The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution
Evolutionary changes of characters formed in ontogeny by developmental induction are modeled for an infinite population and for replicate finite populations under a mutation — drift equilibrium. Induction occurs by interaction of reactants, which must therefore coincide in time intervals of their ab...
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nasplib_isofts_kiev_ua-123456789-649392025-02-10T01:37:36Z The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution Регрессивный тренд сложных фенотипических структур в нейтральной эволюции Dzeverin, I.I. Эволюция и филогения Evolutionary changes of characters formed in ontogeny by developmental induction are modeled for an infinite population and for replicate finite populations under a mutation — drift equilibrium. Induction occurs by interaction of reactants, which must therefore coincide in time intervals of their abilities to react. This mechanism is being damaged in evolution of useless structures by random mutations in genes that control simultaneous formations of reactants, whereas mutational effects on important structures are restrained by selection. The breakdown of induction mechanisms produces increased variability and degeneration in vestigial characters. Quantitative estimations are illustrated by data regarding regressive trends in some groups of mammals. Time spans sufficient for complete loss of vestigial organs obtained from the modelings are much smaller than the periods of macroevolutionary changes. Certain functional value and the genetic correlation with important structures are the most probable mechanisms that could prevent the rapid loss of vestigial structures. Математические модели эволюционных изменений признаков, формирующихся в онтогенезе путем индукции, разработаны для бесконечной популяции, а также для группы конечных популяций, находящихся в состоянии равновесия между мутационным процессом и генетическим дрейфом и имеющих одинаковые исходные свойства. I am indebted to R. Lande for valuable advices and criticisms of earlier drafts of the manuscript. I am indebted to B. M. Mednikov and M. A. Shishkin for some initial ideas on the subject of my research. I am grateful to M. A. Ghazali for help in my work, comments and constructive suggestions. Thanks also are due to O. I. Schmalhausen, E. I. Kozhurina, P. P. Strelkov, I. Hora´cek, and the reviewers for helpful comments and discussions. R. Lande, B. Sige´, M. Machola´n, G. P. Wagner, B. F. J. Manly, S. Gavrilets, R. Burger, B. Hallgr msson, J. Felsenstein, E. P. Martins, M. Turelli kindly presented reprints of articles hardly accessible in the East Europe. V. M. Tytar is acknowledged for improving the English text and discussion. 2007 Article The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution / I.I. Dzeverin // Вестник зоологии. — 2007. — Т. 41, № 1. — С. 53–69. — Бібліогр.: 64 назв. — англ. 0084-5604 https://nasplib.isofts.kiev.ua/handle/123456789/64939 575.8:591.4.068:591.15:599 en Вестник зоологии application/pdf Інститут зоології ім. І.І. Шмальгаузена НАН України |
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Эволюция и филогения Эволюция и филогения Dzeverin, I.I. The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution Вестник зоологии |
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Evolutionary changes of characters formed in ontogeny by developmental induction are modeled for an infinite population and for replicate finite populations under a mutation — drift equilibrium. Induction occurs by interaction of reactants, which must therefore coincide in time intervals of their abilities to react. This mechanism is being damaged in evolution of useless structures by random mutations in genes that control simultaneous formations of reactants, whereas mutational effects on important structures are restrained by selection. The breakdown of induction mechanisms produces increased variability and degeneration in vestigial characters. Quantitative estimations are illustrated by data regarding regressive trends in some groups of mammals. Time spans sufficient for complete loss of vestigial organs obtained from the modelings are much smaller than the periods of macroevolutionary changes. Certain functional value and the genetic correlation with important structures are the most probable mechanisms that could prevent the rapid loss of vestigial structures. |
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Dzeverin, I.I. |
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Dzeverin, I.I. |
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Dzeverin, I.I. |
| title |
The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution |
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The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution |
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The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution |
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The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution |
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The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution |
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regressive trend of complex phenotypic structures in neutral evolution |
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Інститут зоології ім. І.І. Шмальгаузена НАН України |
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2007 |
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Эволюция и филогения |
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The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution / I.I. Dzeverin // Вестник зоологии. — 2007. — Т. 41, № 1. — С. 53–69. — Бібліогр.: 64 назв. — англ. |
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AT dzeverinii theregressivetrendofcomplexphenotypicstructuresinneutralevolution AT dzeverinii regressivnyitrendsložnyhfenotipičeskihstrukturvneitralʹnoiévolûcii AT dzeverinii regressivetrendofcomplexphenotypicstructuresinneutralevolution |
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2025-12-02T12:43:06Z |
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1850400452227629056 |
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UDC 575.8:591.4.068:591.15:599
THE REGRESSIVE TREND OF COMPLEX
PHENOTYPIC STRUCTURES IN NEUTRAL EVOLUTION
I. I. Dzeverin
Schmalhausen Institute of Zoology, NAS of Ukraine,
Bogdan Chmielnicky str., 15, Kyiv, 01601 Ukraine
E-mail: dzeverin@izan.kiev.ua, igor_dzeverin@yahoo.com, igordzeverin@yandex.ru
Accepted 2 October 2006
The Regressive Trend of Complex Phenotypic Structures in Neutral Evolution. Dzeverin I. I. —
Evolutionary changes of characters formed in ontogeny by developmental induction are modeled for an
infinite population and for replicate finite populations under a mutation — drift equilibrium. Induction
occurs by interaction of reactants, which must therefore coincide in time intervals of their abilities to
react. This mechanism is being damaged in evolution of useless structures by random mutations in genes
that control simultaneous formations of reactants, whereas mutational effects on important structures
are restrained by selection. The breakdown of induction mechanisms produces increased variability and
degeneration in vestigial characters. Quantitative estimations are illustrated by data regarding regressive
trends in some groups of mammals. Time spans sufficient for complete loss of vestigial organs obtained
from the modelings are much smaller than the periods of macroevolutionary changes. Certain
functional value and the genetic correlation with important structures are the most probable
mechanisms that could prevent the rapid loss of vestigial structures.
Ke y wo r d s: vestigial organ, threshold character, quantitative character, developmental induction,
neutral evolution, regressive evolution, morphometric variation, mammals.
Ðåãðåññèâíûé òðåíä ñëîæíûõ ôåíîòèïè÷åñêèõ ñòðóêòóð â íåéòðàëüíîé ýâîëþöèè. Äçåâåðèí È. È. —
Ìàòåìàòè÷åñêèå ìîäåëè ýâîëþöèîííûõ èçìåíåíèé ïðèçíàêîâ, ôîðìèðóþùèõñÿ â îíòîãåíåçå
ïóòåì èíäóêöèè, ðàçðàáîòàíû äëÿ áåñêîíå÷íîé ïîïóëÿöèè, à òàêæå äëÿ ãðóïïû êîíå÷íûõ ïî-
ïóëÿöèé, íàõîäÿùèõñÿ â ñîñòîÿíèè ðàâíîâåñèÿ ìåæäó ìóòàöèîííûì ïðîöåññîì è ãåíåòè÷åñêèì
äðåéôîì è èìåþùèõ îäèíàêîâûå èñõîäíûå ñâîéñòâà. Â íîðìå èíäóêöèÿ ïðîèñõîäèò âñëåäñòâèå
âçàèìíîãî âëèÿíèÿ ñïåöèôè÷åñêèõ ðåàãåíòîâ, êîòîðûå äîëæíû, ñëåäîâàòåëüíî, ôîðìèðîâàòüñÿ
â îíòîãåíåçå îäíîâðåìåííî. Â ýâîëþöèè áåñïîëåçíûõ ñòðóêòóð ýòîò ìåõàíèçì íàðóøàåòñÿ ñëó-
÷àéíûìè ìóòàöèÿìè â ãåíàõ, êîíòðîëèðóþùèõ ñðîêè ðàçâèòèÿ ðåàãåíòîâ, à â ýâîëþöèè
ñòðóêòóð, íóæíûõ îðãàíèçìó, íàêîïëåíèå ìóòàöèé ñäåðæèâàåòñÿ åñòåñòâåííûì îòáîðîì. Íàðó-
øåíèÿ ìåõàíèçìîâ èíäóêöèè ñòàíîâÿòñÿ ïðè÷èíîé óâåëè÷åíèÿ èçìåí÷èâîñòè è óïðîùåíèÿ
ñòðîåíèÿ ðóäèìåíòàðíûõ îðãàíîâ âïëîòü äî ïîëíîé èõ óòðàòû. Êîëè÷åñòâåííûå ìîäåëè ýòèõ
ïðîöåññîâ ïðîèëëþñòðèðîâàíû äàííûìè î ðåãðåññèâíûõ òðåíäàõ â ýâîëþöèè ìîðôîëîãè÷åñêèõ
ïðèçíàêîâ â íåêîòîðûõ ãðóïïàõ ìëåêîïèòàþùèõ. Ìîäåëèðîâàíèå ïîêàçàëî, ÷òî îòðåçîê
âðåìåíè, äîñòàòî÷íûé äëÿ ïîëíîé óòðàòû ðóäèìåíòàðíûõ îðãàíîâ, íàìíîãî ìåíüøå, ÷åì îáû÷-
íûå ïåðèîäû ìàêðîýâîëþöèîííûõ èçìåíåíèé. Íåêîòîðîå ôóíêöèîíàëüíîå çíà÷åíèå è ãåíåòè-
÷åñêàÿ êîððåëÿöèÿ ñ âàæíûìè ñòðóêòóðàìè — íàèáîëåå âåðîÿòíûå ìåõàíèçìû, êîòîðûå ìîãóò
ïðåäîòâðàòèòü áûñòðóþ ïîòåðþ ðóäèìåíòîâ.
Êëþ÷åâûå ñ ëîâ à: ðóäèìåíòàðíûé îðãàí, ïîðîãîâûé ïðèçíàê, êîëè÷åñòâåííûé ïðèçíàê,
îíòîãåíåòè÷åñêàÿ èíäóêöèÿ, íåéòðàëüíàÿ ýâîëþöèÿ, ðåãðåññèâíàÿ ýâîëþöèÿ, ìîðôîìåòðè÷åñ-
êàÿ èçìåí÷èâîñòü, ìëåêîïèòàþùèå.
Introduction
Various mechanisms by which complex polygenic phenotypic structures can be established, maintained,
and transformed in evolution are learned from the empirical data on evolutionary dynamics of characters.
Due to these mechanisms some structures become vestigial and disappear in the evolution course, while
others become more complex and more reliable. Organs and systems of organs are examples of such
structures.
Vestnik zoologii, 41(1): 53–69, 2007
© I. I. Dzeverin, 2007
Ýâîëþöèÿ è ôèëîãåíèÿ
This paper concerns the dynamics of diminishing the useless organs in evolution frequently ending up
with a complete loss of them. My task is to describe the neutral evolution of complex phenotypic structures
taking into account both their polygenic determination and developmental events by which such structures
are formed in ontogeny. I hope this class of models may be useful as a first approximation for various
problems in phenotypic evolution.
Theoretical Background
An array of authors have investigated regressive trends of various organs in all main groups of plants
and animals (Sewertzoff, 1939, 1945; Schmalhausen, 1982; Simpson, 1944; Yablokov, 1966; Schemmel,
1984; Parzefall, 1984; Peters, Peters, 1984; Dzwillo, 1984; Jeffery, 2001 et al.). Good examples of regressive
trends can be revealed from the evolution of dental characters in mammals, for example, Chiroptera (Menu,
1985, 1987; Wo/loszyn, 1987) and Primates (Zubov, Khaldeyeva, 1989), or from the limb losses in various
groups of vertebrates (Lande, 1978).
As a rule, the patterns of evolutionary regressive transformations are rather similar for various organs in
different groups. Degenerating, an organ gradually decreases in size, its variability increases, and the structure
becomes more simple. Thus, only a vestigial structure with obvious features of under-development remains.
Eventually the organ disappears, however occasionally it can develop in some individuals of a population as
an atavistic structure, even after a rather long period of time. The reverse evolution of a degenerated organ
can occur in some lineages. The rate of regressive transformation can differ in various lineages, as well as a
sequence of stages of regression. Very often this sequence is opposite to the sequence of their formation in
ontogeny and the suggested sequence of their first emergence in evolution. During each period of its history
a large taxon is represented by a number of lineages with similar trends of evolutionary transformations, and
so various stages of under-development can be revealed in simultaneously existing species. After a very long
period of time the complete loss of a structure can be achieved by the majority or by all species of the taxon.
Regressive trends can be associated with the changes in the patterns of variation. Darwin had assumed
that the lack of selection pressure on unused structures leads to the increase of their variability (Darwin, 1872,
cited after the re-edition: Darwin, 1998). Developing this hypothesis, Schmalhausen (1938, cited after the
re-edition: Schmalhausen, 1982) supposed that the cessation of selection, which had been keeping a certain
structure unchanged, results in an unlimited accumulation of random mutations. Since any newly introduced
mutation changes development in an arbitrary direction independently of any other mutation, as well as
changing the performance of the current genotype, disintegration of an organ and the accumulation of pattern
deformations in development should arise. Diminution, simplification, decreasing correlation between parts
of this organ, increasing variability, and, finally, the complete loss of the organ are the consequences of these
deformations.
Another probable explanation for regressive evolution is that it can be caused by negative selection on
harmful features. For certain cases it is possible to associate observed changes with selection on combinations
of genes determining size decrease, or deceleration of development, or both of these processes, while in other
cases the selection of suppressors of morphogenesis is probable (Lande, 1978). Some classical examples of
regressive evolution (in particular, a loss of lateral fingers and toes in evolution of horses, or limb loss in
snakes) can be explained as the results of negative selection. Besides, in many cases reduced and simplified
organs can be regarded as important adaptations for certain organisms, and selection is supposed to tend to
simplify their structure according to this importance (Yablokov, 1966; Zander, 1984).
For many other regressive processes the adaptive significance remains unknown or unproved.
Depigmentation and eye loss in speleobionts are well-known examples. Eyes may be useless for cave animals
but it has not been proved that they are harmful. This concerns also the final stages of regressive evolution,
when the vestigial organ is already so small, that it can not be substantially deleterious. Adaptive explanations
can be constructed for such trends too (for example, explaining them by the saving of material), but for all
such cases the quantitative examination for input of such changes to fitness is necessary. In certain cases it
is possible to explain regressive processes by indirect selection. Various regressive processes can be induced
either by negative selection or by mutation accumulation (Schemmel, 1984). A combination of mutation and
selection effects seems to be possible too.
A problem with mutational explanation for regressive evolution arises in the quantitative analyses of the
dynamics of gene frequencies. It has been shown that under selective neutrality the mean value of a polygenic
character in a large population should drift in arbitrary direction while its variance should increase linearly
with time (Kimura, 1965; Lande, 1976 a, b). In other words, the termination of selection itself can produce
an increase of organ variability, but not the directed change. The decrease of an organ doesn’t seem to be
more probable during neutral evolution than its increase. Therefore, the long regressive evolution, as a result
of which an organ can be completely lost without any input of negative selection, is hardly probable. The
possibility for such a trend needs an explanation from the genetic standpoint.
Some vestigial organs were studied genetically. It has been shown that they do not differ in the pattern
of genetic determination from other polygenic structures (Wilkens, 1984; Villwock, 1984). Multiple genes
control their regression (Jeffery, 2001). Therefore, quantitative genetic techniques seem to be appropriate in
the study of their evolution. The modeling presented here is based on quantitative genetic approaches to the
study of evolution (review: Falconer, 1985) with introducing the information about some developmental
54 I. I. Dzeverin
events. These approaches were successfully applied to analyze the interface between development and
evolution (Lande, 1979; Riska, 1986, 1989; Wagner, 1988; Wagner et al., 1997; Gavrilets, Hastings, 1994
etc.)
Any structure or character formed by interaction of pre-existing structures in ontogeny is regarded in
this paper as a complex structure or character (with putting more precise definition of complexity off for the
future). An organ or any other complex morphological structure initialized in ontogeny by an induction
process can be an example of such a structure. The variation of formation patterns is analyzed here for an
example of the durations of the abilities of reactants to take part in induction. Apparently it is the most
common example of hereditary variability of developmental processes (Schmalhausen, 1982; Korochkin,
2002). A common effect for many mutations is the shift in time of the realization of some reactions in a
developing organism (Schmalhausen, 1982; Korochkin, 2002). Some models linking genetic and
morphological variation were proposed for developmental inductions, in particular induction effects in
mammalian teeth development (Salazar-Ciudad, Jernvall, 2004).
The Quantitative Model
Assume that an organizer becomes competent to influence responding tissue at the moment X1 and
preserves this ability during an interval of time C1. Assume further, that the responding tissue becomes
competent to develop after being influenced by the organizer at the moment X2 and preserves this ability
during an interval of time C2. Variable X = X1 – X2 (that is an interval of time between the moments, when
the responding tissue and organizer become able to enter a morphogenetic reaction) can be considered as a
quantitative measure of coordination in the development of two reactants. Values of duration in the organizer
and responding tissue competence, C1 and C2, are supposed in this paper to be constant in all specimens of
investigated populations during all the modeled period of evolution.
The differentiation process begins, if simultaneously during some interval of time both the organizer is
able to trigger a reaction, and the responding tissue is able to react. If the formations of these reactants do
not coincide in time, the induction becomes impossible. It is supposed here, that the induction follows the
all-or-nothing pattern, that is the differentiation process either is realized completely, or doesn’t occur at all.
Let Y be an indicator showing whether a set of genes determining the structure was activated by
induction. Three situations are possible for the formation process.
If X < –C2, the reaction is impossible, because the organizer has lost its ability to trigger morhogenesis
too early, still before the responding tissue has attained its ability to differentiate (Y = 0).
If –C2 < X < C1, the formations of the organizer and responding tissue more or less coincide in time,
therefore morphogenesis takes place (Y = 1).
If X > C1, the reaction is impossible, because the organizer has attained its ability to trigger
morphogenesis too late, already after the responding tissue has lost its ability to differentiate (Y = 0).
Suppose X to be a quantitative trait determined by multiple additive genes and distributed in a
population normally with a mean and additive genetic variance in the appropriate scale of measure-
ment. These assumptions do not restrict the generality of the model to a great extent, because certain scale
transformations can substantially increase the similarity between empirical and normal distributions
(Falconer, 1985).
The proportion of organisms, in which the induction has taken place, can be defined using the
formulation of the integral of normal distribution probability as:
. (1)
The trait Y is influenced by X and thus can be studied as a threshold character that is the discrete trait
determined with a latent continuously varying parameter (Falconer, 1985). A trait with such pattern of
variation is a Bernoulli variable with expected value and variance (Statistics, 1989).
The duration of evolution processes, t, is measured in this paper in discrete generations, meaning that
peculiarities of life cycles and repeated reproductions seem not to essentially influence the genetic and
phenotypic structures of the population. Assume, that the investigated structure was established and
maintained by natural selection in the past (t < 0), however after the environmental change in generation
t = 0 this structure loses its adaptive value. It is supposed that this trait became useless but not deleterious,
and could not be an object of direct or indirect negative selection. Therefore, during the time period t > 0
exclusively mutation and random genetic drift determine the dynamics of a given trait.
Consider this dynamics in more detail. Character X was defined as a normally distributed quantitative
trait determined by multiple additive factors. The dynamics of such characters in neutral evolution has been
investigated (Kimura, 1965; Lande, 1976 a, b; Turelli, 1984; Lynch, Hill, 1986; Turelli et al., 1988;
Felsenstein, 1988; Bu�rger et al., 1989; Bu�rger, Lande, 1994; Martins, 1994). If it is assumed that the
population is sufficiently large to ignore random genetic drift and the effects restricting randomness of mating
are insignificant, then the dynamics of such a trait should be determined exclusively by the accumulation of
55Lack of Selection Leads to Regressive Change…
neutral mutations. Major mutations are not analyzed here because their deleterious effects on development
are well known (Korochkin, 2002). Only effects of minor mutations are included to the model.
In any generation t > 0 the distribution of X should remain normal with the expected value:
, (2)
and additive variance:
, (3)
where is the new additive variance introduced by mutation during a generation (Kimura, 1965; Lande,
1976 a). This input is assumed to be unchanged during the period of time under study. Thus, in an infinite
population the mean value of normally distributed and additively determined characters remains constant
while its variation increases without limits due to the accumulation of random mutations.
A different trend is expected for finite population (Lande, 1976 b; Lynch, Hill, 1986; Turelli et al.,
1988). It is important to note that for macroevolutionary periods of time any group must be considered as
having finite size (Turelli et al., 1988). In this case mutation increases the trait variance, however random
genetic drift decreases it. Sooner or later additive variance achieves equilibrium value
, (4)
where NE is the effective population size (Turelli et al., 1988) and then drifts around this expectation. The
expected time span for achieving the equilibrium value (4) is approximately 4NE generations (Turelli et al.,
1988). It does not depend on the initial value of the variance (Turelli et al., 1988). In a finite population
is a random variable distributed normally with expected value:
, (5)
and variance:
, (6)
(Lande, 1976 b; Lynch, Hill, 1986; Turelli et al., 1988). For a population under a mutation — drift
equilibrium, the rate of shifting the mean value depends on , but doesn’t depend on NE (Lynch, Hill, 1986;
Turelli et al., 1988).
A value of a complex character depends both on whether the induction had taken place and on additive
and non-additive genes activated by induction. As usual several induction processes seem to be necessary to
form a complex structure. These complications for the model are analyzed in special sections of this paper.
Results
Dynamics of a threshold character in an infinite population
It is possible to construct a model of evolutionary dynamics for threshold charac-
ter Y in an infinite population (Dzeverin, 2000). The expected value and variance of Y
in generation t is accordingly:
, (7)
and
. (8)
It is evident from (1) and (3) that P(t) decreases with time and consequently
decreases, while at first increases reaching the maximum value when
P(t) = 0.5 and then also decreases.
In a number of biological studies, the coefficient of variation, , is applied
as an important measure for the level of variability (Lande, 1977). The standard error
of
the coefficient of variation in a sample is , where Q is
the
sample estimate of the coefficient of variation, and N is the sample size (Lakin,
1990). For a threshold character the coefficient of variation should be a time-depen-
dent function which can be expressed as
. (9)
It is clear that, as P(t) decreases, the coefficient of variation increases achieving
with time an arbitrarily high value.
These results are illustrated on a numerical example by the fig. 1 and 2. The latent
parameter X is supposed to be determined by purely additive genes. Its initial mean
56 I. I. Dzeverin
value is , the initial variance is , the new additive variance emerged
during a generation is , and the threshold limits both are C1 = C2 = 4.0 in the
accepted scale of measurement. Probabilities for successful developmental induction of
the threshold character, Y(X), in an infinite population are shown in the figure 1. At
the initial state the probability for successful induction is (1–10–4) (fig. 1, A). After 104
generations this probability in the same population is 0.77 (fig. 1, B). After 2 • 104 gen-
erations it is 0.62 (fig. 1, C) and after 4 • 104 generations it is only 0.47 (fig. 1, D). The
dynamics of the threshold character, Y(X), in an infinite population is shown in the fi-
gure 2: 1 is mean value, , 2 is variance, , and 3 is coefficient of variation, .
Time intervals are measured in generations.
Dynamics of a threshold character in populations with limited sizes
The evolutionary dynamics of a threshold character Y determined with latent char-
acter X is evident since we know the dynamics of X as a quantitative character (see
above). Its variance stabilizes at a low level and is being maintained by new mutations
while the mean value drifts in an arbitrary direction. In a finite population there is a
high probability that this drift of mean values should shift a population out of the
limits of the area –C2 < X < C1, in which the formation of the trait is possible (Y = 1).
Denote the magnitude of the shift of the mean after t generations by
. The expected value of this variable is
, (10)
From here an expected number of generations necessary to deviate from the ini-
tial value by a distance DX is
, (11)
57Lack of Selection Leads to Regressive Change…
Fig. 1. Probabilities for successful developmental induction of the threshold character in an infinite
population. The explanations are in the text.
Ðèñ. 1. Âåðîÿòíîñòè óñïåøíîé èíäóêöèè ïîðîãîâîãî ïðèçíàêà â îíòîãåíåçå äëÿ áåñêîíå÷íî áîëüøîé
ïîïóëÿöèè. Îáîçíà÷åíèÿ â òåêñòå.
Thus, most likely, the mean, , deviates from the initial value to an area, in which
the interaction of the responding tissue and organizer is impossible, and the formation
of the organ cannot take place.
Assume a sample of replicate populations starting their evolutionary transforma-
tions from the same point . For each population deviates from this point (at an
average, increases in a half of the sample, and, in a half, it decreases). Within-pop-
ulation variances stabilize while the between-population variance and coefficient of
variation increase owing to divergence of population means. Thus, a proportion of pop-
ulations, which crossed the area –C2 < X < C1 gradually increases. For more and more
populations the mean value of Y exceeds 0. After a long period of time only some pop-
ulations preserve the studied character. If population extinctions are independent from
value (which follows from the assumed condition of the neutrality of this character),
then during a long time a character can be lost by all populations in a group.
An example of neutral dynamics of the statistical parameters of the threshold char-
acter Y(X) in a finite-sized population is shown in the figure 3. Mutation — drift equi-
librium is assumed for all modeled period. Effective population size, NE, is 500. An ana-
lyzed time period is 1.2 • 105 generations. The consecutive estimates of population struc-
tures and statistical parameters are got with intervals of 104 generations. For each con-
secutive step, a mean X value with 99.9% confidence limits of variation,
, and frequency of successful induction, P(Y(X(t)) = 1), are estimat-
ed. The new additive variance emerging during a generation is , and the thre-
shold limits both are C1 = C2 = 4.0 in the accepted scale of measurement. The zone
58 I. I. Dzeverin
Fig. 2. Dynamics of the statistical parameters of the threshold character in an infinite population. The
explanations are in the text.
Ðèñ. 2. Äèíàìèêà ñòàòèñòè÷åñêèõ ïàðàìåòðîâ ïîðîãîâîãî ïðèçíàêà äëÿ áåñêîíå÷íî áîëüøîé
ïîïóëÿöèè. Îáîçíà÷åíèÿ â òåêñòå.
between these limits is marked with grey color, the initial mean value, , is marked
with a dashed line.
An example of neutral dynamics of the statistical parameters of the threshold char-
acter Y(X) in a set of replicate populations is shown in the figure 4. A mutation — drift
equilibrium is assumed for all modeled period. Time is measured in generations. The
consecutive estimates of mean values are shown at the intervals of 100 generations. New
additive variance emerged during a generation is . The threshold limits both are
in the accepted scale of measurement, and the zone between these limits is marked with
grey color. The drift of mean values, , in 10 replicate populations (fig. 4, A) and
the dynamics of between-group standard deviation, (fig. 4, B) are modeled.
A threshold character determination by multiple inductions
For many complex organs it is known that multiple consecutive or simultaneous
induction processes form them. Previous induction is necessary for the next induction
and without a whole series of inductions an organ remains under-developed. As a rule,
a series of inductions takes place, and the responding tissue of the previous induction
becomes the organizer in the next induction (Hadorn, Wehner, 1989). For example,
no less than three or four induction processes occur in the embryogenesis of vertebrates.
Primary induction determines general topography of systems of organs; the secondary
induction determines the development of organs, while the next inductions control the
formation of organ components (Hadorn, Wehner, 1989).
59Lack of Selection Leads to Regressive Change…
Fig. 3. An example of neutral dynamics of the statistical parameters of the threshold character in a finite-
sized population. The explanations are in the text.
Ðèñ. 3. Ïðèìåð íåéòðàëüíîé äèíàìèêè ñòàòèñòè÷åñêèõ ïàðàìåòðîâ ïîðîãîâîãî ïðèçíàêà äëÿ
ïîïóëÿöèè êîíå÷íîãî ðàçìåðà. Îáîçíà÷åíèÿ â òåêñòå.
To take into account the necessity of multiple inductions for the development of
organ (for consecutive inductions, particularly) the proposed model can easily be
extended to multiple latent traits, initializing the beginning of development in some vol-
ume of the multidimensional timing space. As the number of traits increases, the prob-
ability for occuring within the multidimensional hyper-volume decreases with the num-
ber of traits.
In the simplest system only two induction processes form an organ. Consider a
threshold character formed by two developmental inductions, A and B. Induction indi-
cators, YA and YB, depend on latent quantitative characters, XA and XB, respectively.
The mechanism of character determination is the same as described above. A product
Y = YAYB can model a formation of such a character.
If YA and YB are statistically independent, the mean value and variance of a trait
are respectively (Statistics, 1989):
(12)
and
. (13)
Here , , etc., while PA and PB are the probabilities of A and B. They
are the analogues of P in equation (1). It is evident that the expression in brackets is
an estimate for the squared coefficient of variation of Y. Thus,
. (14)
If YA and YB are not independent, a coefficient of correlation between these vari-
ables is
, (15)
60 I. I. Dzeverin
Fig. 4. An example of neutral dynamics of the statistical parameters of the threshold character in a set of
10 replicate populations. The explanations are in the text.
Ðèñ. 4. Ïðèìåð íåéòðàëüíîé äèíàìèêè ñòàòèñòè÷åñêèõ ïàðàìåòðîâ ïîðîãîâîãî ïðèçíàêà â 10 èäåí-
òè÷íûõ ïîïóëÿöèÿõ ñ èäåíòè÷íûìè èñõîäíûìè ñâîéñòâàìè. Îáîçíà÷åíèÿ â òåêñòå.
where PAB is the proportion of organisms, in which both inductions have taken place.
If XA and XB jointly follow bivariate normal distribution with mean vector and
covariance matrix , then
, (16)
where
,
and U is a rectangle limited with the conditions: –CA2 < XA < CA1 and –CB2 < XB < CB1.
General trends in evolution of phenotypic correlation need special investigation.
Taylor series can be used to obtain reasonable approximations for the parameters
of distribution of (Statistics, 1989; Lande, 1977; Manly, 1985). These estimates can be
applied if the deviation of data around a mean value is not too large, Q < 0.1, that is
for analyzing the early stages of regressive processes. Using the first two terms of the
Taylor series the approximation gives
, (17)
, (18)
and
. (19)
The dynamics of correlated threshold characters does not differ essentially from the
dynamics of independent threshold characters. Using the equations (7) — (9), the char-
acter mean and variance for a population considered infinite can be evaluated respec-
tively as
(20)
and
, (21)
Thus, the mean value of a product of two threshold characters decreases, and the
variance increases at first and decreases later owing to the decreasing of the proportion
of specimens having the studied organ developed.
The coefficient of variation of Y also increases (14) or (19) both by increasing vari-
ation in YA and YB, especially if these characters are positively correlated. High nega-
tive correlation can slow down this process. The coefficient of variation of Y increases
faster than coefficients of variation of its components, YA and YB.
These results easily can be extended for a threshold character determined by mul-
tiple inductions. In this case, the indicator of character formation can be described
as (each Yj is 0 or 1).
Induction effects and the inputs of the additive genes
to the value of a quantitative character
Denote a character Z as a product of threshold indicator Y and normally distribut-
ed character W, where Y can be an indicator of multiple inductions as has been descri-
bed in previous section. These components may reflect a developmental mechanism of
character initialization and the input from the genes, which had been activated by the
61Lack of Selection Leads to Regressive Change…
induction. If W and Y are independent, the mean value, variance, and squared coeffi-
cient of variation for Z are (Statistics, 1989):
, (22)
, (23)
and
. (24)
If Y and W are correlated, the approximate formulations for the mean value, vari-
ance, and coefficient of variation of Z can be obtained using the Taylor series like in
the equations (17) — (19).
The dynamics of a trait Z in neutral evolution can be described using the data on
dynamics of Y and W. The dynamics of the threshold indicator has been described by
the equations (7) — (9), while W is a normally distributed quantitative character, and
its dynamics corresponds to equations (2) — (3). Using (22) and (23) character mean
and variance can be evaluated respectively as
, (25)
and
, (26)
For quantitative character W the amount of variation in a generation t is
, (27)
where is new additive variance produced for W by mutation during a generation and
is variance formed by environmental and other non-additive factors. In this case the
coefficient of variation also increases with time. The coefficient of variation of Z also
increases (24) both by increasing of the variation of Y and by the increasing of varia-
tion of W. Negative correlation between Y and W can slow down this process.
These results can be extended for modeling a character determined by various
combinations of consecutive and simultaneous inductions. The mean value of such a
character diminishes in neutral evolution due to both increasing the frequency of spec-
imens in which the character is not being formed and reducing its size in organisms
with this character being manifested. The discovered effects (enhanced variation of
more complicated structures, simplification of such structures and diminishing size,
decreasing proportion of specimens having this structure even in vestigial state) take
place in groups of replicate populations of finite sizes, too. Such modeling can be used
as a representation for the dynamics of a degenerating character in a major taxon sub-
divided into a number of species or other subgroups. Therefore introducing the multi-
ple inductions effects and additive genes inputs to the value of a quantitative character
seems to have made the proposed model more reliable without changing the general
pattern of neutral regressive evolution. Quantitative characters with such mechanisms
of determination tend to be reduced in the evolutionary prospect, too.
Examples
Some examples with empirical data
Pa t t e r n s o f v a r i a t i o n i n v e s t i g i a l s t r u c t u r e s. — The regressive changes
of vestigial organs in comparison with their fully functional homologues are illustrated here
using the data on skeletal and first of all dental structures of some fossil and recent mammals.
Typically the coefficient of variation for functional skeletal elements in mammals
exceeds 0.03–0.10 (Simpson, 1944; for detailed statistics see Yablokov, 1966). Increa-
62 I. I. Dzeverin
sed variation had been detected for functionally unused structures. According to
Simpson, “it is so commonly true that degenerating structures are highly variable that
this may be advanced as an empirical evolutionary generalization” (Simpson, 1944: 39).
For example, the vestigial third upper premolar tooth, P3/, was highly variable
(Q = 0.185 + 0.028), in Ptilodus montanus (Multituberculata, Paleocene of North
America) while well-developed teeth had a typical level of variability
(Q = 0.057 + 0.014 for the length of the first lower molar, M/1) (Simpson, 1944: 39).
Another vestigial tooth, the second upper premolar, P2/, in Hoplophoneus (Carnivora,
Felidae, Oligocene of Asia and North America) was highly variable, too, with asym-
metrical formation, and could be missing in some specimens (Simpson, 1944: 39).
The second upper molar, M2/, is supposed to degenerate in the evolution of
Hyaenidae. In Ictitherium hyaenoides (Hyaenidae, Neogene, China) M2/ was very vari-
able and highly reduced (population mean, M, is 5.4 + 0.28, Q = 0.136 + 0.036) in
comparison with M1/ (M =15.9 + 0.34, Q = 0.88 + 0.015) and could be absent in some
specimens (Kurte´n, 1953). Another species of Ictitherium had normally developed M2/,
while in the modern species Crocuta variabilis M2/ is missing and M1/ is vestigial (see
Kurte´n, 1953 for details). Premolars of Ursus arctos (Ursidae) demonstrate a similar
pattern of variation. They are more or less vestigial and any of them may be missing
(Kurte´n, 1953). For many groups of mammals it had been shown that teeth which are
phylogenetically lost might occasionally be realized once more (see Kurte´n, 1953 for
discussion).
The extreme variation and little correlation with other limb bones had been
revealed for first phalanx of second wing digit in Myotis lucifugus and M. sodalis
(Chiroptera, Vespertilionidae) (Bader, Hall, 1960). This bone has little functional sig-
nificance for the bat wing, so this fact “clearly indicates that the factors which normal-
ly operate to control or limit bone development are absent, or at least greatly modified,
with respect to this element. The almost complete absence of significant correlation
between the phalanx and all other skeletal parts is corroborative evidence. Such varia-
tion is common in aspects of the skeleton or dentition which are non-functional and
presumably under greatly relaxed selective control” (Bader, Hall, 1960: 15).
However, in some cases this typical relation between variation and performance
has not been revealed. Thus, in the teeth of Viverravus acutus and the Didymictus pro-
teus — protenus complex (Viverravidae, Carnivora, Paleogene of North America) those
cusps that should be functionally constrained are actually the most variable (Polly,
1998). The pattern of their variability is better explained by developmental factors than
by the direct action of natural selection (Polly, 1998). Some correlations between limb
bones in Myotis can be explained as being formed by developmental factors, too (Bader,
Hall, 1960).
E vo l u t i o n o f t h i r d u pp e r p r emo l a r s i n b a t s a s a n e x amp l e o f a
r e g r e s s i v e t r e nd. — The evolutionary trends of dental characters in bats are stud-
ied in details (Menu, 1985, 1987; Wo/loszyn, 1987). In particular, the third upper pre-
molar (P3/) is degenerating in various groups of Chiroptera. Its regressive trend started
from a quite well developed state in primitive Paleogene bats, for example, Icaronycteris
(Jepsen, 1966) and Stehlinia (Sige´, 1974). Later the proportion of genera with under-
developed P3/ increases. This tooth is missing in the majority of modern bat genera
while the species of Myotis genus have vestigial P3/ with evident features of under-devel-
opment (Menu, 1985, 1987). Contrary to other vespertilionid bats, Pizonyx vivesi, a bat
closely related to Myotis, has relatively larger P3/ (Menu, 1985).
The under-development of P3/ in Myotis is expressed by diminishing, simplifica-
tion, and lateral exclusion from the toothrow (Menu, 1985, 1987; Dzeverin, 2001).
Already in the fossil species, M. bavaricus from Miocene of Central Europe, the length
of P3/ was more variable (Q = 0.066 for one sample, and Q = 0.075 for another) com-
63Lack of Selection Leads to Regressive Change…
pared to lengths of M/1 (Q exceeds 0.034 and 0.037, respectively) and M/2 (0.035 and
0.042) (Ziegler, 2003). In modern Myotis species all stages of P3/ degeneration span
from almost normally developed, for example, in M. bechsteinii, M. ikonnikovi, up to
completely absent in M. ridleyi and M. rosseti (Hill, Topa´l, 1974; Menu, 1985, 1987;
Dzeverin, 2001). High intraspecific variation of P3/ size is known as well (Hill, Topa´l,
1974; Menu, 1985, 1987; Dzeverin, 2001). Moreover, these teeth can be absent in sep-
arate specimens of a number of Myotis species (Strelkov, 1983; Dzeverin, 2001;
Ghazali, Dzeverin, 2004). In M. blythii P3/ is absent on one or both sides of the
toothrow nearly in 1.4% of individuals (Dzeverin, unpublished data).
For three Myotis species (M. myotis, M. blythii, and M. mystacinus s. l. from the
East Europe) coefficients of variation of the measurements of under-developed teeth
reach 10–40% or even more, that is several times higher than the variability of well-
developed teeth. The height of P3/ turned out to be the most variable character. The
largest coefficient of variation had been found for M. mystacinus (Q = 0.65, SQ = 0.18),
the least ones have been recorded in M. blythii (Q = 0.39, SQ = 0.09), and M. myotis
(Q = 0.42, SQ = 0.09) (Ghazali, Dzeverin, 2004). On the contrary, fully functional M/1
is less variable both in M. mystacinus (Q = 0.22, SQ = 0.046), M. blythii (Q = 0.12,
SQ = 0.029), and M. myotis (Q = 0.23, SQ = 0.044) (Ghazali, Dzeverin, unpublished
data). The extremely high range of variation of P3/ in M. mystacinus agrees with the
well-known data on the high level of degeneration of this tooth in this species (Strelkov,
1983).
Numerical estimations
Most of the variables used in this paper have been estimated for numerous animal
and plant populations (Falconer, 1985; Hedrick, 2000). Statistical estimates for the
main components of variance are not too diverse. Assuming NE = 500 individuals, the
new additive variance per generation being nearly 10-3–10-4 of non-additive variance,
and narrow-sense heritability nearly 0.5 is quite realistic for many purposes (Hedrick,
2000). The probability for ceasing the development of a fully functional character,
P(Y(t = 0)) = 0, can be estimated as being of the order of 10-3 or somewhat lesser for
late inductions, that is for final stages of organ’s development.
Consider effective population size, NE = 500, the new additive variance,
, and threshold limits, , as estimates for a threshold
character, Y(X(t)), in a population under mutation — drift equilibrium. In such a pop-
ulation the additive variance of X should be roughly constant with an average value of
. At an initial point there is a fairly reliable mechanism for
developmental induction, P(Y = 1) = (1–10-4). But later, under the conditions of
selective neutrality and random drift, the population mean should deviate to a zone in
which this induction is not possible. The expected time for such a drift can be estimat-
ed from the equation (11) as 32000 generations to drift away for 8 standard deviations,
and 50000 generations — to drift away for 10 standard deviations, etc. (confer with
fig. 3 and 4). Assuming implies ten times more intervals, that is 320 000
and 500 000 generations for previous examples.
Since a generation period for numerous animals comprises nearly a year, these
time intervals are much smaller than periods of macroevolutionary changes revealed
from paleontologic data. These estimates concern the simplest model of a character
maintained by only a single induction. Characters formed by consecutive inductions
should reduce still even faster (see equations (12) — (21)). If to consider a population
as being infinitely large, the estimated rate of degeneration is comparable with empiri-
cal data on evolutionary regressive processes (Dzeverin, 2000). However, for popula-
tions with limited size, various types of threshold characters described above are expect-
ed to degenerate and vanish in the course of neutral evolution very quickly comparing
64 I. I. Dzeverin
with the macroevolutionary scale of time. This result agrees with Yablokov’s (1966)
hypothesis that common vestigial organs really are fully functional, because genuine
useless organs should rapidly degenerate without selection control. Only atavistic organs
can be supposed to be really useless from this standpoint (Yablokov, 1966). For many
deleterious structures selection seems not to be necessary: mutation destruct them
quicker (Schmalhausen, 1982).
Paleontologic studies have demonstrated that there is a great variety in rates of
regressive changes of morphological characters, and very often these rates are very
small. For example, in evolution of vespertilionid bats, P3/ had been lost in numerous
bat genera at early stages of their evolution (probably in Oligocene and Miocene, when
these genera were emerging). But in Myotis the regressive evolution of this tooth con-
tinues up to the present time, extending dozens times more than the period implied by
the quantitative modeling. Some other teeth demonstrate similar prolonged trends in
these genera, too. Certain functional value and genetic correlation with important struc-
tures are the most probable mechanisms that could prevent the rapid loss of vestigial
structures.
Discussion
Principal features of typical regressive processes are reproduced in the model devel-
oped in this paper. Reducing the probability of developmental induction is reflected in
equations (1), (7), and fig. 1, 2, and 3. Equations (8), (9), (21), (26), (27) and fig. 2
and 4 reproduce the increase in variation of degenerating character. Thus, taking into
account the induction mechanism of character development (equation (1)) and a trend
of structural elements to be reduced, it is possible to expect that the diminishing and
simplification of an organ will occur by a consecutive loss of its components.
Decreasing of its size is described by the equations (20) and (25). The opportunity to
re-express lost structures (that is to develop atavisms) is supposed by the model as well.
Stochastic trends of the modeled characters in replicate lineages are described by the
equations (10) and (11) and illustrated by fig. 3 and 4. Usually these lineages have sim-
ilar trends for character reduction, but characters degenerate with different rates in dif-
ferent lineages.
It may be suggested from the present results that during purely neutral evolution a
character formed by interaction of pre-existing structures gradually reduces and disap-
pears due to disintegration of morphogenetic systems which had to make this interac-
tion possible. Variation of such an organ increases without limits. The disintegration of
pattern formation systems occurs from random neutral mutation and stochastic genet-
ic drift. Thus, the directional process of regressive transformation occurs to be the result
of indirect random processes.
Selection influence on regressive trends is highly probable for natural populations.
The regressive transformations of organs in evolution can be induced by the inactiva-
tion or damage of genetic information by random mutation as well as by negative selec-
tion. Direct or indirect selection can put the brake to the complete loss of vestigial char-
acters. This is possible if such characters are maintained by indirect selection through
pleiotropy with adaptive characters. For example, the genes responsible for the devel-
opment of hind limbs in cetaceans can be supported by indirect selection due to the
genetic correlation either with pelvic bones which serve as points of attachment for uro-
genital musculature or with front limbs (Yablokov, 1966; Lande, 1978).
On the other hand, loss of a character can be induced by negative selection if the
detrimental effect of such a character exceeds any direct or indirect advantages. In a
number of cases it is difficult to distinguish between the random effects and selection
(Manly, 1985). Nevertheless, the rates of regressive evolution, which can be estimated
65Lack of Selection Leads to Regressive Change…
from paleontologic data, are rather small and can be maintained either by mutation or
by rather weak selection. It is enough for weighted selection differential to be of the
order of 10-3–10-4 (Lande, 1978).
Thus, a choice between the hypotheses about mutation and selection inputs on the
regressive process is a serious problem, which is not yet solved. Only preliminary sup-
positions may be done. For these trends successful testing may be grounded on the eval-
uation of character variation. A number of researchers emphasized on a very high
amount of variation in vestigial structures (for example, Darwin, 1998; Schmalhausen,
1982; Simpson, 1944; Yablokov, 1966; Lande, 1978; Peters, Peters, 1984) and in other
structures of little functional significance (for example, Bader, Hall, 1960). Variation of
an organ being transformed by selection decreases, while without selection the varia-
tion should increase (Kimura, 1965; Lande, 1976 a, b, 1979; Lynch, Hill, 1986; Bu�rger,
Lande, 1994; and many other authors). Appropriate statistical tests (t-test on standard
deviation, coefficient of variation, Levene test, etc.) can show this increase in variation.
One of the possible approaches for such testing is the comparison of variation in homol-
ogous organs with different evolutionary trends.
The mechanism of organ loss from the misalignment of reactants implies that genes
necessary for development are not certainly lost. Typically, the genotype may contain
various non-expressed programs for the development of a character, and some evolu-
tionary saltations probably are the results of switching the development over to anoth-
er program (Mednikov, 1987; Shishkin, 1984).
Vestigial characters can become the grounds for reverse evolution and formations
of new characters and structures. The increase of P3/ in the evolution of Pizonyx is pos-
sibly an example of such a trend. The adaptive meaning for this change is quite
unknown. Molecular phylogenetic reconstruction has shown that Pizonyx vivesi is in so
near relation with New World Myotis species that it must be included to this genus
(Stadelmann et al., 2004). Ecologically, Pizonyx is a specialized representative of the
morphological pattern typical for water trawling Myotis species from the subgenus
Leuconoe (Findley, 1972; Dzeverin, 1998; Fenton, Bogdanowicz, 2002). However,
Pizonyx dentition evidently differs from dentitions of Leuconoe as well as other bats
(Menu, 1985).
Besides the developmental mechanism described in this paper, some other process-
es can also increase the phenotypic variation in vestigial characters. In particular, devel-
opmental instability can increase the non-additive component of phenotypic variance.
As usual, the level of bilateral asymmetry is used as a measure of developmental insta-
bility (Van Valen, 1962; Hallgr msson, 1998 and many others). This approach can be
integrated with quantitative genetic analysis of variation and evolution (Gavrilets,
Hastings, 1994). Well-developed organs are expected to be more sustainable in their
development than under-developed ones. However, for dental characters of Myotis
species it has been shown that a pattern of bilateral asymmetry differs from a pattern
of general variability estimated by the coefficient of variation (Ghazali, Dzeverin,
2004). The least asymmetry was found for M. mystacinus. Considerable asymmetry of
P3/ was not revealed. This distinction in patterns of variation needs more investigation.
It is probable that in many cases high correlation with functional characters slows down
the regressive trend of vestigial character (Lande, 1978; Polly, 1998).
However, it is quite probable that correlations of a degenerating character with
other characters themselves tend to decrease under regressive trend. This supposition
agrees with both Schmalhausen’s concept (1982) and empirical data. Fully functional
teeth of Ictitherium were highly correlated while unused teeth varied more independent-
ly from other ones (Kurte´n, 1953). A similar correlation pattern of wing bones in Myotis
(Bader, Hall, 1960) has been already mentioned in this paper. How correlations and
66 I. I. Dzeverin
covariations between complex characters can be changed in evolution is a serious and
important problem for theoretical studies.
The proposed model can probably be applied not only for investigating vestigial
characters. Similar processes of disintegration in interacting structures occur during
other evolutionary trends, for example under domestication (Schmalhausen, 1982;
Korochkin, 2002). Premature or delayed initialization of development in some tissues
or structures may be the basis for transformations in size and shape usually denoted as
heterochronies (Hall, 1984; Korochkin, 2002). It had been supposed that alike the ran-
dom lack of coincidence of reactants may lead to the under-development of certain
characters, an opposite event, that is random mutation-induced coincidence of struc-
tures which normally do not interact, can be the developmental mechanism for the
emergence of new characters (Korochkin, 2002).
The introduction of developmental events to the reconstruction of evolutionary
changes has made possible the description of some important features of regressive
trends. So far as complex phenotypic structures tend to be reduced by mutation inputs,
if stabilizing selection doesn’t prevent this, some limitations must be assumed for long-
termed neutral changes. Some input of selection is expected to be necessary for organs
and other complex structures to stay at the achieved level of complexity.
I am indebted to R. Lande for valuable advices and criticisms of earlier drafts of the manuscript. I am
indebted to B. M. Mednikov and M. A. Shishkin for some initial ideas on the subject of my research. I am
grateful to M. A. Ghazali for help in my work, comments and constructive suggestions. Thanks also are due
to O. I. Schmalhausen, E. I. Kozhurina, P. P. Strelkov, I. Hora´c
�
ek, and the reviewers for helpful comments
and discussions. R. Lande, B. Sige´, M. Machola ´n, G. P. Wagner, B. F. J. Manly, S. Gavrilets, R. Bu�rger,
B. Hallgr msson, J. Felsenstein, E. P. Martins, M. Turelli kindly presented reprints of articles hardly
accessible in the East Europe. V. M. Tytar is acknowledged for improving the English text and discussion.
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