the frozen plasticity theory
1. This theory is based ( I think) on one wrong key assumption that all the offspring need to possess that useful trait which allowed parents to have more offspring than any other pair, for evolution to work. Evolution can still proceed even if none of the immediate descendants possesses the trait, because in the process of evolution what is changing is a species. Important for evolution is therefore the frequency of a trait in a population. A species become taller when there is more tall individuals in the population. Although genotype for some trait of an individual is combination of different alleles this combination is not unique in population. Specific combination, which results in advantageous trait is not vanishing but has the same probability to from as any other combination. Actually if some trait allows to have more offspring the alleles forming that trait are copied more than other alleles and therefore the chance that they will meet again in this combination is increased ( in positive feed-back loop- higher frequency mean higher chance of meeting and that results in even higher frequency and so on). Also the higher variability allows for more combinations to be tested, some of them could be as good as parental, or even better and some could be not as good but still better than the population average. All these possibilities will lead to a higher fitness.
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It is not so important to know how many genes control a trait, all what is needed to be known is variability of the trait in a population. For example when the difference between the highest and lowest male is let’s say 20 cm and height is controlled by (let’s suppose) 10 genes (two alleles for each gene and co-dominance), there are 59049 possible phenotypes. If every genotype had to have its own phenotype, two most similar genotypes would differ by 0.003 mm (for evolution absolutely invisible).Or where there are only two colors (e.g. white and blue) controlled by 10 genes, half of genotypes stand for one color and half for another.
Hallmark of epistasis is that many genotypes stand just for a few phenotypes.
Worth of considering is also a supergene theory. It suggests that traits controlled by alleles of many genes are selected to move closer on a chromosome, what results in a lower probability of the cross-over. This way the trait is inherited as one locus.
2. It is not true that: “Population genetics models usually suggest that each allele can be characterized by a constant, a value that describes the average relative fitness of the carriers of a particular allele“. Not alleles but (logically) phenotypes are associated with different fitness. For example in a case of sickle cell disease there are three genotypes and each one stands for different phenotype. Homozygote with two mutated alleles have abnormal red blood cells that can lead to death (low fitness), homozygote with two normal alleles have functional red blood cells. Heterozygote with one mutated and one normal allele produces a few sickled red blood cells (abnormal) not enough to cause symptoms, but enough to give resistance to malaria. So both homozygotes have a lower fitness than the heterozygotes. Two alleles (normal and mutated) are in an equilibrium due two opposing selection forces. If one of this forces disappear (for example as a result of environmental change mosquitoes would get extinct and malaria would vanish with them) then the frequency of the mutated alele will decrease. No matter how low the frequency will be, its fitness will not increase. So no “frequency dependent selection“ will act againts this decrease.
3.Also a process of freezing seems to be problematic. First of all, not species but induvidual traits could freeze (for example when a color of a fur is frozen, lenght of claws could still be unfrozen). When a trait is so fragile that only one combination can code for it, as the frozen plasticity theory suggests, than any new mutation (any new variability) should destroy it. Therefore strong purifing selection will be acting to sweep away any variability and the trait will never get frozen.
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Response to Marek-g
This theory is (I think) based on one wrong key assumption that all the
offspring need to possess that useful trait which allowed parents to have
more offspring than any other pair, for evolution to work.
Not at all. Darwinian evolution of adaptive traits (that according to frozen plasticity theory could take place only in plastic species) just needs the frequency of carriers of particular adaptive traits among offspring of a carrier of this particular trait to be in average higher than among offspring of a noncarrier.
Evolution can
still proceed even if none of the immediate descendants possesses the trait,
because in the process of evolution what is changing is a species. Important
for evolution is therefore the frequency of a trait in a population.
Most evolutionary biologist will probably not agree with your claim. Darwin would probably argue that frequency of particular trait among offspring of a carrier of particular trait (definitively not in population!) is what counts in (adaptive) evolution. Dawkins (and most of current neodarvinists) would probably argue that number of copies of particular allele that is transmitted to the next generation due to some activity (reproduction or help) of carriers of the allele is what counts.
species become taller when there is more tall individuals in the population.
Although genotype for some trait of an individual is combination of different
alleles this combination is not unique in population. Specific combination,
which results in advantageous trait is not vanishing but has the same
probability to from as any other combination. Actually when some trait allows
to have more offspring the alleles forming that trait are copied more than
other alleles and therefore the chance that they will meet again in this
combination is increased ( in positive feed-back loop- higher frequency mean
higher chance of meeting and that results in even higher frequency and so
on).
While most evolutionary biologist will probably disagree with your arguments, I believe that they contain “a kernel of true”. It shows that in frozen species the group selection (based on competition between population) can outweigh the individual selection (which is rather difficult in plastic species). As it is written in the manuscript of my paper Microevolutionary and macroevolutionary implication of Frozen plasticity theory of adaptive evolution (available at my website):
“The most serious objection of evolutionary biologists against the role of group selection in evolutionary processes consists in the fact that a trait that provides an advantage to a group and simultaneously places the individual that is its carrier at a disadvantage has a low chance of spreading and enduring in nature. Groups in which the altruistic trait spreads would prosper better than groups in which this trait is lacking and the average fitness of the members of this group would be greater; however, selfish individuals who do not exhibit this trait and do not behave altruistically, but only enjoy the advantages provided by the presence of altruists, would have the greatest fitness within these groups. In sexual (frozen) species, any behavioral trait (for example, altruistic behavior) is usually determined by the greater number of genes and many of these genes have (due to epistasis) a context-dependent influence on the particular trait. Consequently the heritability of most traits is low. Under such conditions, altruists emerge from the population as if by chance in families that are completely unrelated and have different phenotypes, i.e. individuals with quite different behavior, with a probability that is determined only by the proportion of particular alleles in the entire population. Thus populations can compete for the greatest average fitness of their members; those that have the greatest proportion of the relevant alleles, resulting in the greatest number of altruists being formed (emerging by chance), will win in this competition. Thus, group and inter-species selection can occur in nature in favor of altruistic traits (because the percentage proportion of alleles in the population is inherited from one generation to the next) and its results cannot be cancelled out by individual selection because the trait itself, altruistic behavior, is not inherited.“
Not to mention that a hallmark of epistasis is that many genotypes stand for
just a few phenotypes.
Not necessarily. When also gene-environment interactions are taken into consideration, the real number of phenotypes can be higher in system with epistasis than in system without epistasis (and same number of genes, alleles and the same amount of environmental variability).
Worth of considering is also a supergene theory. It suggests that traits
controlled by alleles of many genes are selected to move closer on a
chromosome what results in a lower probability of the cross-over. Therefore,
the trait is inherited as one locus.
Yes, the evolution can increase heritability of a trait by building up supergenes. However, due to pleiotropy of most of genes, capacity to build up supergenes is probably rather limited. (The same gene can hardly be part of more than two supergenes.) Moreover, the main source of elasticity of sexual species is probably frequency dependent selection, rather than epistasis. (This subject is discussed in the manuscript entitled Elastic, not plastic species: Frozen plasticity theory and the origin of adaptive evolution in sexually reproducing organisms.)
2. It is not true that: “Population genetics models usually suggest that
each allele can be characterized by a constant, a value that describes the
average relative fitness of the carriers of a particular allele“. Not
alleles but (logically) phenotypes are associated with different fitness. For
example in case of sickle cell disease there are three genotypes and each one
stands for different phenotype. Homozygote with two mutated alleles have
abnormal red blood cells that can lead to death (low fitness), homozygote
with two normal alleles have functional red blood cells. Heterozygote with
one mutated and one normal allele produces a few sickled red blood cells
(abnormal) not enough to cause symptoms, but enough to give resistance to
malaria. So both homozygotes have a lower fitness than the heterozygotes. Two
alleles (normal and mutated) are in an equilibrium due two opposing selection
forces. If one of this forces disappear (for example as a result of
environmental change mosquitoes would get extinct and malaria would vanish
with them) then the frequency of the mutated alele will decrease. No matter
how low the frequency of allele will be, its fitness will not increase. So no
“frequency dependent selection“ will act againts this decrease.
Yes, you are absolutely right, I have to correct this inane error. My sentence should sound: “Population genetics models usually suggest that each genotype (phenotype when the influence of nongenetic factors is taken into consideration in the model) can be characterized by a constant, a value that describes the average relative fitness of carriers of a particular combination of alleles“. However, my argument still holds. For example, the frequency of homozygotes with two mutated s alleles in offspring is a (quadratic) function of frequency of s allele in the population. Therefore, the fitness of Ss heterozygote is very high when s allele is rare and very low when the frequency of s allele is high. Therefore, the fitness of carriers of Ss (or SS or ss) genotype cannot be characterized by any constant (and s allele cannot be fixed in population or removed from a population by selection). Of course, when malaria disappears, the pay off matrix radically changes (the fitness of both ss homozygotes and Ss heterozygotes turns negative) and the mutated s allele disappears (in decreasing rate – the frequency dependent selection against ss homozygotes is still in action) from the population.
Also a process of freezing seems to be a problematic one. First of all, not
species but induvidual traits could freeze (for example when color of fur is
frozen, lenght of claws could still be unfrozen). When a trait is so fragile
that only one combination can code for it as the frozen plasticity theory
suggests, than any new mutation (any new variability) should destroy it.
Therefore strong purifing selection will be acting to sweep away any
variability and the trait will never get frozen.
Again, you are in principle right. Particular traits probably differ in their rate of freezing and especially in resistance to transition from the frozen to the plastic state (see FAQ „Why does the variability of species decrease with the age of the phylogenetic line and why does the maximal diversity (more correctly, the maximal disparity) of phylogenetic lines occur early in the history of the lines?“). However, the autocatalytic nature of the process of accumulation of genetic polymorphism probably ensures that all traits probably get frozen in rather similar time in a particular population. Theoretically, some traits could state plastic through the whole existence of a species. However, the paleontological data suggest that this is probably rather rare – most of the studied species remain unchanged during all their „life“. I am going to include this question to FAQ list.
frozen plasticity - reactions on replies
"Not at all. Darwinian evolution of adaptive traits (that according to frozen plasticity theory could take place only in plastic species) just needs the frequency of carriers of particular adaptive traits among offspring of a carrier of this particular trait to be in average higher than among offspring of a noncarrier."
Right, and the theory of the frozen plasticity expects that none (or that frequency of carriers of particular adaptive traits among offspring of a carrier of this particular trait be in average the same among offspring of a noncarrier, to be precise) of the offspring will possess the trait (because various gene interactions are too complex and regardless how many descendants will parent have, none of them will have the advantageous genotype).However ,when considering quantitative traits there are only three possibilities how can a trait looks in the offspring, its value can be higher, lower or the same (compared to value in parents), regardless of how many genotypes control the trait.
„Most evolutionary biologist will probably not agree with your claim. Darwin would probably argue that frequency of particular trait among offspring of a carrier of particular trait (definitively not in population!) is what counts in (adaptive) evolution.“
I very much appreciate Darwin but his work was pre-genetic and nonmathematical done more than 200 years ago. I will cite more recent opinion.
The changes in populations that are considered evolutionary are those that are inheritable via the genetic material from one generation to the next. Biological evolution may be slight or substantial; it embraces everything from slight changes in the proportion of different alleles within a population (such as those determining blood types) to the successive alterations that led from the earliest protoorganism to snails, bees, giraffes, and dandelions."
- Douglas J. Futuyma in Evolutionary Biology, Sinauer Associates 1986
"The major tenets of the evolutionary synthesis, then, were that populations contain genetic variation that arises by random (ie. not adaptively directed) mutation and recombination; that populations evolve by changes in gene frequency brought about by random genetic drift, gene flow, and especially natural selection; that most adaptive genetic variants have individually slight phenotypic effects so that phenotypic changes are gradual (although some alleles with discrete effects may be advantageous, as in certain color polymorphisms); that diversification comes about by speciation, which normally entails the gradual evolution of reproductive isolation among populations; and that these processes, continued for sufficiently long, give rise to changes of such great magnitude as to warrant the designation of higher taxonomic levels (genera, families, and so forth)."
- Futuyma, D.J. in Evolutionary Biology, Sinauer Associates, 1986;
Or a textbook definition:
"In fact, evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next."
Helena Curtis and N. Sue Barnes, Biology, 5th ed. 1989 Worth Publishers,
“ It shows that in frozen species the group selection (based on competition between population) can outweigh the individual selection (which is rather difficult in plastic species).”
I didn‘t propose the group selection, but individual selection which results in change in frequency of alleles in a population. I do not know if it is even possible to consider competition between populations, because this concept require prevention of a gene flow between the two population to exist and compete in a same place and this two populations could be regarded as two different species.
„Not necessarily. When also gene-environment interactions are taken into consideration, the real number of phenotypes can be higher in system with epistasis than in system without epistasis (and same number of genes, alleles and the same amount of environmental variability).“
If we consider ten genes that control a trait and dominant epistasis there are 59049 possible genotypes and only 11 different phenotypes (the same is for the recessive epistasis).And in a case of inhibition there are only two phenotypes possible no matter how many gene are involved. If environment has strong impact on the phenotype of a trait and in the same time there is high variability in environmental conditions, only alleles able to cooperate with different environmental conditions can spread in a population.
However, my argument still holds. For example, the frequency of homozygotes with two mutated s alleles in offspring is a (quadratic) function of frequency of s allele in the population. Therefore, the fitness of Ss heterozygote is very high when s allele is rare and very low when the frequency of s allele is high. Therefore, the fitness of carriers of Ss (or SS or ss) genotype cannot be characterized by any constant (and s allele cannot be fixed in population or removed from a population by selection).
No, I disagree. Actually fitness of a particular/genotype is constant no matter the frequencies of the alleles are. It is because in the population genetics a relative fitness is used. It is defined as a contribution of the genotype to a next generation compared to the contribution of the other genotypes. What I think you mean is a kind of average fitness of an allele and this "fitness" is not constant (frequency dependent) but in population genetics it is fitness of the phenotypes what is considered and they are constant.
To try to better understand what exactly do you mean, I will cite (if I may) your article "elastic not plastic species..."
"For example, when the frequency of the s allele for sickle cell disease is low in a population living in an endemic malaria area, the allele has a highly positive value for its carriers[11]. Sexual partners of carriers of this allele are homozygotes with two normal alleles; and therefore, only heterozygotes with higher tolerance to malaria, and not homozygotes with two s alleles and therefore with the fatal form of sickle cells disease, will occur among their offspring. When the frequency of the s allele increases, it losses its positive value for carriers as many homozygotes, with the fatal form of sickle cell disease, will spring out among the offspring of a heterozygote."
It is a bit confusing to try to explain this case in terms of „frequency dependent selection“ (and is not necessary either, because it is well understood under model of „ selection against both homozygotes“). Allele (s) participate in two phenotypes with different fitnesses. Unlike an allele for exploitation of an alternative resource, which stands for just one phenotype. This phenotype is advantageous if there is a low frequency of the allele and less advantageous if there is a high frequency of the allele. Because the selection pressure due to the competition is changing. In the case of the sickle cell anemia, when frequency of s allele is low and all phenotypes in which it participate are advantageous (only in Ss), but when the frequency is high there are two different phenotypes (Ss, ss) associated with different fitness and some average fitness or ability of the allele to spread in the population decrease( because a fraction of the allele s is lost in ss homozygotes).
"mutated s allele disappears (in decreasing rate – the frequency dependent selection against ss homozygotes is still in action) from the population."
I don't think it will be with decreasing rate, there is no more frequency dependent selection acting here. Any genotype with allele s is disadvantageous.
"Yes, the evolution can increase heritability of a trait by building up supergenes. However, due to pleiotropy of most of genes, capacity to build up supergenes is probably rather limited. (The same gene can hardly be part of more than two supergenes.)"
I don't understand, why it is difficult to build a supergene due to a effect of pleiotropy, maybe if you can be more specific.
“Again, you are in principle right. Particular traits probably differ in their rate of freezing and especially in resistance to transition from the frozen to the plastic state (see FAQ „Why does the variability of species decrease with the age of the phylogenetic line and why does the maximal diversity (more correctly, the maximal disparity) of phylogenetic lines occur early in the history of the lines?“). However, the autocatalytic nature of the process of accumulation of genetic polymorphism probably ensures that all traits probably get frozen in rather similar time in a particular population. Theoretically, some traits could state plastic through the whole existence of a species.”
I don't think that the major problem is the transition from the frozen to the plastic state (one pregnant female on an island or small population and subsequent inbreeeding could sweep away any variability) but rather from the plastic to the frozen state. Any new advantageous allele would fix in the population. And there will be no variability again. So to make this to work, there have to be a mechanism which will stabilize many alleles in the population. (frequency dependent selection or something else).The main problem is how to retain a variability no how to lose it.
A spread probability of a new allele in a population depends on its ability to form useful phenotypes with as many other alleles as possible from other genes responsible for a specific trait. With increasing variability, it becomes more difficult for allele to achieve this (to enter interlinked web of interactions) unless there is a lot of redundancy (many genotypes stand for a few phenotypes). Anyway, this web is maintained by selection. Therefore, change in selection pressures result in modification of this interactions. I think the major weak point of the theory of the frozen plasticity is that it underestimates or ignores ability of the selection to modify or destroy the web of interaction. It consider selection as something foreign and artificial which stretches species and species is trying resist and return back in its former equilibrium state. But there is no equilibrium without the selection. When a selection pressure disappear, also vanish the “frequency dependent selection”.
In a case of the artificial selection, in short term experiments (when there is no enough time for mutation to emerge) a variability present in a population is used. This process is simply a shift in a frequency of alleles. Some alleles might be lost but not many. Actually, selection becomes ineffective well before variability is depleted, due to decreasing vitality of individuals. When artificial selection pressure stops, natural selection utilize the remaining variability to return the frequency of alleles back ( or closer to) previous state.
“However, the paleontological data suggest that this is probably rather rare – most of the studied species remain unchanged during all their „life“”
Paleontological data is not very much informative. What is it telling us? That in that small fraction of organism that were fossilized, that have been found, that were correctly identified, those that were not altered much by the process of the fossilization itself, there was only a few changes on a fragments of skeletons.
„Can the frozen plasticity theory explain the enigma of invasive species?
According to classical evolutionary theories, native species, which are adapted to local conditions, should outcompete newcoming species. According to the frozen plasticity theory, the ecological success of some newcomers is not so surprising. During the introduction and following lag phase, the genetic polymorphism of an introduced population decreases, which could result in the conversion of a frozen species to the plastic state. Frozen species are best adapted to the conditions existing at the time of their origin (past conditions), while plastic species can adapt to current conditions. Moreover, plastic species can outcompete frozen species in the coevolutionary “arms race”“.
If the above explanation was true than the invasive species should possess some new trait (some new structure or strategy) that was evolved after they become plastic on their new location. And I don’t think this is the case. More plausible explanation is that they become invasive after they have escaped they natural enemies or rivals. Some natural enemies of the invasive species are successfully used for their control (For example Neochetina eichhorniae against the water hyacinth).