What Is Encephalized Relative Brain Size

As recently as the 1960s, some researchers had a logic based on uncorrected absolute size for their evolutionary and/or ecological hypotheses on ence-phalization. Most researchers today (although see Byrne and Corp, 2004, for discussion) assume that encephalization should be studied after some kind of complete or partial control for allometry, often assessed by body size (see Scaling the Brain and Its Connections, Encephalization: Comparative Studies of Brain Size and Structure Volume in Mammals, Principles of Brain Scaling).

Usually, body size allometry is considered a confounding variable and is removed from most analyses of relative brain size. The assumption here is that as a body gets bigger, it takes more brain cells to analyze the information coming from more skin, a bigger retina, larger ears, a bigger nose, as well as to program more motoneurons for bigger and more numerous muscles. It also takes more interneurons to mediate all this added sensory and motor machinery. The brain-body relationship is not 1 to 1. As bodies get bigger, the increase in brain size follows at a slower pace. Not all organs follow this trend; the heart/body relationship, for example, is linear even when the data are not log transformed. The brain is thus a peculiar organ and its relationship with body size may differ from that of other organs. The decreasing slope of the brain-body relationship might mean that ever-larger bodies require proportionally fewer and fewer extra neurons in the brain or that the cost of enlarging the brain increases faster than the cost of enlarging the body. However, metabolic costs, one of the best known costs of encephalization (and the interpretation often cited for the slope of the log-log brain-body line; Martin, 1981; see however, Symonds and Elgar, 2002), decrease with body size. As animals get bigger, there is less surface-to-volume heat loss, body temperatures decrease, and it takes proportionally less energy to fuel a large body compared to a small one.

Another problem with using body size as an allo-metric control is that selection, both natural and sexual, operates on it and that a seemingly small brain relative to a large body may simply mean that there has been stronger selection on an enlarged body than on an enlarged brain. When sexual selection for enlarged bodies leads to gender dimorphism, this presents a further problem, though one possible solution is to take only the brain and body measurements of the gender under the lowest sexual selection pressure. Selection for specific organs that make up a large proportion of the body could also affect total size estimates. Herbivores and folivores have a large digestive system because the low digestibility and nutrient quality of their food requires larger amounts of food and longer digestion. Gorillas and ruminants may thus have a spuriously small relative brain size if allometry controlled via body size is biased by selection on a large digestive system. Some estimates of size (e.g., body length) may be less sensitive to this problem than others (e.g., mass), but the general problem remains. An alternative explanation for small brains in herbivores and folivores would argue that the demands of eating leaves and grass do not select for a large brain relative to body size because these foods are abundant and predictable, but the point is that both explanations are logical.

A third problem with body size is that large bodies are associated with longer generation times. When environments change, there are two ways an animal can modify its response. First, natural selection can increase the frequency over successive generations of alleles (mutated or already appearing in low frequencies) coding for traits that lead to higher fitness in the changed conditions. Alternatively, phenotypic plasticity such as innovation, individual learning, or social learning may allow animals to track the changed conditions. If large brains favor behavioral flexibility and large bodies (and brains; see below) decrease the rate of natural selection via long generation times, then bodies again will not have a neutral effect on brain size. Encephalization might thus follow evolution of enlarged body size, as Nealen and Ricklefs's (2001) analysis of birds suggests (but see Deaner and Nunn, 1999 on primates).

One proposed solution to the problems posed by body size allometry is to use a part of the nervous system itself as a control. This solution also reduces the measurement error inherent to estimates such as body mass, which can change rapidly as a result of food conditions. Harvey and Krebs (1990), Barton (1999), and Deaner et al. (2003) have pointed out that such measurement errors can create spurious positive correlations between relative brain size and other allometrically corrected variables such as life history traits. For example, correcting absolute brain size and longevity by the same erroneous body mass estimate will create a similarly high residual of the two traits in a species whose correct mass is underestimated by the erroneous estimate, and a similarly low residual for the species whose mass is overestimated. These correlated errors may create artificially correlated traits.

When a part of the nervous system is used to remove allometry, we need to specify the higher level centers that are assumed to be more closely involved with cognitively driven encephalization and the lower brain areas that can be used as the control. For this, we depend on neuroanatomy and neuropsychology. The encephalized areas can be very broad, such as the telencephalon in birds and mammals or the supraesophagal lobes in cephalo-pods. The areas chosen for the allometric control could, for example, be the brainstem in birds and mammals and the subesophagal lobes in cephalopods. The lower brain structure could be either that of the species itself or of a primitive evolutionary baseline. Portmann (1946, 1947a, 1947b) pioneered the use of these methods, which were later applied to mammals and cephalopods by Wirz (1950, 1959) and primates, bats, and insectivores by Stephan and collaborators (Stephan et al., 1988, 1991; Baron et al., 1996). In birds, the primitive reference group is usually galliformes, while in mammals, it is insectivores. For this method of removing allometry, there are thus three assumptions: the upper brain structure is the one most closely involved in encephalization, the lower brain structure has been subject only to the allometrically driven selection, and encephalization can best be understood by comparing primitive taxa to more recently encephalized ones. All these assumptions can be questioned.

Whether one uses whole bodies or lower brain structures as controls, there are in essence two statistical approaches to the removal of allometry: residuals and ratios. Residuals use the deviation from the best fit log-log regression as the measure of relative size, often transformed to a standardized scale so that all distributions are comparable from one analysis to another and normalized for parametric statistics. A problem with residuals is that they all change when you add only one new species. If this species has unusual weighting in the data point cloud, this will have a strong effect on all residuals. For example, if you add Rehkamper et al.'s (1991b) 23 hummingbird species to Portmann's (1947a) 140-species database, you tip the best-fit line counterclockwise due to the small body and brain size of hummingbirds. This might introduce an artifact due to the particular flight mode of hummingbirds, which might constrain both brain and body size evolution. You would thus be allowing a taxon that is a special case to influence every single residual.

In analyses that use ratios, the numerator is the brain part predicted to be most closely involved in cognitively driven encephalization (e.g., the neocor-tex of mammals, the mesopallium-nidopallium complex of birds, the vertical lobe system of cepha-lopods, and the mushroom bodies of insects; see below). The denominator is either a structure that encompasses the one in the numerator (e.g., whole brain or telencephalon or supraesophagal lobes or cerebral ganglia) or the lower brain structure not thought to control cognition (e.g., the brainstem, the subesophagal lobes, and the spinal ganglia). Allometric effects are assumed to be (wholly or partly; see below) controlled in ratios, because they apply to both the numerator and denominator.

One problem with ratios is that they are not normally distributed and thus present a statistical problem for parametric statistics. Large ratios tend to get larger faster than do small ratios. For example, parrots and corvids may easily reach values of 20 in a Portmann ratio, while ducks vary only around 1.6. Log transformations of the ratios can solve the problem by compressing the skewed high values (Lefebvre et al., 1997). A second, more important, problem is that ratios may not entirely remove the confounding effect of body mass (Deacon, 1993). If we conclude, for example, that carnivory is associated with large brains and our estimate of relative brain size is confounded with body mass, there is a risk of type 1 error if carnivores also have larger bodies. In this case, the apparent brain-diet relationship could be a spurious effect of the brain-body and diet-body associations.

A third problem is that ratios of variables whose relationship is not 1 to 1 will overestimate one end of the continuum and underestimate the other. The lower the slope is below 1, the more neural structure size (normally plotted on the y axis) of animals that are at low values of the x axis will be overestimated. When the slope is above 1, the reverse will hold, with larger x values being overestimated. It is well known, for example, that expressing relative brain size as the proportion of total body mass represented by the brain will result in higher ratios in chickadees than parrots simply because chickadees are much smaller (Packard and Boardman, 1999). The brain-to-body-size ratio is often used in human paleoanthropology. The same problem may occur if the telencephalon is expressed as a proportion of the whole brain or the neocortex as a proportion of either the brain or the telencephalon (Clark et al., 2001; Burish et al., 2004). If the structures are thought to be progressive, the slopes of the y-x relationship are likely to be higher than 1. This will overestimate the larger-brained species (Barton, 2002), potentially favoring type 1 error of any prediction associating relative brain structure size and cognition.

It may be noted that one quantitative expression of encephalization, Jerison's (1973) encephalization quotient (EQ), combines the advantages and disadvantages of residuals and ratios. EQ expresses relative brain size as the ratio of the observed (unlogged) y value of a given species on a log-log body-brain graph, divided by the unlogged y value of the best fit regression for the x value of the species. If a species has a brain size of 20 g and the y value of the brain-body regression for an equivalently sized animal is 5, then EQ = 4. If the brain mass of a small-brained species of equivalent body size is 2.5, then

EQ = 0.5. Given that EQ is based on a log-log regression, it is statistically better to calculate standardized residuals from this regression, which by definition will be normally distributed, instead of using ratios, which are not. If EQ was intended as a reference to IQ, it is puzzling that Jerison did not express his results as standardized residuals fitted to a mean of 100 and a standard deviation of 16. On this scale, parrots would score around 130, while quail would score around 75. Another problem with EQ is that values calculated from a regression line at one taxonomic level may be biased when they are used to test a hypothesis at another taxonomic level. For example, the EQ values of cetaceans (see Cetacean Brain Evolution) are routinely calculated with respect to the log-log regression line for all mammals. If one then tests a hypothesis on variation within cetaceans only, EQ may hide a confounding negative correlation with body size; small-bodied cetaceans tend to have larger EQs than large-bodied ones (Marino et al., 2006). Allometry can thus still be present in EQ, even if the calculation was initially designed to remove it. Whole Brains or Parts Thereof?

Are larger whole brains the consequence of selection for increased size of some of its components only or is enlargement of the whole brain the means by which larger specific structures evolve? Do these components vary independently of others or are there functional links between anatomically distant areas that cause change in them to occur together? The answer to these questions will depend in part on how much room the components occupy in the brain. The higher the proportion of the whole brain a component structure occupies, the more its enlargement will have a consequence for the size of the whole brain. For example, the mesopallium-nidopallium complex of a crow represents 72% of its telencephalon, which represents 78% of its whole brain. When we say a crow has a large brain, we might really only be saying that it has a large mesopallium. Selection for an enlarged high vocal center (HVC) or hippocampus in a chickadee will not have that effect, because these are small structures compared to the whole brain.

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