This is a glossary of terms that appear in Mendel's paper and other areas of MendelWeb. It is not meant to be exhaustive, and is aimed primarily at students in secondary and undergraduate schools.
The glossary is arranged alphabetically. Although you may find many of the terms familiar, the definitions and explanations frequently raise issues of translation and etymology, and contain links to Mendel's original text, to other documents in MendelWeb, and to resources throughout the World Wide Web. Please send corrections and suggestions to
[email protected]The glossary will continue to expand with successive editions of MendelWeb.
This is a peculiar translation of the German word vermitteln which in modern German means to mediate or to act as a mediator. But even the term "mediated" expresses poorly what Mendel is talking about here; he is describing an alteration or transformation in the fertilized egg of the hybrid that results in that hybrid behaving like one of the constant (or parental) forms found in Pisum. That is, unlike the pea hybrids that produce different kinds of pollen and egg cells, the "constant hybrids" discussed here produce only one sort of cell which results in the production of only those hybrids (rather than in a combination of hybrid and constant forms).
In the English version "Die aufgestellte Ansicht..." is translated as "The theory adduced...," which adds formality, and perhaps a more scientistic feeling to Mendel's original phrase. A more accurate translation might be "The view put forward.." Note that Mendel uses the word theoretischem only once in the paper; where "theory" appears in the translation it is often a rendering of words more accurately translated as "assumption" (e.g. Annahme).
Technically, Mendel's use of "albumen" and "endosperm" is inaccurate, because peas possess neither an albumen nor an endosperm. When Mendel used these terms he was referring to the cotyledons.
AquilegiaColumbine comes from the Latin columbinus, dove-like, apparently referring to the resemblance between the inverted flower and a cluster of doves.
Here Mendel seems to be speculating about a mechanism by which a hybrid embryo could be transformed such that one would not observe the return of parental forms in subsequent generations (as one observes in Pisum). Mendel used the term Stoffaufnahme, which can be translated literally as "substance admission".
We know that Mendel understood that some of the characteristics of his experimental plants were regularly connected with one another, in the way they were inherited. He described these characters alternately as "associated" and "constantly correlated"; and today we would describe the associated or regularly connected characteristics as "linked" genetically. The experiments reported in the paper, however, focus on seven characteristics that did not exhibit such an association or constant correlation.
Mendel uses both Durchschnitts and mittlere to refer to average values and ratios, and it seems that he is talking about the mean in every case. A tutorial on averages will be available soon in MendelWeb.
Mendel had, several years earlier, published a paper (Mendel 1854) on Bruchus pisi, discussing the appearance and effect of the beetle in the context of Brno agriculture. Mendel's research into agricultural "pests" dates to his enrollment in a course in the zoology department of the Vienna Museum, in 1852 (For a discussion, see Orel 1996, p. 75).
Mendel uses "chance" ("Zufall" or "zufällig") in at least two distinct ways: first, to describe the indeterminacy concerning which individual pollen cell will unite with which individual egg cell; and second, to describe the actual fluctuations of his data, relative to a fixed or predicted ratio.
In the first few sections of the paper Mendel uses these terms to refer exclusively to particular aspects of the appearance of the peas and plants. Later, with the introduction of the term "hybrid-character", he sometimes uses "character" to refer both to qualities of appearance and the qualities of internal composition (what we might now call "genetic make-up").
Despite the modest introduction, this sentence presents one of the most important conclusions of the paper; it is the generality of Mendel's claim which motivates the discussion of laws of combination in the following section.
Mendel first uses the combination series to support the claim that each of the seven characters are inherited independently of one another. That is, he argues that the combination series of a two-character or three-character cross, corresponds to the product of the combination series representing each of the individual character crosses. Later in the paper, Mendel uses this same sort of argument to advance a theory about the composition of the reproductive cells of the hybrids.
To get a better idea of how the combination series is used in Mendel's arguments, consider two plants that are both hybrids with respect to one particular character; let S and s to represent the two forms of the character. Suppose you cross these hybrids, and observe that the experimental results can be represented accurately by the series: S + 2Ss + s; that is, you get S and s offspring in a 3:1 ratio, and (waiting another generation) you find that 2/3 of the S offspring must have been themselves hybrids. Then, you may argue, if the series is accurate then the contribution of each parent is known, and can be represented by the series S + s. That is, you can conclude that each parent must have produced both S and s reproductive cells, in equal proportions.
Mendel's use of combination series offers an excellent example of the use of a mathematical model to carry both experiments and arguments forward.
Mendel uses this term to refer exclusively to the information contained in the reproductive, or sex, cells; today we might say he is referring to the "genetic make-up" of these cells. Keep in mind that Mendel's speculation about the composition of the reproductive cells is derived from, and supported by: 1) his observations concerning the appearance of the offspring produced by those cells; and 2) his use of the combination series as a model for the forms of those offspring.
This is a translation of übereinstimmendes, which Mendel uses frequently; elsewhere the Druery-Bateson version translates this word as "agreement."
By translating both vereinigt and verbundenen as conjoined (rather than as "united" or "allied"), Bateson seems to have emphasized the point that the characters combined in the hybrid were joined, but not blended.
Mendel repeatedly notes that the constant combinations that are observed in the offspring from a particular multiple-character cross, are exactly those that appear in the combination series generated by multiplying the combination series of each single-character cross. This is meant to strengthen the view that the combination series provides an accurate representation of any cross; and therefore, to support Mendel's conclusions about the composition of the reproductive cells, which themselves depend on the validity of the combination series representations.
Bateson uses this word to occasionally translate Entwicklung, development; as well as Beschaffenheit, which is elsewhere translated as "composition". The effect of the latter, it seems, is to dissolve some of the ambiguity of Mendel's original language, by distinguishing references to the informational content of the reproductive cells, from references to their material organization.
The constricted form of the pod is characterized by its appearing to be pinched or indented between the spaces occupied by the peas. This is in contrast to the "inflated" (or more convex, or domed) pod, which does not exhibit constrictions between the peas.
Although Gärtner was certainly opposed to at least elements of an evolutionary theory, Bateson's translation of Fortbildung as "continuous evolution" is not particularly accurate; the German term implies both development and improvement (here it probably should be translated as "progressive development"), and one can certainly oppose a directional notion of development, without being opposed to evolution. When Mendel appears to be referring to a theory of evolution, elsewhere in the paper, he consistently uses the term Entwicklung. Whether the latter ought to be translated as "evolution" or "development", given Mendel's knowledge of Darwin and other evolutionists, is a debatable question.
What is perhaps most interesting about this reference to Gärtner's view, is that it demonstrates how different scientists could interpret the results of hybridization experiments as supporting contrary theories about the origin and development of species. For more on this topic, see Jan Sapp's "The Nine Lives of Gregor Mendel".
This is perhaps the earliest use of "control" (Mendel's term is Kontrolle), at least in the biological sciences, to denote an experiment, or set of experiments, run in parallel with others, and differing only in a single respect, or only with respect to environmental factors. In this case, the controls are the plants grown in the greenhouse, while the main experiment is conducted in the open air.
The O.E.D. cites Charles Darwin, in his book Insectivorous Plants (1875), as the first to use the word in this way in English. By 1900, this usage is so well accepted that it appears in Jackson's Glossary of Botanic Terms. But at the time of Mendel's experiments, controls (in the sense used here) were certainly not part of the standard methodology in botany, or in biology generally.
Mendel used the term "korrekt" only once in his paper; elsewhere, when Bateson used the word "correct" to translate the German (e.g. "correct assumption"), Mendel had used the term "richtig" ("right") or one of its cognates. For Mendel, a "correct" experiment was one precise enough to clearly answer a narrow, well-formed question. Unlike most of his predecessors and contemporaries, Mendel investigated plant hybrids by performing experiments that focused on the behavior of single traits. Similarly, these experiments were designed to answer elementary questions about how the particular characteristics of individual plants were inherited from one generation to the next.
Mendel usually used the term Befruchtung, or "fertilization", to refer to the process Bateson translated as "crossing". This involved uniting the pollen from one plant with the eggs of another; Mendel was able to do this using a small brush to take some pollen from the anthers of one flower, and then dust or sprinkle the pollen onto the stigma of the flower of the second plant.
Mendel was primarily interested in cases where the two plants being crossed differed in one or more characteristics; but, at the start of the paper, he was anxious to show both that this process of artificial fertilization did not affect the fertility of the plants, and that his results were not dependent on which parent he chose to provide the pollen and which the eggs.
Mendel emphasizes the care required to perform his experiments in a number of places in the paper. Here, rather than use the term "grown", he uses "cultivated" (angebaut), which calls attention to the important and active role of the experimenter.
Bateson used the term "deduced" to translate of variety of German terms, none of which were the logical term deduzieren. Mendel's choices of terms (e.g. ermitteln [to ascertain or determine], erwiesen [to prove, or show]), clearly emphasize the role of observation and empirical investigation (in addition to logic) in reaching true conclusions.
This is a translation of Mendel's term "bezeichnen".
This is one of several places in the paper in which Mendel discusses the details of, and potential difficulties involved with, carrying out (and perhaps repeating) the experiments he describes. He uses the term "gefährlich", which might be better translated as "dangerous".
Here, Mendel argues that the inheritance of flower color may in fact follow laws, and that such laws may be discovered by the sorts of experiments he is carrying out. He characterizes the opposite view as a willingness to think that flower color in cultivated plants is "random and accidental" (regellose und zufällige).
Dianthus
Mendel uses this term to denote plants, and later characteristics of plants, that have no apparent, or obvious, connection with one another. Thus he writes first of the need to do experiments with plants from diverse orders, and then of testing the "law of development," derived from observing single traits, by examining diverse characters. In the latter case, he means traits like plant height and pea color, that are "diverse" inasmuch as they are different, apparently independent characteristics of the plants.
Mendel uses this term (dominirend) to describe the forms of the characters that appear in the hybrid generation, in which the two parental forms of each character are crossed. The form of the character that does not appear in the hybrids, he calls the recessive.
When Mendel uses the phrase "hybrid egg cells", he is referring to the egg cells produced by the hybrid plant. The egg cells themselves cannot be hybrid because, according to the theory advanced in the last half of the paper, each egg carries only one form of each trait. In modern terminology we would say that each egg cell carries only one allele at each genetic locus.
It is perhaps significant that Bateson uses "endeavor", rather than the plainer word "try", to translate "Versuchen" in this case. Elsewhere, of course, the word "Versuch" is translated as "experiment" by Bateson, rather than as "trial".
Though Mendel uses this term interchangeably with albumen, it should be noted that peas possess neither an endosperm nor an albumen; in the plants with which Mendel was working, the cotyledon carries out these nutritive functions.
In this section Mendel discusses the experiments of Gärtner and Kölreuter concerning the transformation of species. Although 19th century botanists had a rather different view of species than did their contemporaries studying evolution (e.g. in geology and natural history), this section implies Mendel's familiarity with evolutionary theories concerning the origin and transmutability of species. As has been pointed out by Hartl and Orel [1992], and others, Mendel read the German translation of Charles Darwin's Origin of Species, published in 1863; a copy of this book was found in the library of the monastery in Brno, and contained Mendel's notes and commentary in the margins.
The connection between Mendel's views on continuous evolution and his interpretation of his experiments is not obvious. Little is known about whether he thought his findings compatible with the theories advanced by Darwin, and such questions have not always seemed important to modern biologists studying Mendel; when the Bateson translation was published in Peters [1959], a widely read sourcebook in genetics, the concluding section of Mendel's paper was omitted.
One of the great difficulties in performing the botanical experiments described by Mendel, is that each time the experiment is performed, the experimental conditions have changed in numerous ways. Time has passed, the weather is always different, the presence of insects or harmful parasites may change from one season to the next, and, unlike the atoms and particles of physics, no two biological organisms are strictly identical. Mendel therefore had to distinguish between the differences in experimental conditions and results he considered important, and those he did not; a task that was often difficult.
Mendel uses this term ("wesentlich") several times in his paper, most often to distinguish between experimental conditions and results he considered significant, from those he thought accidental or due to chance. That such a distinction always involved interpretation is best seen in his use of the term in final section of the paper.
The first time "evident" is used in the English version, it turns the German double-negative Ein gründlicher Beweiss, which might better have been translated "A thorough demonstration."
Skeat notes that "evident" in used in Chuacer's Treatise on the Astrolabe (1391), perhaps the earliest example of scientific writing in English. Indeed, the term has played an enormous, and perhaps under-appreciated, role in the development (and promotion) of English and American science.
We can contrast this general definition with the specific theory of evolution advanced by Charles Darwin, in Origin of Species; it was Darwin's view that the organisms we see today have all descended from common ancestors through a process of "descent with modification"; and that the most important mechanism of evolution, the primary cause of these modifications through time, has been natural selection.
Although the phrase "history of the evolution" may be a reasonable translation of Mendel's Entwicklungs-Geschichte, and Entwicklungsgeschichte it would be wrong to conclude that Mendel was talking about any particular theory of evolution. Although we know that Mendel was interested in , and read Origin of Species before 1865, we have no evidence that he thought the specifics of Darwin's theory particularly relevent to his experiments with peas. Indeed, Mendel often seems to have used Entwicklungsgeschichte, in contrast to Entwicklung, simply to distinguish the historical development of species from the development of the individual organism.
The use of the term "exhibit", like that of evident, introduces a sense of direct perception, or at least direct visual experience, that is perhaps missing from Mendel's original. For example, the Bateson translation uses "exhibit" to translate the German erhalten, which might better have been translated as "receive" (or even "maintain") in this context.
Although the earliest uses of the English term "experiment" come from alchemy, by the end of the 17th century an "experimental method" was considered to be an essential, and perhaps unique, quality of scientific investigations. Versed in the methods of chemistry and physics, and having recieved training as an experimental physicist at the University of Vienna, Mendel insisted not only on the importance of experiments in the study of plant hybrids, but on carefully designed experiments, by which he seems to have meant experiments modeled on those of physics. In the Introduction to his paper, Mendel mentions the need for detailed experiments (Detail-Versuche), that could discover the patterns of inheritance for particular characteristics; he also has an idea of what constitutes correct experiment, which is mentioned later in the paper.
In the original, Mendel used both "Versuche" and "Experimenten" to refer to experiments. Sometimes he used "Versuche" to refer to individual trials or experiments, while using "Experimenten" for discussions of experimentation per se, or references to the collection of individual experiments; but the logic behind his usage is not obvious.
Although Mendel did use the term genus in its correct taxonomic sense, it is not clear that he was using "family" in such a precise way. In modern taxonomy, we recognize five kingdoms of organisms, and use the categories: Kingdom, Phylum (called Division in plants), Class, Order, Family, Genus and Species, to classify plants and animals. In Mendel's time, however, classification was based on a more limited system, proposed by the botanist and natural historian Carl Linnaeus (1707-1778), and each species of organism was designated by two Latin names, the first denoting the genus and the second the species (e.g. Pisum sativum).
In his investigations, one of Mendel's concerns was how hybridization affected the fertility of plants, and whether or not these effects were relevant to the formulation of laws of inheritance. Today we believe that when members of different species are crossed, their offspring, if they develop at all, will be infertile; but, it can also be the case that hybrids have reduced (or in rare cases enhanced) fertility.
In the Bateson translation, "fertility" and "fertile" are usually translations of the more illustrative terms "Fruchtbarkeit" and fruchtbar.
The word "fixed" appears twice in the Bateson translation: first, in reference to the 2:1 ratio observed between the offspring of the F1 dominants that produced both dominant and recessive F2 characteristics and those that produced only dominant F2 characteristics; and second, in reference to the belief that there are definite limits to how species may be transformed through cross-breeding. An interesting analogy is thus drawn, in the English version, between the discovery of genetic ratios and the discovery of species boundaries. Mendel did not use the same word to describe the two situation in the original, however, using gesichert in the case of ratios, and fest in the case of species limits.
Mendel uses this term most often when discussing ratios, which seem clearest when the number of experimental plants (or seeds) is large. This is only to be expected, because when the number of plants is small, a small number of chance variations have more weight in the computation of averages.
English and American scientists reading the English word "fluctuation", around the turn of the century, would necessarily have thought of statistics and perhaps statistical physics; by 1901, the literature of physics had established a successful way of talking about laws and systematic relations that could be seen despite, or underneath random fluctuations (e.g. particles in a magnetic field). That the Bateson translation used "fluctuation" to translate a word like Störungen (rather than "disturbance" or "interference"), may be more indicative of what the translator considered good scientific thinking, than of Mendel's own thoughts.
Mendel used a term originally borrowed from French, Pincette.
When Mendel writes of successive generations of peas, he means the successive years' offspring from the parental (true-breeding) strains. Thus the first generation from the hybrids (F1), are the offspring of the hybrids, which are themselves the offspring of the parental strains; thus the F1 is actually the second generation from the parental strains.
The generation time for Mendel's peas is approximately one year; that's the time it takes from the appearance of a single pea (in late summer or early Fall) to the appearance of that pea's offspring (the following season).
In biological terminology the name of the genus and species to which an organism belongs is sometimes called its "generic" and "specific" name, respectively. Thus Pisum is the generic name of the plants Mendel was using.
Geum
Mendel's use of the greenhouse in these experiments was extremely important, because it allowed him to run controls, which in turn allowed him to make stronger analyses of both the results his theory predicted, and those that seemed exceptional (e.g. his attributing false impregnation in the garden to the presence of the beetle, "Brucus pisi").
(Although Andrew Faneuil of Boston is said to have built a glass house before 1737, the first greenhouse in the United States is generally attributed to James Beekman, who built one in New York City in 1764.)
Although the term hybrid now enjoys a fairly precise definition, in Mendel's time both hybrid and hybridization were often used to describe cross-fertilization between any species or varieties that were thought by breeders to be significantly different. The term "mule" was then used to denote sterile hybrids. Today, we believe that the offspring of two different species, if they come to be born at all, will be sterile; thus, we would say that what Mendel calls a "hybrid" is really the offspring or progeny of distinct varieties rather than species.
Mendel often stressed the tentative nature of his conclusions, based a they were on a single set of experiments on particular species of plant. But he also stressed the need to continue investigations, not only on Pisum but on other flowering plants as well.
Mendel used the term Hypothese only once in his paper. He used the less formal term Annahme (assumption) many times, and the Bateson version used the terms assumption, theory, and hypothesis to translate it.
Mendel's use of mathematics (the combination series in particular) is important in this respect, because mathematics made it easy to avoid questions of biological mechanism. When he was forced to go beyond mathematics and to use natural language to describe what he saw, his description problems became more difficult. A nice example of the difficulty is seen in his use of the strange phrase "must impress their peculiarity upon" (Eigentümlichkeit aufprägen müssen), to describe dominance.
Here, Mendel reports confirmation of the observations of Gärtner and Kölreuter, each of whom had noted that, over time, the number of parental forms increases at a faster rate than the number of hybrids. Mendel refined their views by describing how this generation of parental and hybrid forms worked for individual traits. That is, he noted that while parental forms, both dominant and recessive, breed true generation after generation, hybrids produce parental and hybrid forms as offspring; therefore, the ratio of parental forms to hybrids increases over time. This increase is dramatically illustrated table in the seventh section of the paper.
Throughout the paper, Mendel reports and speculates about the laws governing the inheritance of traits (what we now call the science of genetics), but he does so without knowing the mechanism responsible for these laws. His use of the term "inclined" (Neigung), is a nice example of the difficulty he had in relating his deterministic findings without a mechanistic language.
According to the OED, the English word independent first appears around 1610, and comes directly from the French indépendant and/or Italian independente. Ultimately, the term derives from the Latin pendere, to hang; a root shared by Mendel's term unabhängig, which he used to refer to the independence of characters.
Today, the term "independent assortment" is used to refer to the behavior of genes on different pairs of chromosomes. But it is also true that genes that are far apart on the same chromosome pair can appear to "sort independently", which is to say that they do not appear to be "linked" any more than genes on different chromosome pairs.
The phrase independent assortment is often used to describe one of Mendel's laws or discoveries, based on the experiments described in this paper. When applied to Mendel's paper, the phrase means that the patterns of inheritance of individual traits, or characters are independent of other studied traits. For example, Mendel argues that the inheritance patterns and ratios for each of his seven characters are uninfluenced by the inheritance patterns and ratios of the others.
Mendel knew nothing of chromosomes, of course (their significance for the study of inheritance was not known during Mendel's lifetime), and many have noted the remarkable fact that he reported the independence of exactly seven traits in Pisum, because geneticists later learned that Pisum has exactly seven pairs of chromosomes! Given Mendel's expertise as a gardener, and his ad hoc selection of seven characters to study (he describes more than a dozen before reporting the seven he selected) it might be reasonable to assume that he knew that seven independent characters was the limit in peas. Unfortunately, the traits Mendel investigated were not on separate chromosome pairs. Indeed, the gene we today think responsible for pod shape, and the gene for stem length, are both on chromosome 4, and are not so far away from each other to appear to sort independently, even in a realtively small sample (see Hartl 1980, p. 16, for a discussion and map of the chromosomes of Pisum, showing the location of Mendel's characters). In his paper, of course, Mendel does not report the results of any specific experiment showing the independence of pod shape and stem length
Mendel used the term unabhängig to describe the independence of traits, and Selbständigkeit to describe the independence of species.
Lathyrus
Lavatera
The "peculiarities" (Mendel uses eigenthümlichen) which were most important to Mendel's study were the bisexual nature of the flower, the ovary positioned at the bottom of the flower, and, most of all, the united sepals (which kept out foreign pollen during reproduction).
When Mendel referred to averages, he was always referring to the mean. The English words "mean" and "median" both come from the Latin medius. "Mode" was not used in this way in English until 1895.
Phaseolus
"Phenotype" was first used in 1909, by the geneticist Wilhelm Johannsen (1857-1927), who coined the terms gene and genotype as well. But Johannsen used the term to refer not just to the appearance of an organism, but to the average appearance of self-fertilizing, apparently "constant" forms. The current sense of the term was developed later, but was well-established in genetics by the mid-1920s (e.g. Sinnott and Dunn [1925], whose genetics textbook was dedicated to "the work of Gregor Mendel"). For more on the history of the terms phenotype and genotype, see Churchill [1974].
Mendel drew the distinction between the forms of characters that appeared in a particular generation (i.e. dominant and recessive) and the "internal nature" of the plants that exhibited those characters (parental and hybrid). This distinction is the basis for the contemporary distinction between the appearance of an organism (its parts as well as its molecules) and the genetic material that, along with the environment in which the organism develops, determines that appearance.
PisumMendel performed most of his experiments on the garden pea, Pisum sativum
Mendel used the phrase "foreign pollen" to describe pollen of unknown origin that might accidentally fertilize one of the flowers on which he was experimenting. The closed keel of the pea flower made this significantly less likely than it would have been in other species of flowering plants.
The meaning of "species" in biology has been the subject of much study and debate since the middle of the 19th century, and the meaning of the term has changed since Mendel's time. Consider the following explanations of "species", the first from a standard early 19th century botany textbook (by the naturalist Asa Gray), and the second from a recent textbook on evolutionary biology (by Douglas J. Futuyma):
"..the members in aggregate of a group of populations that interbreed or potentially interbreed with each other under normal natural conditions; a complex concept." (Futuyma [1986], p. 555).
Mendel was aware that writing about species raised problems of definition and though he certainly considered the term useful, he seems to have felt that the issue of precisely distinguishing between species and varieties was not crucial to his experimental results or his theorizing about the laws governing hybrids. This is especially clear in the original (German) text, where Mendel rarely uses the formal term Species; instead he uses the less-committed term Art (or words composed from it) most often. While Arten was certainly a word for biological species, in botany it was also used as a term for varieties. As these different words were (usually) translated as "species" in the Druery-Bateson version (and in the Stern-Sherwood translation as well), it is understandable that, in English, Mendel seems to use "species" inconsistently and ambiguously.
Issues of translation aside, today we would say that in cases where Mendel talks about different species of plants being crossed and producing fertile hybrids, he was in fact a talking about different varieties of these plants.
To artificially fertilize a particular flower, Mendel would try to remove all the stamens, and then dust the stigma with pollen gathered from the anthers of another flower.
For example, suppose you have a set of data points with the following values:
The mean is obviously 50, and the variance can be calculated as:
![[(10-50)^2 + (10-50)^2 +
(25-50)^2 + (25-50)^2 + (35-50)^2 + (65-50)^2 + (65-50)^2 + (85-50)^2 +
(90-50)^2 + (90-50)^2]/10 = 955](./images/varext.GIF)
Sometimes statistics calculated on a sample of data, drawn from a larger population, are used as estimators of the statistics of tha population; that is, the sample statistics are used to estimate the (unknown) population statistics. When this is the goal, the formula given above is often modified so that n-1, rather than n, is in the denominator. We then have:
On the Statistics Calculation Page the latter formula is referred to as sample variance and the first formula is referred to simply as the variance. You may recognize that, as the size of the data sample gets larger (i.e. for very large n ), the difference between the two forms of variance becomes small. (For more information about statistics and statistics terms, take a look at the Statistics sites on the Reference Page.)
Finally, the variance is usually calculated so that the standard deviation can be calculated. The standard deviation, which is the square-root of the variance, is also a measure of dispersion; but it used more often than variance to indicate the distribution of the data relative to the mean (see, for example, the discussion of the Normal Distribution and Standard Scores that is part of a Basic Statistics course at Arizona State University).
Although Mendel sometimes uses "species" where we would today use "variety" or "strain", he clearly understands that a distinction between varieties is not the same as a distinction between species. He also seems to understand that two varieties are capable of producing fertile offspring when crossed. But he emphasizes, early in the paper, that the decision to classify two organisms as members of different species rather than different varieties may at times appear arbitrary .
Mendel uses the term Varietäten to refer explicitly to biological varieties, but sometimes his use of the term arten seems to also signify a variety (rather than a species).
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