Relating multivariate shapes to genescapes using phenotype-biological process associations for craniofacial shape

Realistic mappings of genes to morphology are inherently multivariate on both sides of the equation. The importance of coordinated gene effects on morphological phenotypes is clear from the intertwining of gene actions in signaling pathways, gene regulatory networks, and developmental processes underlying the development of shape and size. Yet, current approaches tend to focus on identifying and localizing the effects of individual genes and rarely leverage the information content of high dimensional phenotypes. Here, we explicitly model the joint effects of biologically coherent collections of genes on a multivariate trait-craniofacial shape - in a sample of n = 1,145 mice from the Diversity Outbred (DO) experimental line. We use biological process gene ontology (GO) annotations to select skeletal and facial development gene sets and solve for the axis of shape variation that maximally covaries with gene set marker variation. We use our process-centered, multivariate genotype-phenotype (process MGP) approach to determine the overall contributions to craniofacial variation of genes involved in relevant processes and how variation in different processes corresponds to multivariate axes of shape variation. Further, we compare the directions of effect in phenotype space of mutations to the primary axis of shape variation associated with broader pathways within which they are thought to function. Finally, we leverage the relationship between mutational and pathway-level effects to predict phenotypic effects beyond craniofacial shape in specific mutants. We also introduce an online application which provides users the means to customize their own process-centered craniofacial shape analyses in the DO. The process-centered approach is generally applicable to any continuously varying phenotype and thus has wide-reaching implications for complex-trait genetics.

A mathematical framework for evo-devo dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Existing mathematical theory has considered either evolutionary dynamics while neglecting developmental dynamics, or developmental dynamics while neglecting evolutionary dynamics by assuming evolutionary equilibrium. We formulate a mathematical framework that integrates explicit developmental dynamics into evolutionary dynamics. We consider two types of traits: genetic traits called control variables and developed traits called state variables. Developed traits are constructed over ontogeny according to a developmental map of ontogenetically prior traits and the social and non-social environment. We obtain general equations describing the evolutionary-developmental (evo-devo) dynamics. These equations can be arranged in a layered structure called the evo-devo process, where five elementary components generate all equations including those describing genetic covariation and the evo-devo dynamics. These equations recover Lande's equation as a special case and describe the evolution of Lande's G-matrix from the evolution of the phenotype, environment, and mutational covariation. This shows that genetic variation is necessarily absent in some directions of phenotype space if at least one trait develops and enough traits are included in the analysis so as to guarantee dynamic sufficiency. Consequently, directional selection alone is generally insufficient to identify evolutionary equilibria. Instead, "total genetic selection" is sufficient to identify evolutionary equilibria if mutational variation exists in all directions of control space and exogenous plastic response vanishes. Developmental and environmental constraints influence the evolutionary equilibria and determine the admissible evolutionary trajectory. These results show that development has major evolutionary effects.

GestaltMatcher: Overcoming the limits of rare disease matching using facial phenotypic descriptors

The majority of monogenic disorders cause craniofacial abnormalities with characteristic facial morphology. These disorders can be diagnosed more efficiently with the support of computer-aided next-generation phenotyping tools, such as DeepGestalt. These tools have learned to associate facial phenotypes with the underlying syndrome through training on thousands of patient photographs. However, this “supervised” approach means that diagnoses are only possible if they were part of the training set. To improve recognition of ultra-rare diseases, we created GestaltMatcher, which uses a deep convolutional neural network based on the DeepGestalt framework. We used photographs of 21,836 patients with 1,362 rare disorders to define a “Clinical Face Phenotype Space”. Distance between cases in the phenotype space defines syndromic similarity, allowing test patients to be matched to a molecular diagnosis even when the disorder was not included in the training set. Similarities among patients with previously unknown disease genes can also be detected. Therefore, in concert with mutation data, GestaltMatcher could accelerate the clinical diagnosis of patients with ultra-rare disorders and facial dysmorphism.

GestaltMatcher: Overcoming the limits of rare disease matching using facial phenotypic descriptors

The majority of monogenic disorders cause craniofacial abnormalities with characteristic facial morphology. These disorders can be diagnosed more efficiently with the support of computer-aided next-generation phenotyping tools, such as DeepGestalt. These tools have learned to associate facial phenotypes with the underlying syndrome through training on thousands of patient photographs. However, this “supervised” approach means that diagnoses are only possible if they were part of the training set. To improve recognition of ultra-rare diseases, we created GestaltMatcher, which uses a deep convolutional neural network based on the DeepGestalt framework. We used photographs of 21,836 patients with 1,362 rare disorders to define a “Clinical Face Phenotype Space”. Distance between cases in the phenotype space defines syndromic similarity, allowing test patients to be matched to a molecular diagnosis even when the disorder was not included in the training set. Similarities among patients with previously unknown disease genes can also be detected. Therefore, in concert with mutation data, GestaltMatcher could accelerate the clinical diagnosis of patients with ultra-rare disorders and facial dysmorphism.

The completeness and stratification in yeast genotype-phenotype space

Genotype and phenotype are two themes of modern biology. While the running principles in genotype has been well understood (e.g., DNA double helix structure, genetic code, central dogma, etc.), much less is known about the rules in phenotype. In this study we examine a yeast phenotype space that is represented by 405 quantitative traits. We show that the space is convergent with limited latent dimensions, which form surprisingly long-distance chains such that all traits are interconnected with each other. As a consequence, statistically uncorrelated traits are linearly dependent in the multi-dimensional phenotype space and can be precisely inferred from each other. Meanwhile, the performance is much poorer for similar trait inferences but from the genotype space (including DNA and mRNA), highlighting the dimension stratification between genotype space and phenotype space. Since the world we’re living is primarily phenotypic and what we truly care is phenotype, these findings call for phenotype-centered biology as a complement for the cross-space genetic thinking in current biology.

Phylogenetic Comparative Methods and the Evolution of Multivariate Phenotypes

Evolutionary biology is multivariate, and advances in phylogenetic comparative methods for multivariate phenotypes have surged to accommodate this fact. Evolutionary trends in multivariate phenotypes are derived from distances and directions between species in a multivariate phenotype space. For these patterns to be interpretable, phenotypes should be characterized by traits in commensurate units and scale. Visualizing such trends, as is achieved with phylomorphospaces, should continue to play a prominent role in macroevolutionary analyses. Evaluating phylogenetic generalized least squares (PGLS) models (e.g., phylogenetic analysis of variance and regression) is valuable, but using parametric procedures is limited to only a few phenotypic variables. In contrast, nonparametric, permutation-based PGLS methods provide a flexible alternative and are thus preferred for high-dimensional multivariate phenotypes. Permutation-based methods for evaluating covariation within multivariate phenotypes are also well established and can test evolutionary trends in phenotypic integration. However, comparing evolutionary rates and modes in multivariate phenotypes remains an important area of future development.

Continuity in Evolution from Codons to Amino Acids

Continuity plays a crucial role in any discussion on evolution. The genotype-phenotype map focus crucial role in evolutionary biology. A nearness relation in the phenotype space allows distinguishing continuous evolution from discontinuous one. In this paper we have investigated continuity in evolution of amino acids. Uniform structures in the space of amino acids as well as in the set of codons are introduced. Here any codon is a genotype and the corresponding amino acid is the phenotype. We examined the continuity of the genotype-phenotype map with respect different uniform structures of codons.

On Continuity of Evolution of Amino Acids

Continuity plays a crucial role in any discussion on evolution. A nearness relation in the phenotype space allows to distinguish continuous evolution from discontinuous one. The genotype-phenotype map plays a crucial role in evolutionary biology. In this paper we have investigated continuity in evolution of amino acids. Nearness relations in the space of amino acids as well as in the set of codons are introduced. Here any codon is a genotype and the corresponding amino acid is the phenotype. We examined the continuity of the genotype-phenotype map with respect different neighbourhood structures of amino acids.

Modeling Networks of Evolving Populations

The goal of this research is to devise a method of differential equation based modeling of evolution that can scale up to capture complex dynamics by enabling the inclusion of many—potentially thousands—of biological characteristics. Towards that goal, a mathematical model for evolution based on the well-established Fisher-Eigen process is built with a unique and efficient structure. The Fisher-Eigen partial differential equation (PDE) describes the evolution of a probability density function representing the distribution of a population over a phenotype space. This equation depends on the choice of a fitness function representing the likelihood of reproductive success at each point in the phenotype space. The Fisher-Eigen model has been studied analytically for simple fitness functions, but in general no analytic solution is known. Furthermore, with traditional numerical methods, the equation becomes exponentially complex to simulate as the dimensionality of the problem expands to include more phenotypes. For this research, a network model is synthesized and a set of ordinary differential equations (ODEs) is extracted based on the Fisher-Eigen PDE to describe the dynamic behavior of the system. It is demonstrated that, when juxtaposed with full numerical PDE simulations, this ODE model finds well-matched transient and precise equilibrium solutions. This prototype method makes modeling of high-dimensional data possible, allowing researchers to examine and even predict complex dynamic behavior based on a snapshot of a population. KEYWORDS: Evolutionary Modeling; Mathematical Biology; Network Dynamics; Ordinary Differential Equations; Partial Differential Equations; Fisher-Eigen model; Phenotype; Fitness Function