Which Of The Following Would Lead An Animal To A Higher Encephalization Quotient (Eq) As It Evolved?

Both absolute and relative encephalon sizes vary profoundly among and within the major vertebrate lineages. Scientists accept long debated how larger brains in primates and hominins translate into greater cognitive performance, and in particular how to control for the human relationship between the noncognitive functions of the brain and torso size. 1 solution to this problem is to constitute the slope of cognitive equivalence, i.e., the line connecting organisms with an identical bauplan but different body sizes. The original approach to guess this slope through intraspecific regressions was abandoned afterwards it became clear that it generated slopes that were too low by an unknown margin due to estimation fault. Here, we revisit this method. We control for the error problem by focusing on highly dimorphic primate species with big sample sizes and plumbing equipment a line through the hateful values for adult females and males. We obtain the best estimate for the slope of circa 0.27, a value much lower than those constructed using all mammal species and close to the value expected based on the genetic correlation between encephalon size and body size. We also observe that the estimate of cerebral encephalon size based on cognitive equivalence fits empirical cognitive studies better than the encephalization caliber, which should therefore be avoided in time to come studies on primates and presumably mammals and birds in full general. The utilise of residuals from the line of cerebral equivalence may change conclusions concerning the cerebral abilities of extant and extinct primate species, including hominins.

© 2021 The Author(south) Published by S. Karger AG, Basel

Introduction

Although recent ecological approaches to comparative cognition have focused on linking performance in specific cerebral tasks to specific brain regions [eastward.thou., Healy and Krebs, 1996], traditionally comparative cognition has relied on a presumed link between some summary measure of cognitive performance and total brain size [Jerison, 1973]. Scholars have therefore long been searching for a neuroanatomical measure of overall cognitive power, both to compare living species and to estimate the cerebral abilities of extinct ones relative to their extant relatives. The near intuitive measure is a species' brain size (or, peculiarly for extinct species, the highly similar cranial capacity) [Isler et al., 2008]. All the same, because brains also control numerous noncognitive somatic functions, most researchers have agreed that it cannot exist used without decision-making for these somatic functions.

Building on a century-long tradition, Jerison [1973] distinguished betwixt the somatic and the cognitive encephalon functions and proposed that we tin can estimate the portion of the brain dedicated to somatic functions, and thus by subtraction arrive at the size of the cerebral portion. Jerison [1973] fitted regression equations to the brain size-body size data of all available species in many unlike mammalian lineages. Considering this produced a regression slope close to 0.67 in a log-log plot, he interpreted this every bit reflecting a fundamental physiological regularity linking encephalon size to the body's surface area and thus the amount of proprioceptive inputs. This slope could therefore serve as the expected value of the somatic portion of the brain, and the difference from the regression line every bit the estimate of the cognitive portion, i.e., cerebral brain size. Jerison [1973] then proposed the encephalization caliber (EQ), the ratio of a species' actual brain size to its predicted brain size based on the clade-specific brain-torso regression line, to capture its relative cerebral performance. The EQ has become a ordinarily used gauge of the cerebral abilities or intelligence of fauna species. Other researchers have argued the slope is really somewhat college, linking it to metabolic turnover instead and thus suggesting a slope of 0.75 [Martin, 1981; Armstrong, 1983], simply they have not questioned the fundamental EQ approach.

Well-nigh research on basic relationships between encephalon size, body size, and cognitive performance has been conducted on mammals, and in item primates. This research has produced various lines of bear witness arguing against the EQ arroyo. Commencement, its employ assumes that there is no correlation between body size and cognitive performance, only in practice there is a negative correlation between EQ and torso size inside mammalian orders (see below). We should therefore see that bigger mammal species prove a poorer cognitive performance than smaller relatives in the same social club. Nevertheless, the opposite appears to be the instance [Rensch, 1973], suggesting a lower value of the slope. Second, a lower slope would also exist expected given the combined effect of 2 persistent macro-evolutionary trends, i.eastward., (1) brains have increased relative to body size, a miracle we tin can call the Lartet-Marsh rule [Jerison, 1973], and (2) torso size has increased as well, a phenomenon known equally the Cope rule [Alroy, 1998]. As a result, more than recently evolved lineages will tend to have both larger body sizes and larger brain sizes [e.grand., Halley and Deacon, 2017], which artificially inflates the slope of the regression through the total sample. Third, different mammalian lineages unexpectedly show unlike regression slopes of encephalon size on body size [Martin and Harvey, 1985].

These inconsistencies reveal the fundamental flaw in the EQ approach [Deacon, 1990; Striedter, 2005], it assumes that one process (exist information technology proprioception or metabolic turnover) predominates in determining brain size to the extent that cognitive functions produce only minor deviations, so we can estimate their strength by taking ratios or residuals. Instead, nosotros may expect a multifariousness of processes to bear on brain size, with some of them lineage specific and each potentially varying in forcefulness across lineages. Nonetheless, EQs keep to exist used to compare mammalian taxa [e.1000., Boddy et al., 2012], especially extinct ones [e.g., Grabowski et al. 2016; Benoit et al., 2019].

Although EQ approaches are inadequate, no universally accepted alternative has emerged. A major reason is that the notion of overall cognitive ability or functioning remained vague, making it harder to produce an culling measure. In fact, modernistic behavioral ecology generally assumes that animals take bundles of domain-specific cognitive adaptations [Shettleworth, 2010]. Consequently, "overall" cerebral performance does not be and overall brain size does not necessarily provide whatsoever useful information when information technology comes to understanding the animal's ecological niche or social organization. Instead, researchers relate the relative size of specific brain regions to specific cognitive challenges to await for patterns at that level in large comparative surveys. Examples include seed caching and recovery [Healy and Krebs, 1996; Garamszegi and Eens, 2004] or the incidence of feeding innovations [Timmermans et al., 2000] in birds.

Recently, even so, brain size has regained standing every bit a relevant variable. First, forth with the unquestioned selective increase or subtract in certain encephalon parts in response to specific pressures [Barton and Harvey, 2000], mammalian brains are also organized in fundamentally similar ways beyond animals of varying sizes, even across lineages, which produces anticipated allometric relationships among the sizes of the diverse brain regions [Finlay and Darlington 1995; Finlay et al., 2001]. Indeed, many cognitive activities correspond to concerted activity waves throughout the brain rather than existence tied to one particular region [Park and Friston, 2013], suggesting that a subtract or increase in one particular region nether selection will touch the sizes of other parts and thus also the size of the whole brain [Barton, 2006]. 2nd, an important outcome of cognitive abilities that tie together many brain regions is domain-full general intelligence [Burkart et al., 2017]. This concept has historically been applied mainly to humans, and many, implicitly or explicitly, notwithstanding consider it to be uniquely human. In that location is at present mounting show, however, that, at least amidst various mammals [Burkart et al., 2017] and birds [Ashton et al., 2018], domain-full general intelligence can be recognized within species, and that unlike species vary considerably in the strength of this domain-general ability [Deaner et al., 2006; Reader et al., 2011]. The latter finding allows empirical tests of the predictive value of EQ or conceptually similar residuals. Broad comparative analyses of estimated domain-general cognitive abilities accept shown that EQ is a poor predictor of these abilities [Deaner et al., 2007; Reader et al., 2011], and more than express analyses have reached the same conclusion [Alba, 2010; Rumbaugh et al., 1996]. Moreover, as noted above, nigh large-bodied species have greater cognitive abilities than expected based on their EQ values [Rensch, 1973], which tend to decrease with body size within orders. In determination, these more direct, cognition-based tests of EQ-based approaches confirm that they practise not predict cognitive abilities.

Not-EQ Approaches

These conceptual and empirical problems with EQ measures betoken that nosotros need to command for body size in a unlike way. Some scholars have suggested that no control is needed at all [eastward.g., Rensch, 1973; Byrne, 1995; Striedter, 2005], but most accept that regulation of somatic functions requires at least some encephalon resources that are not also available for cognitive functions. Two main alternatives have been proposed. The first set of techniques is similar to the EQ arroyo, as it relies on broad interspecific comparisons. Portmann [1946, 1947] proposed that Galliformes are the most primitive birds and deviations from their interspecific regression equation should exist used to estimate encephalization. Stephan [1960] proposed the same procedure for mammals, using the "basal insectivores" every bit the baseline. This produces a "progression index" for each species. However, due to diverse conceptual and statistical problems [Deacon, 1990] it has found little awarding. This index likewise predicts primate cognitive performance merely marginally better than EQ and far worse than brain size per se [Gibson et al., 2001; Deaner et al., 2007], although information technology is unknown how well it does for other mammals or birds.

Another interspecific approach uses ratios of different brain regions, assuming that one, i.eastward., the numerator, is responsible for the encephalon's cognitive functions, and the other, i.e., the denominator, is responsible for its somatic functions [Krompecher and Lipák, 1966; Passingham, 1982]. This ratio and then estimates the development of cognitive functions relative to expectation. The well-nigh popular measure is the neocortex ratio, i.due east., the size of the neocortex relative to the rest of the brain [Dunbar, 1992]. Notwithstanding, all ratio measures have the fundamental drawback that they lack a clear neurobiological justification [Deacon, 1990; Deaner et al., 2000; Barton, 2006], and the neocortex ratio was favored but considering it yielded the best correlation with the putative selective pressure [Dunbar, 1992]. Like nearly other ratios, the neocortex ratio is clearly correlated with both overall brain and body size, every bit expected based on the fundamental brain allometries [Finlay and Darlington, 2001; Halley and Deacon, 2017]. Thus, its employ depends entirely on the goodness of the fit with presumed selective pressures, risking circularity. If this fit varies beyond taxa, nosotros cannot tell whether a poor fit reflects an imperfect neuroanatomical measure or different selective environments [Stout, 2018]. Moreover, the neocortex ratio does non differentiate betwixt monkeys and apes, which are known to differ in cerebral operation [Gibson et al., 2001]. Too, information technology does non always predict actual cognitive operation in the primate sample as strongly as other measures when we control for phylogenetic nonindependence [due east.g., Deaner et al., 2007]. We volition therefore not further consider ratio measures (simply see Discussion).

The Slope of Cognitive Equivalence

The aim of this paper is to revisit the main remaining culling, i.due east., estimating the slope of cognitive equivalence. Its logic works as follows: we assume (1) that the cognitive functioning of adult individuals within a species does not depend on their body size and (two) that the intraspecific relationship betwixt body size and brain size among adults estimates the extra amount of brain tissue required to sustain the boosted somatic functions in larger individuals because there are no changes in the bauplan or sensory-motor abilities. Therefore, assuming that intraspecific variation in adult size is based on selection on body size lonely, the regression of brain size on body size should give us the slope of cerebral equivalence. If analyses conducted on a range of species converge on a similar slope, the cognitive brain size of a species can then be estimated as the residual of the actual encephalon size of that species from a general line with that slope and some informative intercept.

This is not a new thought. Many estimates of this slope from samples of conspecific individuals of a known trunk and brain mass have been made in the by. Still, they vary considerably. Summarizing previous work, Pilbeam and Gould [1974] noted values between 0.2 and 0.4. The range for individual mammal species with larger samples was somewhat tighter, with average values between 0.23 and 0.25 [e.g., Hemmer, 1971; Röhrs, 1986] for large intraspecific samples. In large multispecies analyses Martin and Harvey [1985] obtained a median value of 0.14 for primates, and in a large recent analysis of birds and mammals Tsuboi et al. [2018] found a value of 0.fifteen; in both cases the values per species were highly variable. This considerable variability arises because empirical slopes within species are ordinarily underestimated [Pagel and Harvey, 1989] by varying margins. Thus, if we can remove this source of fault, this mensurate's utility could be restored.

The high variability in gradient estimates can be explained. The equation for the slope of a regression is [Lande, 1985]:

where Corr(y,10) is the correlation betwixt 10 and y, and σ is the SD. Because virtually all mammals show determinate growth, there is lilliputian variation in torso and brain size. As a upshot, variation due to measurement mistake tin greatly affect the estimated slope of the brain-body relation within a gear up of adults. Moreover, the error appears to exist much larger for body size than for brain size. Encephalon mass or endocranial volume (our estimate for brain size) is rather constant considering during periods of starvation brains keep to receive the same energy flow as during times of plenty, whereas the rest of the body must make do with less. This phenomenon is known as brain sparing [Wells, 2010], resulting in a tiny reduction of brain mass. As a outcome, the estimate of body size, i.e., body mass, is more variable. Not only does the body lose fat and other tissues during starvation, simply it also accumulates fat during times of plenty, whereas the brain does not. The seasonal variation in trunk mass may therefore greatly exceed the i in brain mass, except for a small number of species with seasonal variation in brain mass [Dechmann et al., 2017]. Among females, torso mass likewise varies beyond the reproductive cycle, with college values during pregnancy and lower values toward the end of lactation. Finally, captivity, too, can increase differences in torso weight betwixt wild and captive specimens, particularly in slow-growing species [e.g., Isler et al., 2008; Leigh 1994]. Due to these various processes, the variance in trunk mass at a given size tin can exist upwards to 4 times as high as that in brain mass [Pagel and Harvey, 1989], and the slope will inevitably be underestimated, potentially by up to a gene 2. To reduce this erroneous reduction in the slope approximate, we should include a greater range of intraspecific body sizes in the analysis, reduce the error in the estimation of each betoken past taking averages where possible, and use only wild specimens.

One seemingly obvious way to achieve this is to utilise the means of higher units (species, genera, and families) as information points. This does indeed produce steeper slopes [Martin and Harvey, 1985]. Still, while this so-called taxon level consequence is partly due to the reduction of racket due to varying torso mass, information technology also reflects the combined Cope-Marsh effects noted above, which volition also produce higher slopes for families and orders [Jerison, 1973; Rowe et al., 2011]. Therefore, because nosotros cannot disentangle this Cope-Marsh effect and the estimation error effect, slopes obtained amongst related species or genera demand non reflect cerebral equivalence. However, this slope may withal exist useful, as it provides a convenient upper limit to the bodily slope of cognitive equivalence. The analysis of congeneric slopes past Isler et al. [2008] using independent contrasts yielded a hateful gradient of 0.41 for primates, suggesting that the truthful slope lies somewhere between 0.xv and 0.40.

The all-time option thus remains to obtain intraspecific slopes that are affected as piffling as possible by the error problem. Nosotros can accomplish this past looking for species with a big variation in developed torso size. Using information on dog breeds, which testify a xxx-fold variation in body size, Bronson [1979] obtained a slope of 0.27 based on averages per breed. This would seem to provide an excellent estimate of the slope of cognitive equivalence but, since dog breeds were produced past artificial selection, nosotros cannot be sure that cognitive equivalence was maintained across the whole size range [cf., Martin and Harvey, 1985].

Hither, nosotros consider a variation on this theme. We focus on primates with clear sexual dimorphism in body size and then every bit to minimize error due to the small range in adult body sizes. 2d, nosotros take the ways of males and females then as to reduce the error in individual information points. And 3rd, we only consider data from wild specimens. We then estimate the gradient by fitting a line through the female person and male person average (which nosotros will refer to as the 2-point gradient). We predict that this 2-point slope will be steeper than the slope through all bachelor data points and closer to the true, unbiased value.

This 2-point slope volition be biased when the sexes differ in torso composition, in which case body mass is not a good guess of actual (lean) body size [Schoenemann, 2004]. In humans (not in our sample), men'south bodies are far leaner than women'south bodies, fifty-fifty among foragers [Wells, 2010]. Obviously, the 2-point gradient would so be overestimated. However, such major sex differences in adiposity are not plant amongst nonhuman primates because both arboreality and the loftier mobility nether natural weather condition will strongly limit adiposity and thus reduce any such differences [Heldstab et al., 2016; Sterck et al., 2019]. Past including but animals taken from the wild, nosotros largely eliminate this possible confounding effect.

The 2-indicate gradient will also exist biased when males and females experience differential selection pressures on overall cognitive abilities, in detail due to sexual selection, which by definition may impact the sexes differently. We practice not expect this to exist important because we know of no studies of primate cognition that needed to control for sexual activity [due east.g., Amici et al., 2012; Hopkins et al., 2014; Damerius et al., 2017; see likewise Arden and Adams, 2016, for dogs]. Besides, for humans most experts agree that in that location is no gender difference in intelligence, although some contend for a small difference [Irwing and Lynn, 2005], which may likewise reflect differential socialization rather than a difference in trunk size. Moreover, for primates, Lindenfors et al. [2007] found no bear witness that sexual choice affects the relative neocortex size, the largest role of primate brains. Thus, this supposition seems warranted. Still, for birds, Garamszegi et al. [2005] found a weak positive effect of extra-pair copulation on female person encephalon size. As well, Kotrschal et al. [2012] constitute that males in an Icelandic population of three-spined sticklebacks had far larger brains than females, although they could merely speculate nearly the selective agent (mayhap male-merely parental care). This effect is less likely in our sample because we focused on highly dimorphic species, thus excluding major variation in the mating system. However, to control for the possibility, we will compare species with single-male versus multimale mating. A final possible effect of sexual selection is that at that place may be an upper limit to the males' ability to maintain cognitive equivalence as body mass dimorphism increases, because females are thought to exist at the ecologically optimal size for a given niche. Nosotros therefore also examine the importance of dimorphism every bit a cistron in the slope.

Given these various assumptions and our inability to fully test all of them, it is essential to seek external validation. There are 2 ways of doing this. First, nosotros tin can assess the ecological validity by asking whether the residual brain size values based on the new gradient actually predict cerebral abilities across species and exercise so improve than alternative neuroanatomical measures that have been proposed in the past. This test faces a major hurdle in that we do non know whether the human relationship between the right neuroanatomical measures and cerebral performance is linear, more than linear, or less than linear. This problem is exacerbated by the fact that the performance measures are often normalized or even ordinal. Notwithstanding, since the relationship is necessarily monotonic, the correct measure should always preserve the rank order in cognitive functioning. Although the dissimilar neuroanatomical measures we compare are likely to show high rank correlations among each other, we can still examination their predictive value by assessing the value of the rank correlations with cognitive performance. We found ii published data sets comparing species' cognitive operation for this analysis. A second way to validate the slope value is to compare it with the strength of genetic correlations between brain size and body size [Lande, 1979]. Nosotros will do this in the Discussion, once we have acquired our estimate.

In this written report, we therefore first adamant the slopes of cerebral equivalence for sexually dimorphic primate species. We used 2 samples (one using conservative and another using more relaxed sample size criteria) and assessed the possible effects of sample sizes, mating organization, and sexual dimorphism. Side by side, we validated the slope we obtained by comparing it with the genetic correlation betwixt encephalon and body size and past its rank correlation with published measures of species' cognitive abilities. Finally, nosotros fabricated a first, preliminary assessment of the consequences of adopting this new measure of a species' cerebral abilities, using extinct hominins.

Materials and Methods

We compiled data on the cranial chapters and trunk mass of primates from the studies by Heldstab et al. [2018, 2019]. We selected species with adequately large sample sizes (north ≥v for each sex) to minimize mistake in estimating the mean body and brain size of males and females. We only included wild-caught animals to avoid captivity effects on body mass (usually fattening), and fully adult individuals, every bit evinced by the eruption of the third molar. Finally, we set a minimal mass dimorphism at 1.20 because preliminary analysis, as expected, revealed wildly fluctuating (including negative) estimated two-betoken slopes at values shut to monomorphism. Overall, we had 18 primate species that met these criteria. The brain-torso size slope was and then estimated for each species as the slope of the line connecting the male and female average (the 2-point slope), as well every bit the slope through all of the points. A 2d primate information prepare was produced by including all species with at least ten adult individuals and at least 2 of each sex and mass dimorphism of at least ane.20. This data set up contained 27 species. We expected more variance in the estimate of the gradient. Nosotros refer to these 2 data sets as the conservative and relaxed primate data set, respectively.

We examined the bivariate effects of diverse variables discussed above on the estimated slope: mating system (single male vs. multimale) and female brain size, also as sexual dimorphism (to assess whether it has a positive effect on estimated slope for which we should control), and sample size (too). We also used a model selection approach to place the best-plumbing fixtures model.

For the validation part, we used published data sets to capture cognitive performance, i.e., global cerebral performance [Deaner et al., 2007] and the general intelligence factor g _s1 from Reader et al. [2011].

The independent measures we used are:

1. Body size (P, estimated as trunk mass in g),

2. Encephalon size (Eastward, estimated equally endocranial volume in mL, roughly corresponding to mass in g [Isler et al. 2008]),

3. Encephalization quotient of Jerison [1973] (Due east/[0.12 × P^0.667]), and

4. An gauge of the cerebral brain based on cognitive equivalence (Eastward – [0.065 × P^0.27]), where the exponent 0.27 is the midpoint value of the empirically obtained intraspecific 2-point slopes in the first set of analyses and the intercept based on ane of the smallest-brained mammals, i.e., Sorex minutus, which has a 5-g body mass and a 0.1-g encephalon weight [Bauchot and Stephan, 1966]. This measure out ensures that virtually all mammals have a positive cerebral brain size.

Note that mensurate 4 is an absolute mensurate of the amount of brain tissue bachelor for cerebral tasks, whereas measure three, i.e., the EQ, is a ratio. Thus, 2 species that differ greatly in body size tin have the same EQ, yet the larger of the ii will accept far higher values of measure 4. Note, too, that measure 4 may be negative for ectothermic vertebrates [cf., Jerison, 1973], and thus may only be intuitive for birds and mammals.

Equally noted above, nosotros used rank correlations to assess the fit of these measures.

Results

Estimating the Value of the Gradient of Cognitive Equivalence

Equally expected, the ii-bespeak slopes based on mean values per sex are better than those based on all private points. Using the conservative primate data set up, we plant that the slopes using all of the data points (mean = 0.209 and SEM = 0.020) were on boilerplate 30% less steep than the 2-signal slopes (mean = 0.268 and SEM = 0.020). Likewise, the more conservative data set up, with at to the lowest degree 5 adult individuals of each sex, gave more reliable gradient estimates (lower SEM) than the more relaxed data set up, which also varied less with sexual dimorphism (Tabular array one). Thus, the best estimate of the gradient is 0.27.

Tabular array i.

Effect of changing the minimal cutoff point of sexual dimorphism for inclusion into the analysis of the 2-point slopes for the conservative and the relaxed primate samples

The analyses of the possible effect of confounding variables were performed on the bourgeois primate data set only, and thus using merely species with sexual dimorphism of ≥1.20, where the standard errors of the estimated gradient values had stabilized. Our limited sample size forced united states to do bivariate tests. In these tests, we did not demand to right for phylogenetic nonindependence because the Pagel [1992] λ values of the slopes were <0.001. We found no effect of sample size (r = –0.041, northward = 18; p = 0.87) on the value of the 2-point slope. Likewise, in that location was no effect of sexual dimorphism (r = –0.093; p = 0.71) or of mating system (single male vs. multimale; t _[16] = –ane.39; p = 0.18). Moreover, none of the various possible multivariate models showed anywhere near a significant result and multiple models had a close similarity in overall fit (not shown).

Validating the Value of the Slope

Table ii provides the values of the Spearman rank correlations for the validation studies for each of the five measures used. Overall, as expected because of the need to use ranks only, the results were very close, and the conviction limits for the various measures generally overlapped. Nonetheless, in both cognitive performance measures (data from Deaner et al. [2007] and Reader et al. [2011]), the EQ yielded the lowest correlations, whereas the cognitive brain judge, absolute brain size, and even body size did about equally well.

Table 2.

Validation analyses with multiple information sets of cognitive functioning, using Spearman rank correlations

Word

Value of the Gradient

Nosotros examined the proposition that there is a slope of cognitive equivalence, which predicts the change in brain size, and thus cognitive abilities, corresponding to a change in trunk size in which all of the details of bauplan and sensory-motor abilities are kept constant. Existing estimates of this slope suffer from the problem of measurement error, considering mammals generally have just a narrow range of body sizes, whereas their estimates (trunk mass) can vary widely. We therefore used mean values for males and females in sexually dimorphic species, which have a larger range of body sizes, to estimate the 2-betoken gradient. In general, this approach yielded steeper slopes than regressions through all available data points, confirming the expected reduction in the consequence of mistake on slope estimates and explaining why previous studies frequently found shallower slopes.

Nosotros constitute no effect of possible confounding variables, such as mating system or dimorphism beyond 1.20. The gradient of 0.27 obtained here is the aforementioned as the ane found for dogs, where breeds vary greatly in size [Bronson, 1979], but, as expected, somewhat higher than the value of 0.23 [Hemmer, 1971] or 0.25 [Röhrs, 1986] institute in previous intraspecific mammal studies with big samples that used all private information rather than estimating ii-betoken slopes.

Validation of the Slope Judge

Based on selection experiments on body size in inbred mice lines, Lande [1979, 1985] predicted a 0.36 gradient of log (encephalon size) on log (body size), which would also hold when trunk size changes by drift, and thus also when populations contain selectively neutral genetic variation in body size. Slopes observed after selection experiments on body size in rodents yielded values between 0.2 and 0.iv [Riska and Atchley, 1985], but since these should likewise be afflicted past the fault problem their true value may as well exist ≥0.25. Nevertheless, Lande [1985] suggested that the genetic correlation between encephalon and body size is lower in natural species. Indeed, Grabowski [2016] estimated it for samples of five primate species taken from the wild and found an average value of 0.254, which should be somewhat lower than the truthful slope, given the error in trunk mass used to judge genetic correlation between brain and body. Thus, our approximate of 0.27 for the slope of cognitive equivalence is quite consistent with these estimates of genetic correlation.

We therefore used a line of P^0.27 (where P is body size) every bit the judge of the somatic brain. For estimates of a species' cognitive encephalon we demand to anchor the line (Fig. 1). To achieve positive values for all species in our sample, we took the presumably smallest-brained mammal, i.due east., S. minutus, and forced the curve through its values (average body mass five g and average brain mass 0.one m) [Bauchot and Stephan, 1966]. This leads to the minimum estimated size of the somatic brain every bit E_s = 0.065 x P^0.27, and thus the following approximate of the cognitive brain size: East_c = Eastward – E_s, where E is the species' actual brain size. Figure i illustrates the process.

Fig. one.

Analogy of the difference betwixt EQ and estimates of cognitive brain size. The steep black line gives the Jerison curve for the boilerplate mammalian encephalon and the shallow blue line the curve for the estimate of the somatic brain, which was anchored using the smallest-brained mammal S. minutus (star). 4 hypothetical species (i.e., squares A-D) are included to illustrate the different measures. The black vertical lines are the residuals from the Jerison line; EQ is the ratio of the value for a given betoken and the value of the corresponding indicate on the black line. The blue dashed lines are the estimates of the cerebral encephalon size.

The most important result of the cognitive validation analyses was that the alternative measures, including body size, all perform better than the EQ. The EQ is the ratio of observed to expected brain size and, in Figure 1, the antilog of the residual from the Jerison line. Thus, a very small mammal could have the same ratio as a very large mammal (every bit practise species B and D in Fig. one) even if they differ dramatically in the accented size of the estimated cerebral encephalon (the antilog of the blue dashed vertical lines). Under the EQ, the estimated order of overall cerebral performance would increase every bit follows: A = C < B = D. Nether the cognitive brain estimate deployed hither it would be: A < B < C < D, i.e., the same order as in the absolute brain size or (in this example) the absolute trunk size of the species.

The close similarity in how well the various non-EQ measures predicted actual estimates of overall cognitive abilities is not surprising. Accented brain size is often a reasonable predictor of specific cerebral abilities in studies that did not use the measure based on cognitive equivalence [Benson-Amran et al., 2013; MacLean et al., 2014; Horschler et al., 2019]. The 2 measures are closely correlated and also of course testify potent correlations with body size. Indeed, also the neocortex ratio remains highly correlated with body size [eastward.1000., Stout, 2018]. Although nosotros did not include the neocortex ratio in this study, in the data set used by Dunbar [1992], which uses averages for genera and sexes, the Spearman rank correlation between the two is 0.871 (due north = 38, p < 0.001; nonlinear relationship). Thus, the discrepancies among the various culling approaches (absolute brain size, cognitive equivalence, and neocortex ratio) are quite pocket-sized, and in exercise we will often not have the resolution needed to make up one's mind which of these is the all-time due to the loftier noise in the estimates of cerebral ability.

Based on these highly similar results, 1 could therefore fence that it is both about parsimonious and virtually user-friendly to utilize absolute brain size from now on, every bit has been proposed before. However, we would advise that the modest correction for body size evident in the estimate of the cerebral encephalon is conceptually necessary. First, the cognitive abilities of extremely big animals would nearly certainly exist overestimated. 2d, and virtually chiefly, sexual activity differences in cognitive abilities inside dimorphic species would otherwise be inferred which may well not exist. Nosotros assumed no sex differences in intelligence for nonhuman primates, consistent with the results of the admittedly noisy cognitive tests in diverse species. Just the far more than sophisticated data available for humans also back up this decision: at that place is only a tiny (if any) gender difference in intelligence in humans [Irwing and Lynn, 2005] despite a clear gender difference in brain size [e.g., Martin, 1986] (mean: 1,498 mL for males and 1,326 mL for females). We therefore prefer the judge based on cognitive equivalence.

Patently, this approach reduces the effect of torso size on brain size much more than has traditionally been considered necessary. It is not clear why this is. First, this conclusion may be peculiar to primates, with their large brains for mammals and thus big neocortices [Finlay et al., 2001]. Where cognitive functions take up a large proportion of the overall encephalon size, the relative importance of the somatic functions must become concomitantly smaller. If so, nosotros expect the slope to be lower for other mammalian orders. Second, the size of the somatic brain may exist modest overall because neurons in many brain regions can be involved in multiple networks simultaneously, thus blurring the distinction betwixt somatic and cerebral functions.

The analysis presented here is of course preliminary. It is based on primates only, and on a limited number of species at that, and could not establish whether species differences in slopes were true or merely reflected error. Future work should include all mammals with nontrivial dimorphism in body size, while ensuring the use of fully adult, wild specimens, with values not affected by advanced pregnancy or confounded by seasonal variation in adiposity. Forth with piece of work on other vertebrates, this piece of work may detect that slopes vary among lineages, and generate and test hypotheses on its causes.

Nevertheless, this study confirms that the consequence of torso size on the size of the somatic encephalon (the 2-point slope) varies considerably between mammals (and presumably birds) [Tsuboi et al., 2018] on the i manus and ectothermic vertebrates (fishes, amphibians, and reptiles) on the other hand. The latter vary betwixt 0.4 and 0.5 within species [Tsuboi et al., 2018]. For fishes, Triki et al. [2021] obtained a mean intraspecific slope of 0.49 that is independent of trunk size variation. Furthermore, Triki et al. [2021] studied ane fish species, i.e., the cleaner fish Labroides dimidiatus in more detail. Individual performance in various cognitive tasks was not correlated with trunk size, so that the intraspecific encephalon-body slope of 0.53 of this species indeed represents the gradient of cognitive equivalence. The causes of this major difference between intraspecific slopes in endotherms versus ectotherm vertebrates remain unexplained.

Information technology might be objected that comparing distantly related taxa on their cognitive performance based on encephalon measures just is not advised given the known differences in neuron densities in the brains of different clades [Herculano-Houzel, 2017] and the result on encephalon size of highly divergent bauplans. We fully endorse this view. Comparing cerebral brain estimates among distantly related lineages may non be very revealing, and we should exist very careful. Nonetheless, this restriction does not fence in favor of reviving the EQ approach.

Applications: An Example

Although a thorough application of the new method is across the scope of this newspaper, we can get a commencement impression by comparing the cognitive encephalon gauge with those of Jerison's [1973] EQ for extinct hominins thought to be in the main lineage contributing representatives that formed our own species (thus excluding the robust australopithecines and both Homo floresiensis and H. naledi). Because the new measure produces cognitive brain size estimates that are rather close to overall brain size, the 2 techniques yield a rather different picture (Fig. two). Jerison's [1973] EQ suggests a long period of a continuing, gradual increase in cognitive abilities from 4 Ma until roughly 300 ka, followed past a sudden uptick. The alternative EQ mensurate proposed by Grabowski et al. [2016], which is based on a somewhat shallower slope, gives a similar flick, only without the sudden uptick in the last 300 ka (see their Fig. 2). The cognitive equivalence measure, in dissimilarity, suggests cognitive stasis between 4 and 2 Ma, later on which cognitive abilities steadily increased.

Fig. ii.

Changes in cognitive encephalon size (a) and EQ (b) during hominin evolution. The dates are the median observed age (Ma earlier nowadays). Data are based on Grabowski [2016].

It can be argued that the general blueprint suggested by the cerebral equivalence measure is closer to the current understanding. Thus, the material culture of hominins did not exceed that of the extant great apes [Wynn et al., 2011] until the multifariousness and complication of hominin material culture began in earnest around 2 Ma [e.thousand., Stout, 2011], and there is no great increase in relative brain size over fourth dimension within the human species [Schoenemann, 2013; Grabowski et al., 2016]. However, the paucity of material and the problems inherent in estimating body size from incomplete remains advise circumspection, and this alternative assay should serve more to question the EQ-based interpretation than to back up a specific alternative.

Implications

Comparative tests of adaptive hypotheses to explain brain size evolution in primates sometimes attain incompatible conclusions [Wartel et al., 2019], as practise those on other mammals or birds [Healy and Rowe, 2007]. Among the many reasons for this impasse, i potentially prominent aspect is generally disregarded [Rogell et al., 2019]. These tests invariably include trunk mass as a control variable and so endeavour to explain the remaining variation in brain size, in effect letting the blueprint of covariation among the variables determine the allometric gradient. In practise, therefore, the loftier correlation between trunk size and the other potential explanatory variables may affect the outcome and estimation of the results [Stout, 2018], depending on which set of potential predictors are included in the analysis.

Thus, when we have a validated estimate of the size of the cognitive brain we tin utilise this residual measure equally the response variable, so should get a fairer evaluation of the hypotheses trying to explain encephalon size development. In the end, this may be the most valuable contribution of the kind of analysis undertaken in this paper.

Acknowledgment

We thank Tsuboi Masahito for comments on an before version of this newspaper. C.P.S. thank you the Eugene Dubois Foundation for supporting his stay in Maastricht, The netherlands, which inspired him to accept upward the quest once more.

Statement of Ethics

Information were compiled from published studies.

Conflict of Involvement Statement

The authors declare that they take no conflict of interests.

Funding Sources

This work was supported by the Swiss National Science Foundation (grant No. 310030B_173334/i to R.B. and P2NEP3_188240 to Z.T.).

Author Contributions

C.P.Due south. provided the conceptual basis, and R.B. and Z.T. added major discussion. S.A.H. provided data. S.A.H. and C.P.S. did the analyses. All of the authors wrote the terminal version. A preprint version of this commodity is available on bioRxiv [van Schaik et al., 2021].

Data Availability Statement

The compiled information for this study is accessible at the public repository Figshare (https://doi.org/10.6084/m9.figshare.14346959).

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Author Contacts

Carel P. van Schaik, vschaik@aim.uzh.ch

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Article / Publication Details

First-Page Preview

Received: February 17, 2021
Accepted: May 02, 2021
Published online: July 09, 2021
Result release date: Baronial 2021

Number of Print Pages: 12
Number of Figures: ii
Number of Tables: two

ISSN: 0006-8977 (Print)
eISSN: 1421-9743 (Online)

For boosted information: https://www.karger.com/BBE

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