June 2, 1996

In personal correspondence and unpublished manuscripts, this conclusion has been questioned on various grounds.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.

- 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.

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:

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.

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

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