Raphaël Royauté
email: raphael.royaute@gmail.com

Ned A Dochtermann

Comparing ecological and evolutionary variability within datasets

Keywords: Repeatability, animal personality, individual variation, mixed models, individual niche specialization, functional traits

Many key questions in evolutionary ecology require the use of variance ratios such as heritability, repeatability, and individual resource specialization. These ratios allow researchers to understand how phenotypic variation is structured into genetic and nongenetic components, to identify how much organisms vary in the resources they use or how functional traits structure species communities. Understanding how evolutionary and ecological processes differ among populations and environments therefore often requires the comparison of these ratios across groups (i.e. populations, sexes, species). Inference based on comparisons of ratios can be limited, however. Variance ratios can remain the same across group despite very different values in the numerator and denominator variances. Moreover, evolutionary ecologists are most often interested in differences in specific variance components among groups rather than in differences in variance ratios per se. Recommendations for how to infer whether groups differ in variance are not clear in the literature. Using simulations, we show how questions regarding the estimation of variance components and their differences among groups can be answered with Linear Mixed Models (LMMs). Frequentist and Bayesian frameworks have similar abilities to identify differences in variance components. However, variance differences at higher levels of organization can be difficult to detect with low sample sizes. We provide tools to conduct power analyses to determine the appropriate sample sizes necessary to detect differences in variance of a given magnitude. We conclude by supplying guidelines for how to report and draw inferences based on the comparisons of variance components and variance ratios

SIGNIFICANCE STATEMENT

Many critical questions in ecology and evolution use variance ratios, such as repeatability, heritability, or individual resource specialization, to make inferences about ecological and evolutionary processes. In many cases these inferences rely on the comparison of variance ratios among datasets (populations, sexes, or environments). In this article, we show that current approaches of drawing inferences about group differences from comparisons of ratios are inappropriate because ratios can differ due to differences in the numerator, denominator, or both. We investigated how questions regarding differences in variance ratios and constituent variance components can be evaluated using Linear Mixed Model approaches (LMMs) and provide guidance for appropriate sampling schemes under different scenarios and discuss common pitfalls associated with estimation of differences in variance component among datasets.

INTRODUCTION

Our understanding of many evolutionary and ecological processes is underpinned by an estimation of variance ratios (Table 1). For example, the reporting of repeatability has become pervasive in behavioral studies as it summarizes the amount of variation in behavior attributable to differences among individuals. Informally these differences among individuals can be thought of as differences in their average behaviors. Repeatability then can be interpreted as how much of the overall variation is attributable to individual differences Use of variance ratios like repeatability spans a broad swath of evolutionary ecology (Table 1). This includes the most well-known variance standardized ratio: heritability, and extends to interest in community ecology regarding the distribution of functional trait variation expressed within versus among populations or species [START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF].

While useful for understanding the relative magnitude of variation, variance ratios can be highly misleading when compared between groups [START_REF] Houle | Comparing evolvability and variability of quantitative traits[END_REF][START_REF] Wilson | How should we interpret estimates of individual repeatability?[END_REF].

Comparisons of variance ratios are only narrowly interpretable because these ratios can differ when numerators differ, when denominators differ, or when both differ. Indeed, variance ratios can be equal despite having different numerators and denominators values.

Put another way, differences between groups in ratios like repeatability are not informative as to absolute differences in the magnitudes of variation observed. The proportion of variation attributable to additive genetic variance (Va) [START_REF] Mousseau | Natural selection and the heritability of fitness components[END_REF] Behavioral Ecology

Adjusted Repeatability RA = Vi / (Vi+ Vw)

The proportion of variation attributable to among-individual differences (Vi) relative to either the total variation (Vi+Vf+Vw) or after adjusting for fixed-effects (Vi+Vw) [START_REF] Lessells | Unrepeatable repeatabilities: a common mistake[END_REF] Unadjusted Repeatability RU = Vi / (Vi+Vf +Vw) [START_REF] Nakagawa | Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists[END_REF] Ecology

Individual Niche Specialization

S = WIC / TNW

The proportion of variation attributable to within-individual preference in niche (WIC)

(usually expressed as standard deviations) [START_REF] Bolnick | The ecology of individuals: incidence and implications of individual specialization[END_REF])

Community Ecology

T-ratios TIP/IC = VIP / VIC The proportion of variation attributable to within-population variance (VIP) relative to the community variance (VIC) [START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF] TIC/IR = VIC / VIR The proportion of variation attributable to community variance (VIC) relative to the regional pool variance (VIR) [START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF] Legend: Va: additive genetic variance in a trait, Vi: among-individual variance in trait, Vw: within-individual (i.e. residual) variance in a trait, WIC: within-individual variance in niche preference, TNW: Total niche width, TIP: total amount of trait variation in a community, VIP: within-population variance in trait, VIC: community variance in trait, VIR: regional pool variance

To further illustrate the inferential limits of variance ratios, consider the following scenario: researchers are studying the behaviors and dietary habits of two populations of the mythical Dahu (Dahu desterus; Fig. 1A) at different elevations. These elusive creatures have shorter hind-legs on their left side, thus only allowing for clockwise movement [START_REF] Chartois | Hunting the Dahut: A French Folk Custom[END_REF][START_REF] Jacquat | Le dahu: monographie ethno-étho-biologique publiée à l'occasion de l'exposition inaugurée le 1er avril 1995. Editions de la Girafe, Musée d'histoire naturelle Jenkins SH[END_REF]. While measuring aggressive interactions, researchers find no differences in means between populations and similar behavioral repeatabilities (! = 0.8; Fig. 1B). Put another way, the same relative amount of variation is attributable to individuals in each population. The researchers notice, however, that there are large differences in the among-and within-individual variances of each population. Had researchers only examined repeatabilities and mean differences they would inappropriately conclude that the populations are behaviorally equivalent. Instead, the actual variance estimates reveal that individuals from the high-altitude population are very distinct from one another in their aggressive tendencies while, at low-altitude, individuals

show little departure from the population average (Fig. 1B,C).

These researchers are also curious as to whether the harsher climate at the top of the mountain range leads to a narrower dietary breadth. Researchers predict that individual resource specialization will be higher in the low elevation population, as D.

desterus have more food options to choose from. To the researcher's surprise, they find much higher individual resource specialization in the high-altitude population: S1 = 0.2, S2 = 0.8. Upon examining the specific values of among-and within-individual variation in niche, they find that these differences are a result of the high elevation population having a much narrower total niche width (Fig. 1D) while the within-individual variation in niche preference is equal between populations. This means that it is the difference in diet preference among individuals that drives the difference between the two populations. With more varied resources available at low elevation, each individual can specialize along the total niche axis, yet the breadth of diet preference within-individuals is the same between populations.

For both traits, exclusive reliance on ratios would have led to either inappropriate or incomplete inferences (i.e. inappropriately concluding behavioral equivalence and incompletely recognizing the basis of differences in apparent specialization). Due to these problems with interpretations of variance ratios [START_REF] Houle | Comparing evolvability and variability of quantitative traits[END_REF][START_REF] Dochtermann | The mean matters: going beyond repeatability to interpret behavioural variation[END_REF], what would be of greater use to researchers is to instead evaluate differences in specific variance components.

A statistical framework for comparing variance components

The statistical procedures necessary for the estimation of variance components and ratios within a single population have been the subject of much attention (e.g. mixed models for repeatability: Dingemanse and Dochtermann 2013; animal models for heritability [START_REF] Wilson | An ecologist's guide to the animal model[END_REF]individual niche specialization:Bolnick et al. 2002;[START_REF] Coblentz | The application of Bayesian hierarchical models to quantify individual diet specialization[END_REF] functional trait variation: Nakagawa and Schielzeth 2012; [START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF][START_REF] Carmona | Traits without borders: integrating functional diversity across scales[END_REF]. There is also a long history in quantitative genetics regarding the comparison of variances and covariance structures among groups [START_REF] Shaw | The Comparison of Quantitative Genetic Parameters Between Populations[END_REF][START_REF] Arnold | Hierarchical Comparison of Genetic Variance-Covariance Matrices. Ii Coastal-Inland Divergence in the Garter Snake, Thamnophis elegans[END_REF][START_REF] Roff | Comparing Gmatrices: A Manova Approach[END_REF][START_REF] Roff | There is more than one way to skin a G matrix[END_REF][START_REF] Aguirre | Comparing G: multivariate analysis of genetic variation in multiple populations[END_REF]. Unfortunately, these quantitative genetic approaches have been poorly disseminated across fields (but see [START_REF] Dochtermann | Applying a quantitative genetics framework to behavioural syndrome research[END_REF][START_REF] White | Towards a comparative approach to the structure of animal personality variation[END_REF]). Here we describe and investigate methods for detecting differences in variance components amongst groups. Specifically, we compare the strength and weaknesses of three statistical approaches: comparison of confidence intervals, model comparison with AIC, and Bayesian estimation of the difference in variance components.

While this selection of methods encompasses very different philosophical approaches to data analysis, all three are routinely used in the estimation of repeatability and other ratios.

We consider a scenario where a phenotypic attribute, y, is measured repeatedly for individual organisms occupying one of two different environments (E1 and E2) and in which variation occurs among and within-individuals (VI and VW respectively). In the following sections we focus on differences in individual variation and repeatability. Note, however, that this scenario can also be expanded to the comparison of diet specialization for individuals occupying different environments or how functional traits vary among and within species in two different environments.

An easy way to compare these variance components and their ratios (τ = VI/(VI + VW)) is to estimate the variance components for each environment in separate statistical models. We can then test for differences in variances and ratios by environment based on whether estimate confidence intervals overlap or not. While straightforward, this method suffers from two key limitations. First, basing inference on the overlap of 95 % confidence intervals is overly conservative [START_REF] Barr | Using confidence intervals to test hypotheses[END_REF], especially when sample size is low. It is instead whether the confidence interval for the difference in variances excludes 0 that is relevant for drawing inferences. This difference cannot be directly estimated from the approach we have described. However, statistical significance can still be assessed by comparing the overlap of the 83% confidence intervals for variance components, a threshold that provides a better approximation for an α = 0.05 for the null hypothesis of no difference [START_REF] Schenker | On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals[END_REF][START_REF] Austin | A brief note on overlapping confidence intervals[END_REF][START_REF] Macgregor-Fors | Contrasting Diversity Values: Statistical Inferences Based on Overlapping Confidence Intervals[END_REF][START_REF] Hector | The New Statistics with R: An Introduction for Biologists[END_REF]. Second, by estimating variance components in separate statistical models, the hierarchical structure of the data, i.e. the variance components nested within the environments, has been broken. As a result, potential average differences in the traits of interest are not appropriately tested.

Instead, we suggest that a more appropriate procedure would be the use of a Linear Mixed Model (LMM) where the among-and within-individual variance is estimated for each environment within the same statistical model. This statistical model can be described by the following equation:

" !" = $ # + $ $ &'()*+',-'. + /0 #! + -#!" (equation 1) /0 #! ~ 345(0, Ω %& ); Ω %& = < 4 %& & $ 0 0 4 %& & ( = -#!" ~ 345(0, Ω ) ); Ω ) = < 4 ) & $ 0 0 4 ) & ( =
where " !" describes the phenotypic traits for the ith individual and jth observation. /0 #! , is the deviation from an overall intercept, $ # , for the ith individual. $ $ represents the regression coefficient for the fixed effect of environment (here a contrast coefficient). The random intercepts and residual variance (-#!" ) both follow a multivariate normal distribution, and Ω %& and Ω ) , are the variance-covariance matrices at the among-and within-individual levels respectively.

The diagonal elements of these matrices represent the among-and withinindividual variances in each environment: E1 and E2. The off-diagonal elements represent the cross-environment correlation (set to 0 if individuals are only ever evaluated in one of the two environments). This formulation has the advantage of allowing considerable flexibility in the specification of the statistical models considered [START_REF] Dingemanse | Quantifying individual variation in behaviour: mixed-effect modelling approaches[END_REF]. LMMs are now available for most statistical software and their generalized extensions can accommodate non-normal error distributions (Table 2).

Upon fitting LMMs, several methods are then available to determine whether a variance ratio or components of the ratio differ by environment. Specific hypotheses of which variance component differs across environment can be easily tested via model comparison. For example, a model where only the among-individual variance differs by environment can be compared to a null model where the among and within-individual variance are kept constant across developmental environments [START_REF] Royauté | Current energy state interacts with the developmental environment to influence behavioural plasticity[END_REF].

These models can be estimated within a frequentist framework via restricted maximum likelihood or a Bayesian framework and suitable decision criteria can be used to determine which model best fits the data. In the case of restricted maximum likelihood estimation, it is also possible to use likelihood ratio tests to compare these models. Note however that the proper degrees of freedom to apply to each model is unclear and additional care should be taken when using this method [START_REF] Pinheiro | Mixed-Effects Models in S and S-PLUS[END_REF][START_REF] Santostefano | Interacting with the enemy: indirect effects of personality on conspecific aggression in crickets[END_REF]). We recommend calculating these degrees of freedom by considering each variance component as a full parameter for more conservative testing (see also the tutorial in ESM3).

Table 2 Packages and softwares allowing to test for differences in variance components using Linear Mixed Models (LMM) along with parameter estimation method (maximum likelihood (ML), restricted maximum likelihood (REML), hierachical likelihood (H-ML) or Bayesian framework) and inference method (Likelihood Ratio tests (LRT), AIC, bootstrapping or credible interval for ΔV). This list is not comprehensive and is instead based on widely-used commercial softwares and R packages In many cases, researchers are also interested in whether the difference in variance components have a biologically meaningful effect. In other words, when asking questions about whether variance components vary between environments, we are mostly interested in the magnitude of the difference in these components across environments. While model comparison of LMMs can help us understand whether a statistically detectable difference is observable across environments, the magnitude of the difference can only be determined by examining the difference in variance components among environment: ΔV estimated as VE2 -VE1 in our case. When the trait of interest is expressed as standard deviation units (i.e.

mean centered and scaled to the standard deviation of the dataset across all populations and environments), this difference can be considered an effect size for the magnitude of the difference among variance components, thus making comparisons across studies possible [START_REF] Royauté | When the mean no longer matters: Developmental diet affects behavioral variation but not population averages in the house cricket (Acheta domesticus)[END_REF][START_REF] Hamilton | Genetic conservation and management of the California endemic, Torrey pine (Pinus torreyana Parry): Implications of genetic rescue in a genetically depauperate species[END_REF]Royauté and Dochtermann 2017). Note that ΔV could also be expressed on a ratio scale (VE2/VE1) or on a log-additive scale (log(VE2) -log (VE1)). We will return to the topic of statistical significance vs. appropriate effect sizes later in the paper. For now, we simply consider ΔV on an additive scale with data expressed in standard unit deviations because it allows the most straightforward interpretation and functions in cases where a variance component is zero or approaching zero. ΔV can be calculated from the maximum likelihood estimates in a frequentist framework but calculation of the uncertainty around this estimate is not straightforward and requires additional steps such as bootstrapping. In a Bayesian framework, the calculations are much simpler given that the distribution of ΔV can be directly estimated by taking the difference in the posterior distribution of VE2 -VE1. The posterior mode of ΔV can then be interpreted as the estimated strength of ΔV, with credible intervals representing the precision around this estimate.

In summary, approaches based on LMM and their generalized extensions allow great flexibility and are well suited to study questions related to how variation in phenotypic traits varies at multiple levels of organization. In the next section, we describe the performance of LMMs to detect differences in variance components.

METHODS

The simulations described below focus on interpretation in the context of behavioral repeatability. However, it is worth noting again that inferences about the ability to estimate and detect differences in variances generalizes to the components of the ratios described in Table 1.

Data simulations

To compare the performance of statistical procedures for detecting differences in variance components and variance ratios, we performed a series of simulations based on the scenarios illustrated in Fig. 2. In these scenarios a phenotypic attribute y is measured in two different environments (E1 and E2) and variation occurs among and within individuals (VI and VW respectively). In scenarios A through C the repeatability (τ) differs by an equal amount between the two environments (∆τ = 0.3), but the underlying driver of this difference is either due to a difference in the among-individual variance (A), in the withinindividual variance (B) or in both the among and within-individual variance (C). Note that for scenario C, the total variance remains the same between environments. In scenarios D and E, we explore cases where the variance ratios are equal among environment, either because all variance components are equal as well (D) or in spite of differences in all variance components (E) (see Table S1 for exact values for all parameters).

Using the R statistical environment (R Core Team 2020), we generated 500 datasets for each of the following combinations:

• Sample size varying from 20 to 200 individuals by increments of 20 for each environment (sample size was equal between the two environments)

• Number of repeated measures taken on each individual varying from 2 to 6 repeated measures by increments of 1

• Five different scenarios of known difference in variance ratios as described in Fig. 1 and Table S1.

Each dataset was simulated by sampling from a Gaussian distribution for the random (among-individual values) and the error (within-individual) terms. This resulted in a total of 125,000 datasets on which we tested three different statistical procedures to detect differences in variance components and variance ratios. We provide all R code for data generation and analysis in the Electronic Supplementary Materials (ESM1). S1). Scenarios

Comparison of confidence interval overlap from separate mixed models

We first compared the overlap of 83 % confidence intervals for variance component when estimated from separate linear mixed models. We specified one mixed model for environment 1 and one for environment 2. These models are a simplified version of the one presented in equation ( 3):

! !" = # # + %& #! + ' #!" (equation 2) ()* #! ~ -(0, 1 $% ); ' #!" ~ -(0, 1 & )
The experimental units in the environment of interest are included as random effects and no additional fixed effect are needed. Upon fitting these models, we computed 83 % confidence intervals for the among and within-individual variance. Datasets where these intervals did not overlap were considered as statistically different.

Frequentist LMM with AIC model comparison

Our second approach was to fit the LMM approach described above and test for the for the significance of the difference in among-and within-individual variance using likelihood ratio tests. Specifically, we specified four different mixed models corresponding to the four different possibilities by which variance components may differ [START_REF] Royauté | Current energy state interacts with the developmental environment to influence behavioural plasticity[END_REF][START_REF] Bucklaew | The effects of exposure to predators on personality and plasticity[END_REF]):

• Model 1: a null model where the among (VI) and within-individual variance (VW)

was kept constant among environments.

iterations and thinning interval of 10 iterations). We used priors that were minimally informative for the variance components (See ESM1 and ESM3 for prior specification and a discussion on priors).

Probability of correct model identification, precision, bias and accuracy estimations

We calculated the probability of detecting the model with the correct difference in variance components (hereafter "abridged" to probability of correct model identification), precision, relative bias and accuracy under each scenario and sampling design to compare the performance of maximum likelihood and Bayesian mixed models. For Method 1 (overlap of 83 % intervals), we assigned values of 1 when significant differences in variance components were detected in directions predicted by the data generating process, and 0 otherwise. For Method 2, we calculated the probability of correct model identification as the proportion of times the model with the lowest AIC matched the generating model. For

Method 3, we calculated whether a given model detected a difference in variance components based on the overlap of the 95 % credible intervals of the ΔV posterior distribution with 0. As in Method 1, we then assigned values of 0 or 1 based on whether the detected difference matched with the data generation process of the corresponding scenario. We calculated the probability of correct model identification as the proportion of analyzed datasets in which we detected differences in the direction predicted by each scenario and statistical method. Precision, indicating the similarity of the results produced by simulations with a given scenario, was calculated as the difference between 25 % and 75 % quantiles of estimates (van de Pol 2012). To calculate the relative bias (in %) for each statistical approach by scenario, we calculated the mean difference between the expected value and the value observed in each of the 500 simulations. Finally, we report the root mean square of error (RMSE) for each scenario and sample sizes. This metric calculates how close estimates are to the expected values and serves as an estimate of the accuracy of each statistical approach by scenario.

RESULTS

The probability of correctly detecting differences in variance components did not differ substantially between frequentist and Bayesian methods of estimation (Fig. 3). The highest probability of correct model identification was observed for cases where the variance ratio differs as a result of changes to the within-individual variance (scenario B) or when variation remained equal between environments (scenario D). The statistical power to differentiate between alternative scenarios (i.e. scenarios A, C and E) was lower, especially with small sample sizes and low number of repeated measures (Fig. 3). Importantly, no statistical method seemed to outperform all others across scenarios. Our results are consistent with previous simulations showing that the among-individual variance component is particularly difficult to estimate at small sample sizes [START_REF] Dingemanse | Quantifying individual variation in behaviour: mixed-effect modelling approaches[END_REF]. In scenarios B and D, the correct differences among variance components were identified > 80 % of the time, even at low sample sizes (Fig. 3). In all other scenarios this threshold was only reached with high sample sizes and a high number of repeated measures. For scenarios C and E-which correspond to cases where the variance ratio differs as a result of among-individual variance (C) or when the variance ratio remains the same despite changes to both among-and within-individual variance (E)-datasets with only 2 repeated measures per individual never achieved a probability of identifying the generating model above 0.8, even with sample sizes above 200 units per environment (i.e. a minimum of 800 total measurements, Fig. 3). Increasing the number of repeated measures only marginally alleviated the problem. For example, in scenario C, only datasets with 4 or more repeated measures per individual reached statistical power above 0.8 with sample sizes above 120 individuals per environment, which is higher than many ecological or evolutionary studies can provide under realistic scenarios.

Note that for AIC model comparison, we calculated power as the number of times the best model corresponded to the generating model. A more conservative approach is to calculate the proportion of times the best model is at least 2 AIC units lower than the second model. This method corresponds to a common threshold to detect statistically distinct models [START_REF] Burnham | Practical use of the information-theoretic approach[END_REF]. When using this more conservative threshold (Fig. S1), datasets generated according to scenarios A and D were never statistically distinguishable from non-generating models, although the correct model was consistently ranked as the best model. This discrepancy is likely because when the generating model does not include differences in the within-individual variability (scenarios A and D), sampling error is erroneously identified as heterogeneity. At smaller sample sizes this error is greater on average, and thus detectable. At larger sample sizes this sampling error is smaller but more easily detected and therefore manifests as a difference between groups. To address this, in addition to measures of variance differences like the described ΔV statistic, researchers should also compare mean-standardized variance estimates like the coefficient of variation or Houle's evolvability between groups [START_REF] Houle | Comparing evolvability and variability of quantitative traits[END_REF][START_REF] Hansen | Heritability is not Evolvability[END_REF][START_REF] Dochtermann | The mean matters: going beyond repeatability to interpret behavioural variation[END_REF].

The comparison of relative bias, precision, and accuracy among statistical methods produced mixed results. On average, Bayesian LMMs consistently underestimated the among-individual variance for scenarios in which the among-individual variance differed between environments (scenarios A, C, and E) resulting in a bias at small sample sizes (Fig. S2). However, Bayesian LMMs also had higher precision and accuracy compared to maximum likelihood (Fig. S3, S4). This means that Bayesian estimates tend to be consistently more conservative than maximum likelihood regarding the magnitude of the among-individual variance but that these estimates nonetheless more closely matched simulation conditions.

DISCUSSION

Comparing variability across datasets is important for many questions in evolutionary ecology (e.g. Table 1). However, variance ratios are not sufficient to address questions about how variation is expressed across environments, populations, or sexes. The inability to determine why groups differ based on ratios is in addition to the numerous conceptual and theoretical problems inherent to the estimation of variance ratios [START_REF] Houle | Comparing evolvability and variability of quantitative traits[END_REF][START_REF] Hansen | Heritability is not Evolvability[END_REF]. Instead, many questions require the direct comparison of variances.

What are appropriate sample sizes for detecting differences in variance?

Our simulations show that regardless of the statistical methods used, comparing variance components across groups is a "data hungry" question. Scenarios where the among-individual variance differed between environments were particularly hard to detect at low sample sizes. Note that our objective was not to provide a full exploration of parameter space. Instead, we focused on a subset of scenarios that are likely to be common in ecology and evolution (Fig. 2). Based on our simulations, the probability to detect differences in variance components will depend in large part on the ability to estimate the among-individual variance component (VI). In the most complex case where differences occur among and within-individuals (scenario E), researchers would require a minimum of 1,600 observations to correctly detect differences (i.e, 200 individuals measured 4 times in each environment). This is far higher than sample sizes needed for single populations, where moderate repeatabilities only need ∼100 observations to be estimated with > 0.8 power (at least 25 individuals measured 4 times to detect a repeatability of 0.3; see [START_REF] Dingemanse | Quantifying individual variation in behaviour: mixed-effect modelling approaches[END_REF].

Given these challenges, we recommend that researchers conduct power calculations prior to the experiment whenever possible (see R code for a priori power analyses in ESM2 compares all components by environment (posterior medians and 95 % credible intervals estimated from a Bayesian mixed model with model 4, note that frequentist confidence interval can also be reported using nonparametric bootstrapping as shown in ESM3). Finally, because aggression does not differ on average between populations, lnVR is an appropriate metric to report the effect size for the difference in variance between populations.

We provide a synthetic guide for which statistical tests and effect sizes are most appropriate depending on the nature of the dataset in = 128.76 [107.57; 148.40], Pmcmc = 1.00). This difference is also biologically relevant since the effect sizes are also > 1 (lnVRI = 1.38 [1.10, 1.66]; ΔVRW = 1. 48 [1.31, 1.64]). Biologically, this means that the high elevation population is composed of individuals that are more distinct in behavior compared to the low elevation population.

While we limited our conceptual example to comparisons between two environments, the LMM approach we propose is by no mean restricted to two-groups comparisons. For example, Jenkins (2011) used model comparison to tease apart the relative influence of sex, species and their interaction on the expression of behavioral variation in kangaroo rats. Similarly, [START_REF] Coblentz | The application of Bayesian hierarchical models to quantify individual diet specialization[END_REF] show how model selection combined with Bayesian GLMM can allow the comparison of indices of diet specialization within and among species. In both cases, model selection can provide a first pass at whether differences in variance components are detectable among groups, while specific pairwise comparisons of effect sizes (using ΔV or other metrics) will allow discernment of the most pronounced differences in variance component. Regardless of the statistical approach used, we suggest it is important that researchers clearly outline the direction and, when possible, magnitude of the expected effects in their predictions.

Finally, our conceptual examples focus exclusively on the case of "well-behaved" data with normal error distributions. While these comparisons can be made with generalized extensions to LMMS (i.e. GLMMs), researchers must take extra precautions when calculating and comparing the within-individual variances (i.e. the residual variance).

Indeed, in the case of non-Gaussian data, the residual variance depends on both the link function used and how the software deals with overdispersion (additive vs. multiplicative overdispersion). [START_REF] Nakagawa | Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists[END_REF])) provides a very useful and extensive guide explaining how the correct residual variation can be calculated.

CONCLUSIONS

Variance ratios are straightforward metrics to describe how various ecological and evolutionary processes occur. However, comparing these ratios across studies or group can be misleading if poor attention is given to the specific variance components making up those ratios. More importantly, a lack of difference in these ratios does not mean that variation is expressed equally among groups. Given these limitations, we advocate for techniques allowing the estimation of differences in each variance components rather than focusing solely on variance ratios. The statistical tools allowing comparison of trait variation have become increasingly sophisticated and now allow asking very precise questions. Specifically, we can now ask how trait variation is generated and how variation differs among groups. However, despite the availability of these tools, researchers interested in ecological and evolutionary variation must remain careful in their study designs. As our simulations show, scenarios involving differences in among-individual variance are particularly difficult to detect without substantial sample sizes. Finally, we hope the statistical approaches and tools for power analysis presented here will allow for appropriate comparisons of trait variation in ecological and evolutionary studies.

Fig. 1

 1 Fig. 1 Reliance on variance ratios can lead to misleading inferences. (A) The elusive Dahu (Dahu dexterus) in its natural environment. (B) Two populations of Dahus living at different elevations do not differ in their repeatability of aggressive interactions (τ). (C) By plotting the individual aggression scores over the course of multiple measurements, it is clear that individuals are more distinct in their aggressive behavioral strategies at high elevation. This inference cannot be made by investigating repeatability alone. (D) The two population have very different resource specialization indices (S). A more accurate inference is that individuals do not differ in niche width (WIN), it is instead the total niche wdith (TNW) that is narrower in the high-alttitude population. Code available here: https://osf.io/5aw42/. Illustration: Philippe Semeria (CC BY 3.0 license)

Fig. 2

 2 Fig. 2 Scenarios used in simulations detailing how differences or lack of difference in repeatability (right-side column) can arise from different patterns in the underlying variance components (left-side column; exact values can be found in TableS1). Scenarios

A

  -C correspond to cases where the total variation differs between two environments (E1 and E2) due to differences in the among-individual variance (VI, A), the within-individual variance (VW, B) or both (C). Scenarios D-E indicate cases where the ratios remain constant across environments, because all variance components are identical (D) or in spite of variance component being different among environments (E)

Fig. 3

 3 Fig. 3 Effect of sampling design on the probability of correct model identification by scenario type and statistical modeling approach. Each point represents the probability of detecting the correct differences in variance averaged over 500 simulated datasets for a given sample size (n: number of individuals measured in each population, reps: number of repeated measures per individuals). A represents a scenario where only the amongindividual variance (VI) varies between environments, B represents a case where the within-individual variance (VW) varies between environments, and both among and withinindividual variance vary between environments in scenario C. In scenario D, all variance components are equal while in scenario E, variance components are different but variance ratios are equal across environments. Dashed lines correspond to 80 % threshold similar to recommendations for power analyses.

Fig. 4

 4 Fig.4A) Flowchart showing decision rules regarding how to test for differences in variance components, which metrics to report and which effect sizes can be calculated, along with their definitions in table format. B) Reporting example based on the simulated case study in Fig.1B, C. The first Table used REML model selection with AIC to compare the support for different hypotheses for how variance components of aggression may differ between the low and high elevation populations. The best model is one where among and within-individual variances are higher in the high elevation population. The second Table compares all components by environment (posterior medians and 95 % credible intervals estimated from a Bayesian mixed model with model 4, note that frequentist confidence interval can also be reported using nonparametric bootstrapping as shown in ESM3). Finally, because aggression does not differ on average between populations, lnVR is an appropriate metric to report the effect size for the difference in variance between populations.

  Fig. 4A. Returning to our dahu example, an appropriate analysis of the difference in aggression variance would follow the tables and figures from Fig. 4B. Here the repeatability is unchanged between environments (posterior median [95 % credible interval]; Δτ = -0.01 [-0.06; 0.04], probability of difference: Pmcmc = 0.68). However, the high-elevation population shows significantly higher variation among and within-individuals (ΔVRI = 493.89 [370.25; 648.69], Pmcmc = 1.00; ΔVRW

Table 1

 1 Examples variance ratios found in the the ecological and evolutionary literature

	Discipline	Variance ratio	Definition	Description	References
	Quantitative	Heritability	h 2 = Va / Vp
	Genetics

Acknowledgments

We thank the participants of the Statistical Quantification of Individual Differences (SQuID) Symposium at the 2016 ISBE Congress for helpful discussions. We also thank Russel Bonduriansky, Ben Bolker and four anonymous reviewers for helpful comments on a previous version of this manuscript. This study was funded by NSF IOS-1557951 (to NAD) and the Department of Biological Sciences at North Dakota State University.

Funding

This study was funded by NSF IOS-1557951 (to NAD) and the Department of Biological Sciences at North Dakota State University.

Availability of data and material

All code and data for simulations is available on the Open Science Framework's project for this article: https://osf.io/5aw42/

Code availability

All code and data for simulations is available on the Open Science Framework's project for this article: https://osf.io/5aw42/

Declarations

Conflicts of interest/Competing interests

The authors declare no conflict of interest

Author contribution

Each author contributed equally to the design, analysis and writing of the manuscript. For each dataset combination, we then compared each model's Aikaike's Information Criterion value (AIC). AIC allows the comparison of relative fit of statistical models and models with lower AIC values indicate better support relative to competing models. These simulations and this analytical framework are similar to previously used approaches [START_REF] Shaw | The Comparison of Quantitative Genetic Parameters Between Populations[END_REF]Jenkins 2011;[START_REF] Tüzün | Pesticide-induced changes in personality depend on the urbanization level[END_REF]). These models were specified using the nlme package for mixed models [START_REF] Pinheiro | Mixed-Effects Models in S and S-PLUS[END_REF] using Restricted Maximum Likelihood (REML).

Ethics approval

Not applicable

Consent to participate

Not applicable

Consent for publication

Bayesian LMM and difference in variance components

We next fit a mixed model where variances among and within units were allowed to vary between environments (as in model 4 described above) to each randomly generated dataset. We calculated the posterior mode for the difference in variance components (calculated as ∆V = VE2 -VE1) and estimated the 95 % credible intervals based on the Highest Posterior Density of this distribution. 95 % credible intervals excluding 0 were taken to indicate statistically detectable differences in variance components among environments. All models were run with the MCMCglmm package (Hadfield 2010) using default iteration settings to shorten computing time (13000 iterations, 3000 burn-in How to report results? Statistical significance vs. effect sizes Given the issues discussed above, how should researchers interested in ecological and evolutionary variation design their studies and report their findings? We suggest that researchers report their results in a manner that focuses on the magnitude of the difference in variability between experimental groups rather than solely focus on statistical significance.

To this effect, we believe that reporting the results of the full model rather than just the most parsimonious model will be most appropriate in most cases (i.e. model 4 in our conceptual example). This is because model selection only gives information on whether differences among groups are statistically detectable. In contrast, questions regarding the magnitude and precision of the estimated differences are answerable only with interpretation of the most complete statistical model (see tutorial in ESM3).

In addition to presenting results of the full model, we suggest that measures of effect sizes for the differences in variance component also be presented. As reported above, ΔV provides a simple metric to estimate the magnitude of these differences, but it is by no mean the only one. In our theoretical example, the mean trait value did not differ by environments, but in many cases mean and variance are related. In such cases, using comparisons based on Houle's (1992) I 2 value or coefficients of variation for each component as opposed to variance component themselves can be preferable [START_REF] Hansen | Heritability is not Evolvability[END_REF][START_REF] Dochtermann | The mean matters: going beyond repeatability to interpret behavioural variation[END_REF]. Effect sizes based on the coefficient of variation can also be calculated within an LMM framework as described by [START_REF] Nakagawa | Meta-analysis of variation: ecological and evolutionary applications and beyond[END_REF] (see also [START_REF] Carmona | Traits without borders: integrating functional diversity across scales[END_REF][START_REF] Fontana | Individual-level trait diversity predicts phytoplankton community properties better than species richness or evenness[END_REF] for approaches relevant to functional trait diversity).

Supporting Information (SI) and Electronic Supplementary Materials (ESM)

ESM 1 Raw data from simulations along with R code for data analysis and figures (https://osf.io/5aw42/) ESM 2 R code for conducting a priori power analysis (https://osf.io/5aw42/) ESM 3 R tutorial for comparing variance components using nlme, MCMCglmm and brms packages (https://osf.io/5aw42/) Table S1 Scenarios tested in simulations to estimate the power to detect differences in variance components of varying magnitude


The Uses of Symptoms of Mental Health in the Long 20 th Century

Nicolas Pierre Boileau, Aix-Marseille Université, LERMA, UR 853, Aix-en-Provence, France 'To link madness and writing is to perpetuate one of the greatest commonplaces of our modernity' (Cape 2010: 7). Such statement is especially relevant when one considers the madness of the creative mind (Downie 2005: 49), the social implications of psychiatric treatment (Wall 2018), or more generally the understanding of the madness of literary creation (Felman 1978) and the very quality of language and the linguistic inventions of those regarded as mad (Ferrer 1990;Lecercle 1996). One also immediately sees this theme as also having a long history, readily connecting it with medieval studies of melancholia and lunacy or, in an Anglophone context, with the Shakespearean explorations of irrationality1 . In recent years, the collective work by Charley Baker et al. (2010) has mapped out the state of such a topic in the 20 th and 21 st centuries. They have renewed the interest in the question of mental illness in the contemporary era by carefully analysing the categories of medical treatment and the evolution of their fictionalisation.

One of the reasons for literature's interest in madness might be found in the symptom of psychic disorder itself, which can be conceived as something else than a 'cyphered message' (Zizek 1992: 175), through which, in orthodox Freudian theory, 'the subject gets back… the truth about his desire, the truth that he was not able to confront'. (Zizek 1992: 175) The symptom can be defined outside its analogy to a physical symptom, which is as a sign to be interpreted in relation to some organic dysfunction and causing pain the doctor seeks to assuage. In Lacanian, contemporary psychoanalytic theory, the symptom is a subjective solution that enables each and everyone to knot together different aspects of their life into a whole that holds; a scaffolding (Moment of Being) it is the very essence of their subjective response to the world, the very cause of their discomfort with their being, inherently unsatisfactory, and that which can be manipulated or at least manoeuvred from in therapy and through writing (Lacan 2005).

The question I want to raise in this work is how, thanks to the Modernist forays into the workings of the mind and the body, literature produces, instead of simply reproducing, symptoms, how the symptoms produced are decoded or made decipherable in a way that medicine leaves out (outside strict causality), but also how the represented illness defies cure and care and resists the attempts currently made to erase symptoms through biomedicine, instead of working from and around them. The book will not seek to establish what would inevitably be a long list of symptomssuch as what can be found in the Diagnostic Statistical Manual of Mental Disorders (DSM-V) for exampleor to chronicle the evolution of symptomatology as shown in fiction in the long 20th century (the phrase 'long 20th century' is intended to indicate that I will be looking at works produced between 1925 and the 2020s). I would like to resist such temptation for a taxonomical approach and side with Bonikowski when he says that we should not play 'a game of symptom or diagnosis spotting' (Bonikowski 2013: 6). What this book will explore instead is the discrepancy between the way doctors deal with symptomsfor now, suffice it to say that from a medical point of view symptoms are the signs of an illness which patients want to control if not get rid of, and which biomedical science endeavours to eraseand the way literature uses and produces symptoms, especially linguistic ones, to invent characters and account for the experience of symptoms and their significance at the subjective level. The definition of symptoms as a sure sign of an illness that must be cured is what literature disputes, as can be seen in the representation of psychic disorders in the long 20 th century. Or I could rephrase this by saying that Septimus is a paradigmatic example of the dangers there are in wanting to cure someone like him.

The idea for this book is based on the premise that Mrs Dalloway sets an example in which the author goes beyond the logical explanation of psychological symptoms. I hope to show that there is a way of looking at Septimus's symptoms without hoping to make him fit into the nosography of shell-shock, to restore his own singularity. (say a few words about how the repressive hypothesis and influence of social discourse has been much worked upon by critics including Abel  but less has been said about Septimus's delirium and the way his own truth is not listened to)

The notion of symptoms has rarely been central to studies of literature and madness, often as a result of a lack of clarity as to what symptoms mean and how they are used in therapy, as well as the ongoing, raging debates there exist in the field of mental health care. Very often, critics and readers have endorsed or resisted diagnostic categorisation; some have followed in the footsteps of dominant medical discoursescurrently neurological and biomedical; others have criticised the medical biases and prejudices that diagnoses and methods of treatment reflected; in other words, literary critics have contended with notions of normality, commonality and statistical representations while affirming that subjects were being subjected, reified and stigmatised by psychiatric and 'mental health' discourses. Literary critics in the medical humanities field have accepted the authority of the symptom as a sure sign of illness and a reliable symbol/ sign to be interpreted. However, to use Pett's words, I do not intend, 'in celebrating the principles and practices of the humanities, and particularly those of literary studies,' to suggest that 'both literature and literary studies [are] more sophisticated and more capacious in their approach to representing and interpreting illness' than they really are. (Pett 2019: 56) I do not intend to be a clinician where I analyse literature, but rather to try and see what it is writers teach clinicians and how they 'always precede' the theoretical framework elaborated to account for the function of symptoms (Lacan 2001: 192-93).

This book will look at British, mostly English, literature of the 20 th century, and is based on two hypotheses: first, that the mad person characterised by delirium, lack of coherence and an enigmatic response to the world, like Septimus Smith in Mrs Dalloway, has more or less disappeared over the course of the 20th century as a literary trope, a development that mirrors that of biomedical psychiatry2 ; secondly, that there has been little consideration for the impact of 'mental health' symptoms and diagnoses in and on literary representations of madness and psychic disorders. The evolution of symptomatology towards contemporary 'discreet disease categories,' to use a phrase by Micale, has more or less been treated as an insignificant oddity bearing no relation to the question of madness. I want to see how these discreet symptoms enable us to confirm both the functions they play in the subjective response to life and the way they invite us to redefine the medical binary of health/illness. With the expression 'discreet disease categories', Micale suggests that the nosography in 'mental health' treatment gradually discarded the notion of symptom clusters with the improvement of biomedicine and now observes other formations which resist the effect of biomedical treatment (Micale 1993: 503). This echoes the works currently carried out by the Freudian School and NLS analysts, Leguil, Maleval, Miller and Laurent on the new spectrum of psychosis and what they call 'generalised' madness.

What happens, indeed, if the symptom is regarded not as that which should be disposed of but as the subjective response to a world that subjects can never fully grasp because of their existence through and in language? The reason for this inability to grasp what their existence means lies in the fact that there is no essence of a subject's sense of being (no meaning or definition of who the subject is). Moreover, subjects only exist in language and therefore can only be situated in their relation to the law of language and the symbolic place they come to occupy (Lacan 1975). Bearing this in mind, what would be the effect of considering that the symptom is there to ensure that subjects understand how humble and frail they are in relation to language and as one of the ways of accessing a world that supersedes language itself? -These are many questions that matter for the understanding of literature. The fact that the emergence of 'mental health' care coincided with a global, artistic movement now called Modernism invites us to think about the way in which the history of medical treatment in the 20 th centuryranging from the advent of cognitive psychology and its scientific apparatus to an understanding of the multiple fractures within the fields of psychiatry and psychoanalysishelps understand new figures of madness in literature, and contributes to producing new symptoms that are not metaphors (Sontag 1978;1989).

Modernism emerged at about the same time as Freudian psychoanalysis did and the aim of this book is to also show that to a certain extent, Woolf preceded Freud in her exploration of the symptom and contributed to fashioning another approach that is now more common, especially in writers from the 1990s-onwards: namely in the writings of the end of the century, the notions of discreet symptoms have become prevalent, very often seen in secondary characters who, like Septimus, haunts the narrative so much that their understanding becomes crucial. In order to explore these questions, the following novels will be studied: Virginia Woolf's Mrs Dalloway (1925), Patrick McGrath's Asylum (1996), Pat Barker's Regeneration Trilogy (1991-95), Doris Lessing's The Fifth Child (1988), Alan Hollinghurst's The Line of Beauty (2004), Rachel Cusk's Trilogy (2014-2018) and Ali Smith's Seasonal Quartet . The corpus has been selected for the following reasons: first, the novels chosen are all somehow connected to Woolf and the Modernist era, in ways that I shall explore, so that a history of the evolution of the uses of symptoms can be delineated through a careful analysis of the novels. Woolf's Mrs Dalloway resonates with all these novels either in their themes (World War I and post-traumatic stress disorder), or in the presence of secondary characters whose madness or disorders affect the story and the structure of the works, or their voices: Cusk and Smith apart, but only as I argue because of appearances, what manifests in these novels is the absence of the characters' voices, their mutism or their silencing following the pattern of Septimus; the modernist or neo-modernist aspects of these works is constantly re-affirmed because of the novelists' primary concern with subjectivity, an exploration of the unsaid and its effect on the subject's apprehension of life. I argue that their connection lies in an exploration of their characters' solutions in order to make do without the capacity to articulate their experiencethese novels explore the symptom of psychic disorder as a way of considering the limits of literature and the failure of language that is ever so central to Mrs Dalloway.

Secondly, these novels have never been discussed together and some of them have never featured in studies of psychic disorder and symptom analysis. I think it is fruitful to track down symptoms in overt manifestations of psychic disorders (section 1) as well as in discreet ones (sections 2 and 3), which is arguably the modality of psychic disorders of our contemporary era (Gaspard 2010: 357-371). Lastly, most, if not all, of these texts form part of a cycle in their author's writing, either by being overtly part of a trilogy, having a sequel, or by being themselves connected to a certain period of production. It is as if none of these novels stood on their own, as if their authors were fully aware that symptoms are not written out, or off, without consequences. This is the sign that symptoms persist, because they are not simply a 'cyphered message', but the singular skein of meanings which structure one's being into a functioning entity in the world.

My argument is divided into three sections. The first section focuses on the patientdoctor relationship; the second one on what happens when medical care is not represented and how symptoms are revealed through the trace they leave on the subject's body; the third will be interested in a modality of contemporary symptoms, namely the new forms of introspection and stream-of-consciousness invented by Ali Smith and Rachel Cusk in response to contemporary forms of social disconnection.

I.

Doctors' misdiagnoses: Symptoms, Meaning and Function This first section is dedicated to three novels which reflect the relationship between patients and doctors in the formation of psychological symptoms. It looks at the symptom as a narrative tool subverting medical and psychiatric treatment. Taking the examples of Mrs Dalloway and its modernist aesthetics (chapter 1), in which the symptom is silenced and unheard in its function, I will consider more contemporary novels that continue to explore the production of meanings linked to the characters' symptoms. Following in the footsteps of the template set by Woolf, I will analyse Patrick McGrath's Asylum, which enables me to point to the fundamental role played by interpretation in the life of the symptom, notably in its being located in sexuality and the body (chapter 2); and secondly, through Pat Barker's Regeneration Trilogy, which owes so much to Woolf and develops her idea that failed medical treatment is in fact conducive to successful symptom formations (chapter 3).

a. Symptomatic Silence in Mrs Dalloway

The first chapter is dedicated to Mrs Dalloway, a 1925 novel in which Septimus Warren Smith features as perhaps one of the last 'delirious' patients in British fiction. For the doctors who treat Septimus, he is pathologically silent and unable to act; yet, Septimus keeps speaking to himself and his wife tries to ensure that he does not, by interrupting him constantly. Woolf chooses to make us listen to him. I argue that this is the symptom that needs focusing on: Septimus's silence is a very singular, subjective response to a world that he feels estranged from. The chapter delves into the repressive causality that bars access to an interpretation of the symptom that would be more structural than meaningful. By showing how the symptom is not, as Freudian interpretation argued at the time, solely to be interpreted, but can also be read as a meaningless formation evocative of a peculiar response to the world (Lacan), then the discourse of psychiatry is not only defeated and satirized, it is presented as requiring a reformwhich is exactly what Richard Dalloway and Sir Bradshaw want to do, although they remain unaware of this.

b. The Absence of Meaning vs Psychiatric Interpretative Method in Asylum by Patrick McGrath

Another landmark in the history of British writing about psychiatry is McGrath's novels, which have surprisingly led to very little critical interest in recent years. I show that the psychiatrist depicted in Asylum is a mock detective because his approach to psychiatric symptoms is to try and make them signify something so that they make sense from the point of view of causality. His authority derives from his method in which the meaning of the patients' symptoms is forced upon the subject's story. In his treatment of Stella, Dr. Cleave's method fails because he wants her silence to be the sign of her concealing something. The text instead reveals that it is impossible for her to articulate her own story in a dialectical fashion, making her incapable of appropriating the story the psychiatrist elaborates on her behalf. In this novel which starts off as a story of unfaithfulness, and ends up as a tragedy, the relationship between patient and doctor identified in Mrs Dalloway is revisited: silence, forceful interpretation, repressive hypothesis, all these elements are renegotiated by the author. McGrath's text shows an evolution: the repressive hypothesis of the Freudian unconscious, even if the story is set in the 1950s, no longer holds in the 1990s, and the author's choice of various stories superimposing proves an efficient strategy in order to better camouflage the absence of his main protagonist's story, ironically called Stella.

c. From Physical Symptoms to Subjective Creations in Pat Barker's Regeneration trilogy

Pat Barker's Trilogy evidently replays some of the themes contained in Mrs Dalloway, if only because both novels focus on the trauma of World War I. After showing how the Freudian influence plays a role in the psychiatrist's handling of his patients' symptoms, notably by offering an interpretative model that the patients laugh at, I argue that Prior, the only entirely fictional character, provides Rivers with a new way of approaching the symptom his patient suffers from. This new method results in great improvement: not only is Prior stripped of the symptom that most impeded him at firstmutismbut he also becomes a diarist, a way for him to find his voice well beyond the reductive speech acts that he is capable to produce when in hospital. Behavioural therapy might have been happy enough to have enabled him to speak again but without questioning the subject's place in discourse and in relation to others, therapy would have rendered Prior's use of language inefficient. Prior in fact becomes more in control of his symptoms when the logic of his choice of sexual partners is more apparent and he can form relationships he could only look at with irony before.

II.

The Symptom and the Body: Discreet Signs of Psychological Troubles In the second section, I focus on symptomatic readings of dysfunctional relationships, in relation but not restricted to sexuality and I look at novels in which the characters are not seen in the therapeutic scene, as if the symptom was now meant to be erased via medication and no longer thought or spoken about. I start with Doris Lessing's The Fifth Child (chapter 4), which relates the way a woman tries to live with her disabled child and how their relationship becomes symptomatic of her mortifying identification with motherhood. Then, I analyse Alan Hollinghurst's The Line of Beauty (chapter 5), in which the psychic disorders of the family's daughter are treated as an inconsequential nuisance while cocaine and AIDS subvert and distort all relationships.

a. The Body as Dangerous jouissance in The Fifth Child by Doris Lessing Doris Lessing's The Fifth Child explores the question of disability and the subjective experience of it for a mother whose son, for lack of medical help, remains an enigma. The fifth child of a couple immediately possesses the qualities of a misfit, without ever being clearly diagnosed. Quite rapidly, this last child is the agent of a split in the family's happiness which had, so far, outlived all the expectations. The novel interestingly approaches the body as a source of both pleasure and pain, strength and weakness, and a psychic rather than physical reality for the woman and mother, Harriet. When Harriet gives birth to her fifth child, her family is already marked by opprobriumwhy have so many kids when contraceptives exist?and excess, but the fifth child will inevitably come to stand for the punishment they must face for indulging in the excessive pleasure of begetting and parenting. What my chapter does is explore the partnership between mother and son not as pathological but on the contrary, as the condition for each of them to survive and perhaps even for Harriet to exist. By locating her son's symptom at the place where she fails to be a mother, Harriet ensures that even more than her other children, Ben should be regarded as the epitome of the jouissance she craves for: an unbridled body marked by no self-consciousness.

b. Homosexuality, AIDS and Psychological Resistance in The Line of Beauty by Alan Hollinghurst

It should come as a surprise to see this Booker-Prize winning novel listed in a book on literature and madness. If the novel seems interested in illness, it is only insofar as it focuses on AIDS, the illness that kills two of Nick Guest's lovers while Nick goes through the 1980s discovering the life of the well-off from his unacknowledged position of marginality. AIDS is the illness that brings about a certain vision of the body and creates a sense of unease and realism to the text. However, one character shouldn't be neglected: Catherine, the Feddens' daughter, whom Nick befriends straightaway and with whom she is partnered. Catherine is manic-depressive, as the diagnosis would have gone back in the 1980s, and she is known to self-harm. This secondary character enables the author to analyse the behavioural symptoms that set her as a pathological figure who can structurally be placed alongside the dysfunction and troubles experienced by some gay men in the novel and illuminate them. Hollinghurst finds in Catherine a way of rending the veil of literary propriety and the traditional template of the comedy of mannerswith which Woolf also had to grapplein order to question how a subject can be overwhelmed when they are assigned to an identification that is so strict it is mortifying.

III. Voices, Contemporary Symptoms and Social Cohesion

In the last section, the book will turn to voices, silences and body-free modes of expression in contemporary refashionings of the Modernist stream-of-consciousness technique by studying Rachel Cusk's Trilogy (chapter 6) and Ali Smith's Seasonal Quartet (chapter 7). This will enable me to conclude by analysing new modes of enjoyment (jouissance) and new symptoms in which the story one tells matters less than the core of enigmatic, opaque behaviour these new symptoms are able to produce.

a.

Voices and the Return of Silence in Cusk's Trilogy With Cusk's trilogy we return to silence as a symptom: 'Without wishing to sound melodramatic, it was creative death after Aftermath. That was the end. I was heading into total silence -an interesting place to find yourself when you are quite developed as an artist.' (Kellaway 2014) This is how Cusk describes her own rebirth into literature in an interview following the publication of Outline (2014), a novel which is now part of a trilogy with Transit (2016) and Kudos (2018). Aftermath, an autobiographical essay on the end of her marriage, had been published two years before and in what has now become customary in her career, it had caused more outrage than praise. Like A Life's Work (2001) before, and The Last Supper (2009), Aftermath was misunderstood by critics and readers alike, who got confused as to what the work was trying to achieve: its innovative format, intermingling fiction with essayistic reflections, was regarded as a stylistic flaw that made her point all the more unclear and debatable. Yet, what Cusk describes also inscribes her in a Modernist stance that foregrounds the crisis and failure of meaning and communication that writing tries to stitch up. Inevitably, Woolf scholars will find in Cusk's reflection a reminder of Woolf's similar anxiety about and drive towards silencethe much-quoted sentence of Woolf's first novel ("I want to write a novel about silence, the things people don't say. But the difficulty is immense." (VO, 232)) is bound to sound very similar to what Cusk faced after her digression into non-fiction. It is therefore very paradoxical that she should have come out of this artistic depression with three novels replete with chatter, small talk and every possible mode of endless conversation and uninterrupted monologues. Could this entanglement of silence and excessive talk be a symptom of her neo-Modernist endeavour (Latham 2016) to articulate meaning against contemporary forms of social disconnection?

b. Voices and Symptomatic Forms of Social Disconnection in Ali Smith's Seasonal Quartet

The last chapter and conclusion of the book will look at another symptom of subjects seeking forms of attachment in contemporary Britain. Ali Smith's Seasonal Quartet was written during and in the wake of the campaign for Brexit and in it she conveys her analysis of the more profound fractures within society this political agenda led to, enhanced or was the consequence of. The novels were published very recently, thus they enable us to momentarily close this exploration by closing a century of literary productions that began with the publication of Mrs Dalloway. They also enable us to raise questions about new ways of writing the psyche in an age that would like to reduce subjects to consumers, critical thinkers to gullible and non-ideological persons, communitarians to dangers, etc. Pitting people against one another because of age, sex, class and aspirations, Ali Smith allows them to create their own response in a language characterized by lack of cohesion, lack of correction and stability, a language that is therefore and perhaps like all social productions mad.

See in particular H. Suhamy's concern that such a common theme be reduced to a simple equation of madness to freedom(Suhamy 1989: 9). The theme has long been commented upon by critics. See for example the issue "Shakespeare et la folie". Revue philosophique de la France etde l'étranger. (123) 1937, p. 128.

The use of specific neuroleptics has enabled most medicated patients to have fewer symptoms of incoherent delirium.