Mendel tracked the segregation of parental genes and their appearance in the offspring as dominant or recessive traits. He recognized the mathematical patterns of inheritance from one generation to the next. Mendel's Laws of Heredity are usually stated as:. Parental genes are randomly separated to the sex cells so that sex cells contain only one gene of the pair. Offspring therefore inherit one genetic allele from each parent when sex cells unite in fertilization.
The genetic experiments Mendel did with pea plants took him eight years and he published his results in During this time, Mendel grew over 10, pea plants, keeping track of progeny number and type. Mendel's work and his Laws of Inheritance were not appreciated in his time. It wasn't until , after the rediscovery of his Laws, that his experimental results were understood.
After his death, Mendel's personal papers were burned by the monks. Luckily, some of the letters and documents generated by Mendel were kept in the monastery archives. Because the seven pea plant characteristics tracked by Mendel were consistent in generation after generation of self-fertilization, these parental lines of peas could be considered pure-breeders or, in modern terminology, homozygous for the traits of interest.
Mendel and his assistants eventually developed 22 varieties of pea plants with combinations of these consistent characteristics. Mendel not only crossed pure-breeding parents, but he also crossed hybrid generations and crossed the hybrid progeny back to both parental lines.
These crosses which, in modern terminology, are referred to as F 1 , F 1 reciprocal, F 2 , B 1 , and B 2 are the classic crosses to generate genetically hybrid generations. Before Mendel's experiments, most people believed that traits in offspring resulted from a blending of the traits of each parent.
However, when Mendel cross-pollinated one variety of purebred plant with another, these crosses would yield offspring that looked like either one of the parent plants, not a blend of the two.
For example, when Mendel cross-fertilized plants with wrinkled seeds to those with smooth seeds, he did not get progeny with semi-wrinkly seeds. Instead, the progeny from this cross had only smooth seeds.
In general, if the progeny of crosses between purebred plants looked like only one of the parents with regard to a specific trait, Mendel called the expressed parental trait the dominant trait. From this simple observation, Mendel proposed his first principle, the principle of uniformity ; this principle states that all the progeny of a cross like this where the parents differ by only one trait will appear identical.
Exceptions to the principle of uniformity include the phenomena of penetrance , expressivity , and sex-linkage , which were discovered after Mendel's time. When conducting his experiments, Mendel designated the two pure-breeding parental generations involved in a particular cross as P 1 and P 2 , and he then denoted the progeny resulting from the crossing as the filial, or F 1 , generation. Although the plants of the F 1 generation looked like one parent of the P generation, they were actually hybrids of two different parent plants.
Upon observing the uniformity of the F 1 generation, Mendel wondered whether the F 1 generation could still possess the nondominant traits of the other parent in some hidden way. To understand whether traits were hidden in the F 1 generation, Mendel returned to the method of self-fertilization. Here, he created an F 2 generation by letting an F 1 pea plant self-fertilize F 1 x F 1.
This way, he knew he was crossing two plants of the exact same genotype. This technique, which involves looking at a single trait, is today called a monohybrid cross. The resulting F 2 generation had seeds that were either round or wrinkled. Figure 4 shows an example of Mendel's data. When looking at the figure, notice that for each F 1 plant, the self-fertilization resulted in more round than wrinkled seeds among the F 2 progeny.
These results illustrate several important aspects of scientific data:. In Figure 4, the result of Experiment 1 shows that the single characteristic of seed shape was expressed in two different forms in the F 2 generation: either round or wrinkled. Also, when Mendel averaged the relative proportion of round and wrinkled seeds across all F 2 progeny sets, he found that round was consistently three times more frequent than wrinkled.
This proportion resulting from F 1 x F 1 crosses suggested there was a hidden recessive form of the trait. Mendel recognized that this recessive trait was carried down to the F 2 generation from the earlier P generation.
As mentioned, Mendel's data did not support the ideas about trait blending that were popular among the biologists of his time. As there were never any semi-wrinkled seeds or greenish-yellow seeds, for example, in the F 2 generation, Mendel concluded that blending should not be the expected outcome of parental trait combinations. Mendel instead hypothesized that each parent contributes some particulate matter to the offspring. He called this heritable substance "elementen. Indeed, for each of the traits he examined, Mendel focused on how the elementen that determined that trait was distributed among progeny.
We now know that a single gene controls seed form, while another controls color, and so on, and that elementen is actually the assembly of physical genes located on chromosomes.
Multiple forms of those genes, known as alleles , represent the different traits. For example, one allele results in round seeds, and another allele specifies wrinkled seeds.
One of the most impressive things about Mendel's thinking lies in the notation that he used to represent his data. Mendel's notation of a capital and a lowercase letter Aa for the hybrid genotype actually represented what we now know as the two alleles of one gene : A and a. Moreover, as previously mentioned, in all cases, Mendel saw approximately a ratio of one phenotype to another. When one parent carried all the dominant traits AA , the F 1 hybrids were "indistinguishable" from that parent.
However, even though these F 1 plants had the same phenotype as the dominant P 1 parents, they possessed a hybrid genotype Aa that carried the potential to look like the recessive P 1 parent aa. After observing this potential to express a trait without showing the phenotype, Mendel put forth his second principle of inheritance: the principle of segregation.
According to this principle, the "particles" or alleles as we now know them that determine traits are separated into gametes during meiosis , and meiosis produces equal numbers of egg or sperm cells that contain each allele Figure 5. Mendel had thus determined what happens when two plants that are hybrid for one trait are crossed with each other, but he also wanted to determine what happens when two plants that are each hybrid for two traits are crossed.
Mendel therefore decided to examine the inheritance of two characteristics at once. Based on the concept of segregation , he predicted that traits must sort into gametes separately.
By extrapolating from his earlier data, Mendel also predicted that the inheritance of one characteristic did not affect the inheritance of a different characteristic. Mendel tested this idea of trait independence with more complex crosses. First, he generated plants that were purebred for two characteristics, such as seed color yellow and green and seed shape round and wrinkled.
These plants would serve as the P 1 generation for the experiment. In this case, Mendel crossed the plants with wrinkled and yellow seeds rrYY with plants with round, green seeds RRyy. From his earlier monohybrid crosses, Mendel knew which traits were dominant: round and yellow. So, in the F 1 generation, he expected all round, yellow seeds from crossing these purebred varieties, and that is exactly what he observed. Mendel knew that each of the F 1 progeny were dihybrids; in other words, they contained both alleles for each characteristic RrYy.
He then crossed individual F 1 plants with genotypes RrYy with one another. This is called a dihybrid cross. Mendel's results from this cross were as follows:. Next, Mendel went through his data and examined each characteristic separately. He compared the total numbers of round versus wrinkled and yellow versus green peas, as shown in Tables 1 and 2.
The proportion of each trait was still approximately for both seed shape and seed color. In other words, the resulting seed shape and seed color looked as if they had come from two parallel monohybrid crosses; even though two characteristics were involved in one cross, these traits behaved as though they had segregated independently. From these data, Mendel developed the third principle of inheritance: the principle of independent assortment.
According to this principle, alleles at one locus segregate into gametes independently of alleles at other loci. Such gametes are formed in equal frequencies. More lasting than the pea data Mendel presented in has been his methodical hypothesis testing and careful application of mathematical models to the study of biological inheritance.
The resulting hybrids in the F 1 generation all had violet flowers. In the F 2 generation, approximately three quarters of the plants had violet flowers, and one quarter had white flowers.
In his publication, Mendel reported the results of his crosses involving seven different characteristics, each with two contrasting traits. A trait is defined as a variation in the physical appearance of a heritable characteristic.
The characteristics included plant height, seed texture, seed color, flower color, pea pod size, pea pod color, and flower position. For the characteristic of flower color, for example, the two contrasting traits were white versus violet. To fully examine each characteristic, Mendel generated large numbers of F 1 and F 2 plants, reporting results from 19, F 2 plants alone. His findings were consistent. What results did Mendel find in his crosses for flower color? First, Mendel confirmed that he had plants that bred true for white or violet flower color.
Regardless of how many generations Mendel examined, all self-crossed offspring of parents with white flowers had white flowers, and all self-crossed offspring of parents with violet flowers had violet flowers. In addition, Mendel confirmed that, other than flower color, the pea plants were physically identical.
Once these validations were complete, Mendel applied the pollen from a plant with violet flowers to the stigma of a plant with white flowers. After gathering and sowing the seeds that resulted from this cross, Mendel found that percent of the F 1 hybrid generation had violet flowers. Conventional wisdom at that time would have predicted the hybrid flowers to be pale violet or for hybrid plants to have equal numbers of white and violet flowers. In other words, the contrasting parental traits were expected to blend in the offspring.
Importantly, Mendel did not stop his experimentation there. He allowed the F 1 plants to self-fertilize and found that, of F 2 -generation plants, had violet flowers and had white flowers. This was a ratio of 3. When Mendel transferred pollen from a plant with violet flowers to the stigma of a plant with white flowers and vice versa, he obtained about the same ratio regardless of which parent, male or female, contributed which trait.
This is called a reciprocal cross —a paired cross in which the respective traits of the male and female in one cross become the respective traits of the female and male in the other cross. For the other six characteristics Mendel examined, the F 1 and F 2 generations behaved in the same way as they had for flower color.
One of the two traits would disappear completely from the F 1 generation only to reappear in the F 2 generation at a ratio of approximately Table 1. Upon compiling his results for many thousands of plants, Mendel concluded that the characteristics could be divided into expressed and latent traits.
He called these, respectively, dominant and recessive traits. Dominant traits are those that are inherited unchanged in a hybridization. Recessive traits become latent, or disappear, in the offspring of a hybridization. The recessive trait does, however, reappear in the progeny of the hybrid offspring.
An example of a dominant trait is the violet-flower trait. For this same characteristic flower color , white-colored flowers are a recessive trait. The fact that the recessive trait reappeared in the F 2 generation meant that the traits remained separate not blended in the plants of the F 1 generation. Mendel also proposed that plants possessed two copies of the trait for the flower-color characteristic, and that each parent transmitted one of its two copies to its offspring, where they came together.
Moreover, the physical observation of a dominant trait could mean that the genetic composition of the organism included two dominant versions of the characteristic or that it included one dominant and one recessive version.
Conversely, the observation of a recessive trait meant that the organism lacked any dominant versions of this characteristic. So why did Mendel repeatedly obtain ratios in his crosses? To understand how Mendel deduced the basic mechanisms of inheritance that lead to such ratios, we must first review the laws of probability.
Probabilities are mathematical measures of likelihood. The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of opportunities for the event to occur.
It is also possible to calculate theoretical probabilities by dividing the number of times that an event is expected to occur by the number of times that it could occur. Empirical probabilities come from observations, like those of Mendel. Theoretical probabilities come from knowing how the events are produced and assuming that the probabilities of individual outcomes are equal.
A probability of one for some event indicates that it is guaranteed to occur, whereas a probability of zero indicates that it is guaranteed not to occur. An example of a genetic event is a round seed produced by a pea plant. When the F 1 plants were subsequently self-crossed, the probability of any given F 2 offspring having round seeds was now three out of four. In other words, in a large population of F 2 offspring chosen at random, 75 percent were expected to have round seeds, whereas 25 percent were expected to have wrinkled seeds.
Using large numbers of crosses, Mendel was able to calculate probabilities and use these to predict the outcomes of other crosses. Mendel demonstrated that the pea-plant characteristics he studied were transmitted as discrete units from parent to offspring.
As will be discussed, Mendel also determined that different characteristics, like seed color and seed texture, were transmitted independently of one another and could be considered in separate probability analyses.
For instance, performing a cross between a plant with green, wrinkled seeds and a plant with yellow, round seeds still produced offspring that had a ratio of green:yellow seeds ignoring seed texture and a ratio of round:wrinkled seeds ignoring seed color. The characteristics of color and texture did not influence each other. The product rule of probability can be applied to this phenomenon of the independent transmission of characteristics.
The product rule states that the probability of two independent events occurring together can be calculated by multiplying the individual probabilities of each event occurring alone.
To demonstrate the product rule, imagine that you are rolling a six-sided die D and flipping a penny P at the same time. The outcome of rolling the die has no effect on the outcome of flipping the penny and vice versa. There are 12 possible outcomes of this action Table 2 , and each event is expected to occur with equal probability.
For example, consider how the product rule is applied to the dihybrid cross: the probability of having both dominant traits in the F2progeny is the product of the probabilities of having the dominant trait for each characteristic, as shown here:. On the other hand, the sum rule of probability is applied when considering two mutually exclusive outcomes that can come about by more than one pathway.
The sum rule states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities. What is the probability of one coin coming up heads and one coin coming up tails? This outcome can be achieved by two cases: the penny may be heads PH and the quarter may be tails QT , or the quarter may be heads QH and the penny may be tails PT.
Either case fulfills the outcome. You should also notice that we used the product rule to calculate the probability of PH and QT, and also the probability of PT and QH, before we summed them. Again, the sum rule can be applied to show the probability of having just one dominant trait in the F2 generation of a dihybrid cross:.
To use probability laws in practice, it is necessary to work with large sample sizes because small sample sizes are prone to deviations caused by chance. The large quantities of pea plants that Mendel examined allowed him calculate the probabilities of the traits appearing in his F 2 generation. The seven characteristics that Mendel evaluated in his pea plants were each expressed as one of two versions, or traits.
The physical expression of characteristics is accomplished through the expression of genes carried on chromosomes. The genetic makeup of peas consists of two similar or homologous copies of each chromosome, one from each parent. Each pair of homologous chromosomes has the same linear order of genes. In other words, peas are diploid organisms in that they have two copies of each chromosome. The same is true for many other plants and for virtually all animals.
Diploid organisms utilize meiosis to produce haploid gametes, which contain one copy of each homologous chromosome that unite at fertilization to create a diploid zygote. For cases in which a single gene controls a single characteristic, a diploid organism has two genetic copies that may or may not encode the same version of that characteristic.
Gene variants that arise by mutation and exist at the same relative locations on homologous chromosomes are called alleles. Mendel examined the inheritance of genes with just two allele forms, but it is common to encounter more than two alleles for any given gene in a natural population. Two alleles for a given gene in a diploid organism are expressed and interact to produce physical characteristics. The observable traits expressed by an organism are referred to as its phenotype.
When true-breeding plants in which one parent had yellow pods and one had green pods were cross-fertilized, all of the F 1 hybrid offspring had yellow pods. That is, the hybrid offspring were phenotypically identical to the true-breeding parent with yellow pods. However, we know that the allele donated by the parent with green pods was not simply lost because it reappeared in some of the F 2 offspring. Therefore, the F 1 plants must have been genotypically different from the parent with yellow pods.
The P 0 plants that Mendel used in his experiments were each homozygous for the trait he was studying. Diploid organisms that are homozygous at a given gene, or locus, have two identical alleles for that gene on their homologous chromosomes.
When P 0 plants with contrasting traits were cross-fertilized, all of the offspring were heterozygous for the contrasting trait, meaning that their genotype reflected that they had different alleles for the gene being examined. Our discussion of homozygous and heterozygous organisms brings us to why the F 1 heterozygous offspring were identical to one of the parents, rather than expressing both alleles. In all seven pea-plant characteristics, one of the two contrasting alleles was dominant, and the other was recessive.
Mendel called the dominant allele the expressed unit factor; the recessive allele was referred to as the latent unit factor. We now know that these so-called unit factors are actually genes on homologous chromosome pairs. For a gene that is expressed in a dominant and recessive pattern, homozygous dominant and heterozygous organisms will look identical that is, they will have different genotypes but the same phenotype.
The recessive allele will only be observed in homozygous recessive individuals Table 4. Several conventions exist for referring to genes and alleles.
Furthermore, we will use uppercase and lowercase letters to represent dominant and recessive alleles, respectively. Therefore, we would refer to the genotype of a homozygous dominant pea plant with violet flowers as VV , a homozygous recessive pea plant with white flowers as vv , and a heterozygous pea plant with violet flowers as Vv. When fertilization occurs between two true-breeding parents that differ in only one characteristic, the process is called a monohybrid cross, and the resulting offspring are monohybrids.
Mendel performed seven monohybrid crosses involving contrasting traits for each characteristic. On the basis of his results in F 1 and F 2 generations, Mendel postulated that each parent in the monohybrid cross contributed one of two paired unit factors to each offspring, and every possible combination of unit factors was equally likely. To demonstrate a monohybrid cross, consider the case of true-breeding pea plants with yellow versus green pea seeds.
The dominant seed color is yellow; therefore, the parental genotypes were YY for the plants with yellow seeds and yy for the plants with green seeds, respectively. A Punnett square , devised by the British geneticist Reginald Punnett, can be drawn that applies the rules of probability to predict the possible outcomes of a genetic cross or mating and their expected frequencies.
To prepare a Punnett square, all possible combinations of the parental alleles are listed along the top for one parent and side for the other parent of a grid, representing their meiotic segregation into haploid gametes. Then the combinations of egg and sperm are made in the boxes in the table to show which alleles are combining. Each box then represents the diploid genotype of a zygote, or fertilized egg, that could result from this mating. Because each possibility is equally likely, genotypic ratios can be determined from a Punnett square.
If the pattern of inheritance dominant or recessive is known, the phenotypic ratios can be inferred as well. For a monohybrid cross of two true-breeding parents, each parent contributes one type of allele.
In this case, only one genotype is possible. All offspring are Yy and have yellow seeds Figure 4. Figure 4.
In the P 0 generation, pea plants that are true-breeding for the dominant yellow phenotype are crossed with plants with the recessive green phenotype. This cross produces F 1 heterozygotes with a yellow phenotype. Punnett square analysis can be used to predict the genotypes of the F 2 generation. Therefore, the offspring can potentially have one of four allele combinations: YY , Yy , yY , or yy Figure 4.
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