Were the conclusions of Finlay and Darlington (1995) distorted?

Were the Conclusions of Finlay and Darlington (1995) Distorted by their Failure to Control for Taxonomic Grouping, Body Size, and Part-Whole Correlations?

Richard B. Darlington and Barbara L. Finlay

June 2, 1996

Finlay and Darlington (1995), here abbreviated F&D, argued for the existence of constraints in brain evolution--constraints that apparently force all the major parts of the brain except the olfactory bulb to maintain certain sizes relative to one another. More specifically, F&D showed that across 131 mammalian species studied by Heinz Stephan and colleagues, the sizes of all major brain parts except the olfactory bulb could be predicted with surprising accuracy from the size of the brain as a whole, by simple regression analysis using the logs of structure and brain sizes.

In personal correspondence and unpublished manuscripts, this conclusion has been questioned on various grounds. Two questions in particular have been raised:

1. Isn't a simple regression analysis invalid because it treats species as independent observations, while in fact species are related by evolution? Shouldn't one use instead a method like Comparative Analysis by Independent Contrasts (CAIC) (Purvis and Rambaut, 1995), to take into account the interrelatedness of species?

2. Might the correlations between whole brain size and brain structure sizes be produced by the facts that (a) they are part-whole correlations, (b) they don't control for body size?

The purpose of this note is to respond to these questions.

Independent Observations and CAIC

CAIC is quite similar to using ordinary regression techniques but adding to the regression model terms for taxonomic units--order, family, etc. CAIC requires a complete or nearly complete taxonomy of the species analyzed--something we didn't have for the 131 species for which we had structure-size data. However, the ordinary regression method can be applied with whatever amount of taxonomic data the user has. We therefore applied that approach, entering dummy variables for order (bats versus insectivores versus primates) and primate suborder (simians versus prosimians). To be precise, after expressing all sizes in log form, we predicted the size of each neural structure (except the neocortex and olfactory bulb) simultaneously from two sets of variables:

The SIZE set included the sizes of the neocortex and olfactory bulb, plus their squares and the simple interaction or crossproduct between them.
The TAXONOMY set included the aforementioned variables measuring order and suborder.

The "unique contribution" of a set of variables is the amount R² drops when the set is removed from the model. The list below shows the ratio of the unique contribution of the SIZE set to that of the TAXONOMY set, for predicting the logged sizes of 9 neural structures. Numbers above 1 mean SIZE has the larger unique contribution. Items are ranked from high to low ratios.

Ratio of Size/Taxonomy Contributions
STUCTURE	RATIO
Paleocortex	810.97
Striatum	503.05
Diencephalon	469.91
Septum	91.98
Mesencephalon	82.60
Medulla	79.44
Cerebellum	77.48
Schizocortex	67.39
Hippocampus	54.09

All ratios are far above 1, meaning the contribution of taxonomy is trivial in comparison to that of the size variables. This strongly suggests that the omission of taxonomic controls from our previous analysis had little effect on the results.

But suppose the effects in question occur not at the level of order and suborder, but occur instead at lower levels--at the level of the family or genus. We did not directly test this possibility. There are two answers to that objection. First, as we mentioned at the time, the total unexplained variation is remarkably small, and includes random measurement error, within- species differences, and other sources of variance. That lessens the likelihood that family and genus-level effects are important. Second, in general the higher the level of a taxonomic split, the more important the differences the split produces. Differences between chimpanzees and macaques are large in one sense, but they're very small in comparison to the differences between primates and bats or shrews. Therefore if the effects of order and suborder are trivial, it is reasonable to assume that the effects of family and genus are even smaller.

This analysis strongly suggests that our inability to fully control for taxonomy had very little effect on our conclusions.

Might the results of this analysis be distorted by the fact that the slopes of regression lines might change from order to order? Inspection of Figure 1 in our Science paper suggests that such differences in slope are trivial, but we supplemented that impression with the following analysis, which is somewhat similar to the one just described. We used regression to predict each logged structure size from 5 variables simultaneously: logged brain size, two dummy variables differentiating among orders, and two order*logbrainsize interaction terms. We then expressed the proportion of variance explained uniquely by the two interaction terms as a proportion of the total variance explained by the model. This addresses the question of how important within-order differences in slope are as a component of the total model. The proportions thus calculated are:

Proportional Contributions of Slope Differences
STRUCTURE	RATIO
Szhizocortex	.0127
Paleocortex	.0110
Mesencephalon	.0106
Septum	.0080
Hippocampus	.0078
Medulla	.0044
Diencephalon	.0027
Cerebellum	.0012
Striatum	.00073
Neocortex	.00037

These are ranked from high to low. Even the highest value barely exceeds 1%, and the lowest is far below that. Interestingly the neocortex, the structure of greatest interest in this respect, is the lowest. We also found that in our data, when simple regressions predicting logged structure size from logged brain size are run separately by order, the neocortex gets the highest slope in all 3 orders. This further supports the conclusion that taxonomic variables add little to our analysis.

Controlling for body size

The second question was whether the correlations between whole brain size and brain structure sizes might be produced by the facts that (a) they are part-whole correlations, (b) they don't control for body size. To study this possibility, we computed the correlations between neocortex size and the size of other brain structures, controlling for the following:

Body size
Taxonomy (order and suborder )
The body size*taxonomy interaction

The last term is to control for the possibility that body size relates to neural structure size differently in different orders and suborders. Since the correlations are between different structures, the part-whole problem is eliminated. As usual, all sizes were in log form. The correlations were as follows:

Neocortex correlations controlling for order, body size, and their interaction
STRUCTURE	Correlation
Diencephalon	.907
Striatum	.871
Cerebellum	.830
Schizocortex	.774
Septum	.747
Hippocampus	.737
Mesencephalon	.664
Medulla	.623
Paleocortex	.425
Olfactory bulb	.116

Correlations are ordered from high to low. Thus we see that even with all the aforementioned variables controlled, neocortex size correlates highly with the sizes of most other structures.

References

Finlay, Barbara and Richard Darlington (1995), "Linked regularities in the development and evolution of mammalian brains," Science 268:1578-1584

Purvis, A. and A. Rambaut (1995), "Comparative analysis by independent contrasts (CAIC): an Apple Macintosh application for analysing comparative data," Computer Applications for the Biosciences, 11: 247-251

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