How general is cognitive ability in non-human animals? A meta-analytical and multi-level reanalysis approach

Abstract

General intelligence has been a topic of high interest for over a century. Traditionally, research on general intelligence was based on principal component analyses and other dimensionality reduction approaches. The advent of high-speed computing has provided alternative statistical tools that have been used to test predictions of human general intelligence. In comparison, research on general intelligence in non-human animals is in its infancy and still relies mostly on factor-analytical procedures. Here, we argue that dimensionality reduction, when incorrectly applied, can lead to spurious results and limit our understanding of ecological and evolutionary causes of variation in animal cognition. Using a meta-analytical approach, we show, based on 555 bivariate correlations, that the average correlation among cognitive abilities is low (r = 0.185; 95% CI: 0.087–0.287), suggesting relatively weak support for general intelligence in animals. We then use a case study with relatedness (genetic) data to demonstrate how analysing traits using mixed models, without dimensionality reduction, provides new insights into the structure of phenotypic variance among cognitive traits, and uncovers genetic associations that would be hidden otherwise. We hope this article will stimulate the use of alternative tools in the study of cognition and its evolution in animals.

1. Introduction

In humans, general intelligence can be broadly defined as the cognitive ability to reason, solve problems, think abstractly and acquire knowledge [1]. Applying factor-analytical procedures to large cognitive test batteries consistently reveals a single factor that loads positively, both for phenotypes and genotypes, and can explain a significant amount of variation in human intelligence [2–4]. Today, the concept of general intelligence, denoted as the psychometric factor g, is described as one of the most replicated findings in cognitive science [3,5,6], although there remains debate around its nature and existence [7,8]. In humans, g typically explains around 50% of variance in test performance [5] and has been suggested to have a clear genetic basis [4,9]. In comparison, the study of individual differences in cognitive abilities of non-human animals is still in its infancy [6,10,11]. Nonetheless, individual differences in performance on cognitive test batteries in animals have been proposed to amount to differences in intelligence quotient in humans (e.g. [12,13]). However, it is not clear whether these analogies are warranted as overall support for g in non-human animals has not yet been assessed quantitatively.

The existence of ‘g’ predicts positive among-individual correlations in performance on tasks from various cognitive domains. However, most studies of g in non-human animals have taken the ‘individual gambit’, i.e. they assume that phenotypic correlations correspond to among-individual correlations [14,15]. This assumption, common in many fields of study in animal behaviour [16], can be problematic because phenotypic correlations from single measurements reflect a mixture of processes occurring at the among- and within-individual levels. This distinction is important; among-individual correlations are derived from average trait values among individuals, while within-individual correlations arise when changes in trait values are correlated within individuals across subsequent measurements due to within-individual plasticity and/or correlated measurement error. The individual gambit is particularly risky for traits with low repeatability [15,17], which is the case for cognitive performance in non-human animals (r = 0.15–0.28; reviewed in [18]). In other words, issues with the individual gambit can arise when the covariance among cognitive traits is due to correlated measurement error or an unidentified variable affecting all traits. The individual gambit can be avoided by using multivariate mixed-effect models (MMMs) to partition (co)variance patterns at the among- versus within-individual levels [17,19]. MMMs are particularly useful when investigating trade-offs [20] or multivariate correlation structures such as in the study of general intelligence [21]. However, the application of this framework to the study of cognitive traits remains scarce, mostly because (i) studies used single measurements per individual and/or (ii) studies elected to reduce dimensionality using factor-analytical procedures to convert cognitive performance across tasks to a single general factor.

To date, only a few animal studies have studied the genetic architecture of cognitive abilities (e.g. [21]). Instead, most studies of g in animals take the ‘phenotypic gambit’, which assumes that the strength and direction of selection on observed phenotypes is sufficient to predict evolutionary trajectories [22–24]. This represents a major limitation, because various genetic mechanisms (e.g. linkage disequilibrium, pleiotropy and G × E interactions) can inhibit or alter the evolutionary response to selection [25,26]. Many quantitative geneticists have cautioned against inferring genetic patterns from phenotypic correlations (i.e. Cheverud's conjecture; [27]), particularly for traits with low heritability [25,28,29], such as behavioural and cognitive traits [30,31]. In humans, for instance, the genetic expression of cognitive traits in children differs for different maternal environments, implying that the environment interacts with genes [32]. In animals, however, the phenotypic gambit is still a major, and often unstated, assumption that limits our understanding of the adaptive value of general cognitive abilities. Again, this gambit can be overcome by using MMMs. When relatedness between individuals is known, MMMs can be used to decompose the phenotypic (co)variance into additive genetic (co)variances. This approach allows researchers to use the multivariate breeders' equation to predict the evolutionary response to selection on multiple traits [25,33,34]. Otherwise, estimating selection on g involves making critical assumptions that are probably false, as selection does not necessarily act along the single trait combination that harbours the most variance (i.e. other trait combinations might be important for fitness) [34–36]. Moreover, interpreting selection on composite characters (i.e. PC axes) is notoriously hard [36–38].

Studying individual differences in a multitude of cognitive tasks is a fundamental prerequisite to understanding the evolution of cognition [39,40], which provides a strong motivation to identify and overcome the above-noted limitations. In this study, we address the following questions: (i) is there evidence for g in non-human animals based on current factor-analytical methods? (2) Are we missing any insights by using a dimensionality reduction approach? To answer these questions, we first qualitatively assessed the recent use of factor-analytical procedures to estimate general intelligence. We then used a meta-analytical approach to quantitatively estimate the support for g in animals. Finally, we conducted a re-analysis using a recent example from the scientific literature to evaluate and discuss the current application of statistical methods in studies of general intelligence in non-human animals. We demonstrate how not reducing dimensionality, and instead using a (co)variance partitioning approach, can provide different and new insights into the evolution of cognitive abilities.

2. Review and meta-analysis

(a). Methods

(i). Data collection

We followed the preferred reporting items for systematic reviews and meta-analyses (PRISMA; [41]) approach to collect the datasets used in the current study. After screening articles, we initially collected 49 published articles on general cognitive abilities (i.e. ‘general intelligence’ or ‘g’) in non-human animals (see Methods and electronic supplementary material, table S1). Following further evaluation of each study, we kept a total of 33 studies that provided sufficient information for our meta-analysis. We excluded comparative studies that assessed correlated cognitive performance across species or on humans. We extracted the vast majority of studies on general intelligence in animals with the exception of a few studies concerned with directly comparing between human and non-human social and physical cognition (e.g. [42,43]). Each selected dataset included 10–241 individuals (median = 32) that measured performance across 3–13 cognitive tasks (median = 6). From these datasets, we extracted, when available, details of principal component analysis (PCA) or factor analysis (FA), estimates from factor loadings and variance explained by the first and second component or factor (e.g. PC1). In total, we extracted information from 42 factor-analytical procedures aimed at estimating variance explained by a ‘general factor’. Furthermore, when available, we extracted bivariate phenotypic correlation of performance between cognitive tasks (23/33 = 70% of studies). Further details on data collection are provided in the electronic supplementary material.

(ii). Meta-analytic models

We limited our meta-analytic models to bivariate phenotypic correlations between cognitive performance scores since they were readily available and provided information regarding statistical relationships before dimensionality reduction. We extracted a total of 555 individual bivariate phenotypic correlations from 23 studies providing correlation matrices of performance among cognitive tasks. We used a meta-analytical approach to estimate average correlation coefficients, accounting for variation in sample size. More precisely, we performed different multi-level meta-analytical models using the ‘metafor’ package [44] in R [45] to estimate the overall mean correlation coefficient of bivariate cognitive performance relationships. The use of multi-level, i.e. hierarchical, meta-analytical models, allowed correlations to be explicitly modelled within the different levels or factors [46]. For each model, we used standardized correlation coefficients, using Fisher's Z-transformation, as a response variable. In our most complex model, we considered species identity (n = 11) and study identity (n = 23) as random factors, controlling for any shared variance among these factors. We also assessed the extent of variation among correlation coefficients in each meta-analytical model by calculating heterogeneities (I²). In meta-analytical models, overall statistical heterogeneity refers to the variation in effect sizes between studies [47]. Along with the overall heterogeneity (I²_total), measured as between-study variance divided by the total variance [47], we also provide estimates of heterogeneity for each random factor [46]. I² values of 25%, 50% and 75% are generally considered to be low, moderate and high levels of heterogeneity, respectively [47]. A high level of heterogeneity can be interpreted as evidence for strong variation in effect sizes among levels of factors (e.g. studies or species). We also investigated whether our meta-analysis showed any bias in publication by conducting a type of Egger's regression by adding the sampling standard error as a moderator in our more complex multi-level model [46,48]. If the intercept of Egger's regression is significantly different from zero, then there is evidence for publication bias. This usually indicates that large effect sizes (i.e. correlation) with large sampling variance (i.e. small sample size) are more prevalent than expected, potentially overestimating the overall effect size. We did not compute other meta-regression models since measuring the effects of moderators was not central to addressing the aims of this study.

(b). Results

(i). Dataset summary

Variance explained by g in non-human studies, extracted from the first component or factor (e.g. PC1), ranged from 17.0 to 64.6%, and the average variance is nearly identical whether PCA is considered alone or combined with FA (table 1). Only half the studies provided information on the second component or factor (e.g. PC2), which explained 5.0–32.0% of total variance (table 1). Using studies that provided the first two components, we found that, on average, PC1 only explained 11.9% more variance than PC2. Despite this small difference, 72% of studies that provided the first two components interpreted PC1 as general intelligence. Furthermore, out of the 25 studies performing PCAs, only 10% provided a statistical test for the significance of the extracted component (e.g. permutation test), making it difficult to judge the reliability of the component. In fact, 90% of studies using PCAs assessed the significance of components using the ‘eigenvalue > 1’ rule (table 1). We also found significant differences in the rules used to estimate the value or significance of factor loadings. Rough rules such as ‘factor loadings larger than’ 0.3, 0.4 and 0.5 were observed in most studies.

Table 1.

Descriptive statistics of published factor-analytical procedures used to extract a general intelligence factor in the non-human animal literature. Presented are the total number of factor-analytical procedures for all studies (i.e. PCA, EFA and CFA), studies that used PCA only and studies that used PCA without control variables (e.g. anxiety and exploration). The median number of tested individuals and the median number of factors included per factor-analytical procedure are provided next. The median proportion of variance explained by the first two components is then provided. Finally, the percentage of studies that used the ‘eigenvalue greater than 1’ rule to extract a general factor of intelligence is provided.

	all studies	PCA only	PCA without controls
no. factor-analytical procedures	42	30	25
no. tested individuals/procedure	40	33	40
no. factors included/procedure	6	6	5
variance explained – first component	0.32	0.32	0.32
variance explained – second component	0.22	0.21	0.23
Eigen > 1 rule utilization	82.5%	90.0%	88.0%

(ii). Meta-analytical models

According to our simplest meta-analytical model (intercept-only) excluding random effects, mean correlation coefficient among cognitive traits was estimated at 0.163 [95% CI: 0.147–0.178]. A multi-level meta-analytical model including random effects revealed a similar overall correlation between performance across cognitive task (r = 0.185; figure 1). These results suggest that shared variance between pairs of cognitive abilities (r²) ranges from 0.027 to 0.034. In our multi-level meta-analytical model, total heterogeneity (I²_total) was 63.21%, suggesting that the degree of variation in effect sizes between studies was moderate to high [47,49,50]. Statistical noise (i.e. sampling variance or error) explained 37% of the total variance in estimated correlation coefficients, a value similar to values found in other across-species meta-analyses [18,49]. A significant amount of total heterogeneity was attributable to species (I²_species = 51.16%), while the remaining variance was due to studies within species (I²_{species/study} = 12.05%). These results suggest that species identity plays a key role in correlation coefficients among cognitive traits. Our study, however, cannot differentiate between potential explanations for this result. It could be explained by differences in general versus modular abilities among species. It could also reflect, among other things, differences in experimental designs, testing environments or the match between the cognitive test battery and the ecology of the species. Further research is needed to address these possibilities. Finally, there was little evidence of publication bias as the intercept of Egger's regression did not differ from zero (b₀ = 0.048, 95% CI: −0.072 to 0.169).

Figure 1.

Results from the meta-analytic model. Average correlation coefficients (±95% CIs) are presented for each species. The total number of extracted correlations (r) and the median sample size (n) per correlation are also provided for each species. The multi-level model including random effects of species and study identity estimates an average correlation of 0.185 (95% CI: 0.087–0.287).

3. Case study

(a). Methods

In addition to our meta-analysis, we present a case study from a recent study of g in non-human animals. By doing so, we hope to highlight some limitations of the current methods used in the study of g and provide alternatives. The study in question [13] provides a rare assessment of the broad-sense heritability (H²) and gene-by-environment interactions (G × E) in cognitive performance in non-human animals. The authors measured performance in five cognitive tasks on male mice from 58 full-sib litters, each of which had two siblings maintained in standard laboratory conditions (control; 116 individuals) while two other siblings had access to a running wheel and were exposed to novel environments on a daily basis (enriched; 115 individuals). The five cognitive tasks were the Lashley maze, passive avoidance, T-maze, odour discrimination, and spatial water maze. In summary, Sauce et al. [13] applied exploratory FA (EFA) to extract scores of ‘general cognitive ability’ (GCA) and used univariate mixed models to estimate that the H² of GCA was 0.15 in enriched environments compared with 0.55 in controlled, non-enriched, environments. Furthermore, in their study, Sauce et al. [13] found no evidence for G × E interaction in general intelligence based on GCA scores (for further details, refer to the study in question [13]). Here, we re-analysed the five traits measured in [13], along with the GCA factor scores extracted from the EFA. All models were run in ASReml-R [51]. For reproducibility, detailed methods and codes are provided in the electronic supplementary material.

First, we ran univariate mixed models with the environment fitted as a fixed effect and litter identity fitted as a random intercept to estimate H² in control versus enriched environments for each of the five tests and the GCA scores (as used in [13]). In these models, the variance attributed to litter identity as a random effect represents the among-litter variance (V_LIT). Here, the among-litter variance is analogous to the among-individual variance when traits are measured repeatedly on the same individuals (in which case individual identity would be put as a random effect instead of litter identity). The remaining variance was the residual variance (V_e). We calculated broad-sense heritability as H² = 2 × V_LIT/(V_LIT + V_e).

Second, we used random regressions [52] to estimate the amount of among-litter variance in intercepts (V_int), slopes (V_slp), and the correlation between intercept and slope (r_int-slp) of the relationship between each trait and the environment. Evidence for the presence of random slopes (as opposed to a single common slope) was assessed by the likelihood ratio test comparing a model that included all three above parameters against a model that included V_int only.

Finally, we used a multivariate mixed model (MMM) to estimate all of the correlations among the five traits at the among- and within-litter levels. The MMM included all five traits as dependent variables, and a V_LIT and V_e fitted to each trait. In addition, the MMM included a correlation structure at both the among- and within-litter levels. Hence, all 10 correlations between all five traits were computed at the among-litter level (r_LIT) and the residual (within-litter) level (r_e).

(b) Results

(i). Among- and within-litter variance

The among-litter variance (V_LIT) was relatively low in both control and enriched environments for most traits (electronic supplementary material, table S2; figure 2). The patterns of V_LIT and V_e in GCA scores were almost identical to the pattern found in the Lashley maze (figure 2). The four other traits showed contrasting patterns of change in V_LIT and V_e in control versus enriched environments (figure 2). Only passive avoidance showed a statistical difference in variance components in control versus enriched environments (figure 2), with significant increases in both V_LIT and V_e in enriched environments (electronic supplementary material, table S2).

Figure 2.

(a) Among-litter variance, (b) within-litter variance and (c) broad-sense heritability in five learning tasks measured on male mice from 58 full-sib litters, each of which had two siblings maintained in standard laboratory conditions (control; 116 individuals), while the two other siblings had access to a running wheel and were exposed to novel environments on a daily basis (enriched; 115 individuals). Mice were tested on a battery of five tasks, including (i) Lashley maze (mean number of errors across three trials; black open circles), (ii) passive avoidance (ratio of avoidance latency by baseline latency; red triangles), (iii) T-maze alternation (trial at first four correct choices in a row; green plus sign), (iv) odour discrimination (mean errors across three trials; blue × sign) and (v) spatial water maze (mean path length in cm across trials 1–2; indigo diamond). Also shown are estimates for the factor scores extracted from an exploratory factor analysis and interpreted as ‘GCA’ in [13]. Note that standard errors are not shown (see electronic supplementary material, table S2). (Online version in colour.)

(ii). Random slope models

As initially reported [13], there was no statistical support for random slopes in GCA according to the environment (electronic supplementary material, table S3). Again, the estimates in GCA were almost identical to those estimated for the Lashley maze (electronic supplementary material, table S3; figure 3a,b). Adding random slopes significantly improved model fit for the passive avoidance test (electronic supplementary material, table S3), indicating that litters significantly differed in how their scores in the passive avoidance test changed from the control to the enriched environment, i.e. significant G × E interaction. This result matches the significant differences in V_LIT above, where variation among litters was low in the control environment but high in the enriched environment (figure 3c).

Figure 3.

Litter-specific reaction norms (grey lines; N = 58) in (a) the factor scores extracted from an exploratory factor analysis and interpreted as ‘GCA’ by Sauce et al. [13] and five learning tasks measured on male mice, including the (b) Lashley maze, (c) passive avoidance, (d) T-maze alternation, (e) odour discrimination and (f) spatial water maze. Grey lines in panels show predicted trajectories as function of the environment, relative to the population mean (indicated by ‘0’ on the y-axis).

(iii). Among- and within-litter correlations

Correlations at the among-litter level were mostly weak and non-significant, except for the negative correlation between the passive avoidance and odour discrimination tests (electronic supplementary material, table S4; figure 4a). By contrast, there were four positive and significant correlations at the residual level (electronic supplementary material, table S4; figure 4b).

Figure 4.

‘Heat maps’ displaying the (a) among-litter and (b) within-litter correlations between five learning tasks measured on 231 male mice, including the Lashley maze, passive avoidance, T-maze alternation, odour discrimination and spatial water maze. Correlations significantly different from 0 are denoted by asterisks (***; see electronic supplementary material, table S4 for 95% confidence intervals). (Online version in colour.)

4. Discussion

(a). Is there evidence of g in non-humans?

Our meta-analysis suggests that the strength of evidence for g in non-human animals is currently weak. Although the average variance explained by g in previous studies is 32%, the average phenotypic correlation among performance in cognitive tasks is low (r = 0.185; figure 1). This important divergence might be explained by issues regarding key assumptions of the statistical methods used. Using PCA and FA requires evidence that the multivariate structure differs from random [53]. This key assumption was rarely assessed in studies we extracted (for exceptions, see [54,55]), making it difficult to evaluate the biological pertinence of extracted components. Indeed, previous work has shown that first components extracted from uncorrelated multivariate structures can explain >40% of variance by chance alone (e.g. [56,57]). Therefore, studies interpreting the first extracted component as general intelligence without statistical evidence of a non-random correlation structure are making a major assumption. Furthermore, the mean difference in variance explained by PC1 and PC2 was small (i.e. 11%), suggesting that first extracted components were rarely unique axes representing a ‘general factor’. Considering these limitations and a weak overall correlation among performance in cognitive tasks, we argue that evidence for g in non-human animals is currently poor. Moreover, in comparison to human literature, most animal studies have used low sample size and a small number of tasks representative of only a few cognitive domains [6,11], thus providing less information regarding the biological extent and significance of general intelligence. Our analysis suggests that the use and test of PCA in most studies on g in animals (1993–2019) is inadequate given current statistical standards for these tests. This conclusion concurs with recent statistical discussions in the fields of evolutionary biology and animal behaviour [56–58]. Guidelines for the use of dimensionality reduction methods can be found in the statistic literature and are outside the scope of this study (e.g. [53,59]).

(b). Are we missing any insights by using dimensionality reduction approaches?

As shown in the case study, reduction of dimensionality can lead to inaccurate conclusions. Re-analysing each task separately shows the extracted GCA scores only appropriately represented one of the five cognitive tasks assayed (figure 2). Indeed, the task with the largest loading (i.e. Lashley maze) followed identical variance patterns as the extracted GCA scores. Because the GCA scores are almost perfectly correlated with performance in the Lashley maze (r = 0.99), conclusions from the initial analysis are only relevant for this task and not the other four, which show very different variance patterns. A similar problem is likely to arise in other studies where loadings differ widely between tasks; it is thus crucial that authors report factor loadings, assess their statistical significance, and provide information on (co)variances of unreduced factors if they choose to compute g using dimension reduction techniques [53,56]. It is only appropriate to use dimension reduction methods when there is sufficient evidence to do so [56].

Multivariate analysis of performance across all tasks showed weak associations between the five cognitive traits (figure 4). Importantly, the only statistically significant among-litter correlation was negative, a result that goes against predictions of general intelligence [3–5]. Indeed, g assumes positive phenotypic correlation of performance across tasks, reflecting a single latent intelligent factor. Our re-analysis also provides evidence that passive avoidance followed variance patterns that were opposite to extracted GCA scores. Broad-sense heritability of passive avoidance was actually higher in the enriched environment compared with the control environment (figure 2c). Again, this result is contrary to the initial findings [13] on GCA.

The final major difference revealed by our re-analysis is that, counter to the original analysis, we found evidence of G × E interaction in passive avoidance performance (figure 3), with litters differing in their response to the environment. Specifically, genotypes varied in how they responded to the environment; while there was little to no genetic variation for this trait in the control environment, a great deal of genetic variation was present in the enriched environment (electronic supplementary material, table S2; figure 3c). This finding provides rare empirical evidence of G × E interaction in a cognitive trait in non-human animals (for another example, see [60]). Overall, our re-analysis provides a strong demonstration of how reducing dimensionality can result in loss of critical information and greatly alter our interpretation of the correlation structure among cognitive abilities.

(c). Alternative ways to study animal (general) cognition

Considering the weak support for g in non-human animals highlighted in this study, we suggest as a gainful alternative the study of (co)variance patterns across cognitive abilities. Understanding how cognitive traits are structured and how selection acts independently (or not) on each trait is required before making conclusions regarding the evolution of cognitive abilities. At the phenotypic level, g assumes positive among-individual correlations across different cognitive abilities. If measured traits correlate weakly at the phenotypic level, then one might conclude there is little evidence for general intelligence. However, unless the repeatability of all traits is close to 1, there is always the possibility that the phenotypic correlations differ from the underlying pattern of (co)variance at the among-individual level. In our case study, a multivariate approach demonstrated how performance across tasks correlated only weakly. Moreover, variance patterns differed among cognitive tasks, suggesting that the biological underpinnings of performance might differ depending on the nature of the task assayed. Consequently, we argue that the use of dimensionality reduction methods can limit our ability to capture meaningful (co)variance patterns in (general) cognitive abilities.

So far, only a handful of studies have used MMMs to examine (co)variance patterns at different biological levels in animal cognition studies. Most of these genetic and among-individual correlations were weak (e.g. [21]), while some were negative (e.g. [61,62]), similar to the negative among-litter correlation we found between passive avoidance and odour discrimination. Such negative covariance suggests the presence of trade-offs in performance between cognitive tasks and goes against predictions of g. They underline the importance of partitioning phenotypic (co)variances to detect associations between traits at levels that are relevant for our understanding of the evolution of cognition. For instance, previous work suggests that speed–accuracy trade-offs may occur within individuals [63] and/or among individuals [62]. The former might be explained by temporal or contextual changes in the cost of errors for individuals [63], while in the latter, individuals might exhibit different cognitive styles expressed by consistent individual differences in speed–accuracy [39,62]. To test whether the speed–accuracy trade-off occurs at the among- versus within-individual levels, one has to sample both speed and accuracy repeatedly to be able to estimate the among- and within-individual correlations [17,20]. This example demonstrates how using a repeated-measure sampling design and focusing on multi-level correlation structures can increase our biological understanding and facilitate the development of evolutionary-relevant hypothesis.

As mentioned above, the study of phenotypic multi-level trait structure is a leap towards a better understanding of general intelligence and its underlying components. However, studies investigating correlation structures among cognitive abilities should be cautious if seeking to make evolutionary inferences from phenotypic variance patterns. This ‘phenotypic gambit’ remains an unstated assumption of many animal cognition and animal behaviour studies. Combining mixed models with appropriate relatedness data allows researchers to precisely overcome this gambit's assumption [19,64]. Using univariate mixed models, we demonstrated how changes in H² for one trait (i.e. passive avoidance) followed a pattern that was completely opposite to predictions based on GCA scores. Moreover, we found evidence of G × E interaction in that same trait, implying that genotypes differed in their response to the environment. Disparities between these findings and the original analysis provide strong evidence against dimensionality reduction when making evolutionary inferences. To this effect, estimating selection on cognitive abilities will be ultimately required, and it will be easier to interpret selection on original traits than on a composite character such as g [36–38]. Note that it would be possible to project selection estimates on PCs back into the original trait space [65], but such an approach may be needed only when traits are highly multicollinear (which appears not to be the case with cognitive traits, see above).

As the number of studies providing genetic information increases (e.g. [13,21,61,66]), comparison of the phenotypic and genetic correlations across cognitive traits will greatly advance our understanding of factors that maintain individual variation in cognitive traits and potential overarching structures. For instance, in the human literature, general intelligence is typically explained by a common genetic basis (i.e. high heritability of g; [4]). Recently, work on pheasants (Phasianus colchicus) found important disparities between phenotypic and genetic correlation trait structures, with the phenotypic structure supporting a modular view of cognition, while the genetic structure supported a general factor [21]. Similarly, population-level studies find positive phenotypic correlations between the size of brain components, but this is not mirrored in genetic correlations [67]. Clearly, research is needed to further address the causes of (co)variances at different hierarchical levels among cognitive traits, and possible links to underlying brain structure.

(d). Recommendations

In the light of insights gained from our re-analysis, we provide recommendations for future research that specifically aims to assess individual differences across a multitude of cognitive traits:

• (1)Hierarchical, i.e. multi-level, models partitioning phenotypic (co)variance are required to increase our understanding of trait structure and discern potential underlying mechanisms. Researchers have to measure cognitive performance in several tasks, but should also seriously consider taking repeated measures to allow partitioning of the (co)variance. This can become a research question in its own right: are these task performances correlated at the among- or within-individual level, or not at all? Which type of tasks correlate strongly, and at which level? We argue that increasing our understanding of multi-level association between cognitive abilities should be prioritized before estimating general intelligence.
• (2)Dimensionality reduction techniques allow the prediction of underlying construct(s); they are thus useful in our quest to understand general intelligence. However, dimensionality reduction methods should only be used when there is sufficient evidence to do so and be accompanied by statistical assessments using appropriate methods [53,56]. Furthermore, we suggest that dimensionality reduction methods be used in addition to variance partitioning, and that correlation matrices always be included. In addition, it is crucial that reduction methods be applied at the appropriate hierarchical level (e.g. among-individual). Interestingly, it is possible to apply dimensionality reduction on (co)variance matrices after variance partitioning. For example, after having quantified the genetic variance–covariance matrix (G, or the among-individual matrix I), one can run an eigenanalysis of G to derive the trait combinations in which there is the most genetic variance [68]. Another alternative would be to use structural equation models (SEMs) that allow hierarchical structures accounting for different levels of variance [69–71]. This way, researchers could provide more in-depth results reflecting biologically relevant information, while also testing hypotheses related to general intelligence. This would be an effective method to differentiate between domain-specificity and domain-generality.
• (3)While using MMMs to estimate different phenotypic-level structures is informative in its own right, it is only the first step towards identifying genetic and environmental associations among performance traits through larger-scale quantitative genetic studies. Future studies should aim at measuring cognitive abilities between related individuals [21,64] and ultimately estimate multivariate selection on traits [35,71,72].
• (4)Finally, we are aware that our suggestions might require an increase amount of research effort. However, simple but effective methods could facilitate this transition for future studies. For example, one way forward could be to reduce the number of tasks studied to allocate more research efforts toward estimating the genetic variance associated with a few cognitive traits. Species that are easy to maintain or test in large numbers (e.g. insects, fish, etc.) could expand our statistical opportunities while also broadening the number of taxa studied in the animal kingdom; indeed, our literature review shows a clear mammal and avian bias. Species that are suited for experimental breeding designs (e.g. half-sib/full-sib) allowing quantitative genetic methods could be prioritized when seeking evolutionary hypotheses [19]. Breeding designs might be particularly useful to avoid the issue of assessing repeatability in tasks that involve learning and memory [18], because each individual offspring can be tested only once and the (co)variance structure is estimated at the sire level. Another simple and effective strategy is the use of planned missing data designs (PMDDs), where data are randomly and deliberately missed during data collection [73,74]. Although still in their infancy, PMDD and data imputation procedures should be considered as promising tools to ensure sufficient power to address research questions on animal general intelligence.

5. Conclusion

Factor-analytical procedures were first developed for studying general intelligence in humans [2]. Prior to the advent of high-speed computers, these approaches aimed at reducing dimensionality of large datasets. Once more powerful statistical approaches became viable, the human literature on g moved towards alternative statistical tools such as structural equation modelling and multivariate genetic analyses [4,5]. To this day, most studies on general intelligence in non-human animals have used these same factor-analytical procedures that human studies have mostly left behind. Here, we showed how reducing dimensionality can lead to spurious interpretations and mask important patterns within the field of general intelligence in non-human animals. Overall, our results suggest that current evidence for g is weak in non-human animals. We hope we provided researchers interested in studying the evolution of cognitive traits with valuable statistical and methodological alternatives that will generate insightful research in the field of animal cognition.

Data accessibility

This article has no additional data.

Authors' contributions

M.-A.P. conducted the meta-analysis and wrote the first draft of the manuscript with input from J.M.-F.; D.Y.K. performed the literature search and V.C. conducted the re-analysis of the case study. All authors participated in elaborating the study, in addition to writing and revising the manuscript.

Competing interests

The authors declare no conflict of interests.

Funding

This work was supported by the NSERC through Discovery Grants to J.M.-F. and V.C., a Discovery Accelerator Supplemental grant to J.M.F. and a CGS D scholarship to M.A.P. J.M.F. holds a University Research Chair in Cognitive Ecology from the University of Ottawa.