The parental feeding practices (PFPs) of excessive restriction of food intake (‘restriction’) and pressure to increase food consumption (‘pressure’) have been argued to causally influence child weight in opposite directions (high restriction causing overweight; high pressure causing underweight). However child weight could also ‘elicit’ PFPs. A novel approach is to investigate gene-environment correlation between child genetic influences on BMI and PFPs. Genome-wide polygenic scores (GPS) combining BMI-associated variants were created for 10,346 children (including 3,320 DZ twin pairs) from the Twins Early Development Study using results from an independent genome-wide association study meta-analysis. Parental ‘restriction’ and ‘pressure’ were assessed using the Child Feeding Questionnaire. Child BMI standard deviation scores (BMI-SDS) were calculated from children’s height and weight at age 10. Linear regression and fixed family effect models were used to test between- (n = 4,445 individuals) and within-family (n = 2,164 DZ pairs) associations between the GPS and PFPs. In addition, we performed multivariate twin analyses (n = 4,375 twin pairs) to estimate the heritabilities of PFPs and the genetic correlations between BMI-SDS and PFPs. The GPS was correlated with BMI-SDS (β = 0.20, p = 2.41x10 -38 ). Consistent with the gene-environment correlation hypothesis, child BMI GPS was positively associated with ‘restriction’ (β = 0.05, p = 4.19x10 -4 ), and negatively associated with ‘pressure’ (β = -0.08, p = 2.70x10 -7 ). These results remained consistent after controlling for parental BMI, and after controlling for overall family contributions (within-family analyses). Heritabilities for ‘restriction’ (43% [40–47%]) and ‘pressure’ (54% [50–59%]) were moderate-to-high. Twin-based genetic correlations were moderate and positive between BMI-SDS and ‘restriction’ (r A = 0.28 [0.23–0.32]), and substantial and negative between BMI-SDS and ‘pressure’ (r A = -0.48 [-0.52 - -0.44]. Results suggest that the degree to which parents limit or encourage children’s food intake is partly influenced by children’s genetic predispositions to higher or lower BMI. These findings point to an evocative gene-environment correlation in which heritable characteristics in the child elicit parental feeding behaviour.

It is widely believed that parents influence their child’s BMI via certain feeding practices. For example, rigid restriction has been argued to cause overweight, and pressuring to eat to cause underweight. However, recent longitudinal research has not supported this model. An alternative hypothesis is that child BMI, which has a strong genetic basis, evokes parental feeding practices (‘gene-environment correlation’). To test this, we applied two genetic methods in a large sample of 10-year-old children from the Twins Early Development Study: a polygenic score analysis (DNA-based score of common genetic variants associated with BMI in genome-wide meta-analyses), and a twin analysis (comparing resemblance between identical and non-identical twin pairs). Polygenic scores correlated positively with parental restriction of food intake (‘restriction’; β = 0.05, p = 4.19x10 -4 ), and negatively with parental pressure to increase food intake (‘pressure’; β = -0.08, p = 2.70x10 -7 ). Associations were unchanged after controlling for all genetic and environmental effects shared within families. Results from twin analyses were consistent. ‘Restriction’ (43%) and ‘pressure’ (54%) were substantially heritable, and a positive genetic correlation between child BMI and ‘restriction’ (r A = 0.28), and negative genetic correlation between child BMI and ‘pressure’ (r A = -0.48) emerged. These findings challenge the prevailing view that parental behaviours are the sole cause of child BMI by supporting an alternate hypothesis that child BMI also causes parental feeding behaviour.

Funding: We gratefully acknowledge the ongoing contribution of the participants in the Twins Early Development Study (TEDS) and their families. TEDS is supported by a program grant to RP from the UK Medical Research Council (MR/M021475/1 and previously G0901245), with additional support from the US National Institutes of Health (AG046938). The research leading to these results has also received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ grant agreement n° 602768 and ERC grant agreement n° 295366. RP is supported by a Medical Research Council Professorship award (G19/2). SS is supported by the MRC/IoPPN Excellence Award and by the US National Institutes of Health (AG046938). High performance computing facilities were funded with capital equipment grants from the GSTT Charity (TR130505) and Maudsley Charity (980). TAM is supported by a Sir Henry Dale Fellowship, jointly funded by the Wellcome Trust and the Royal Society (107706/Z/15/Z). This study represents independent research part-funded by the National Institute for Health Research (NIHR) Biomedical Research Centre at South London and Maudsley NHS Foundation Trust and King’s College London. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. High performance computing facilities were funded with capital equipment grants from the GSTT Charity (TR130505) and Maudsley Charity (980). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data Availability: The dataset analysed during the current study is restricted due to participant confidentially. Restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. The Twins Early Development Study is a third party that owns the data, and information about data access is available here: https://www.teds.ac.uk/research/collaborators-and-data/teds-data-access-policy . Requests should be made via the data request form supplied, which are then reviewed by the TEDS Executive committee. Data will be made available on request to interested researchers in the same fashion in which it was made available to the authors, allowing data sharing for novel collaborations leading to new publications.

The goals of this study were to test for gene-environment correlation between children’s BMI and PFPs, using a twin design and a BMI GPS. We hypothesised that: (i) children’s BMI GPS would be positively associated with parental restriction and negatively associated with parental pressure, even after accounting for shared genetic and environmental family influences; and (ii) parental restriction and parental pressure would be moderately heritable, and that genetic influence on PFPs would be partly explained by genetic influence on children’s BMI.

Children’s DNA can also be used to test for gene-environment correlation. Genome-wide meta-analyses have made great progress in identifying common single nucleotide polymorphisms (SNPs) that are associated with body mass index (BMI) in adults and children[ 19 ]. These can be combined to calculate a genome-wide polygenic score (GPS) that indexes individual-specific propensity to higher or lower BMI, along a continuum, although in the aggregate the GPS explains only a small proportion of variance in BMI (approximately 3%)[ 20 ]. Nevertheless, children’s BMI GPS can therefore be used to test the hypothesis that parents develop their feeding practices specifically in response to their child’s weight, as indicated by a correlation between child BMI GPS and PFPs. A caveat to this is that a parent’s feeding practices may reflect their own genetic predisposition to be of a higher or lower BMI, rather than that of their children. In this way, a correlation between child BMI GPS and PFPs may simply reflect a child’s genetic predisposition to be of a higher or lower BMI, which they inherit from their parent with whom they share 50% of their DNA. In addition, genetic effects related to adult BMI discovered in genome-wide association studies could potentially incorporate effects of PFPs if they were to causally influence child BMI, and its trajectory into adulthood. However, within-family designs can circumvent both of these limitations to some extent. Studying variation in PFPs according to variation in BMI GPS within non-identical co-twins accounts for both genetic and environmental shared effects within families (e.g. parental genetic predisposition to be of higher or lower BMI). By applying both quantitative and molecular genetic methods, and utilising statistical approaches to account for shared family effects, we intended to address the various limitations presented by the individual methods.

Testing whether children genuinely cause their parents’ behaviour presents challenges. It is not possible–practically or ethically–to randomise children to have overweight or underweight, and examine how parents respond. Genetic approaches provide a powerful alternative method of interrogating the role of children in causing their parents’ behaviour towards them, especially for child characteristics with an established genetic basis. To date, no study has applied genetically sensitive methods to test for gene-environment correlation in parental feeding behaviour. Family and twin studies have shown that Body Mass Index (BMI), is highly heritable in both adulthood and late childhood (~70%)[ 14 – 16 ]. Twin designs can also be used to test if parental behaviour has a heritable component, by comparing within-pair resemblance for identical and fraternal twin pairs in childhood. If found, this indicates that parental behaviour is explained to some extent by variation in children’s genotype–termed evocative gene-environment correlation[ 17 ]. Twin designs can also be extended to the analysis of multiple variables to establish if genetic influence on a particular child characteristic (e.g. weight) also predicts the parental behaviour of interest (e.g. PFPs). If such analyses show that a child characteristic is genetically correlated with parenting traits, it indicates that these child characteristics influence parenting behaviours. A meta-analysis of 32 twin studies of different types of parenting behaviour reported an average heritability estimate of 24%, indicating that children’s genotype is predictive of a moderate amount of variation in parental behaviour[ 18 ].

A wealth of cross-sectional findings are consistent with these hypotheses[ 8 ], but another plausible explanation for the observed correlations is that parents are responding to their child’s emerging characteristics, not simply causing them. Parents may only adopt restrictive strategies when a child shows a tendency toward overeating, or gains excessive weight; and they may pressure their child to eat only if he or she is a poor eater, or has underweight. The few longitudinal studies testing bidirectionality have shown that children’s weight prospectively predicts PFPs[ 9 – 13 ]. Furthermore, three studies showed no prospective association from PFPs to child weight[ 10 ], and the studies reporting bidirectional relationships found stronger associations from child weight to parental behaviour than the reverse direction[ 9 , 11 ]. Although these findings point towards children’s weight eliciting PFPs, the possibility of residual confounding in observational studies hinders conclusions about causation–temporality does not necessarily mean causality.

The home and family environment has been studied for decades with the assumption that it is a crucial determinant of children’s health and development. Since the onset of the childhood obesity crisis at the turn of the century, the spotlight has turned onto environmental factors associated with variation in adiposity, in the hope that modifiable elements may be identified as intervention targets. Perhaps unsurprisingly, parental behaviours have received a great deal of attention. Parents are widely considered to be the ‘gatekeepers’ to their children’s food, and powerful shapers of their developing eating behaviour[ 1 – 3 ]. Two types of parental feeding practices (PFPs) in particular have been hypothesised to play a causal role in children’s ability to develop good self-regulation of food intake and consequently determine their weight. Excessive restriction of the type and amount of food a child is allowed to eat (‘restriction’) has been hypothesised to lead to overeating when parental restriction is no longer in place, because the child will potentially then hanker after the foods he or she is not usually allowed to eat–the so-called ‘forbidden fruit effect’[ 1 , 4 , 5 ]. On the other hand, overly pressuring a child to eat, or to finish everything on the plate (‘pressure’), is thought to be anxiety-provoking for a child with a poor appetite, and serves only to increase undereating further, and compromise weight gain[ 6 , 7 ].

As shown in the twin analyses ( Fig 3 and Supplementary S3 Table ), variation in child BMI-SDS is partly caused by non-shared environmental influences, which correlate significantly with non-shared environmental influences for ‘restriction’ (r E = 0.20) and ‘pressure’ (r E = -0.29). We therefore performed MZ twin difference analyses to examine these relationships more closely. In contrast to child BMI-SDS MZ difference scores, most twins did not differ in their PFP (Supplementary S1 Fig ). Nevertheless, we found that child BMI-SDS difference scores predicted both differences in ‘restriction’ (β = 0.14, t(1484) = 7.98, p = 2.88x10 -15 , R 2 = 0.041) and ‘pressure’ (β = -0.25, t(1498) = -12.26, p = 5.12x10 -33 , R 2 = 0.09). These findings suggest that there are common non-shared environmental sources of variance for both PFP and child BMI; within identical twin pairs who share 100% of their genetic and shared environmental influence, parents apply more restrictive feeding practices on the twin with the higher BMI, and more pressuring feeding practices on the twin with the lower BMI score.

We performed multivariate genetic analyses (a correlated factors model) to establish the heritability of ‘restriction’ and ‘pressure’ and to test the extent to which genetic influence on child BMI-SDS elicited PFPs as indicated by the magnitude of genetic correlations between BMI, ‘restriction’, and ‘pressure’. Fig 3 shows the variance components (A, C and E) for each measured phenotype, as well as the genetic, shared environmental and non-shared environmental correlations between phenotypes derived from the correlated factors model (see Supplementary S1 Table for fit statistics and model comparisons, and Supplementary S2 Table for intra-class correlations). Heritability estimates (A) were moderate to high for parental ‘restriction’ (43%, 95% CI [40%, 47%]) and parental ‘pressure’ (54%, 95% CI [50%, 59%]); heritability of child BMI-SDS was high (78%, 95% CI [72%, 84%]). Consistent with the findings from the GPS analyses, there was a significant, positive moderately sized genetic correlation between child BMI-SDS and parental ‘restriction’ (r A = 0.28, 95% CI [0.23, 0.32]), indicating that some of the genetic effects that predispose a child to a higher BMI also elicit more food restriction by their parent. A sizeable significant negative genetic correlation was observed between child BMI-SDS and parental ‘pressure’ (r A = -0.48, 95% CI [-0.52, -0.44]), indicating that many of the genetic effects that predispose a child to a lower BMI elicit greater parental pressure on the child to eat.

Model 1 describes results using BMI GPS of unrelated individuals to predict PFPs, where β GPS indicates the change in the outcome trait per one standard deviation increase in the BMI GPS. Model 2 summarises results using BMI genome-wide polygenic scores in a sample of DZ co-twins using a family fixed-effects model, where β GPS indicates the increase in PFPs within DZ pairs, per one standard deviation increase in BMI GPS within DZ pairs. Model 2 analyses were performed using the combined DZ sample, and same-sex DZ pairs and opposite-sex DZ pairs only. The dotted lines represent the beta coefficient estimates for Model 1. * = p<0.05; ** = p<0.01; *** = p<0.001.

To establish the association between children’s BMI GPS and PFPs entirely without confounding by genetic and environmental family factors shared by twin pairs, we performed family fixed-effect analyses in dizygotic (DZ) co-twins. This analysis examined the extent to which parents vary their ‘restriction’ and ‘pressure’ across twin pairs in response to differences in their BMI GPS. As shown in Fig 2 , beta coefficients for BMI GPS predicting PFPs remained largely stable when comparing unrelated individuals (Model 1) and DZ twin pairs (Model 2). For unrelated individuals (Model 1) child BMI-SDS significantly positively predicted ‘restriction’ and significantly negatively predicted ‘pressure’, as previously reported. The magnitude of the within-family estimates for the combined (same-sex and opposite-sex) DZ co-twins (Model 2) were virtually the same as those for the unrelated individuals for the relationships between BMI GPS and ‘restriction’ (t(2054) = 3.50, p = 7.10x10 -3 , Adj. R 2 model = 0.724) and BMI GPS and ‘pressure’ (t(2103) = -4.82, p = 1.52x10 -6 , Adj. R 2 model = 0.641) (R 2 magnitudes for Model 2 are large because all shared factors among family members, including genetic and environmental influences, are accounted for). These findings indicate that even when shared family effects are completely accounted for, children’s BMI GPS is significantly associated with PFPs, providing additional evidence that children’s genetic predisposition to BMI evokes certain parental feeding responses. When repeating Model 2 analyses separately for same-sex and opposite-sex DZs, magnitudes of effect sizes ( Fig 2 ) remained consistent for the prediction of ‘pressure’ in same-sex DZ pairs (t(1118) = -3.36, p = 8.02x10 -4 , Adj. R 2 model = 0.607) and opposite-sex DZ pairs (t(984) = -3.49, p = 5.12x10 -4 , Adj. R 2 model = 0.678). Although BMI GPS in opposite-sex DZs was a significant predictor of within-family differences in ‘restriction’ (t(966) = 3.76, p = 1.82x10 -4 , Adj. R 2 model = 0.731), same-sex DZ data did not show a significant within-family association (t(1087) = 1.21, p = 0.23, Adj. R 2 model = 0.719), indicating that within a family environment, GPS differences in BMI between same-sex DZ twins are not related to differences in parental ‘restriction’.

Child BMI-SDS was significantly positively correlated with ‘restriction’ (β = 0.19, t(4004) = 12.09, p = 4.45x10 -33 , R 2 = 0.035), such that parents were more restrictive over their child’s food intake if the child had a higher BMI. In contrast, child BMI-SDS was significantly negatively correlated with ‘pressure’ (β = -0.24, t(4058) = -15.59, p = 3.14x10 -53 , R 2 = 0.056), such that parents exerted higher amounts of pressure on their child to eat, if their child was leaner. ‘Restriction’ and ‘pressure’ were significantly positively correlated (β = 0.15, t(4207) = 9.51, p = 3.08x10 -21 , R 2 = 0.021), suggesting that parents who tend to exert higher levels of ‘restriction’ also exert a more pressuring feeding style, to some extent.

Discussion

Summary of findings We describe the first study to test for gene-environment correlation for parental feeding behaviour in relation to child weight, using a twin design and children’s DNA. Results support our hypothesis that parents’ feeding practices are evoked, in part, by their children. Parental ‘restriction’ and ‘pressure’ were positively and negatively associated with child BMI respectively, in keeping with many previous cross-sectional studies[8]. We applied novel genetic methods to show, for the first time, that children’s BMI GPS was significantly positively associated with ‘restriction’ and negatively associated with ‘pressure’, even after accounting for the potentially confounding shared familial effects (both genetic and environmental). This suggests that children’s genetic influence on weight explains part of the observed phenotypic associations. Our twin analysis provided quantitative estimates of the total variance in parental feeding practices explained by children’s genotype. Heritability was substantial for both ‘restriction’ (43%) and ‘pressure’ (54%), indicating that children’s genes explain about half of the variation in parental feeding behaviour. Multivariate twin analysis established the extent to which parental feeding behaviour was determined by children’s genetic influence on BMI specifically. The genetic correlations between children’s BMI and both ‘restriction’ (r A = 0.28) and pressure (r A = -0.48) were moderate, indicating overlap between the genes that influence parental feeding behaviour and children’s BMI. A potential confounder of the association between child GPS and parental feeding behaviour, was the parent’s own genetic propensity to a higher or lower BMI. Children inherit half of each of their parents’ genetic material, so the expected correlation between a child’s GPS with that of their parent’s is 0.50. A parent’s genetic predisposition to be of a higher or lower BMI may also influence the way they feed their children, which could introduce a passive (rather than ‘evocative’) gene-environment correlation. For example, a parent with a higher BMI may be more restrictive over their child’s food intake, but their child also inherits their parent’s susceptibility to be of a higher BMI. Restrictive feeding may therefore simply be a marker for a child’s genetic predisposition to be of a higher BMI that is transmitted to them by their parent, rather than a causal risk factor (the same could be true for a more pressuring feeding style and lower BMI). In line with this, parental BMI (indexing parental GPS) was significantly positively associated with parental restriction indicating that parents of a higher weight exert greater restriction over their children’s food intake (β = 0.08); although the association with parental pressure was not significant. Adjustment for parental BMI did not attenuate the associations between child GPS and either restriction or pressure, suggesting it was not confounding the relationship between parental feeding behaviour and child BMI GPS. Nevertheless, adjustment for parental BMI cannot completely remove confounding from parental BMI, nor can it account for the potential effect of longer-term BMI on parental feeding behaviours. However, in order to rule out confounding by any parental characteristics (both genetic and environmental), we took advantage of a family fixed-effect design, which held the effects of family constant while testing the association between the child BMI GPS and parental feeding practices in DZ co-twins. The within-family analysis allowed us to demonstrate that even after accounting for all genetic and environmental familial effects, parents vary their feeding behaviour for each child depending on their GPS–larger GPS differences between pairs were associated with more pronounced differences in parental feeding behaviour. The magnitudes of the between- and within-family associations between parental feeding behaviour and child GPS were virtually the same, with the exception of the relationship between child GPS and ‘restriction’ in same-sex twins, strengthening the evidence that children evoke parental responses based on their genetic predispositions for BMI. Nevertheless, as expected, and consistent with the small amount of variance explained in BMI by the GPS, the size of the associations between the BMI GPS and PFPs were small.

Other relevant research The findings from this study accord with those from twin studies of many other types of parenting behaviours that have also tended to show moderate heritability. A meta-analysis of 32 child twin studies on maternal positivity, negativity, affect and control in relation to parenting showed an average heritability of 24%[18], indicating widespread, child-driven genetic influences on parental behaviour. The heritability estimates for ‘restriction’ (43%) and ‘pressure’ (54%) were somewhat higher than the average heritability estimate for the parenting styles considered in the meta-analysis (24%), but in keeping with the magnitude of the heritability of negative parenting styles observed across early childhood (~55%)[21]. In addition to providing evidence for gene-environment correlation, results from the MZ discordance design also indicated that non-shared environmental influences for child BMI and PFPs are correlated as well. This suggests that child BMI and PFPs are also related due to common non-shared environmental influences. However, the MZ discordance design was not able to shed light on the causal direction–i.e. if child BMI causes PFPs or if PFPs cause child BMI–because our variables were measured at the same time. The few prospective studies that have attempted to establish the cause-effect relationship in the parent-child dynamic using bidirectional analyses have suggested either only a small effect of restriction and/or pressure on child weight, or none[9–11,13]. Prospective studies therefore suggest that PFPs may be less important than is commonly assumed. The well-established strong genetic influence on children’s weight–in the order of 70–80%[15,16]–also supports the hypothesis that parents influence child weight via genetic inheritance more than by creating an ‘obesogenic’ family environment. However, it cannot be ruled out that genetic effects related to BMI in the parents also contribute to an obesogenic environment if gene-environment correlation was at play, further passively reinforcing the child’s inherited genetic propensities. The shared environmental influence on BMI in late childhood is also low[15,16]. In the current study, the shared environmental influence on parental feeding behaviour was the proportion of variance that was common to both twins in a pair (invariant within families). It therefore likely reflects variation in feeding behaviour that was parent-driven rather than child-directed. These estimates indicated that a substantial proportion of variation in both ‘restriction’ (C = 43%) and ‘pressure’ (C = 37%) also originated in the parent. Experimental studies in the form of large well-designed randomised controlled trials (RCTs) are needed to truly test the hypothesis that PFPs causally modify children’s weight gain trajectories. Very few of these have been conducted to date, and they have focused on the preschool years. Nevertheless, two landmark studies have indicated that parental behaviour may, in fact, be influential in early life. NOURISH[22] was an Australian RCT that randomised 352 parents and infants to receive a feeding intervention (including using low amounts of pressure, and employing child-responsive methods of food restriction) during the period of complementary feeding; 346 families were randomised to the standard care control group. At three to four years of age, children in the intervention group had better appetite control than those in the control group, and there were fewer children with overweight; although this did not reach statistical significance[23]. INSIGHT[24], a US RCT, randomised 145 new mothers to a responsive parenting intervention that focused on feeding infants only in response to their hunger and satiety signals (but neither pressuring nor restricting their milk and food intake), during milk-feeding and complementary feeding; 145 mothers were randomised to a control group. At one year significantly fewer infants in the intervention group had overweight (6%) compared to the control group (13%). These RCTs indicate that parental feeding behaviour can modify young children’s eating behaviour and weight gain. However, these studies were conducted in infants and young preschool children so it is unclear whether these findings are generalisable to older children. The genetic correlations between children’s BMI and parental feeding behaviour were modest, and were far from complete (i.e. less than 1.0), indicating that other genetically-determined child characteristics are also influencing parental feeding behaviour. Children’s appetite is under strong genetic control; twin studies–including this sample–have shown high heritability for appetite[25,26] and shared heritability with BMI[27]. Appetite is associated with the BMI GPS in this sample and has been shown to mediate part of the GPS-BMI association[28]. It is therefore likely that child appetite also influences parental feeding behaviour[25,26]. In support of this, prospective and within-family studies have provided evidence that within the context of parental feeding, parents respond not only to their child’s weight but also to their eating styles. A large prospective population-based study used bidirectional analyses to show that parents whose children were excessively fussy at baseline increased their pressure over time[29]. A reverse relationship also pertained, but the temporal association from child to parent was stronger. A large within-family study of preschool twins showed that parents varied their pressuring feeding style when their twins were discordant for food fussiness[30]. The fussier twin was pressured more than their co-twin, also in support of a child-driven model of parental feeding behaviour. It stands to reason that a child who is a picky eater is pressured to try some of their vegetables or to eat more overall. Along the same lines, a natural response from a parent who has a child who shows a tendency toward excess intake and a relatively pronounced preference for foods rich in sugar or fat, is to enforce some restriction. We also found a positive phenotypic correlation between ‘restriction’ and ‘pressure’ (β = 0.15), indicating that parents who exert higher levels of restriction on their children also tend to pressure them more. This suggests that some parents have a more controlling feeding style in general.

Implications and future research The relationship between parental behaviour and children’s emerging characteristics appears to be reciprocal and complex. The current findings suggest that parents’ natural feeding responses to child weight are to exert greater restriction of food intake on children with a higher BMI, and to pressure a thinner child to eat. However, these strategies may not be effective in the long run. RCTs have suggested that PFPs can have a lasting and important impact on children’s weight and eating behaviour in the early years, although whether or not these findings apply to older children has yet to be determined. It is well established that genetic influence on BMI in younger children is lower, and the shared environmental effect is higher, than it is in older children[15,16]. This suggests that parental influence diminishes as children grow older, gain independence and spend increasing time outside the home with peers rather than parents[31]. Large RCTs that follow children from early life to later childhood are needed to establish if PFPs influence the weight of older children.

Strengths & limitations A strength of this study is that we used several genetically sensitive methodological approaches to explore the directionality of relationships between child BMI and PFPs, yielding consistent results. PFPs were measured using the Child Feeding Questionnaire, which has well established criterion and construct validity, as well as good internal and test-retest reliability[32]. This instrument has been used widely in previous research into child weight, allowing the findings from this study to be directly compared to a wealth of existing results. A potential limitation is that heritability estimates from twin studies rely on the assumption that MZs and DZs share their environment in terms of the trait in question to the same extent, so-called the ‘equal environments assumption’; if this is violated, the findings are invalid. Therefore if parents feed MZs more similarly than DZs simply because they are identical, this would artificially inflate the MZ correlation and, consequently, heritability. However, if MZs are fed more similarly than DZs because parents are responding to their genetically determined BMI or traits that share genetic influence with BMI such as appetite, differences in feeding experience across MZs and DZs do not constitute a violation of the equal environments assumption because these differences in feeding practices are being driven by greater genetic similarity between MZs than DZs. In addition, if parents’ reports of how similarly they fed their twins were biased by their perceived zygosity (i.e. reported treatment was not a true reflection of actual treatment, but related to the twins being MZ or DZ), this would also render the heritability estimates unreliable. However, this seems unlikely given previous findings that parents’ reports about their twins’ are not biased by their beliefs about their zygosity, using the ‘mistaken zygosity’ design[33]. Another limitation was the lack of parental genotypes assessments. Parental BMI is by no means a perfect proxy for their genotypic predisposition to higher or lower BMI; the most powerful approach would be to have parental genotypes whereby the non-transmitted alleles from the parents (which relate to their own BMI and behaviour, but not to that of their child) can be entirely separated from the child’s genotype[34]. Nevertheless, the within-family analysis controlled for all family-level genetic and environmental effects, and the magnitudes of the relationships between child BMI and PFPs were unaffected. A further limitation is that we were unable to validate self-reported parental BMI, which may have been inaccurate and could potentially bias our results. Additionally, it may be possible that PFPs are largely explained by environmental factors that influence children’s BMI. As the BMI GPS is not yet strong enough to be a sufficient proxy to separate genetic and environmental effects on child BMI, we were unable to test this question empirically. However, considerable genetic correlations between child BMI and PFPs derived from the twin model renders this explanation unlikely. Lastly, BMI was only reported at one time point, but PFPs are likely to be driven by the child’s emerging BMI throughout the developmental years. However, BMI-associated SNPs and BMI GPS are associated with weight gain trajectories from infancy throughout childhood, so the BMI GPS in fact captures a long window of child BMI[14,35].