Our results show that ETFDs work as designed. They are generally unbiased when assumptions are met, and unlike the CTD, they are not overly sensitive to violations of assumptions so long as D
is interpreted broadly, as an estimate of genetic non-additivity in general (including gene-by-age interaction effects) rather than as dominance in particular. Our results also highlight that the key trade-off in using ETFDs is one of complexity versus accuracy. By attempting to estimate a large number of parameters, many of which use overlapping information, the precision of ETFD estimates suffers (see the full ETFD model estimates in – and parameter covariances in ). The ETFD estimates in , for example, are much less precise than those from the CTD. Nevertheless, ETFD estimates tend to be unbiased under a much wider range of scenarios than CTD estimates, and because of this, are almost universally more accurate than are CTD estimates. This improved accuracy can be quantified by empirical researchers using ETFDs by comparing a goodness of fit index of an ETFD only estimating a few parameters (e.g., A
, and E
) versus an ETFD estimating all parameters. The difference between these two fit indices provides an idea of how important using an ETFD is over a simpler model (e.g., the CTD) given the phenotype in question.
The trend of increasing accuracy with increasing complexity repeats itself within the ETFD models: Stealth
estimates are accurate across a wider range of scenarios than are NTFD estimates (), and Cascade
estimates are accurate across a wider range of scenarios than are Stealth
estimates (–). For example, the mean accuracy values (lower being more accurate) across the ten scenarios for A
were .140 for the CTD, .069 for the NTFD, .049 for the Stealth
, and .045 for the Cascade.
As expected, the Cascade
results were virtually identical except in cases where assumptions regarding mating in the Stealth
Nevertheless, the question remains: given the increased difficulty in fitting the models and collecting the requisite data, is it worth it to use ETFDs? Our results cannot provide an answer to this question, but they do provide guidance. For all the problems associated with the CTD, the combined CTD parameters of A
do provide decent estimates of broad sense heritability. If a researcher’s goal is primarily to understand broad sense heritability, or to understand broad sense genetic covariances in a multivariate setting, the CTD is adequate, and using ETFDs is probably not worth the hassle unless extended family data already exists. To the degree that any genetic non-additivity or spousal similarity exists, however, CTD models can wildly under- or overestimate shared environmental effects (see –). Thus, if one’s interest is in characterizing the effects of the environment in any way—including arguing that shared environmental effects are small—the CTD is a singularly bad method. Similarly, if one’s interest is in understanding the relative importance of additive versus non-additive genetic variation, the CTD provides little help. In these latter situations, researchers should seriously consider the use of ETFDs. These conclusions are not merely based on the simulation results of this paper. Coventry and Keller (2005)
compared the parameter estimates of every available Stealth
model run up to that time to the estimates that would have been obtained using the CTD on the same data and phenotype. Consistent with prediction, they found that CTD results gave predictably distorted pictures of the makeup of genetic variation and the common environment.
For researchers who already have the data needed to fit the Stealth
models, our results suggest the Cascade
model should be used over existing ETFD models. However, an argument could be made from our results that the NTFD represents a good compromise between the accuracy of the Cascade
and the simplicity of the CTD. NTFD estimates tended to be less precise and slightly more biased than Cascade
estimates, but these differences were minor compared to the difference between the ETFD estimates as a group and the CTD estimates. Of course, the major limitation of the NTFD is that the source of shared environmental effects (due to sibling effects or vertical transmission from parents) cannot be discerned, and when both shared environmental sources are present, estimated parameters will be biased. In a separate piece (Medland & Keller, 2009
), we discuss which relative types provide the most power for detecting different parameters in the Cascade
, which should be of service to investigators interested in collecting new data for any ETFD (see also Heath et al., 1985
Hill, Goddard, and Visscher (2008)
recently argued that most genetic variance in most traits is additive in nature. If VD
~ 0 for most traits, then CTD estimates of VA
should be accurate in the absence of assortative mating and vertical transmission, and thus ETFDs would often be overkill. While we agree with Hill et al’s (2008)
conclusion that genetic variation is likely to be mostly additive in nature for most traits, we disagree with potential conclusions drawn from this paper (e.g., Wahlberg, 2009
) that non-additive genetic variance is typically small and insignificant. A meta-analysis of results from the Stealth
design (Coventry & Keller, 2005
) found that typically D
0 and, on average across 38 phenotypes, D
was nearly as large as A
, being a full 75% of A
. These Stealth
results showing evidence for substantial non-additive genetic variance are much more convincing than Hill et al.’s (2008)
twin-only analysis, in which correlations of monozygotic and dizygotic twins were compared across 86 phenotypes: as we have shown (–), the relative magnitude of VA
cannot be accurately ascertained using twins alone. Moreover, because natural selection erodes additive genetic variation much faster than non-additive genetic variance, theory suggests that traits related to Darwinian fitness should have relatively high degrees of non-additive genetic variation (Haldane, 1932
; Wright, 1929
), and indeed empirical reviews show that non-additive genetic variance in non-human animals is similar in magnitude to additive genetic variance among fitness-related traits (Crnokrak & Roff, 1995
). Thus, without empirical investigation, we think it would be premature to take solace in the hope that non-additive genetic variance is low enough for most traits for CTD estimates to be generally unbiased.
There are several limitations with the current approach to understanding the bias, precision, and accuracy of parameter estimates from twin-family designs. First, as mentioned above, our procedure for automating model fitting meant that the results from reduced ETFD models were optimistic. However, as we argued in the Methods section, this probably produced a negligible degree of bias in our results. A more important source of bias in our results, which worked in the opposite direction, is that a human could not guide each fitting process interactively due to the automated way models were fit. A non-negligible number (around 2–8%) of model runs produced outlier estimates, poorly reproduced the observed covariance matrices, and probably failed to find the true maximum likelihood estimates. An experienced modeler could have detected these situations and taken remedial measures, such as changing start values, to improve the fit of the model. This suggests that the ETFD results presented in this paper appear less precise than they will be when fit interactively on real data.
Another limitation to the current approach was that we investigated only a very small portion of the space of possible parameters that might exist in the real world. For example, we did not investigate alternative modes of vertical transmission or spousal similarity due to convergence, both of which can be modeled in the Cascade
. We also did not investigate any number of alternative scenarios that might occur and cause bias in all the models investigated here, such as mixed models of assortative mating (Reynolds, Baker, & Pedersen, 2000
), additional types of gene-environment interactions and correlations, higher-order epistasis, in utero effects, and special MZ-twin environments. This latter issue is particularly important. At the heart of all twin models, including ETFDs, is the comparison between MZ and DZ twins. If some non-genetic factor such as in utero effects increases MZ twin resemblance, all models described in this paper will overestimate A
and especially D
. Furthermore, for simplicity, we did not investigate sex-specific estimates in this paper, which would have had similar biases but lower precision than those presented here. Given this, none but the largest sex-specific effects are likely to be detectable with even the largest available extended twin family datasets. A final limitation to our study is that only univariate models were investigated. Although univariate parameter estimates are interesting in their own rights, ETFD models become more interesting in a multivariate context. For example, parental warmth may be negatively associated with adolescent depression in children (Operario, Tschann, Flores, & Bridges, 2006
), but the reasons for this association are unclear. ETFD models can discern whether this association is due to the same genes affecting both warmth and depression risk or to parental warmth being culturally transmitted to offspring in the form of lower depression risk. Our paper did not assess the parameter characteristics in such multivariate models, although there is no reason to believe that the quality of multivariate parameter estimates would be substantially different than univariate ones. Despite these limitations, the current paper represents the fullest exploration to date of how different real world scenarios affect estimates from twin-family designs.
We have argued that the most commonly used design in behavioral genetics, the CTD, is inadequate for understanding the relative magnitude of shared environmental effects or the ratio of additive to non-additive genetic variation. Our results demonstrate that, irrespective of power or sample size, estimates of these two quantities from CTDs cannot be interpreted with any degree of confidence unless strong assumptions—no assortative mating, no gene-environment covariance, and that either non-additive genetic variance or shared environmental variance is zero—have been verified. ETFDs, on the other hand, provide unbiased and fairly accurate estimates of this information. More complex ETFDs, such as the Cascade, are unbiased under an even wider range of scenarios and provide additional details on the makeup of shared environmental effects that may itself be of interest. The principal reasons why ETFDs are rarely used in behavioral genetics is that they are more difficult to use and that little extended twin family data exists suitable for their use. We hope that the current paper clarifies the rationale for using ETFDs and encourages researchers to collect extended twin family data when circumstances warrant their use.