A genome-wide association study identifies multiple loci associated with mathematics ability and disability

Preliminary Evidence for a Positive Relation Between the COMT rs4680 Met/Met Genotype and Math Achievement

To identify if COMT polymorphisms interact with executive functions as predictors of math skills, we assessed 38 adolescents (mean age = 16.4 ± 0.80 years, IQ > 80) from a larger study of high-school students screened for their mathematical abilities. Adolescents were genotyped for the COMT Val158Met polymorphism (grouped as Met/Met or Val-carriers) and completed the WRAT math achievement test, working-memory, inhibitory-control, and shifting tasks. Met/Met-carriers achieved higher WRAT scores than the Val-carriers (W = 229, p = .009). Genotype group was a moderate-to-strong predictor of WRAT scores (β = 0.56 to 0.74). No genotype/executive-function interaction was detected. Our findings suggest that the rs4680 Met/Met genotype is positively associated with math achievement.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

The principle of procreative beneficence and its implications for genetic engineering

Molecular genetic engineering technologies such as CRISPR/Cas9 have made the accurate and safe genetic engineering of human embryos possible. Further advances in genomics have isolated genes that predict qualities and traits associated with intelligence. Given these advances, prospective parents could use these biotechnologies to genetically engineer future children for genes that enhance their intelligence. While Julian Savulescu's Principle of Procreative Beneficence (PPB) argues for the moral obligation of prospective parents to use in-vitro fertilization and preimplantation genetic diagnosis to make eugenic selections of embryos for intelligence, the PPB could imply obligations to genetically engineer selected embryos for intelligence as well. I argue that the PPB implies an additional moral obligation for prospective parents to genetically engineer the embryonic germline identity of selected embryos for genes that predict intelligence. Objections to my argument for the PPB's extension are also discussed.

Quantity as a Fish Views It: Behavior and Neurobiology

An ability to estimate quantities, such as the number of conspecifics or the size of a predator, has been reported in vertebrates. Fish, in particular zebrafish, may be instrumental in advancing the understanding of magnitude cognition. We review here the behavioral studies that have described the ecological relevance of quantity estimation in fish and the current status of the research aimed at investigating the neurobiological bases of these abilities. By combining behavioral methods with molecular genetics and calcium imaging, the involvement of the retina and the optic tectum has been documented for the estimation of continuous quantities in the larval and adult zebrafish brain, and the contributions of the thalamus and the dorsal-central pallium for discrete magnitude estimation in the adult zebrafish brain. Evidence for basic circuitry can now be complemented and extended to research that make use of transgenic lines to deepen our understanding of quantity cognition at genetic and molecular levels.

Neuropilin 2/Plexin-A3 Receptors Regulate the Functional Connectivity and the Excitability in the Layers 4 and 5 of the Cerebral Cortex

The functions of cortical networks are progressively established during development by series of events shaping the neuronal connectivity. Synaptic elimination, which consists of removing the supernumerary connections generated during the earlier stages of cortical development, is one of the latest stages in neuronal network maturation. The semaphorin 3F coreceptors neuropilin 2 (Nrp2) and plexin-A3 (PlxnA3) may play an important role in the functional maturation of the cerebral cortex by regulating the excess dendritic spines on cortical excitatory neurons. Yet, the identity of the connections eliminated under the control of Nrp2/PlxnA3 signaling is debated, and the importance of this synaptic refinement for cortical functions remains poorly understood. Here, we show that Nrp2/PlxnA3 controls the spine densities in layer 4 (L4) and on the apical dendrite of L5 neurons of the sensory and motor cortices. Using a combination of neuroanatomical, ex vivo electrophysiology, and in vivo functional imaging techniques in Nrp2 and PlxnA3 KO mice of both sexes, we disprove the hypothesis that Nrp2/PlxnA3 signaling is required to maintain the ectopic thalamocortical connections observed during embryonic development. We also show that the absence of Nrp2/PlxnA3 signaling leads to the hyperexcitability and excessive synchronization of the neuronal activity in L5 and L4 neuronal networks, suggesting that this system could participate in the refinement of the recurrent corticocortical connectivity in those layers. Altogether, our results argue for a role of semaphorin-Nrp2/PlxnA3 signaling in the proper maturation and functional connectivity of the cerebral cortex, likely by controlling the refinement of recurrent corticocortical connections.SIGNIFICANCE STATEMENT The function of a neuronal circuit is mainly determined by the connections that neurons establish with one another during development. Understanding the mechanisms underlying the establishment of the functional connectivity is fundamental to comprehend how network functions are implemented, and to design treatments aiming at restoring damaged neuronal circuits. Here, we show that the cell surface receptors for the family of semaphorin guidance cues neuropilin 2 (Nrp2) and plexin-A3 (PlxnA3) play an important role in shaping the functional connectivity of the cerebral cortex likely by trimming the recurrent connections in layers 4 and 5. By removing the supernumerary inputs generated during early development, Nrp2/PlxnA3 signaling reduces the neuronal excitability and participates in the maturation of the cortical network functions.

The Polygenic Nature and Complex Genetic Architecture of Specific Learning Disorder

Specific Learning Disorder (SLD) is a multifactorial, neurodevelopmental disorder which may involve persistent difficulties in reading (dyslexia), written expression and/or mathematics. Dyslexia is characterized by difficulties with speed and accuracy of word reading, deficient decoding abilities, and poor spelling. Several studies from different, but complementary, scientific disciplines have investigated possible causal/risk factors for SLD. Biological, neurological, hereditary, cognitive, linguistic-phonological, developmental and environmental factors have been incriminated. Despite worldwide agreement that SLD is highly heritable, its exact biological basis remains elusive. We herein present: (a) an update of studies that have shaped our current knowledge on the disorder’s genetic architecture; (b) a discussion on whether this genetic architecture is ‘unique’ to SLD or, alternatively, whether there is an underlying common genetic background with other neurodevelopmental disorders; and, (c) a brief discussion on whether we are at a position of generating meaningful correlations between genetic findings and anatomical data from neuroimaging studies or specific molecular/cellular pathways. We conclude with open research questions that could drive future research directions.

Evidence for specificity of polygenic contributions to attainment in English, maths and science during adolescence

How well one does at school is predictive of a wide range of important cognitive, socioeconomic, and health outcomes. The last few years have shown marked advancement in our understanding of the genetic contributions to, and correlations with, academic attainment. However, there exists a gap in our understanding of the specificity of genetic associations with performance in academic subjects during adolescence, a critical developmental period. To address this, the Avon Longitudinal Study of Parents and Children was used to conduct genome-wide association studies of standardised national English (N = 5983), maths (N = 6017) and science (N = 6089) tests. High SNP-based heritabilities (h2SNP) for all subjects were found (41-53%). Further, h2SNP for maths and science remained after removing shared variance between subjects or IQ (N = 3197-5895). One genome-wide significant single nucleotide polymorphism (rs952964, p = 4.86 × 10-8) and four gene-level associations with science attainment (MEF2C, BRINP1, S100A1 and S100A13) were identified. Rs952964 remained significant after removing the variance shared between academic subjects. The findings highlight the benefits of using environmentally homogeneous samples for genetic analyses and indicate that finer-grained phenotyping will help build more specific biological models of variance in learning processes and abilities.

Genome-wide association analysis of cognitive function in Danish long-lived individuals

Cognitive function is a substantially heritable trait related to numerous important life outcomes. Several genome-wide association studies of cognitive function have in recent years led to the identification of thousands of significantly associated loci and genes. Individuals included in these studies have rarely been nonagenarians and centenarians, and since cognitive function is an important component of quality of life for this rapidly expanding demographic group, there is a need to explore genetic factors associated with individual differences in cognitive function at advanced ages. In this study, we pursued this by performing a genome-wide association study of cognitive function in 490 long-lived Danes (age range 90.1-100.8 years). While no genome-wide significant SNPs were identified, suggestively significant SNPs (P < 1 × 10^-5) were mapped to several interesting genes, including ZWINT, CELF2, and DNAH5, and the glutamate receptor genes GRID2 and GRM7. Additionally, results from a gene set over-representation analysis indicated potential roles of gene sets related to G protein-coupled receptor (GPCR) signaling, interaction between L1 and ankyrins, mitogen-activated protein kinase (MAPK) signaling, RNA degradation, and cell cycle. Larger studies are needed to shed further light on the possible importance of these suggestive genes and pathways in cognitive function in nonagenarians and centenarians.

Identification of novel loci associated with infant cognitive ability

It is believed that genetic factors play a large role in the development of many cognitive and neurological processes; however, epidemiological evidence for the genetic basis of childhood neurodevelopment is very limited. Identification of the genetic polymorphisms associated with early-stage neurodevelopment will help elucidate biological mechanisms involved in neuro-behavior and provide a better understanding of the developing brain. To search for such variants, we performed a genome-wide association study (GWAS) for infant mental and motor ability at two years of age with mothers and children recruited from cohorts in Bangladesh and Mexico. Infant ability was assessed using mental and motor composite scores calculated with country-specific versions of the Bayley Scales of Infant Development. A missense variant (rs1055153) located in the gene WWTR1 reached genome-wide significance in association with mental composite score (meta-analysis effect size of minor allele βmeta = -6.04; 95% CI: -8.13 to -3.94; P = 1.56×10-8). Infants carrying the minor allele reported substantially lower cognitive scores in both cohorts, and this variant is predicted to be in the top 0.3% of most deleterious substitutions in the human genome. Fine mapping and region-based association testing provided additional suggestive evidence that both WWTR1 and a second gene, LRP1B, were associated with infant cognitive ability. Comparisons with recently conducted GWAS in intelligence and educational attainment indicate that our phenotypes do not possess a high genetic correlation with either adolescent or adult cognitive traits, suggesting that infant neurological assessments should be treated as an independent outcome of interest. Additional functional studies and replication efforts in other cohorts may help uncover new biological pathways and genetic architectures that are crucial to the developing brain.

Longitudinal Effects of the Home Learning Environment and Parental Difficulties on Reading and Math Development Across Grades 1-9

This study focuses on parental reading and mathematical difficulties, the home literacy environment, and the home numeracy environment as well as their predictive role in Finnish children’s reading and mathematical development through Grades 1–9. We examined if parental reading and mathematical difficulties directly predict children’s academic performance and/or if they are mediated by the home learning environment. Mothers (n = 1590) and fathers (n = 1507) reported on their reading and mathematical difficulties as well as on the home environment (shared reading, teaching literacy, and numeracy) when their children were in kindergarten. Tests for reading fluency, reading comprehension, and arithmetic fluency were administered to children in Grades 1, 2, 3, 4, 7, and 9. Parental reading difficulties predicted children’s reading fluency, whereas parental mathematical difficulties predicted their reading comprehension and arithmetic fluency. Familial risk was associated with neither formal nor informal home environment factors, whereas maternal education had a significant relationship with both, with higher levels of education among mothers predicting less time spent on teaching activities and more time spent on shared reading. In addition, shared reading was significantly associated with the development of reading comprehension up to Grades 3 and 4, whereas other components of the home learning environment were not associated with any assessed skills. Our study highlights that taken together, familial risk, parental education, and the home learning environment form a complex pattern of associations with children’s mathematical and reading skills.

Neurobiological origins of individual differences in mathematical ability

Mathematical ability is heritable and related to several genes expressing proteins in the brain. It is unknown, however, which intermediate neural phenotypes could explain how these genes relate to mathematical ability. Here, we examined genetic effects on cerebral cortical volume of 3-6-year-old children without mathematical training to predict mathematical ability in school at 7-9 years of age. To this end, we followed an exploration sample (n = 101) and an independent replication sample (n = 77). We found that ROBO1, a gene known to regulate prenatal growth of cerebral cortical layers, is associated with the volume of the right parietal cortex, a key region for quantity representation. Individual volume differences in this region predicted up to a fifth of the behavioral variance in mathematical ability. Our findings indicate that a fundamental genetic component of the quantity processing system is rooted in the early development of the parietal cortex.

Behavior and Molecular Genetic Approaches to Comorbidity

Purpose of Review

This review provides an overview of studies that used behavioral genetic methods to understand the genetic and environmental influences that lead to comorbidity, the co-occurrence of two or more developmental disorders in the same individual.

Recent Findings

Comorbidity is primarily explained by shared genetic influences for most pairs of disorders that have been studied, including attention deficit hyperactivity disorder (ADHD) and learning disabilities, conduct disorder and ADHD, anxiety and depression, and anxiety and autism spectrum disorder (ASD). Molecular genetic studies indicate that the etiologies of developmental disorders are highly multifactorial, with dozens or even hundreds of genes acting in combination with environmental risk factors to lead to each individual disorder and the extensive comorbidity between disorders. Due to this complexity, current state-of-the-art studies are now combining molecular genetic data from multiple large samples to begin to achieve adequate statistical power to identify the specific genetic polymorphisms that lead to comorbidity.

Summary

An extensive literature demonstrates the pervasiveness and potential importance of comorbidity between developmental disorders, and results of family, twin, and molecular genetic studies indicate that these comorbidities may be largely explained by shared genetic influences. Additional studies are ongoing to identify the specific genetic polymorphisms that increase risk for each developmental disorder and comorbidity between disorders.

The functional database of the ARCHI project: Potential and perspectives

More than two decades of functional magnetic resonance imaging (fMRI) of the human brain have succeeded to identify, with a growing level of precision, the neural basis of multiple cognitive skills within various domains (perception, sensorimotor processes, language, emotion and social cognition …). Progress has been made in the comprehension of the functional organization of localized brain areas. However, the long time required for fMRI acquisition limits the number of experimental conditions performed in a single individual. As a consequence, distinct brain localizations have mostly been studied in separate groups of participants, and their functional relationships at the individual level remain poorly understood. To address this issue, we report here preliminary results on a database of fMRI data acquired on 78 individuals who each performed a total of 29 experimental conditions, grouped in 4 cross-domains functional localizers. This protocol has been designed to efficiently isolate, in a single session, the brain activity associated with language, numerical representation, social perception and reasoning, premotor and visuomotor representations. Analyses are reported at the group and at the individual level, to establish the ability of our protocol to selectively capture distinct regions of interest in a very short time. Test-retest reliability was assessed in a subset of participants. The activity evoked by the different contrasts of the protocol is located in distinct brain networks that, individually, largely replicate previous findings and, taken together, cover a large proportion of the cortical surface. We provide detailed analyses of a subset of regions of relevance: the left frontal, left temporal and middle frontal cortices. These preliminary analyses highlight how combining such a large set of functional contrasts may contribute to establish a finer-grained brain atlas of cognitive functions, especially in regions of high functional overlap. Detailed structural images (structural connectivity, micro-structures, axonal diameter) acquired in the same individuals in the context of the ARCHI database provide a promising situation to explore functional/structural interdependence. Additionally, this protocol might also be used as a way to establish individual neurofunctional signatures in large cohorts.

Shared genetic aetiology between cognitive performance and brain activations in language and math tasks

Cognitive performance is highly heritable. However, little is known about common genetic influences on cognitive ability and brain activation when engaged in a cognitive task. The Human Connectome Project (HCP) offers a unique opportunity to study this shared genetic etiology with an extended pedigree of 785 individuals. To investigate this common genetic origin, we took advantage of the HCP dataset, which includes both language and mathematics activation tasks. Using the HCP multimodal parcellation, we identified areals in which inter-individual functional MRI (fMRI) activation variance was significantly explained by genetics. Then, we performed bivariate genetic analyses between the neural activations and behavioral scores, corresponding to the fMRI task accuracies, fluid intelligence, working memory and language performance. We observed that several parts of the language network along the superior temporal sulcus, as well as the angular gyrus belonging to the math processing network, are significantly genetically correlated with these indicators of cognitive performance. This shared genetic etiology provides insights into the brain areas where the human-specific genetic repertoire is expressed. Studying the association of polygenic risk scores, using variants associated with human cognitive ability and brain activation, would provide an opportunity to better understand where these variants are influential.

Genome-wide analysis of adolescent psychotic-like experiences shows genetic overlap with psychiatric disorders

This study aimed to test for overlap in genetic influences between psychotic-like experience traits shown by adolescents in the community, and clinically-recognized psychiatric disorders in adulthood, specifically schizophrenia, bipolar disorder, and major depression. The full spectra of psychotic-like experience domains, both in terms of their severity and type (positive, cognitive, and negative), were assessed using self- and parent-ratings in three European community samples aged 15-19 years (Final N incl. siblings = 6,297-10,098). A mega-genome-wide association study (mega-GWAS) for each psychotic-like experience domain was performed. Single nucleotide polymorphism (SNP)-heritability of each psychotic-like experience domain was estimated using genomic-relatedness-based restricted maximum-likelihood (GREML) and linkage disequilibrium- (LD-) score regression. Genetic overlap between specific psychotic-like experience domains and schizophrenia, bipolar disorder, and major depression was assessed using polygenic risk score (PRS) and LD-score regression. GREML returned SNP-heritability estimates of 3-9% for psychotic-like experience trait domains, with higher estimates for less skewed traits (Anhedonia, Cognitive Disorganization) than for more skewed traits (Paranoia and Hallucinations, Parent-rated Negative Symptoms). Mega-GWAS analysis identified one genome-wide significant association for Anhedonia within IDO2 but which did not replicate in an independent sample. PRS analysis revealed that the schizophrenia PRS significantly predicted all adolescent psychotic-like experience trait domains (Paranoia and Hallucinations only in non-zero scorers). The major depression PRS significantly predicted Anhedonia and Parent-rated Negative Symptoms in adolescence. Psychotic-like experiences during adolescence in the community show additive genetic effects and partly share genetic influences with clinically-recognized psychiatric disorders, specifically schizophrenia and major depression.

Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic

Brain disorders are often investigated in isolation, but very different conclusions might be reached when studies directly contrast multiple disorders. Here, we illustrate this in the context of specific learning disorders, such as dyscalculia and dyslexia. While children with dyscalculia show deficits in arithmetic, children with dyslexia present with reading difficulties. Furthermore, the comorbidity between dyslexia and dyscalculia is surprisingly high. Different hypotheses have been proposed on the origin of these disorders (number processing deficits in dyscalculia, phonological deficits in dyslexia) but these have never been directly contrasted in one brain imaging study. Therefore, we compared the brain activity of children with dyslexia, children with dyscalculia, children with comorbid dyslexia/dyscalculia and healthy controls during arithmetic in a design that allowed us to disentangle various processes that might be associated with the specific or common neural origins of these learning disorders. Participants were 62 children aged 9 to 12, 39 of whom had been clinically diagnosed with a specific learning disorder (dyscalculia and/or dyslexia). All children underwent fMRI scanning while performing an arithmetic task in different formats (dot arrays, digits and number words). At the behavioral level, children with dyscalculia showed lower accuracy when subtracting dot arrays, and all children with learning disorders were slower in responding compared to typically developing children (especially in symbolic formats). However, at the neural level, analyses pointed towards substantial neural similarity between children with learning disorders: Control children demonstrated higher activation levels in frontal and parietal areas than the three groups of children with learning disorders, regardless of the disorder. A direct comparison between the groups of children with learning disorders revealed similar levels of neural activation throughout the brain across these groups. Multivariate subject generalization analyses were used to statistically test the degree of similarity, and confirmed that the neural activation patterns of children with dyslexia, dyscalculia and dyslexia/dyscalculia were highly similar in how they deviated from neural activation patterns in control children. Collectively, these results suggest that, despite differences at the behavioral level, the brain activity profiles of children with different learning disorders during arithmetic may be more similar than initially thought.

Specific learning disability in mathematics: a comprehensive review

Math skills are necessary for success in the childhood educational and future adult work environment. This article reviews the changing terminology for specific learning disabilities (SLD) in math and describes the emerging genetics and neuroimaging studies that relate to individuals with math disability (MD). It is important to maintain a developmental perspective on MD, as presentation changes with age, instruction, and the different models (educational and medical) of identification. Intervention requires a systematic approach to screening and remediation that has evolved with more evidence-based literature. Newer directions in behavioral, educational and novel interventions are described.

Rare Copy Number Variants in Array-Based Comparative Genomic Hybridization in Early-Onset Skeletal Fragility

Early-onset osteoporosis is characterized by low bone mineral density (BMD) and fractures since childhood or young adulthood. Several monogenic forms have been identified but the contributing genes remain inadequately characterized. In search for novel variants and novel candidate loci, we screened a cohort of 70 young subjects with mild to severe skeletal fragility for rare copy-number variants (CNVs). Our study cohort included 15 subjects with primary osteoporosis before age 30 years and 55 subjects with a pathological fracture history and low or normal BMD before age 16 years. A custom-made high-resolution comparative genomic hybridization array with enriched probe density in >1,150 genes important for bone metabolism and ciliary function was used to search for CNVs. We identified altogether 14 rare CNVs. Seven intronic aberrations were classified as likely benign. Five CNVs of unknown clinical significance affected coding regions of genes not previously associated with skeletal fragility (ETV1-DGKB, AGBL2, ATM, RPS6KL1-PGF, and SCN4A). Finally, two CNVs were pathogenic and likely pathogenic, respectively: a 4 kb deletion involving exons 1-4 of COL1A2 (NM_000089.3) and a 12.5 kb duplication of exon 3 in PLS3 (NM_005032.6). Although both genes have been linked to monogenic forms of osteoporosis, COL1A2 deletions are rare and PLS3 duplications have not been described previously. Both CNVs were identified in subjects with significant osteoporosis and segregated with osteoporosis within the families. Our study expands the number of pathogenic CNVs in monogenic skeletal fragility and shows the validity of targeted CNV screening to potentially pinpoint novel candidate loci in early-onset osteoporosis.

Cognitive genomics: Searching for the genetic roots of neuropsychological functioning

OBJECTIVE

Human cognition has long been known to be under substantial genetic control. With the complete mapping of the human genome, genome-wide association studies for many complex traits have proliferated; however, the highly polygenic nature of intelligence has made the identification of the precise genes that influence both global and specific cognitive abilities more difficult than anticipated.

METHOD

Here, we review the latest developments in the genomics of cognition, including a discussion of methodological advances in the genetic analysis of complex traits, and shared genetic contributions to cognitive abilities and neuropsychiatric disorders.

RESULTS

A wealth of twin and family studies have provided compelling evidence for a strong heritable component of both global and specific cognitive abilities, and for the existence of "generalist genes" responsible for a large portion of the variance in diverse cognitive abilities. Increasingly sophisticated analytic tools and ever-larger sample sizes are now facilitating the identification of specific genetic and molecular underpinnings of cognitive abilities, leading to optimism regarding possibilities for novel treatments for illnesses related to cognitive function.

CONCLUSIONS

We conclude with a set of future directions for the field, which will further accelerate discoveries regarding the biological pathways relevant to cognitive abilities. These, in turn, may be further interrogated in order to link biological mechanisms to behavior. (PsycINFO Database Record

A Genome-Wide Association Study Identifies Genetic Variants Associated with Mathematics Ability

Mathematics ability is a complex cognitive trait with polygenic heritability. Genome-wide association study (GWAS) has been an effective approach to investigate genetic components underlying mathematic ability. Although previous studies reported several candidate genetic variants, none of them exceeded genome-wide significant threshold in general populations. Herein, we performed GWAS in Chinese elementary school students to identify potential genetic variants associated with mathematics ability. The discovery stage included 494 and 504 individuals from two independent cohorts respectively. The replication stage included another cohort of 599 individuals. In total, 28 of 81 candidate SNPs that met validation criteria were further replicated. Combined meta-analysis of three cohorts identified four SNPs (rs1012694, rs11743006, rs17778739 and rs17777541) of SPOCK1 gene showing association with mathematics ability (minimum p value 5.67 × 10⁻¹⁰, maximum β −2.43). The SPOCK1 gene is located on chromosome 5q31.2 and encodes a highly conserved glycoprotein testican-1 which was associated with tumor progression and prognosis as well as neurogenesis. This is the first study to report genome-wide significant association of individual SNPs with mathematics ability in general populations. Our preliminary results further supported the role of SPOCK1 during neurodevelopment. The genetic complexities underlying mathematics ability might contribute to explain the basis of human cognition and intelligence at genetic level.

Dyscalculia and the Calculating Brain

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

Functional polymorphisms in BDNF and COMT genes are associated with objective differences in arithmetical functioning in a sample of young adults

BACKGROUND

Understanding the molecular genetics of complex human behaviors and functions remains a substantial challenge for the neurosciences. Previous studies have shown a genetic basis for individual differences in mathematical functioning; however, the specific genes remain to be completely identified. In the present study, we explored the possibility that 2 functional polymorphisms in candidate genes could be associated with differences in arithmetical performance.

METHODS

A computerized test to analyze performance in basic arithmetical calculations (additions and subtractions) was applied to 168 healthy young Colombian participants using the PEBL (Psychology Experiment Building Language) battery. DNA samples were genotyped for 2 functional SNPs in candidate genes: brain-derived neurotrophic factor (BDNF)-Val66Met and catechol-O-methyltransferase (COMT)-Val158Met.

RESULTS

We found significant differences for arithmetical processing scores between genotypes. For BDNF, Val/Val subjects had a worse performance (p value: 0.025) and for COMT, Val/Val carriers had a better performance (p value: 0.006). A multivariate model, including both BDNF and COMT genes, accounted for 7.1% of the variance in math processing scores.

DISCUSSION

To our knowledge, this is the first study finding associations of polymorphisms in BDNF and COMT genes with quantitative measures of numerical aptitude in healthy young participants. A future study of other genes involved in neural plasticity could be helpful to identify genetic correlates of arithmetical functioning, which will be important for the understanding of normal human behaviors and related neuropsychiatric disorders.

Lack of replication for the myosin-18B association with mathematical ability in independent cohorts

Twin studies indicate that dyscalculia (or mathematical disability) is caused partly by a genetic component, which is yet to be understood at the molecular level. Recently, a coding variant (rs133885) in the myosin-18B gene was shown to be associated with mathematical abilities with a specific effect among children with dyslexia. This association represents one of the most significant genetic associations reported to date for mathematical abilities and the only one reaching genome-wide statistical significance. We conducted a replication study in different cohorts to assess the effect of rs133885 maths-related measures. The study was conducted primarily using the Avon Longitudinal Study of Parents and Children (ALSPAC), (N = 3819). We tested additional cohorts including the York Cohort, the Specific Language Impairment Consortium (SLIC) cohort and the Raine Cohort, and stratified them for a definition of dyslexia whenever possible. We did not observe any associations between rs133885 in myosin-18B and mathematical abilities among individuals with dyslexia or in the general population. Our results suggest that the myosin-18B variant is unlikely to be a main factor contributing to mathematical abilities.

Neural cell adhesion molecule NrCAM regulates Semaphorin 3F-induced dendritic spine remodeling

Neuron-glial related cell adhesion molecule (NrCAM) is a regulator of axon growth and repellent guidance, and has been implicated in autism spectrum disorders. Here a novel postsynaptic role for NrCAM in Semaphorin3F (Sema3F)-induced dendritic spine remodeling was identified in pyramidal neurons of the primary visual cortex (V1). NrCAM localized to dendritic spines of star pyramidal cells in postnatal V1, where it was coexpressed with Sema3F. NrCAM deletion in mice resulted in elevated spine densities on apical dendrites of star pyramidal cells at both postnatal and adult stages, and electron microscopy revealed increased numbers of asymmetric synapses in layer 4 of V1. Whole-cell recordings in cortical slices from NrCAM-null mice revealed increased frequency of mEPSCs in star pyramidal neurons. Recombinant Sema3F-Fc protein induced spine retraction on apical dendrites of wild-type, but not NrCAM-null cortical neurons in culture, while re-expression of NrCAM rescued the spine retraction response. NrCAM formed a complex in brain with Sema3F receptor subunits Neuropilin-2 (Npn-2) and PlexinA3 (PlexA3) through an Npn-2-binding sequence (TARNER) in the extracellular Ig1 domain. A trans heterozygous genetic interaction test demonstrated that Sema3F and NrCAM pathways interacted in vivo to regulate spine density in star pyramidal neurons. These findings reveal NrCAM as a novel postnatal regulator of dendritic spine density in cortical pyramidal neurons, and an integral component of the Sema3F receptor complex. The results implicate NrCAM as a contributor to excitatory/inhibitory balance in neocortical circuits.

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

Understanding the genetic basis of cognitive traits could aid the development of numeracy and literacy skills in children. Here the authors show that reading and mathematics have a large overlapping genetic component and suggest that a child's learning environment has a key role in creating differences between them.

Are 22q11.2 distal deletions associated with math difficulties?

Approximately 6% of school-aged children have math difficulties (MD). A neurogenetic etiology has been suggested due to the presence of MD in some genetic syndromes such as 22q11.2DS. However, the contribution of 22q11.2DS to the MD phenotype has not yet been investigated. This is the first population-based study measuring the frequency of 22q11.2DS among school children with MD. Children (1,564) were identified in the schools through a screening test for language and math. Of these children, 152 (82 with MD and 70 controls) were selected for intelligence, general neuropsychological, and math cognitive assessments and for 22q11.2 microdeletion screening using MLPA. One child in the MD group had a 22q11.2 deletion spanning the LCR22-4 to LCR22-5 interval. This child was an 11-year-old girl with subtle anomalies, normal intelligence, MD attributable to number sense deficit, and difficulties in social interactions. Only 19 patients have been reported with this deletion. Upon reviewing these reports, we were able to characterize a new syndrome, 22q11.2 DS (LCR22-4 to LCR22-5), characterized by prematurity; pre- and postnatal growth restriction; apparent hypotelorism, short/upslanting palpebral fissures; hypoplastic nasal alae; pointed chin and nose; posteriorly rotated ears; congenital heart defects; skeletal abnormalities; developmental delay, particularly compromising the speech; learning disability (including MD, in one child); intellectual disability; and behavioral problems. These results suggest that 22q11.2 DS (LCR22-4 to LCR22-5) may be one of the genetic causes of MD.

A genome wide association study of mathematical ability reveals an association at chromosome 3q29, a locus associated with autism and learning difficulties: a preliminary study

Mathematical ability is heritable, but few studies have directly investigated its molecular genetic basis. Here we aimed to identify specific genetic contributions to variation in mathematical ability. We carried out a genome wide association scan using pooled DNA in two groups of U.K. samples, based on end of secondary/high school national academic exam achievement: high (n = 419) versus low (n = 183) mathematical ability while controlling for their verbal ability. Significant differences in allele frequencies between these groups were searched for in 906,600 SNPs using the Affymetrix GeneChip Human Mapping version 6.0 array. After meeting a threshold of p<1.5×10⁻⁵, 12 SNPs from the pooled association analysis were individually genotyped in 542 of the participants and analyzed to validate the initial associations (lowest p-value 1.14 ×10⁻⁶). In this analysis, one of the SNPs (rs789859) showed significant association after Bonferroni correction, and four (rs10873824, rs4144887, rs12130910 rs2809115) were nominally significant (lowest p-value 3.278 × 10⁻⁴). Three of the SNPs of interest are located within, or near to, known genes (FAM43A, SFT2D1, C14orf64). The SNP that showed the strongest association, rs789859, is located in a region on chromosome 3q29 that has been previously linked to learning difficulties and autism. rs789859 lies 1.3 kbp downstream of LSG1, and 700 bp upstream of FAM43A, mapping within the potential promoter/regulatory region of the latter. To our knowledge, this is only the second study to investigate the association of genetic variants with mathematical ability, and it highlights a number of interesting markers for future study.

Why do spatial abilities predict mathematical performance?

Spatial ability predicts performance in mathematics and eventual expertise in science, technology and engineering. Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics. Understanding the nature of this association can inform educational practices and intervention for mathematical underperformance. Using data on two aspects of spatial ability and three domains of mathematical ability from 4174 pairs of 12-year-old twins, we examined the relative genetic and environmental contributions to variation in spatial ability and to its relationship with different aspects of mathematics. Environmental effects explained most of the variation in spatial ability (~70%) and in mathematical ability (~60%) at this age, and the effects were the same for boys and girls. Genetic factors explained about 60% of the observed relationship between spatial ability and mathematics, with a substantial portion of the relationship explained by common environmental influences (26% and 14% by shared and non-shared environments respectively). These findings call for further research aimed at identifying specific environmental mediators of the spatial-mathematics relationship.

KIAA0319 and ROBO1: evidence on association with reading and pleiotropic effects on language and mathematics abilities in developmental dyslexia

Substantial heritability has been reported for developmental dyslexia (DD), and KIAA0319 and ROBO1 appear as more than plausible candidate susceptibility genes for this developmental disorder. Converging evidence indicates that developmental difficulties in oral language and mathematics can predate or co-occur with DD, and substantial genetic correlations have been found between these abilities and reading traits. In this study, we explored the role of eight single-nucleotide polymorphisms spanning within KIAA0319 and ROBO1 genes, and DD as a dichotomic trait, related neuropsychological phenotypes and comorbid language and mathematical (dis)abilities in a large cohort of 493 Italian nuclear families ascertained through a proband with a diagnosis of DD. Marker-trait association was analyzed by implementing a general test of family-based association for quantitative traits (that is, the Quantitative Transmission Disequilibrium Test, version 2.5.1). By providing evidence for significant association with mathematics skills, our data add further result in support of ROBO1 contributing to the deficits in DD and its correlated phenotypes. Taken together, our findings shed further light into the etiologic basis and the phenotypic complexity of this developmental disorder.

Why do we differ in number sense? Evidence from a genetically sensitive investigation

Basic intellectual abilities of quantity and numerosity estimation have been detected across animal species. Such abilities are referred to as 'number sense'. For human species, individual differences in number sense are detectable early in life, persist in later development, and relate to general intelligence. The origins of these individual differences are unknown. To address this question, we conducted the first large-scale genetically sensitive investigation of number sense, assessing numerosity discrimination abilities in 837 pairs of monozygotic and 1422 pairs of dizygotic 16-year-old twin pairs. Univariate genetic analysis of the twin data revealed that number sense is modestly heritable (32%), with individual differences being largely explained by non-shared environmental influences (68%) and no contribution from shared environmental factors. Sex-Limitation model fitting revealed no differences between males and females in the etiology of individual differences in number sense abilities. We also carried out Genome-wide Complex Trait Analysis (GCTA) that estimates the population variance explained by additive effects of DNA differences among unrelated individuals. For 1118 unrelated individuals in our sample with genotyping information on 1.7 million DNA markers, GCTA estimated zero heritability for number sense, unlike other cognitive abilities in the same twin study where the GCTA heritability estimates were about 25%. The low heritability of number sense, observed in this study, is consistent with the directional selection explanation whereby additive genetic variance for evolutionary important traits is reduced.

Genome-wide association study of receptive language ability of 12-year-olds

PURPOSE

Researchers have previously shown that individual differences in measures of receptive language ability at age 12 are highly heritable. In the current study, the authors attempted to identify some of the genes responsible for the heritability of receptive language ability using a genome-wide association approach.

METHOD

The authors administered 4 Internet-based measures of receptive language (vocabulary, semantics, syntax, and pragmatics) to a sample of 2,329 twelve-year-olds for whom DNA and genome-wide genotyping were available. Nearly 700,000 single-nucleotide polymorphisms (SNPs) and 1 million imputed SNPs were included in a genome-wide association analysis of receptive language composite scores.

RESULTS

No SNP associations met the demanding criterion of genome-wide significance that corrects for multiple testing across the genome ( p < 5 × 10 -8). The strongest SNP association did not replicate in an additional sample of 2,639 twelve-year-olds.

CONCLUSIONS

These results indicate that individual differences in receptive language ability in the general population do not reflect common genetic variants that account for more than 3% of the phenotypic variance. The search for genetic variants associated with language skill will require larger samples and additional methods to identify and functionally characterize the full spectrum of risk variants.

Epigenetic analysis of neurocognitive development at 1 year of age in a community-based pregnancy cohort

Multiple studies show that molecular genetic changes and epigenetic modifications affect the risk of cognitive disability or impairment. However, the role of epigenetic variation in cognitive development of neurotypical young children remains largely unknown. Using data from a prospective, community-based study of mother-infant pairs, we investigated the association of DNA methylation patterns in neonatal umbilical cord blood with cognitive and language development at 1 year of age. No CpG loci achieved genome-wide significance, although a small number of weakly suggestive associations with Bayley-III Receptive Communication scales were noted. While umbilical cord blood is a convenient resource for genetic analyses of birth outcomes, our results do not provide conclusive evidence that its use for DNA methylation profiling yields epigenetic markers that are directly related to postnatal neurocognitive outcomes at 1 year of age.

Curious cases: Altered dose-response relationships in addiction genetics

Dose-response relationships for most addictive substances are "inverted U"-shaped. Addictive substances produce both positive features that include reward, euphoria, anxiolysis, withdrawal-relief, and negative features that include aversion, dysphoria, anxiety and withdrawal symptoms. A simple model differentially associates ascending and descending limbs of dose-response curves with rewarding and aversive influences, respectively. However, Diagnostic and Statistical Manual (DSM) diagnoses of substance dependence fail to incorporate dose-response criteria and don't directly consider balances between euphoric and dysphoric drug effects. Classical genetic studies document substantial heritable influences on DSM substance dependence. Linkage and genome-wide association studies identify modest-sized effects at any locus. Nevertheless, clusters of SNPs within selected genes display 10(-2)>p>10(-8) associations with dependence in many independent samples. For several of these genes, evidence for cis-regulatory, level-of-expression differences supports the validity of mouse models in which levels of expression are also altered. This review documents surprising, recently defined cases in which convergent evidence from humans and mouse models supports central influences of altered dose-response relationships in mediating the impact of relevant genomic variation on addiction phenotypes. For variation at loci for the α5 nicotinic acetylcholine receptor, cadherin 13, receptor type protein tyrosine phosphatase Δ and neuronal cell adhesion molecule genes, changed dose-response relationships conferred by gene knockouts in mice are accompanied by supporting human data. These observations emphasize desirability of carefully elucidating dose-response relationships for both rewarding and aversive features of abused substances wherever possible. They motivate consideration of individual differences in dose-response relationships in addiction nosology and therapeutics.

New insights into the genetic mechanism of IQ in autism spectrum disorders

Autism spectrum disorders (ASD) comprise a number of underlying sub-types with various symptoms and presumably different genetic causes. One important difference between these sub-phenotypes is IQ. Some forms of ASD such as Asperger’s have relatively intact intelligence while the majority does not. In this study, we explored the role of genetic factors that might account for this difference. Using a case–control study based on IQ status in 1657 ASD probands, we analyzed both common and rare variants provided by the Autism Genome Project (AGP) consortium via dbGaP (database of Genotypes and Phenotypes). We identified a set of genes, among them HLA-DRB1 and KIAA0319L, which are strongly associated with IQ within a population of ASD patients.

Genetic and environmental contributions to brain activation during calculation

Twin studies have long suggested a genetic influence on inter-individual variations in mathematical abilities, and candidate genes have been identified by genome-wide association studies. However, the localization of the brain regions under genetic influence during number manipulation is still unexplored. Here we investigated fMRI data from a group of 19 MZ (monozygotic) and 13 DZ (dizygotic) adult twin pairs, scanned during a mental calculation task. We examined both the activation and the degree of functional lateralization in regions of interest (ROIs) centered on the main activated peaks. Heritability was first investigated by comparing the respective MZ and DZ correlations. Then, genetic and environmental contributions were jointly estimated by fitting a ACE model classically used in twin studies. We found that a subset of the activated network was under genetic influence, encompassing the bilateral posterior superior parietal lobules (PSPL), the right intraparietal sulcus (IPS) and a left superior frontal region. An additional region of the left inferior parietal cortex (IPC), whose deactivation correlated with a behavioral calculation score, also presented higher similarity between MZ than between DZ twins, thus offering a plausible physiological basis for the observable inheritance of math scores. Finally, the main impact of the shared environment was found in the lateralization of activation within the intraparietal sulcus. These maps of genetic and environmental contributions provide precise candidate phenotypes for further genetic association analyses, and illuminate how genetics and education shape the development of number processing networks.

Twins Early Development Study (TEDS): a genetically sensitive investigation of cognitive and behavioral development from childhood to young adulthood

The Twins Early Development Study (TEDS) is a large longitudinal sample of twins born in England and Wales between 1994 and 1996. The focus of TEDS has been on cognitive and behavioral development, including difficulties in the context of normal development. TEDS began when multiple births were identified from birth records and the families were invited to take part in the study; 16,810 pairs of twins were originally enrolled in TEDS. More than 10,000 of these twin pairs remain enrolled in the study to date. DNA has been collected for more than 7,000 pairs, and genome-wide genotyping data for two million DNA markers are available for 3,500 individuals. The TEDS families have taken part in studies when the twins were aged 2, 3, 4, 7, 8, 9, 10, 12, 14, and 16 years of age. Data collection is currently underway to assess the adult destinations of the twins as they move from school to university and the workplace. Between January 2012 and December 2014, all of the TEDS twins will turn 18, and the study will transition to an adult sample. TEDS represents an outstanding resource for investigating the developmental effects of genes and environments on complex quantitative traits from childhood to young adulthood and beyond.

A common variant in myosin-18B contributes to mathematical abilities in children with dyslexia and intraparietal sulcus variability in adults

The ability to perform mathematical tasks is required in everyday life. Although heritability estimates suggest a genetic contribution, no previous study has conclusively identified a genetic risk variant for mathematical performance. Research has shown that the prevalence of mathematical disabilities is increased in children with dyslexia. We therefore correlated genome-wide data of 200 German children with spelling disability, with available quantitative data on mathematic ability. Replication of the top findings in additional dyslexia samples revealed that rs133885 was a genome-wide significant marker for mathematical abilities (P(comb) = 7.71 × 10(-10), n = 699), with an effect size of 4.87%. This association was also found in a sample from the general population (P = 0.048, n = 1080), albeit with a lower effect size. The identified variant encodes an amino-acid substitution in MYO18B, a protein with as yet unknown functions in the brain. As areas of the parietal cortex, in particular the intraparietal sulcus (IPS), are involved in numerical processing in humans, we investigated whether rs133885 was associated with IPS morphology using structural magnetic resonance imaging data from 79 neuropsychiatrically healthy adults. Carriers of the MYO18B risk-genotype displayed a significantly lower depth of the right IPS. This validates the identified association between rs133885 and mathematical disability at the level of a specific intermediate phenotype.

MMPs and soluble ICAM-5 increase neuronal excitability within in vitro networks of hippocampal neurons

Matrix metalloproteinases (MMPs) are zinc-dependent endopeptidases that are released from neurons in an activity dependent manner. Published studies suggest their activity is important to varied forms of learning and memory. At least one MMP can stimulate an increase in the size of dendritic spines, structures which represent the post synaptic component for a large number of glutamatergic synapses. This change may be associated with increased synaptic glutamate receptor incorporation, and an increased amplitude and/or frequency of α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) mini excitatory post-synaptic currents (EPSCs). An associated increase in the probability of action potential occurrence would be expected. While the mechanism(s) by which MMPs may influence synaptic structure and function are not completely understood, MMP dependent shedding of specific cell adhesion molecules (CAMs) could play an important role. CAMs are ideally positioned to be cleaved by synaptically released MMPs, and shed N terminal domains could potentially interact with previously unengaged integrins to stimulate dendritic actin polymerization with spine expansion. In the present study, we have used multielectrode arrays (MEAs) to investigate MMP and soluble CAM dependent changes in neuronal activity recorded from hippocampal cultures. We have focused on intercellular adhesion molecule-5 (ICAM-5) in particular, as this CAM is expressed on glutamatergic dendrites and shed in an MMP dependent manner. We show that chemical long-term potentiation (cLTP) evoked changes in recorded activity, and the dynamics of action potential bursts in particular, are altered by MMP inhibition. A blocking antibody to β₁ integrins has a similar effect. We also show that the ectodomain of ICAM-5 can stimulate β₁ integrin dependent increases in spike counts and burst number. These results support a growing body of literature suggesting that MMPs have important effects on neuronal excitability. They also support the possibility that MMP dependent shedding of specific synaptic CAMs can contribute to these effects.

Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years.

The Imaging and Cognition Genetics Conference 2011, ICG 2011: A Meeting of Minds

In June 2011, 70 researchers from the disciplines of cognitive science, genetics, psychology, psychiatry, neurobiology, and computer science gathered in Os, Norway, for the first Imaging and Cognition Genetics meeting. The aim of the conference was to discuss progress, enhance collaboration, and maximize the sharing of resources within this new field. In this Perspective, we summarize the major themes that emerged from ICG 2011. The first is the importance of defining cognitive and imaging phenotypes and endophenotypes suitable for genetic analysis. These can come from differential psychology, cognitive science, structural MRI, tractography, and functional imaging. The second theme is the emergence of new methods for the analysis of complex traits. These include advanced computational and statistical techniques for analyzing complex datasets, and new ways of interpreting data from genome-wide association studies, such as jointly evaluating the contribution of SNPs in specific genes and pathways rather than considering single SNPs in isolation. The final theme is the importance of establishing functional correlates of newly identified genetic variants.

Child development and molecular genetics: 14 years later

Fourteen years ago, the first article on molecular genetics was published in this journal: Child Development, Molecular Genetics, andWhat to Do With Genes Once They Are Found (R. Plomin & M. Rutter, 1998). The goal of the article was to outline what developmentalists can do with genes once they are found. These new directions for developmental research are still relevant today. The problem lies with the phrase “once they are found”: It has been much more difficult than expected to identify genes responsible for the heritability of complex traits and common disorders, the so-called missing heritability problem. The present article considers reasons for the missing heritability problem and possible solutions.

The role of NrCAM in neural development and disorders--beyond a simple glue in the brain

NrCAM is a neuronal cell adhesion molecule of the L1 family of immunoglobulin super family. It plays a wide variety of roles in neural development, including cell proliferation and differentiation, axon growth and guidance, synapse formation, and the formation of the myelinated nerve structure. NrCAM functions in cell adhesion and modulates signaling pathways in neural development through multiple molecular interactions with guidance and other factors. Alterations in NrCAM structure/expression are associated with psychiatric disorders such as autism and drug addiction and with tumor progression. The mechanisms of NrCAM participation in development and how these might be perturbed in disorders are reviewed.

Understanding Heritability: What it is and What it is Not

Commentators generally found our exposition of the concept of heritability helpful for psychologists, suggesting that we largely accomplished our primary goal. Many provided supplemental and helpful perspectives on concepts we addressed. A few of the comments indicated that we may not have been completely successful in making clear our secondary goal, which was to outline how heritability estimates confound a plethora of influences. In this response, we thus emphasize that we do not claim that specific kinds of complexity, or, even worse, intractable complexity, pervade the genetics of behavioural traits. Rather, our claim is that genetics is riddled with complexity of many degrees and kinds, and heritability is a poor indicator of either degree or kind of underlying genetic complexity. Copyright © 2011 John Wiley & Sons, Ltd.