Limits...
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.

Show MeSH
Localization of the visible phenotypic subspace.(A) A loglog plot of the distribution of degeneracy levels among visible                            phenotypes. Each point denotes the expected number of distinct                            phenotypes with a certain degeneracy level for a given developmental                            plan and is an average over 10,000 different plans. Note that the point                            associated with degeneracy level 0 (i.e., hidden phenotypes) is not                            included. These developmental plans frequently give rise to phenotypes                            with degeneracy levels higher than 103, and in rare cases,                            higher than 103.5. Given that the total number of genotypes                            is 214 a single phenotype can be produced by                            6%–20% genotypes. (B) A contour plot of                            the gain function induced by a given developmental plan (all                            developmental plans produce qualitatively similar results). The gain                            function,                                    gain(dg,dp),                            denotes the probability that the Hamming distance between two phenotypes                            is dp, given that the distance between the                            two genotypes that produced them is dg. (C)                            The distribution of pairwise phenotypic Hamming distances among randomly                            selected phenotypes (not produced by a developmental plan), distinct                            visible phenotypes (considering every visible phenotype only once,                            regardless of frequency), and visible phenotypes including all                            occurrences of each phenotype. The pairwise Hamming distances between                            randomly selected phenotypes follows a binomial distribution, with mean                            distance 7 (for phenotypes of length 14). Distinct visible phenotypes                            are closer to one another, with the mean distance 5.976. When weighting                            by the frequency of the visible phenotypes, the distance is reduced,                            with a mean distance 4.607.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2562988&req=5

pcbi-1000202-g003: Localization of the visible phenotypic subspace.(A) A loglog plot of the distribution of degeneracy levels among visible phenotypes. Each point denotes the expected number of distinct phenotypes with a certain degeneracy level for a given developmental plan and is an average over 10,000 different plans. Note that the point associated with degeneracy level 0 (i.e., hidden phenotypes) is not included. These developmental plans frequently give rise to phenotypes with degeneracy levels higher than 103, and in rare cases, higher than 103.5. Given that the total number of genotypes is 214 a single phenotype can be produced by 6%–20% genotypes. (B) A contour plot of the gain function induced by a given developmental plan (all developmental plans produce qualitatively similar results). The gain function, gain(dg,dp), denotes the probability that the Hamming distance between two phenotypes is dp, given that the distance between the two genotypes that produced them is dg. (C) The distribution of pairwise phenotypic Hamming distances among randomly selected phenotypes (not produced by a developmental plan), distinct visible phenotypes (considering every visible phenotype only once, regardless of frequency), and visible phenotypes including all occurrences of each phenotype. The pairwise Hamming distances between randomly selected phenotypes follows a binomial distribution, with mean distance 7 (for phenotypes of length 14). Distinct visible phenotypes are closer to one another, with the mean distance 5.976. When weighting by the frequency of the visible phenotypes, the distance is reduced, with a mean distance 4.607.

Mentions: Having established that large regulatory networks lead to a small number of visible phenotypes, we turn to the statistical characteristics of the visible, phenotypic subspace. We focus on developmental plans for which r = k (e.g., the number of TFs matches the number of target genes). As demonstrated above, these developmental plans produce the most restricted set of visible phenotypes. Unless otherwise indicated, we set r = k = 14 to allow for the complete enumeration of all genotypes. We consider the distribution of frequency levels among the visible phenotypes. We calculate for each phenotype j, a degeneracy level, nj, denoting the number of different genotypes that produce it (visible phenotypes correspond to those phenotypes for which nj>0). The distribution of degeneracy levels fits a generalized power-law distribution (Figure 3A), implying that there are a few very common (frequent) phenotypes and many rare ones. These findings replicate those on the highly nonuniform frequencies of folding geometries in the RNA secondary structure genotype/phenotype map [20].


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

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

Localization of the visible phenotypic subspace.(A) A loglog plot of the distribution of degeneracy levels among visible                            phenotypes. Each point denotes the expected number of distinct                            phenotypes with a certain degeneracy level for a given developmental                            plan and is an average over 10,000 different plans. Note that the point                            associated with degeneracy level 0 (i.e., hidden phenotypes) is not                            included. These developmental plans frequently give rise to phenotypes                            with degeneracy levels higher than 103, and in rare cases,                            higher than 103.5. Given that the total number of genotypes                            is 214 a single phenotype can be produced by                            6%–20% genotypes. (B) A contour plot of                            the gain function induced by a given developmental plan (all                            developmental plans produce qualitatively similar results). The gain                            function,                                    gain(dg,dp),                            denotes the probability that the Hamming distance between two phenotypes                            is dp, given that the distance between the                            two genotypes that produced them is dg. (C)                            The distribution of pairwise phenotypic Hamming distances among randomly                            selected phenotypes (not produced by a developmental plan), distinct                            visible phenotypes (considering every visible phenotype only once,                            regardless of frequency), and visible phenotypes including all                            occurrences of each phenotype. The pairwise Hamming distances between                            randomly selected phenotypes follows a binomial distribution, with mean                            distance 7 (for phenotypes of length 14). Distinct visible phenotypes                            are closer to one another, with the mean distance 5.976. When weighting                            by the frequency of the visible phenotypes, the distance is reduced,                            with a mean distance 4.607.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000202-g003: Localization of the visible phenotypic subspace.(A) A loglog plot of the distribution of degeneracy levels among visible phenotypes. Each point denotes the expected number of distinct phenotypes with a certain degeneracy level for a given developmental plan and is an average over 10,000 different plans. Note that the point associated with degeneracy level 0 (i.e., hidden phenotypes) is not included. These developmental plans frequently give rise to phenotypes with degeneracy levels higher than 103, and in rare cases, higher than 103.5. Given that the total number of genotypes is 214 a single phenotype can be produced by 6%–20% genotypes. (B) A contour plot of the gain function induced by a given developmental plan (all developmental plans produce qualitatively similar results). The gain function, gain(dg,dp), denotes the probability that the Hamming distance between two phenotypes is dp, given that the distance between the two genotypes that produced them is dg. (C) The distribution of pairwise phenotypic Hamming distances among randomly selected phenotypes (not produced by a developmental plan), distinct visible phenotypes (considering every visible phenotype only once, regardless of frequency), and visible phenotypes including all occurrences of each phenotype. The pairwise Hamming distances between randomly selected phenotypes follows a binomial distribution, with mean distance 7 (for phenotypes of length 14). Distinct visible phenotypes are closer to one another, with the mean distance 5.976. When weighting by the frequency of the visible phenotypes, the distance is reduced, with a mean distance 4.607.
Mentions: Having established that large regulatory networks lead to a small number of visible phenotypes, we turn to the statistical characteristics of the visible, phenotypic subspace. We focus on developmental plans for which r = k (e.g., the number of TFs matches the number of target genes). As demonstrated above, these developmental plans produce the most restricted set of visible phenotypes. Unless otherwise indicated, we set r = k = 14 to allow for the complete enumeration of all genotypes. We consider the distribution of frequency levels among the visible phenotypes. We calculate for each phenotype j, a degeneracy level, nj, denoting the number of different genotypes that produce it (visible phenotypes correspond to those phenotypes for which nj>0). The distribution of degeneracy levels fits a generalized power-law distribution (Figure 3A), implying that there are a few very common (frequent) phenotypes and many rare ones. These findings replicate those on the highly nonuniform frequencies of folding geometries in the RNA secondary structure genotype/phenotype map [20].

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