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An end to endless forms: epistasis, phenotype distribution bias, and nonuniform evolution.

Borenstein E, Krakauer DC - PLoS Comput. Biol. (2008)

Bottom Line: Ancestral phenotypes, produced by early developmental programs with a low level of gene interaction, are found to span a significantly greater volume of the total phenotypic space than derived taxa.We suggest that early and late evolution have a different character that we classify into micro- and macroevolutionary configurations.These findings complement the view of development as a key component in the production of endless forms and highlight the crucial role of development in constraining biotic diversity and evolutionary trajectories.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, Stanford University, Stanford, California, United States of America. ebo@stanford.edu

ABSTRACT
Studies of the evolution of development characterize the way in which gene regulatory dynamics during ontogeny constructs and channels phenotypic variation. These studies have identified a number of evolutionary regularities: (1) phenotypes occupy only a small subspace of possible phenotypes, (2) the influence of mutation is not uniform and is often canalized, and (3) a great deal of morphological variation evolved early in the history of multicellular life. An important implication of these studies is that diversity is largely the outcome of the evolution of gene regulation rather than the emergence of new, structural genes. Using a simple model that considers a generic property of developmental maps-the interaction between multiple genetic elements and the nonlinearity of gene interaction in shaping phenotypic traits-we are able to recover many of these empirical regularities. We show that visible phenotypes represent only a small fraction of possibilities. Epistasis ensures that phenotypes are highly clustered in morphospace and that the most frequent phenotypes are the most similar. We perform phylogenetic analyses on an evolving, developmental model and find that species become more alike through time, whereas higher-level grades have a tendency to diverge. Ancestral phenotypes, produced by early developmental programs with a low level of gene interaction, are found to span a significantly greater volume of the total phenotypic space than derived taxa. We suggest that early and late evolution have a different character that we classify into micro- and macroevolutionary configurations. These findings complement the view of development as a key component in the production of endless forms and highlight the crucial role of development in constraining biotic diversity and evolutionary trajectories.

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Potential and visible phenotypes as a function of the regulatorydimension, r.The phenotypic dimension is set tok = 18. All curvesrepresent the average of 1,000 different developmental matrices. (A) Thenumber of potential phenotypes (2r) and the number of distinct visible phenotypes as a functionof the regulatory dimension. (B) The percentage of visible phenotypesout of the potential phenotypes, corresponding to a sigmoidal function.(C) The marginal contribution of each genetic element to the increase inthe number of visible phenotypes. Formally, ifV(r) denotes the number of visiblephenotypes as a function of r, then the marginalcontribution is defined asV(r)/V(r−1),and is evidently linear (with slope of −0.044; least squaresregression).
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pcbi-1000202-g002: Potential and visible phenotypes as a function of the regulatorydimension, r.The phenotypic dimension is set tok = 18. All curvesrepresent the average of 1,000 different developmental matrices. (A) Thenumber of potential phenotypes (2r) and the number of distinct visible phenotypes as a functionof the regulatory dimension. (B) The percentage of visible phenotypesout of the potential phenotypes, corresponding to a sigmoidal function.(C) The marginal contribution of each genetic element to the increase inthe number of visible phenotypes. Formally, ifV(r) denotes the number of visiblephenotypes as a function of r, then the marginalcontribution is defined asV(r)/V(r−1),and is evidently linear (with slope of −0.044; least squaresregression).

Mentions: Consider a developmental model with regulatory dimension r andphenotypic dimension k. There are 2r genotypes which could produce a maximum of 2r phenotypes. However, the developmental plan maps several genotypesinto the same phenotype (giving rise to degeneracy), and consequently generatesa much smaller number of distinct phenotypes. We refer to the set of phenotypesproduced by a given developmental plan as visible phenotypes,and examine the number of visible phenotypes and the number of potentialphenotypes as a function of r (Figure 2A). We find that while thenumber of visible phenotypes increases with the regulatorydimension, r, their fraction, out of the number of potentialphenotypes, rapidly declines, with around 5% of the potentialphenotypes remaining visible (Figure 2B) whenr = k. Inother words, the expansion of the genotypic space, which also promotes anexpansion in the number of possible genotypic configurations, also brings aboutan increased canalization, masking the expansion in the number of new visiblephenotypes. This is further exemplified by the marginal contribution of eachgenetic element (e.g., each transcription factor), measured as the relativeincrease in the number of visible phenotypes obtained by adding a new geneticelement. This declines from about two-fold for the first few elements, to lessthan 1.4 as r reaches k (Figure 2C). As per the mathematical analysisbelow, this can be attributed to the effect of an unbalanced sample ofD entries and the multiplicative effect of the nonuniformdistribution of each element in the phentype. Interestingly, the functiondescribing the fraction of visible phenotypes (Figure 2B) is sigmoidal, with the greatestchange in the fraction of visible phenotypes occurring at regulatory dimensionson the order of half the phenotypic dimension. Thus for smaller regulatorycircuits, a large fraction of potential phenotypes remain visible, whereas forlarger regulatory circuits, the greater fraction of the phenotypic space ishidden and inaccessible to selection and evolutionary transformation.


An end to endless forms: epistasis, phenotype distribution bias, and nonuniform evolution.

Borenstein E, Krakauer DC - PLoS Comput. Biol. (2008)

Potential and visible phenotypes as a function of the regulatorydimension, r.The phenotypic dimension is set tok = 18. All curvesrepresent the average of 1,000 different developmental matrices. (A) Thenumber of potential phenotypes (2r) and the number of distinct visible phenotypes as a functionof the regulatory dimension. (B) The percentage of visible phenotypesout of the potential phenotypes, corresponding to a sigmoidal function.(C) The marginal contribution of each genetic element to the increase inthe number of visible phenotypes. Formally, ifV(r) denotes the number of visiblephenotypes as a function of r, then the marginalcontribution is defined asV(r)/V(r−1),and is evidently linear (with slope of −0.044; least squaresregression).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2562988&req=5

pcbi-1000202-g002: Potential and visible phenotypes as a function of the regulatorydimension, r.The phenotypic dimension is set tok = 18. All curvesrepresent the average of 1,000 different developmental matrices. (A) Thenumber of potential phenotypes (2r) and the number of distinct visible phenotypes as a functionof the regulatory dimension. (B) The percentage of visible phenotypesout of the potential phenotypes, corresponding to a sigmoidal function.(C) The marginal contribution of each genetic element to the increase inthe number of visible phenotypes. Formally, ifV(r) denotes the number of visiblephenotypes as a function of r, then the marginalcontribution is defined asV(r)/V(r−1),and is evidently linear (with slope of −0.044; least squaresregression).
Mentions: Consider a developmental model with regulatory dimension r andphenotypic dimension k. There are 2r genotypes which could produce a maximum of 2r phenotypes. However, the developmental plan maps several genotypesinto the same phenotype (giving rise to degeneracy), and consequently generatesa much smaller number of distinct phenotypes. We refer to the set of phenotypesproduced by a given developmental plan as visible phenotypes,and examine the number of visible phenotypes and the number of potentialphenotypes as a function of r (Figure 2A). We find that while thenumber of visible phenotypes increases with the regulatorydimension, r, their fraction, out of the number of potentialphenotypes, rapidly declines, with around 5% of the potentialphenotypes remaining visible (Figure 2B) whenr = k. Inother words, the expansion of the genotypic space, which also promotes anexpansion in the number of possible genotypic configurations, also brings aboutan increased canalization, masking the expansion in the number of new visiblephenotypes. This is further exemplified by the marginal contribution of eachgenetic element (e.g., each transcription factor), measured as the relativeincrease in the number of visible phenotypes obtained by adding a new geneticelement. This declines from about two-fold for the first few elements, to lessthan 1.4 as r reaches k (Figure 2C). As per the mathematical analysisbelow, this can be attributed to the effect of an unbalanced sample ofD entries and the multiplicative effect of the nonuniformdistribution of each element in the phentype. Interestingly, the functiondescribing the fraction of visible phenotypes (Figure 2B) is sigmoidal, with the greatestchange in the fraction of visible phenotypes occurring at regulatory dimensionson the order of half the phenotypic dimension. Thus for smaller regulatorycircuits, a large fraction of potential phenotypes remain visible, whereas forlarger regulatory circuits, the greater fraction of the phenotypic space ishidden and inaccessible to selection and evolutionary transformation.

Bottom Line: Ancestral phenotypes, produced by early developmental programs with a low level of gene interaction, are found to span a significantly greater volume of the total phenotypic space than derived taxa.We suggest that early and late evolution have a different character that we classify into micro- and macroevolutionary configurations.These findings complement the view of development as a key component in the production of endless forms and highlight the crucial role of development in constraining biotic diversity and evolutionary trajectories.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, Stanford University, Stanford, California, United States of America. ebo@stanford.edu

ABSTRACT
Studies of the evolution of development characterize the way in which gene regulatory dynamics during ontogeny constructs and channels phenotypic variation. These studies have identified a number of evolutionary regularities: (1) phenotypes occupy only a small subspace of possible phenotypes, (2) the influence of mutation is not uniform and is often canalized, and (3) a great deal of morphological variation evolved early in the history of multicellular life. An important implication of these studies is that diversity is largely the outcome of the evolution of gene regulation rather than the emergence of new, structural genes. Using a simple model that considers a generic property of developmental maps-the interaction between multiple genetic elements and the nonlinearity of gene interaction in shaping phenotypic traits-we are able to recover many of these empirical regularities. We show that visible phenotypes represent only a small fraction of possibilities. Epistasis ensures that phenotypes are highly clustered in morphospace and that the most frequent phenotypes are the most similar. We perform phylogenetic analyses on an evolving, developmental model and find that species become more alike through time, whereas higher-level grades have a tendency to diverge. Ancestral phenotypes, produced by early developmental programs with a low level of gene interaction, are found to span a significantly greater volume of the total phenotypic space than derived taxa. We suggest that early and late evolution have a different character that we classify into micro- and macroevolutionary configurations. These findings complement the view of development as a key component in the production of endless forms and highlight the crucial role of development in constraining biotic diversity and evolutionary trajectories.

Show MeSH