Biologists have long been interested in the evolution of the brain. Its’ sheer size differs greatly across different groups of mammals, and is of course greatly expanded in humans. Part of this variability is because species differ in body size, and we need to understand the nature of this relationship before we can say anything sensible about the evolution of brain size and its possible link to cognitive abilities. Despite decades of comparative studies, however, puzzling aspects of the relationship between mammalian brain and body mass continue to defy satisfactory explanation. Why this relationship seems to be so variable across taxonomic groups and taxonomic levels, why brain size appears to lag behind body size when larger species evolve, what dictates the way that brain and body size co-evolve, and what all of this means for meaningfully measuring differences between species in the size of the brain relative to the body, are amongst the unresolved questions. To try and answer these questions, we analysed a large data set on 1500 species of mammals, using powerful computational methods for estimating evolutionary rates of change on the branches of phylogenetic trees. Our analyses uncovered some surprising results, overturning long-held assumptions and considerably simplifying our understanding of the brain-body size relationship.

We started in a similar way to previous researchers, by log-transforming our data and fitting linear statistical models. This has been standard in the study of biological scaling relationships (“allometry”) – including brain-body relationships, for at least 100 years. Various explanations have been put forward for the shape of the brain-body mass relationship, including constraints imposed by mass-specific metabolic rate or by the way brain size needs to increase with body size in proportion to the bodily surface area serviced by the nervous system. As had been found before, however, fitting linear models showed substantially different brain-body mass relationships across the different orders of mammals (primates, bats, cetaceans, and so on). The relationship was steeper in some orders than in others, and ‘grade-shifts’ between groups in how encephalised they are could also be observed. This would not support any one general model of scaling.

Looking more closely at our scatter plots, however, we noticed something interesting. The overall relationship appeared not to be linear, but curved, or quadratic. We tested this formally, and found that, indeed, a quadratic model fitted the data much better than a linear model, overturning a 100-year old assumption. This was very clear when we used a linear statistical model to calculate relative brain sizes for each group of mammals. If a linear model was a good fit, there should be no correlation between the slope of the relationship in the brain-body mass relationship and body mass itself. Yet there was a negative correlation: the slope was lower in larger-bodied mammals (e.g., Figure 1).  Our quadratic model removed this artefact. Importantly, our results showed that all of the previously observed complexity in the mammalian brain-body size relationship evaporates after accounting for the true brain-body mass relationship, and they change how brain-body size relationships should be studied in the future. The quadratic relationship needs to be accounted for when studying relative brain size (‘encephalization’); the many studies that have attempted to identify how relative brain size correlates with behavior and cognitive abilities now need to be reconsidered in light of this curvilinear scaling.

Figure 1: Using linear models to estimate the relationship between brain and body mass across mammalian families reveals a size-dependency, implying that these models fail to properly account for the effects of body mass.

Our results help to resolve the puzzling complexity in the brain-body mass relationship. After accounting for the quadratic relationship, the tendency to observe allometric slopes (the steepness of the relationship) that are lower among more closely related species disappeared. This so-called ‘taxon-level’ effect had previously been given quite elaborate explanations, such as brain size lagging behind when selection acts on body size.  Such complicated explanations are no longer necessary in light of our model. We could detect no significant variation across taxonomic groups in either slopes or intercepts (‘grade-shifts’). Hence, relative brain size evolution in mammals can be studied using a single – rather than taxon-specific – model of the underlying relationship between brain and body size.

Applying this model reveals that rates of change in brain size varied dramatically across the tree of life (see Figure 2), exhibiting episodic bursts of change indicative of strong selection. Evolutionary increases in relative brain size were driven primarily by changes in brain rather than body size. Contradicting some suggestions in the literature, we can therefore conclude that most of the variability in rates of relative brain size evolution are a result of selection on brain functions, rather than a side-effect of selection on body size. All groups of mammals showed some rapid bursts of evolutionary change, but this was most pronounced in rodents, carnivores and - especially – primates. Bats, in contrast, showed very low rates of relative brain size evolution after a rapid change at the origin of this group. We were also able to re-examine the old idea of a consistent trend for relative brain size to increase through time, the so-called ‘Marsh-Lartet rule’. We found this to be clearly the case only in carnivores and primates, with rodents showing some sign of a weaker trend. This is revealed by a simple metric: in primates, brain size has increased on about 80% of the branches of the phylogenetic tree, compared to only about 60% of the branches on which body size has increased. And the branch leading to humans exhibits one of the fastest rates of all, twenty-three times higher than the background rate observed across all mammals. Evidently, something changed at the origin of the primates that set the stage for escalating brain size evolution, ultimately leading to the remarkable computational powers of the human brain. What that something was will be for future research to discover.

Figure 2: Phylogenetic tree of mammals with branches scaled to show evolutionary rates of change in relative brain mass. Some of the biggest rates can be seen in some very charismatic taxa, including humans, lions, and elephants.

One thing we cannot answer at this point is why there is a curve in the brain-body mass relationship. We looked to see whether this could be explained by the way that connectivity within brains have to change with overall size, or whether the scaling of energy demands was responsible, but we drew a blank. What we can say is that the curve seems to be a general phenomenon in warm-blooded animals, as we also found it across bird species. Hence, whatever the explanation, it would have to apply to animals with differently organized brains and very different biological and ecological constraints. Whether this remains true when we examine an even greater diversity of animals remains to be seen.