their alleles will not segregate independently during gamete formation. As a result, test crosses involving alleles of linked genes will yield phenotypic ratios that stray from the classic Mendelian ratios. Also in the case of linked genes, the phenotypic ratio will show higher numbers of offspring with the parental genotypes than offspring with the recombinant genotypes.
Make your own fly
Breeding flies is an exciting way to learn genetics. There are many possible allele combinations within a fruit fly, and you can explore them via the interactive image below. Just click on a genotype button from each category below to make your own customized fly (Drosophila melanogaster).
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Phenotypic ratio helps us to predict gene expression in the future generations of organisms. In phenotypic ratio calculations, we map out specific parental alleles and predict the probability of how they will be expressed in their offspring. Knowledge of allele dominance is required, although it is possible to figure out very simple parental genetic makeup by looking at observable traits (phenotypes) in their young. Phenotypic ratio is a term that describes probability of finding the patterns and frequency of genetic trait outcomes in the offspring of organisms. A phenotype is an observable or measurable characteristic and is the result of expressed genes. For example, by noting the traits in a long-haired, pink-nosed and a short-haired, black-nosed guinea pig breeding pair, we can calculate the probability of their offspring having pink or black noses and short or long hair. The number of times each phenotype is expected to occur according to strict calculation determines the phenotypic ratio. Different colors of the same species = different phenotypesBefore finding out how to find the phenotypic ratio, it is worth brushing up on several terms used in the field of genetics.
The phenotypic ratio is the number of times a specific combination of alleles appears in the predicted phenotypes of any offspring. Genetic information relating to the studied trait must be known. It is also possible to work out which parent alleles are dominant or recessive by studying the phenotypes of their offspring. This is an example of Mendelian inheritance or inheritance patterns that occur in offspring after sexual reproduction between two organisms. The name comes from Gregor Mendel who – at first rather unwittingly – experimented with pea-plant crosses in his monastery’s garden. These observations led to our understanding of dominant and recessive traits. Mendel’s statue at his monastery in Brno, Czech RepublicPhenotypic ratio calculations are easy to perform using Punnett squares or with specially-developed phenotypic ratio calculators. As most observable traits are the result of multiple allele combinations (sometimes at completely different loci) such calculations can be extremely complex. For the purposes of this article, we will pretend that a single allele is responsible for a single trait. Not only can we calculate the chance of a certain phenotype appearing in the first generation (F1) of a breeding pair, we can also predict the effects of breeding through subsequent generations. Although early horse and dog breeders knew nothing about DNA, they knew how to produce animals with different traits over time. Selective breeding has brought us the huge range of domesticated breeds we are familiar with today. ‘Purebred’ dogs are the result of phenotypic calculationsTo work out the phenotypic ratio of a monohybrid cross, let us return to the guinea pig example. We have two opposite-sex guinea pigs – the female has long hair; the male short hair. Short- and long-haired versionsThe hair length is, for this example’s purposes, determined by a single allele. Both parents carry a complete set of DNA that includes instructions for both hair lengths and both come from very long lines that only include their particular hair length. When studying generations, the first set of parents is labeled the P1 (parental) generation. Their litters are called the F1 (first filial) generation; litters produced by the F1 generation are noted as the F2 generation, and so on. To find out which of the short and long hair alleles is recessive, we need either have studied that allele beforehand or – as was the case for thousands of years – look at the phenotypes of the offspring after they are born. Without knowing which hair-length allele is dominant, we cannot predict a reliable outcome. The female guinea pig produces four offspring. All of these have long hair. With this information, we can surmise that the long-hair gene is dominant. From this point on, we use LL, Ll, and ll to represent three potential outcomes for future generations – LL is a homozygous allele for long hair, Ll a heterozygous allele for long hair, and ll a homozygous recessive allele for short hair. We can almost predict the outcomeIn the monohybrid cross Punnett square below, all F1 offspring are heterozygous for long hair (Ll). We now know the long-haired mother is homozygous for this allele (LL). If she were heterozygous (Ll) we would expect 50% of any offspring to be short-haired. You can see how this works in the next LL/Ll/ll Punnett square. As the father has short hair and short hair is produced by a recessive gene, he must have the ll allele. In a Punnett square, the mother’s alleles are noted at the top and the father’s at the side. The dominant allele is always listed first. Mother in red (LL), father in blue (ll) – offspring (purple) are a mix of both (Ll)As all four offspring are long-haired, a phenotypic ratio calculation is redundant. We only need to measure the phenotypic ratio when more than one phenotype exists. In this example, there are two possible genotypic outcomes – long hair and short hair – but only long hair is expressed (phenotype). There is a 100% visibility rate in the single dominant phenotype. As there is no second phenotype, there is no phenotypic ratio. If we did put this result as a ratio, it would be 4:0. The genotypic ratio, however, does not look at the observable trait (the phenotype) but at potential allele combinations. In this case, there is only one phenotype – Ll – but three potential combinations are involved using these alleles whether they are expressed or not – LL, Ll, and ll. The genotypic ratio is, therefore, 0:4:0. Genotype and phenotypeWe have now worked out that all four offspring have heterozygous Ll alleles that favor long-hair but carry the short-haired gene. This means we have the knowledge to encourage short-haired offspring in future generations. When we take one of these offspring and create a mating pair with a short-haired guinea pig, we can predict that around 50% of this second generation will be short-haired, as seen in the following Punnett square. We can now predict some short-haired offspringIn this case, there is more than one potential phenotype – both short and long-haired F2 litters are possible when breeding with the F1 generation (Ll). There is a 50% visibility rate for either the dominant or recessive phenotype. To calculate the phenotypic ratio, we look at the observable traits – long (dominant) and short (recessive) phenotypes. Two babies have long hair (Ll) and two have short hair (ll). This gives us a phenotypic ratio of 2:2. This can be rounded down to 1:1. The genotypic ratio, however, calculates the probability of all potential allele combinations: LL, Ll, and ll (in that order). In this example, the result is 0:2:2. If breeders concentrated on one phenotype, less useful features could appear. There is no use in breeding a fast racehorse if it has inherited heart problems from either parent. This is why breeders and geneticists look for more than one feature to encourage in or block from future generations. When two phenotypes are in play, we call this a dihybrid cross. Bred to winIn the guinea pig example, we notice that a small number of babies have very tiny ears when both parents of these litter have big ears. We can represent this particular allele with the letter E. Here, the small ear gene is recessive and both parents have the Ee allele, where E represents the phenotype for big ears and e small ears. It is now possible to predict the phenotypic ratio of short-haired small-eared, short-haired big-eared, long-haired small-eared, and long-haired big-eared babies from various breeding pairs. This is done using a dihybrid cross Punnett square or a phenotypic ratio calculator. Color-coded phenotype predictionsIn the above Punnett square, there are nine potential genotypic outcomes:
However, due to dominant and recessive alleles, there are only four possible phenotypic outcomes:
The phenotypic ratio calculation result requires us to count the colored squares that relate to phenotype and add them up. We then list them as ratios, starting with the largest number. This gives us the following result: 9:3:3:1. We can expect offspring from these parents to have a nine times higher chance of having long hair and big ears than short hair and small ears; a three times higher probability of having long hair and big ears than either long or short hair with small ears. Ear shape – probably the result of multiple allelesA genotypic ratio calculation, on the other hand, does not consider phenotype but the nine potential allele combinations. This would produce 1:2:1:2:4:2:1:2:1. Add a third phenotype to the mix and the potential outcomes of gene expression in the next generation increase. Pink or black?If most guinea pigs in a litter have pink noses (NN or Nn) and just one or two have black noses (nn), pink noses can be considered dominant. This article will not deal with more complex topics such as co-dominance as the purpose here is to make the phenotypic ratio concept clear. We can now calculate the phenotypic ratio of the offspring of two guinea pigs. To save ink, we do not have to list the entire allele list for each parent, just the three alleles in their possible combinations, as in the example below. It gets more complicated the more alleles you includeWhen we look at the phenotypic ratio, we look at the eight potential combinations of the three expressed phenotypes:
This gives us eight possible phenotypic results. Remember, a genotypic result would look at all possible allele combinations, whether or not these genes are expressed. In the above example, the genotypic ratio would read 1:2:2:2:4:8:4:4:2:2:4:1:2:4:2:1:2:1:4:2:2:1:2:1:2:1 – where LLEENN is represented by the first number and lleenn by the last. There are twenty-six possible expressed and non-expressed allele combinations. We can now work out the phenotypic ratio or a trihybrid cross. Order is arranged according to probability. Where probability is the same, results are ordered according to the dominant gene traveling from left to right (L to N). From this calculation, we can expect most pups to have long hair, big ears and pink noses. If we specifically want a short haired, small eared, pink nosed baby, the law of probability tells us that the parents will have to produce about twenty-seven pups.Bibliography
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