Cuvier's principle of correlation. Principles of carrying out detailed correlation of well sections. Page 21. Review questions and assignments

A living organism is a single whole in which all parts and organs are interconnected. When the structure and functions of one organ change in the evolutionary process, this inevitably entails corresponding or, as they say, correlative changes in other organs associated with the former physiologically, morphologically, through heredity, etc.

Example: One of the most significant, progressive changes in the evolution of arthropods was the appearance in them of a powerful external cuticular skeleton. This inevitably affected many other organs - a continuous skin-muscular sac could not function with a hard outer shell and broke up into separate muscle bundles; the secondary body cavity lost its reference value, and it was replaced by a mixed body cavity of a different origin (myxocoel), which mainly performs a trophic function; body growth took on a periodic character and began to be accompanied by molts, etc. In insects, there is a clear correlation between the respiratory organs and blood vessels. With a strong development of the trachea, delivering oxygen directly to the place of its consumption, blood vessels become redundant and disappear.

M. Milne-Edwards (1851)

Milne-Edwards (1800–1885) - French zoologist, foreign correspondent of the St. Petersburg Academy of Sciences (1846), one of the founders of morphophysiological studies of marine fauna. Pupil and follower of J. Cuvier.

The evolution of organisms is always accompanied by differentiation of parts and organs.

Differentiation consists in the fact that initially homogeneous parts of the body gradually differ more and more from each other both in form and in functions, or are subdivided into parts that are different in function. Specializing to perform a certain function, they at the same time lose the ability to perform other functions and thus become more dependent on other parts of the body. Consequently, differentiation always leads not only to the complication of the organism, but also to the subordination of parts to the whole - simultaneously with the morphophysiological dismemberment of the organism, the reverse process of forming a harmonious whole, called integration, takes place.

Question

Haeckel-Muller biogenetic law (also known as "Haeckel's law", "Muller-Haeckel's law", "Darwin-Muller-Haeckel's law", "basic biogenetic law"): every living being in its individual development (ontogenesis) repeats in to some extent the forms passed by its ancestors or its species (phylogenesis). He played an important role in the history of the development of science, but at present, in its original form, it is not recognized by modern biological science. According to the modern interpretation of the biogenetic law, proposed by the Russian biologist A.N. Severtsov at the beginning of the 20th century, in ontogenesis there is a repetition of the signs not of adult individuals of the ancestors, but of their embryos.

In fact, the "biogenetic law" was formulated long before the advent of Darwinism. The German anatomist and embryologist Martin Rathke (1793-1860) in 1825 described gill slits and arches in mammalian and bird embryos - one of the most striking examples of recapitulation. In 1828, Karl Maksimovich Baer, based on Rathke's data and on the results of his own studies of the development of vertebrates, formulated the law of germline similarity: “Embryos successively move in their development from general type traits to more and more special traits. Last of all, signs develop that indicate that the embryo belongs to a certain genus, species, and, finally, development ends with the appearance of the characteristic features of this individual. Baer did not attach evolutionary meaning to this “law” (he never accepted Darwin’s evolutionary teachings until the end of his life), but later this law began to be considered as “embryological proof of evolution” (see Macroevolution) and evidence of the origin of animals of the same type from a common ancestor.

The "biogenetic law" as a consequence of the evolutionary development of organisms was first formulated (rather vaguely) by the English naturalist Charles Darwin in his book On the Origin of Species in 1859: , in its adult or personal state, all members of the same large class"

Two years before the formulation of the biogenetic law by Ernst Haeckel, a similar formulation was proposed by the German zoologist Fritz Müller, who worked in Brazil, on the basis of his research on the development of crustaceans. In his book "For Darwin" (Für Darwin), published in 1864, he emphasizes in italics the idea: "the historical development of the species will be reflected in the history of its individual development."

A brief aphoristic formulation of this law was given by the German naturalist Ernst Haeckel in 1866. The brief formulation of the law is as follows: Ontogeny is the recapitulation of phylogeny (in many translations - “Ontogeny is a quick and brief repetition of phylogeny”).

Examples of the fulfillment of the biogenetic law

A vivid example of the fulfillment of the biogenetic law is the development of a frog, which includes the stage of a tadpole, which in its structure is much more similar to fish than to amphibians:

In the tadpole, as in lower fish and fish fry, the basis of the skeleton is the notochord, which only later becomes overgrown with cartilaginous vertebrae in the trunk part. The skull of the tadpole is cartilaginous, and well-developed cartilaginous arches adjoin it; gill breathing. The circulatory system is also built according to the fish type: the atrium has not yet divided into the right and left halves, only venous blood enters the heart, and from there it goes through the arterial trunk to the gills. If the development of the tadpole stopped at this stage and did not go any further, we should have no hesitation in classifying such an animal as a superclass of fish.

The embryos of not only amphibians, but also all vertebrates without exception, also have gill slits, a two-chambered heart, and other features characteristic of fish in the early stages of development. For example, a bird embryo in the first days of incubation is also a tailed fish-like creature with gill slits. At this stage, the future chick reveals similarities with lower fish, and with amphibian larvae, and with the early stages of development of other vertebrates (including humans). At subsequent stages of development, the embryo of a bird becomes similar to reptiles:

And while in the chicken embryo, until the end of the first week, both the hind and forelimbs look like the same legs, while the tail has not yet disappeared, and feathers have not yet formed from the papillae, in all its characteristics it is closer to reptiles than to adult birds.

The human embryo goes through similar stages during embryogenesis. Then, between approximately the fourth and sixth weeks of development, it transforms from a fish-like organism to an organism indistinguishable from an ape fetus, and only then acquires human features.

Haeckel called this repetition of ancestral traits during the individual development of an individual recapitulation.

Dollo's law of irreversibility of evolution

an organism (population, species) cannot return to its former state, which was in the series of its ancestors, even after returning to their habitat. It is possible to acquire only an incomplete number of external, but not functional, similarities with their ancestors. The law (principle) was formulated by the Belgian paleontologist Louis Dollo in 1893.

The Belgian paleontologist L. Dollo formulated the general position that evolution is an irreversible process. This position was then repeatedly confirmed and received the name of Dollo's law. The author himself gave a very brief formulation of the law of irreversibility of evolution. He was not always correctly understood and sometimes caused not quite well-founded objections. According to Dollo, "an organism cannot return, even partially, to the previous state already realized in the series of its ancestors."

Examples of Dollo's Law

The law of irreversibility of evolution should not be extended beyond its applicability. Terrestrial vertebrates are descended from fish, and the five-fingered limb is the result of the transformation of the paired fin of fish. The terrestrial vertebrate can again return to life in the water, and the five-fingered limb at the same time takes on the general form of a fin. The internal structure of the fin-shaped limb - the flipper retains, however, the main features of the five-fingered limb, and does not return to the original structure of the fish fin. Amphibians breathe with lungs, They have lost the gill breathing of their ancestors. Some amphibians returned to a permanent life in the water and again acquired gill breathing. Their gills are, however, larval external gills. The internal gills of the fish type have disappeared forever. In tree-climbing primates, the first toe is reduced to a certain extent. In humans, descended from climbing primates, the first finger of the lower (hind) limbs again underwent significant progressive development (in connection with the transition to walking on two legs), but did not return to some initial state, but acquired a completely unique shape, position and development.

Consequently, not to mention the fact that progressive development is often replaced by regression, and regression is sometimes replaced by new progress. However, development never goes back along the path already traveled, and it never leads to a complete restoration of the previous states.

Indeed, organisms, moving into their former habitat, do not completely return to their ancestral state. Ichthyosaurs (reptiles) have adapted to living in water. At the same time, their organization remained typically reptilian. The same goes for crocodiles. Mammals living in the water (whales, dolphins, walruses, seals) have retained all the features characteristic of this class of animals.

The law of organ oligomerization according to V.A. Dogel

In multicellular animals, in the course of biological evolution, there is a gradual decrease in the number of initially isolated organs that perform similar or identical functions. In this case, the organs can be differentiated and each of them begins to perform different functions.

Discovered by V. A. Dogel:

“As differentiation proceeds, oligomerization of organs occurs: they acquire a certain localization, and their number decreases more and more (with progressive morphophysiological differentiation of the remaining ones) and becomes constant for a given group of animals”

For the annelids type, body segmentation has a multiple, unsteady character, all segments are homogeneous.

In arthropods (derived from annelids), the number of segments:

1. in most classes is reduced

2. becomes permanent

3. individual segments of the body, usually combined into groups (head, chest, abdomen, etc.), specialize in performing certain functions.

The purpose of correlation analysis is to identify an estimate of the strength of the connection between random variables (features) that characterizes some real process.
Problems of correlation analysis:
a) Measurement of the degree of connection (tightness, strength, severity, intensity) of two or more phenomena.
b) The selection of factors that have the most significant impact on the resulting attribute, based on measuring the degree of connectivity between phenomena. Significant factors in this aspect are used further in the regression analysis.
c) Detection of unknown causal relationships.

The forms of manifestation of interrelations are very diverse. As their most common types, functional (complete) and correlation (incomplete) connection.
correlation manifests itself on average, for mass observations, when the given values of the dependent variable correspond to a certain number of probabilistic values of the independent variable. The connection is called correlation, if each value of the factor attribute corresponds to a well-defined non-random value of the resultant attribute.
Correlation field serves as a visual representation of the correlation table. It is a graph where X values are plotted on the abscissa axis, Y values are plotted along the ordinate axis, and combinations of X and Y are shown by dots. The presence of a connection can be judged by the location of the dots.
Tightness indicators make it possible to characterize the dependence of the variation of the resulting trait on the variation of the trait-factor.
A better indicator of the degree of tightness correlation is linear correlation coefficient. When calculating this indicator, not only the deviations of the individual values of the attribute from the average are taken into account, but also the magnitude of these deviations.

The key issues of this topic are the equations of the regression relationship between the resulting feature and the explanatory variable, the least squares method for estimating the parameters of the regression model, analyzing the quality of the resulting regression equation, building confidence intervals for predicting the values of the resulting feature using the regression equation.

Example 2

System of normal equations.
a n + b∑x = ∑y
a∑x + b∑x 2 = ∑y x
For our data, the system of equations has the form
30a + 5763 b = 21460
5763 a + 1200261 b = 3800360
From the first equation we express A and substitute into the second equation:
We get b = -3.46, a = 1379.33
Regression equation:
y = -3.46 x + 1379.33

2. Calculation of the parameters of the regression equation.
Sample means.

Sample variances:

standard deviation

1.1. Correlation coefficient
covariance.

We calculate the indicator of closeness of communication. Such an indicator is a selective linear correlation coefficient, which is calculated by the formula:

The linear correlation coefficient takes values from –1 to +1.
Relationships between features can be weak or strong (close). Their criteria are evaluated on the Chaddock scale:
0.1 < r xy < 0.3: слабая;
0.3 < r xy < 0.5: умеренная;
0.5 < r xy < 0.7: заметная;
0.7 < r xy < 0.9: высокая;
0.9 < r xy < 1: весьма высокая;
In our example, the relationship between feature Y and factor X is high and inverse.
In addition, the coefficient of linear pair correlation can be determined in terms of the regression coefficient b:

1.2. Regression Equation(evaluation of the regression equation).

The linear regression equation is y = -3.46 x + 1379.33

The coefficient b = -3.46 shows the average change in the effective indicator (in units of y) with an increase or decrease in the value of the factor x per unit of its measurement. In this example, with an increase of 1 unit, y decreases by an average of -3.46.
The coefficient a = 1379.33 formally shows the predicted level of y, but only if x=0 is close to the sample values.
But if x=0 is far from the sample x values, then a literal interpretation can lead to incorrect results, and even if the regression line accurately describes the values of the observed sample, there is no guarantee that this will also be the case when extrapolating to the left or to the right.
By substituting the corresponding values of x into the regression equation, it is possible to determine the aligned (predicted) values of the effective indicator y(x) for each observation.
The relationship between y and x determines the sign of the regression coefficient b (if > 0 - direct relationship, otherwise - inverse). In our example, the relationship is reverse.
1.3. elasticity coefficient.
It is undesirable to use regression coefficients (in example b) for a direct assessment of the influence of factors on the effective attribute in the event that there is a difference in the units of measurement of the effective indicator y and the factor attribute x.
For these purposes, elasticity coefficients and beta coefficients are calculated.
The average coefficient of elasticity E shows how many percent the result will change on average in the aggregate at from its average value when changing the factor x 1% of its average value.
The coefficient of elasticity is found by the formula:

The elasticity coefficient is less than 1. Therefore, if X changes by 1%, Y will change by less than 1%. In other words, the influence of X on Y is not significant.
Beta coefficient shows by what part of the value of its standard deviation the value of the effective attribute will change on average when the factor attribute changes by the value of its standard deviation with the value of the remaining independent variables fixed at a constant level:

Those. an increase in x by the value of the standard deviation S x will lead to a decrease in the average value of Y by 0.74 standard deviation S y .
1.4. Approximation error.
Let us evaluate the quality of the regression equation using the absolute approximation error. The average approximation error is the average deviation of the calculated values from the actual ones:

Since the error is less than 15%, this equation can be used as a regression.
Dispersion analysis.
The task of analysis of variance is to analyze the variance of the dependent variable:
∑(y i - y cp) 2 = ∑(y(x) - y cp) 2 + ∑(y - y(x)) 2
Where
∑(y i - y cp) 2 - total sum of squared deviations;
∑(y(x) - y cp) 2 - sum of squared deviations due to regression (“explained” or “factorial”);
∑(y - y(x)) 2 - residual sum of squared deviations.
Theoretical correlation ratio for a linear relationship is equal to the correlation coefficient r xy .
For any form of dependence, the tightness of the connection is determined using multiple correlation coefficient:

This coefficient is universal, as it reflects the tightness of the connection and the accuracy of the model, and can also be used for any form of connection between variables. When constructing a one-factor correlation model, the multiple correlation coefficient is equal to the pair correlation coefficient r xy .
1.6. Determination coefficient.
The square of the (multiple) correlation coefficient is called the coefficient of determination, which shows the proportion of the variation of the resultant attribute explained by the variation of the factor attribute.
Most often, giving an interpretation of the coefficient of determination, it is expressed as a percentage.
R 2 \u003d -0.74 2 \u003d 0.5413
those. in 54.13% of cases, changes in x lead to a change in y. In other words, the accuracy of the selection of the regression equation is average. The remaining 45.87% of the change in Y is due to factors not taken into account in the model.

Bibliography

Econometrics: Textbook / Ed. I.I. Eliseeva. - M.: Finance and statistics, 2001, p. 34..89.
Magnus Ya.R., Katyshev P.K., Peresetsky A.A. Econometrics. Initial course. Tutorial. - 2nd ed., Rev. – M.: Delo, 1998, p. 17..42.
Workshop on econometrics: Proc. allowance / I.I. Eliseeva, S.V. Kurysheva, N.M. Gordeenko and others; Ed. I.I. Eliseeva. - M.: Finance and statistics, 2001, p. 5..48.

In the first quarter of the 19th century, great advances were made in such areas of biological science as comparative anatomy and paleontology. The main achievements in the development of these areas of biology, especially in comparative anatomy, belong to the French scientist J.L. Cuvier. He systematically compared the structure and functions of the same organ or an entire system of organs through all sections of the animal kingdom. Investigating the structure of the organs of vertebrates, Cuvier found that all the organs of an animal are parts of a single integral system. As a result, the structure of each organ naturally correlates with the structure of all others. No part of the body can change without a corresponding change in other parts. This means that each part of the body reflects the principles of the structure of the whole organism. So, if an animal has hooves, its entire organization reflects a herbivore lifestyle: the teeth are adapted to grinding coarse plant foods, the jaws have a certain shape, the stomach is multi-chambered, the intestines are very long, etc. Cuvier called the correspondence of the structure of animal organs to each other the principle of correlations (correlativity). Cuvier successfully applied the principle of correlations in paleontology. He restored the appearance of a long-vanished organism from individual fragments that have survived to this day.

In the course of his research, Cuvier became interested in the history of the Earth, terrestrial animals and plants. As a result of great work, he came to the following conclusions:

The earth has changed its appearance throughout its history;

Simultaneously with the change of the Earth, its population also changed;

Changes in the earth's crust occurred even before the appearance of living beings.

Cuvier was convinced of the impossibility of the emergence of new forms of life and proved that the species of living organisms modern to us have not changed, at least since the time of the pharaohs. But Cuvier considered the most significant objection to the theory of evolution to be the apparent absence of transitional forms between modern animals and those whose remains were found during excavations.

Numerous paleontological data, however, irrefutably testified to the change in the forms of animals on Earth. The real facts came into conflict with the biblical legend. At first, supporters of the immutability of living nature explained such contradictions by the fact that those animals that Noah did not take into his ark during the Flood died out. The unscientific nature of this conclusion was refuted when various degrees of antiquity of extinct animals were established. Then Cuvier put forward the theory of catastrophes. According to this theory, the cause of extinction was periodically occurring major geological disasters that destroyed vegetation and animals over large areas. Then this territory was populated by species that penetrated from neighboring regions.

The followers and students of Cuvier, developing his teaching, went further, arguing that catastrophes covered the entire globe. After each catastrophe, a new act of divine creation followed. They numbered 27 such catastrophes and acts of creation.

Anatomists, long before the emergence of evolutionary doctrine, observed that the position and structure of various organs in the body are in a regular relationship with each other.

At the beginning of the XIX century. the famous French comparative anatomist and paleontologist Georges Cuvier established the law of the coexistence of organs, which he called the lawnom of correlation, which helped him to reconstruct entire skeletons from the scattered remains of the bones of fossil animals. A similar law - the mutual balancing of organs - was also discovered by his contemporary Geoffroy Saint-Hilaire.

C. Darwin attached great importance to both of these laws, and in the chapter on correlative changes in organs, he analyzed the significance of changes in the ratio between organs in the process of evolution. The adaptation of an animal to certain conditions of existence does not affect any one organ, but causes a whole series of correlative changes in other organs. A change in the function of any organ entails a change in the functions of other organs. For example, the adaptation of mammals to carnivorous nutrition not only caused changes in the teeth and intestines, which are directly related to eating meat food, but the limbs also changed accordingly: large claws formed on the fingers, strong muscles developed. In herbivores, in addition to teeth adapted to grinding plants, the stomach and intestines adapted to digesting plant food, the limbs also changed: the five-fingered limb of the horse's ancestors turned into a one-fingered limb with a hoof, adapted for fast running, which is necessary when living in open steppe spaces .

The law of correlation has played an enormous role in paleontology. Having studied in detail the chain of functional relationships of organs in modern forms, the paleontologist got the opportunity, having only parts of the animal in his hands, to restore the entire animal. Having fragments of a skull with large horns in his hands, the paleontologist has every right to assert that the spine of this animal had large spinous processes, to which powerful muscles were attached, supporting a heavy head, and the limbs were adapted to walking on two fingers, as is observed in all modern artiodactyl animals.

The law of correlation also plays an enormous role in comparative anatomy and embryology. With the victory of the evolutionary doctrine, the static idea of correlations as a constant coexistence of organs was abandoned, and the law of the ratio of organs began to be understood as a process of interconnection of parts of an organism in individual and historical development. According to this understanding of correlations, they were divided into two categories:

1) physiological, or individual, correlations, i.e., the interconnections of parts and organs in individual development,

2) phylogenetic correlations, or coordinations (A. N. Severtsov), that is, the interconnections of organs in historical development.

The doctrine of correlations plays a large role in evolutionary doctrine. It explains the cases when an insignificant hereditary change causes a complex chain of coordinating changes in the organism, significantly changing the previous attitude of the organism to the environment.