Facial phenotype is influenced by genes and environment; however, little is known about their relative contributions to normal facial morphology. The aim of this study was to assess the relative ...genetic and environmental contributions to facial morphological variation using a three-dimensional (3D) population-based approach and the classical twin study design.
3D facial images of 1380 female twins from the TwinsUK Registry database were used. All faces were landmarked, by manually placing 37 landmark points, and Procrustes registered. Three groups of traits were extracted and analysed: 19 principal components (uPC) and 23 principal components (sPC), derived from the unscaled and scaled landmark configurations respectively, and 1275 linear distances measured between 51 landmarks (37 manually identified and 14 automatically calculated). The intraclass correlation coefficients, rMZ and rDZ, broad-sense heritability (h2), common (c2) and unique (e2) environment contributions were calculated for all traits for the monozygotic (MZ) and dizygotic (DZ) twins.
Heritability of 13 uPC and 17 sPC reached statistical significance, with h2 ranging from 38.8% to 78.5% in the former and 30.5% to 84.8% in the latter group. Also, 1222 distances showed evidence of genetic control. Common environment contributed to one PC in both groups and 53 linear distances (4.3%). Unique environment contributed to 17 uPC and 20 sPC and 1245 distances.
Genetic factors can explain more than 70% of the phenotypic facial variation in facial size, nose (width, prominence and height), lips prominence and inter-ocular distance. A few traits have shown potential dominant genetic influence: the prominence and height of the nose, the lower lip prominence in relation to the chin and upper lip philtrum length. Environmental contribution to facial variation seems to be the greatest for the mandibular ramus height and horizontal facial asymmetry.
The paper describes a new approach to constructing exact solutions of nonlinear partial differential equations that employs separation of variables using special (nonlinear integral) transformations ...and the splitting principle. To illustrate its effectiveness, the method is applied to nonlinear reaction–diffusion type equations that involve variable coefficients and arbitrary functions. New exact functional separable solutions as well as generalized traveling wave solutions are obtained.
The paper is concerned with different classes of nonlinear Klein-Gordon and telegraph type equations with variable coefficients
c(x)u
tt
+ d(x)u
t
= a(x)u
x
x
+ b(x)u
x
+ p(x) f (u),
where f (u) is ...an arbitrary function. We seek exact solutions to these equations by the direct method of symmetry reductions using the composition of functions u = U (z) with z = φ (x, t). We show that f (u) and any four of the five functional coefficients a(x), b(x), c(x), d(x), and p(x) in such equations can be set arbitrarily, while the remaining coefficient can be expressed in terms of the others. The study investigates the properties and finds some solutions of the overdetermined system of PDEs for φ (x, t). Examples of specific equations with new exact functional separable solutions are given. In addition, the study presents some generalized traveling wave solutions to more complex, nonlinear Klein-Gordon and telegraph type equations with delay.
Craniofacial morphology is highly heritable, but little is known about which genetic variants influence normal facial variation in the general population. We aimed to identify genetic variants ...associated with normal facial variation in a population-based cohort of 15-year-olds from the Avon Longitudinal Study of Parents and Children. 3D high-resolution images were obtained with two laser scanners, these were merged and aligned, and 22 landmarks were identified and their x, y, and z coordinates used to generate 54 3D distances reflecting facial features. 14 principal components (PCs) were also generated from the landmark locations. We carried out genome-wide association analyses of these distances and PCs in 2,185 adolescents and attempted to replicate any significant associations in a further 1,622 participants. In the discovery analysis no associations were observed with the PCs, but we identified four associations with the distances, and one of these, the association between rs7559271 in PAX3 and the nasion to midendocanthion distance (n-men), was replicated (p = 4 × 10−7). In a combined analysis, each G allele of rs7559271 was associated with an increase in n-men distance of 0.39 mm (p = 4 × 10−16), explaining 1.3% of the variance. Independent associations were observed in both the z (nasion prominence) and y (nasion height) dimensions (p = 9 × 10−9 and p = 9 × 10−10, respectively), suggesting that the locus primarily influences growth in the yz plane. Rare variants in PAX3 are known to cause Waardenburg syndrome, which involves deafness, pigmentary abnormalities, and facial characteristics including a broad nasal bridge. Our findings show that common variants within this gene also influence normal craniofacial development.
Several studies have highlighted differences in the facial features in a White European population. Genetics appear to have a major influence on normal facial variation, and environmental factors are ...likely to have minor influences on face shape directly or through epigenetic mechanisms.
The aim of this longitudinal cohort study is to determine the rate of change in midline facial landmarks in three distinct homogenous population groups (Finnish, Latvian, and Welsh) from 12.8 to 15.3 years of age. This age range covers the pubertal growth period for the majority of boys and girls.
A cohort of children aged 12 were monitored for facial growth in three countries Finland (n = 60), Latvia (n = 107), and Wales (n = 96). Three-dimensional facial surface images were acquired (using either laser or photogrammetric methods) at regular intervals (6-12 months) for 4 years. Ethical approval was granted in each country. Nine midline landmarks were identified and the relative spatial positions of these surface landmarks were measured relative to the mid-endocanthion (men) over a 4-year period.
This study reports the children who attended 95 per cent of all scanning sessions (Finland 48 out of 60; Latvia 104 out of 107; Wales 50 out of 96). Considerable facial variation is seen for all countries and sexes. There are clear patterns of growth that show different magnitudes at different age groups for the different country groups, sexes, and facial parameters. The greatest single yearly growth rate (5.4 mm) was seen for Welsh males for men-pogonion distance at 13.6 years of age. Males exhibit greater rates of growth compared to females. These variations in magnitude and timings are likely to be influenced by genetic ancestry as a result of population migration.
The midline points are a simple and valid method to assess the relative spatial positions of facial surface landmarks. This study confirms previous reports on the subtle differences in facial shapes and sizes of male and female children in different populations and also highlights the magnitudes and timings of growth for various midline landmark distances to the men point.
We present a number of new generalized separable, functional separable, periodic and antiperiodic exact solutions to non-linear delay reaction–diffusion equations of the formut=kuxx+F(u,w),where ...u=u(x,t) and w=u(x,t−τ), with τ being the delay time. The generalized separable solutions are sought in the form u=∑n=1NΦn(x)Ψn(t), with the functions Φn(x) and Ψn(t) to be determined in the analysis. Most of the equations considered contain one or two arbitrary functions of a single argument or one arbitrary function of two arguments of special form. All solutions involve free parameters (in some cases, infinitely many parameters) and so can be suitable for solving certain problems and testing approximate analytical and numerical methods for non-linear delay PDEs. Some results are extended to non-linear delay partial differential equations of any order.
•Non-linear delay reaction–diffusion equations are considered.•New generalized and functional separable solutions are presented.•Most equations contain arbitrary functions of one argument.•Some equations contain an arbitrary function of two arguments.•Some solutions involve infinitely many free parameters.
Facial Genetics: A Brief Overview Richmond, Stephen; Howe, Laurence J; Lewis, Sarah ...
Frontiers in genetics,
10/2018, Volume:
9
Journal Article
Peer reviewed
Open access
Historically, craniofacial genetic research has understandably focused on identifying the causes of craniofacial anomalies and it has only been within the last 10 years, that there has been a drive ...to detail the biological basis of normal-range facial variation. This initiative has been facilitated by the availability of low-cost hi-resolution three-dimensional systems which have the ability to capture the facial details of thousands of individuals quickly and accurately. Simultaneous advances in genotyping technology have enabled the exploration of genetic influences on facial phenotypes, both in the present day and across human history. There are several important reasons for exploring the genetics of normal-range variation in facial morphology. - Disentangling the environmental factors and relative parental biological contributions to heritable traits can help to answer the age-old question "why we look the way that we do?" - Understanding the etiology of craniofacial anomalies; e.g., unaffected family members of individuals with non-syndromic cleft lip/palate (nsCL/P) have been shown to differ in terms of normal-range facial variation to the general population suggesting an etiological link between facial morphology and nsCL/P. - Many factors such as ancestry, sex, eye/hair color as well as distinctive facial features (such as, shape of the chin, cheeks, eyes, forehead, lips, and nose) can be identified or estimated using an individual's genetic data, with potential applications in healthcare and forensics. - Improved understanding of historical selection and adaptation relating to facial phenotypes, for example, skin pigmentation and geographical latitude. - Highlighting what is known about shared facial traits, medical conditions and genes.
We consider heat and diffusion equations with finite relaxation time which ensure a finite speed of propagation of disturbances. We use the Cattaneo–Vernotte model for the heat flux and obtain a ...number of exact solutions to the corresponding linear differential-difference heat equation. We also give exact solutions to two one-dimensional Stokes problem for a differential-difference mass/heat transfer equation (without a source and with a linear source) with a periodic boundary condition.
We describe a number of exact solutions to non-linear differential-difference heat equations of the formT¯t=divf(T)∇T+g(T¯),T¯=T(x,t+τ),where τ is the relaxation time. In addition, we obtain some exact solutions to non-linear systems of two coupled reaction–diffusion equations with finite relaxation time and present several exact solutions of non-linear reaction–diffusion equations with time-varying delay of the formut=kuxx+F(u,w),w=u(x,t−τ),where τ=τ(t).
All equations in question contain arbitrary functions or free parameters. Their solutions can be used to solve certain problems and test numerical methods for non-linear partial differential-difference equations (delay partial differential equations).
•Heat/diffusion differential-difference equations with delay are considered.•Solutions to a Stokes problem with a periodic boundary condition are given.•Exact solutions to non-linear differential-difference heat equations are obtained.•Non-linear systems of coupled reaction–diffusion equations are considered.•Some equations and systems contain arbitrary functions.
The paper deals with one-dimensional nonlinear delay reaction–diffusion equations with varying transfer coefficients of the form ut=G(u)uxx+F(u,ū), where u=u(x,t) and ū=u(x,t−τ), with τ denoting ...the delay time. Generalized and functional separable solutions for this class of equations have been obtained and presented for the first time; these equations have not been known to have such solutions so far. To construct these solutions and solutions of some other delay PDEs, we developed a few exact methods that rely on using invariant subspaces for corresponding nonlinear differential operators. Many of the results are extendable to more complex nonlinear reaction–diffusion equations with several delay times, τ1,…,τm, and equations with time-varying delay, τ=τ(t). All of the equations considered involve several free parameters (or an arbitrary function) and so their solutions can be suitable for testing approximate analytical and numerical methods for nonlinear delay reaction–diffusion equations. The exact methods described may also be applied to other classes of nonlinear delay PDEs.
The idea that symmetry in facial traits is associated with attractiveness because it reliably indicates good physiological health, particularly to potential sexual partners, has generated an ...extensive literature on the evolution of human mate choice. However, large-scale tests of this hypothesis using direct or longitudinal assessments of physiological health are lacking. Here, we investigate relationships between facial fluctuating asymmetry (FA) and detailed individual health histories in a sample (n = 4732) derived from a large longitudinal study (Avon Longitudinal Study of Parents and Children) in South West England. Facial FA was assessed using geometric morphometric analysis of facial landmark configurations derived from three-dimensional facial scans taken at 15 years of age. Facial FA was not associated with longitudinal measures of childhood health. However, there was a very small negative association between facial FA and IQ that remained significant after correcting for a positive allometric relationship between FA and face size. Overall, this study does not support the idea that facial symmetry acts as a reliable cue to physiological health. Consequently, if preferences for facial symmetry do represent an evolved adaptation, then they probably function not to provide marginal fitness benefits by choosing between relatively healthy individuals on the basis of small differences in FA, but rather evolved to motivate avoidance of markers of substantial developmental disturbance and significant pathology.
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