Biology Reference
In-Depth Information
BOX 10.3
META-ANALYSIS
In most of the comparative studies described in this topic, we are asking whether
two variables are correlated across species. For example, in Chapter 2 we asked
whether sexual dimorphism is correlated with mating system across primates,
and found that it is (Fig. 2.6). However, in some cases, the relevant question is
not whether variables are correlated, but rather whether consistent patterns
occur across species. Meta-analysis provides a method for this, and is becoming
an increasingly important tool in all the areas discussed in this topic (Arnqvist &
Wooster, 1995).
To illustrate the usefulness of meta-analysis, imagine that we are interested in
whether female mammals are able to adjust their offspring sex ratio in response
to their maternal condition, as originally suggested by Trivers and Willard
(1973), or whether genetic sex determination constrains them from doing this.
Imagine that data had been collected on eight species. Two studies showed a
significantly positive correlation between maternal condition and offspring sex
ratio, with better condition females being more likely to produce sons, as
predicted by Trivers and Willard. One study showed a significantly negative
correlation between maternal condition and offspring sex ratio, with better
condition females being less likely to produce sons, in the opposite direction to
that predicted by Trivers and Willard. The remaining five studies showed no
significant correlation between maternal condition and sex ratio.
One possible conclusion from this data would be that Trivers and Hare
hypothesis is not supported, and that the positive results could just have arisen
by chance. However, this conclusion throws away data on the direction of the
non-significant results and relies on the implicit assumption that all the studies
were equally good, with the same sample size. This can lead to incorrect
conclusions. For example, suppose that the two positive results were from large
studies of 150 individuals, while all the others were from small studies of 10
individuals. In this case, we would want the larger studies (which were both
positive) to carry more weight towards the final conclusion, because there is a
greater probability that they show the 'correct' result. Furthermore, suppose
that all the non-significant results were in the positive direction, so that we
actually had seven studies showing the predicted direction, and only one not.
In this case, we would have a consistent pattern and the non-significant results
could potentially be explained by a low sample size. Overall, this closer
examination of sample size and directionality would have changed our
conclusion, and given support to the Trivers and Willard hypothesis.
Meta-analysis was developed to solve these problems of sample size and
directionally. Firstly, instead of just counting whether a study is significant or not,
it uses a standard measure of effect size, the correlation coefficient
r
(where
r
2
is
the proportion of variance in the data explained - here it would be the proportion
of the variance in the sex ratio explained by maternal condition). Secondly, it gives
more weight to studies with larger sample sizes. A meta-analysis of the real
ungulate data shows that although there is much variation, there is consistent
