Mendel’s Peas

If you are already familiar with the work of Mendel and Punnett, skip to Mendel's Peas and Punnett and His Square.

In the mid 1800’s, an Austrian monk named Gregor Mendel decided he should try to understand how inherited traits are controlled.  He needed a model organism he could work with in his research facility, a small garden in the monastery, and a research plan.  His plan was designed to test a hypothesis for the inheritance of trait variation.

The Model:

Since Mendel and his monks could obtain different varieties of peas that differed in easy to observe traits such as flower color, seed color and seed shape, and he could grow these peas in his garden, he chose peas as the model organism for conducting his inheritance control study. A model is easy to work with and often what you learn from the model you can apply to other organisms.

The Hypothesis:

While many biologists were interested in trait inheritance, at the time Mendel conducted his experiments none of the biologists had published evidence that inheritance could be predicted.  Mendel made this bold statement.  His hypothesis was that he could observe “mathematical” regularities in the appearance of a trait that was passed on from parents to their offspring.  Mendel had the idea that mathematical regularities could be observed and could be used to explain the biology of inheritance!

The Plan:

Mendel’s experimental plan was designed to test the hypothesis.  He identified true breeding lines of peas by allowing them to self pollinate (which we will refer to as "selfing") and examining their offspring. Pea plants have flowers that contain both male and female reproductive parts; if a pea flower is left undisturbed, the male and female gametes from the same flower will combine to produce seeds, the next generation.  If the pea always made offspring like itself, Mendel had his true breeding line.  He then made planned crosses between lines that differed by just one trait (monohybrid crosses). The controlled monohybrid cross was the first step in his experiment that allowed him to look for mathematical regularities in the data for three generations.  Table 1 below shows the data from a series of these monohybrid cross experiments.  

The Analysis:

By summarizing his data in a single table, Mendel could look for those hypothesized math regularities. A regularity is a repeated observation.

Data Table 1: Mendel's Result from Crossing Peas
Character Cross and Phenotypes F1 F2 number F2 ratio
Seed form Round X Wrinkled All round 5474 Round 1850 Wrinkled 2.96 to 1
Cotyledon color Yellow X Green All yellow 6022 Yellow 2001 Green 3.01 to 1
Seed coat color* Gray X White All gray 705 Gray 224 White 3.15 to 1
Pod form Inflated X Constricted All inflated 882 Inflated 299 Consricted 2.95 to 1
Pod color Green X Yellow All green 428 Green 152 Yellow 2.82 to 1
Flower position Axial X Terminal  All axial 651 Axial 207 Terminal 3.14 to 1
Stem length Tall X Short All tall 787 Tall 277 Short 2.84 to 1
*Gray seed coat also had purple flowers; White seed coat had white flowers

Mendel’s table demonstrates that he was serious about the math.  He generated large numbers of offspring that allowed him to observe mathematical ratios.  From his table of data, we can see mathematical patterns appear with every monohybrid cross he made.

F1:  All the plants had the same phenotype as one of the parents.

F2:  Both phenotypes are present, the phenotype that was not expressed in the F1 appears again in the F2, but is always the least frequently produced.  The average ratio is about 3:1 for the two phenotypes.

What was striking to Mendel was that every chacter in his study exhibited the same kind of mathematical pattern.  This suggested that the same fundamental processes inside the plant's reproductive cells were at work controlling the inheritance of each trait. 

Now Mendel had the task of providing a description of the fundamental biology process controlling each of these traits.  He needed to come up with ideas that no one had yet proposed to explain biology. 

New Idea #1: 

The traits expressed in the pea plant were controlled by some kind of particle. These hereditary particles are stable and passed on intact from parent to offspring through the sex cells. (NOTE: Sex cells or gametes were not a new idea, Mendel was aware that biologists knew sexually reproducing plants and animals needed to make gametes.)  We now call these particulate factors genes and will use that term in the rest of this reading.

New Idea #2: 

Genes are stable, and genes can have alternative versions (alleles). 

New Idea #3:  

Genes are in pairs in somatic cells and these paired genes separate during gamete formation.  Each gamete will have one gene from the pair of genes. The segregating of the paired genes from the somatic cells of the parent into gametes is random.  Because segregation is random, a parent that has two different alleles for a gene pair will make two kinds of gametes and makes these gametes at equal frequencies.

From Mendel’s ideas, we can see that in a situation in which there was a normal version of a gene (we can call it the R gene) and an alternate version (r), the plant could produce gametes with just the R gene or just the r gene.

New Idea #4: 

Plant flowers are designed to allow male gametes (pollen) to combine randomly with the female gametes (egg).  When the gametes randomly come together, they bring the genes they carry to the same zygote. This means plants could have the genotype RR, Rr, or rr in families that have both the R and r alleles.

New Idea #5: 

Mendel proposed that the genes controlling a trait not only paired in somatic cells, they also interacted in controlling the traits of the plants.  For the traits in his experiment, he proposed that one allele interacted with the other in a dominant fashion.  That means a plant that is the genotype RR would have the same phenotype as an Rr plant.  The R allele is dominant to the r allele. 

Ideas and Data advance science

Those were Mendel’s new ideas; he used them to make sense of his experiment data and observations. Let’s think like Mendel and apply those ideas.

All the F1s were the same

Mendel’s new ideas could explain this observation. Since his parents were true breeding, he was always making a cross between homozygous parents.  Homo means the same, so the parents had two copies of the same version of the gene.

RR  X  rr   Rr

Since the R is dominant to r, then the Rr offspring (named the F1) look the same (have the same phenotype) as the RR parent. Therefore only one phenotype is observed in the F1.  But the F1 genotype is different from either parent.  It is heterozygous (two different alleles).

Figure 5. Mendel used letters to represent the genes (he called them particulate factors) that he proposed were found in pairs in the cells of the pea plants. These could vary in form (alleles) and segregate when sex cells (gametes) were formed as the plants prepared to sexually reproduce. (Image credit: A. Kohmetscher)

The F2s:  both traits appear in about a 3:1 ratio

Mendel could explain the reappearance of the recessive trait and the ratio by combining the idea of genes with the idea of random segregation.  Mendel used simple algebra to explain this result.

First he wrote out a mathematical expression to account for the gametes made in the male part of the F1 flower or in the female part.

(1/2 R   +  1/2 r)  =  all the gametes made

Next he reasoned that if pollen randomly united with the egg to combine the genes in the gametes, then algebra could be used to predict the result by multiplying the gamete expressions.

(1/2 R   +  1/2 r)   X    (1/2 R   +  1/2 r)  = all the F2 offspring made

If we do the multiplication above we get …

(1/4 RR   +  1/4 Rr  + 1/4 Rr +  1/4 rr)   =  (1/4 RR + 1/2 Rr + 1/4 rr) = predicted fractions of F2 genotypes


If this math is causing your brain to lose focus, you might be experiencing what Mendel’s contemporaries experienced when they read his published research paper.  While many biologists were motivated to understand how the variation among animals and plants was controlled and inherited, it took biologists 30 years to recognize that Mendel’s new ideas to explain inheritance of traits in peas could be applied to inheritance of traits in other living organisms.

One possible explanation for this 30 year delay in appreciation is that it was difficult for biologists to understand how math could explain biology. One biologist that did understand what Mendel was describing was Punnett.  Punnett decided to convert Mendel’s algebra into a more graphic representation of the process of gamete segregation and random union.