Pierre De Villemereuil

Oscar E Gaggiotti

Pierre De

A new F ST -based method to uncover local adaptation using environmental variables

Keywords: genome-scan, local adaptation, environment, F model, Bayesian methods, false discovery rate

Genome-scan methods are used for screening genome-wide patterns of DNA polymorphism to detect signatures of positive selection. There are two main types of methods: (i) "outlier" detection methods based on FST that detect loci with high differentiation compared to the rest of the genome, and (ii) environmental association methods that test the association between allele frequencies and environmental variables.

• We present a new FST-based genome-scan method, BayeScEnv, which incorporates environmental information in the form of "environmental differentiation". It is based on the F model, but, as opposed to existing approaches, it considers two locus-specific effects; one due to divergent selection, and another due to various other processes different from local adaptation (e.g. range expansions, differences in mutation rates across loci or background selection). The method was developped in C++ and is avaible at http://github.com/devillemereuil/bayescenv.

• A simulation study shows that our method has a much lower false positive rate than an existing FST-based method, BayeScan, under a wide range of demographic scenarios. Although it has lower power, it leads to a better compromise between power and false positive rate.

• We apply our method to a human dataset and show that it can be used successfully to study local adaptation. We discuss its scope and compare it to other existing methods.

Introduction

One of the most important aims of population genomics [START_REF] Luikart | The power and promise of population genomics: from genotyping to genome typing[END_REF] is to uncover signatures of selection in genomes of non model species. Of special interest is the process of local adaptation, whereby populations experiencing different environmental conditions undergo adaptive, selective pressures specific to their local habitat. As a result, populations evolve traits that provide an advantage in their local environment. Many experimental approaches focused on potentially adaptive traits have been developed to test for local adaptation (reviewed in [START_REF] Blanquart | A practical guide to measuring local adaptation[END_REF], but only recently it has become possible to make inferences about the genomic regions involved in local adaptation processes. Indeed, the advent of next generation sequencing (NGS, [START_REF] Shendure | Next-generation DNA sequencing[END_REF] has fostered the development of so-called genome-scan methods aimed at identifying regions of the genome subject to selection. These methods are now widely used in studies of local adaptation [START_REF] Faria | Advances in Ecological Speciation: an integrative approach[END_REF].

There are two main types of genome-scan methods. The first type detects 'outlier' loci using locus-specific F ST estimates, which are compared to either an empirical distribution [START_REF] Akey | Interrogating a High-Density SNP Map for Signatures of Natural Selection[END_REF], or to a distribution expected under a neutral model of evolution [START_REF] Beaumont | Identifying adaptive genetic divergence among populations from genome scans[END_REF][START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. The rationale behind these methods is that local adaptation leads to strong genetic differentiation between populations, but only at the selected loci (or marker loci linked to them). Thus, loci with very high F ST compared to the rest of the genome are suspected to be under strong local adaptation and are referred to as outliers. The outlier approach was further extended to statistics akin to F ST [START_REF] Bonhomme | Detecting selection in population trees: the Lewontin and Krakauer test extended[END_REF][START_REF] Günther | Robust Identification of Local Adaptation from Allele Frequencies[END_REF], and also to other unrelated statistics [START_REF] Duforet-Frebourg | Genome Scans for Detecting Footprints of Local Adaptation Using a Bayesian Factor Model[END_REF]. One limitation of these methods is that they are not designed to test hypotheses about the environmental factors underlying the selective pressure.

A second type of methods focuses on environmental variables and aims at associating patterns of allele frequency to environmental gradients. The rationale is that selective pressures should create associations between allele frequencies at the selected loci and the causal environmental variables [START_REF] Coop | Using Environmental Correlations to Identify Loci Underlying Local Adaptation[END_REF]. In the presence of population structure, performing a simple linear regression would be an error-prone approach [START_REF] De Mita | Detecting selection along environmental gradients: analysis of eight methods and their effectiveness for outbreeding and selfing populations[END_REF][START_REF] De Villemereuil | Genome scan methods against more complex models: when and how much should we trust them?[END_REF]. Instead, existing methods account for population structure by modelling the allele frequency covariation across populations [START_REF] Coop | Using Environmental Correlations to Identify Loci Underlying Local Adaptation[END_REF][START_REF] Frichot | Testing for Associations between Loci and Environmental Gradients Using Latent Factor Mixed Models[END_REF][START_REF] Guillot | Detecting correlation between allele frequencies and environmental variables as a signature of selection. A fast computational approach for genome-wide studies[END_REF]. One disadvantage of most of these approaches is that the parameters that capture the effect of demographic history on genetic differentiation do not have a clear biological interpretation, which in turn makes the rejection of the null model hard to interpret in terms of detection of local adaptation. Especially, note that although the elements of the covariance matrix estimated by [START_REF] Coop | Using Environmental Correlations to Identify Loci Underlying Local Adaptation[END_REF] could in principle be interpreted as parametric estimates of the pairwise and population-specific F ST , this is only true when levels of genetic drift are low [START_REF] Nicholson | Assessing Population Differentiation and Isolation from Single-Nucleotide Polymorphism Data[END_REF].

It is important to note that, regardless of the type of genome-scan method under consideration, processes other than local adaptation might be responsible for the observed spatial patterns in allele frequency or F ST . These include demographic processes such as allele surfing [START_REF] Edmonds | Mutations arising in the wave front of an expanding population[END_REF] or hierarchical population structure [START_REF] Excoffier | Detecting loci under selection in a hierarchically structured population[END_REF], large differences in mutation rate across loci [START_REF] Edelaar | Comparisons between QST and FST-how wrong have we been?[END_REF], hybrid incompatibility following secondary contact [START_REF] Kruuk | A comparison of multilocus clines maintained by environmental adaptation or by selection against hybrids[END_REF] and background selection [START_REF] Charlesworth | Measures of divergence between populations and the effect of forces that reduce variability[END_REF].

It is therefore possible that some of the loci identified as outliers are in fact false positives. Accounting for processes other than selection would require introducing parameters that could appropriately capture the effect of these other processes.

Here, we present a method that incorporates features of the two types of genome-scans described above. The objective is to allow inferences about the environmental factors underlying selective pressures, and simultaneously better discriminate between true and false genetic signatures of local adaptation. Note that our new method focuses only on local adaptation driven by a focal environmental variable and, therefore, differs from other F ST -based methods that carry out "blind" genome scans. Thus, this new approach is aimed at testing hypothesis about specific drivers of local adaptation such as altitude [START_REF] Bigham | Identifying Signatures of Natural Selection in Tibetan and Andean Populations Using Dense Genome Scan Data[END_REF][START_REF] Foll | Widespread Signals of Convergent Adaptation to High Altitude in Asia and America[END_REF], salinity [START_REF] Larsson | Concordance of allozyme and microsatellite differentiation in a marine fish, but evidence of selection at a microsatellite locus[END_REF][START_REF] Daub | Evidence for Polygenic Adaptation to Pathogens in the Human Genome[END_REF], pathogens [START_REF] Fumagalli | Signatures of Environmental Genetic Adaptation Pinpoint Pathogens as the Main Selective Pressure through Human Evolution[END_REF][START_REF] Daub | Evidence for Polygenic Adaptation to Pathogens in the Human Genome[END_REF], etc.

Our method is based on the Bayesian approach first proposed by [START_REF] Beaumont | Identifying adaptive genetic divergence among populations from genome scans[END_REF] and later extended by [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. The original formulation considers population-and locus-specific F ST 's, which are described by a logistic model with three parameters: a locus-specific term, α i , that captures the effect of mutation and some forms of selection, a population-specific term, β j , that captures demographic effects (e.g. N e and migration) and a locus-by-population interaction term, γ ij , that reflects the effect of local adaptation. The estimation of the first two terms benefits from sharing information across loci or populations, but this is not the case for the interaction term, which is therefore poorly estimated [START_REF] Beaumont | Identifying adaptive genetic divergence among populations from genome scans[END_REF], but see [START_REF] Riebler | Bayesian Variable Selection for Detecting Adaptive Genomic Differences Among Populations[END_REF]. In practice signatures of local adaptation are therefore inferred from the locus-specific effects (α i ) under the assumption that large positive values reflect adaptive selection. The implicit assumption is that background selection and mutation should not have much of an effect on this term. In order to relax this assumption and to better estimate the interaction term we introduce environmental data so that γ ij = g i E j , where E j is the "environmental differentiation" observed in population j and g i is a locus-specific coefficient.

In what follows, we first describe in detail the probabilistic model underlying our Bayesian approach. We then evaluate its performance using simulated data and then present an application using a human dataset. Finally, we discuss the scope of our method and compare it with other existing genome-scan approaches.

Statistical model

Modelling allele frequencies using the F model Our new genome-scan approach is based on the F model [START_REF] Beaumont | Identifying adaptive genetic divergence among populations from genome scans[END_REF][START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF] and extends the software BayeScan [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF] by incorporating environmental data so as to explicitly consider local adaptation scenarios. Full details of the F model are given by [START_REF] Gaggiotti | Quantifying population structure using the F-model[END_REF], so here we only provide a brief description. The core assumptions of the F model is that all populations share a common pool of migrants, but that their effective sizes and immigration rates are population-specific. Thus, population structure at each locus is described by local F ST 's that measure genetic differentiation between each local population and the migrant pool.

The F model uses the multinomial-Dirichlet likelihood for the allele counts a ij = (a ij1 , . . . , a ijKi ) at locus i within population j (where K i is the number of distinct alleles at locus i) with parameters given by the migrant pool allele frequencies, f i = (f i1 , . . . , f iKi ), and a population-and locus-specific parameter of similarity,

θ ij = 1 -F ij ST F ij ST : a ij ∼ multDir(θ ij f i1 , . . . , θ ij f iKi ), (1)
where multDir stands for the multinomial-Dirichlet distribution.

Although, for the sake of simplicity, we only present here the formulation for co-dominant data, the software implementing our approach also allows for dominant data (e.g. AFLP markers) using the same probabilistic model as [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. Note finally that, for bi-allelic co-dominant markers (e.g. SNP markers), the likelihood reduces to a beta-binomial model.

Alternative models to explain population structure

Our purpose is to better discriminate between true signals of local adaptation and spurious signals left by other processes. Therefore, we assume that genetic differentiation at individual loci is influenced by three type of effects: (i) genome-wide effects due to demography, (ii) a locus-specific effect due to local adaptation caused by the focal environmental variable, and (iii) locus-specific effects unrelated to the focal environmental variable.

Although in principle one could consider all seven alternative models that can be constructed with different combinations of these three effects, most of them would not have any biological meaning. For example, all models should include genome-wide effects associated with genetic drift. Additionally, we do not consider the two types of locus-specific effects simultaneously in a full model. The reason for this is that the inclusion of α i along with g i is not justified biologically. This is because the joint effect of local adaptation and another locus-specific effect such as allele surfing or background selection on the same locus is extremely unlikely either because of the strong effect of genetic drift in the first instance or the implausibility of a favourable variant arising and increasing in frequency in a highly conserved region subject to strong purifying selection. Thus, we focus on three different models to explain the genetic structuring at individual loci.

Null model of population structure Under the null hypothesis that all loci are neutral, the local differentiation parameter F ij ST will be driven only by local population demography and, hence, should be common to all loci:

log F ij ST 1 -F ij ST = log 1 θ ij = β j . (2)
A high β j value means that the population j is strongly differentiated from the pool of migrants. This could be due to a lack of immigration from the other populations, a reduced effective size, or a particular spatial structure.

Alternative model of local adaptation

In this model, we focus on a particular signature left by a process of local adaptation. If selection is driven by a putative environmental factor, we expect that genetic differentiation for the locus or loci under selection will be stronger than expected under neutrality for populations with strong environmental differentiation. Any measure of distance between the environmental value of population j and the average environment could serve as a measure of differentiation. For the sake of simplicity, we here only consider the absolute value. Furthermore, in order to facilitate the calibration of prior distributions, we consider standardised environmental values with unit variance. To model the effect of local adaptation on locus i, we consider the impact of environmental differentiation E j of population j on the locus, we thus modify Eq. 2 as follows:

log F ij ST 1 -F ij ST = β j + g i E j , (3)
where g i quantifies the sensitivity of locus i to the environmental differentiation.

Alternative model of locus-specific effect Local adaptation with respect to the focal environmental variable is not the only evolutionary phenomenon that could lead to departures from the neutral model. Other phenomena that could produce such locus-specific effects include local adaptation due to other unknown factors, large differences in mutation rate across loci, the so-called allele surfing phenomenon [START_REF] Edmonds | Mutations arising in the wave front of an expanding population[END_REF] and background selection [START_REF] Charlesworth | Background Selection 20 Years on: The Wilhelmine E. Key 2012 Invitational Lecture[END_REF]. This is accounted for by using the following parametrisation for local differentiation:

α i β j g i E j θ ij a ij f i
log F ij ST 1 -F ij ST = α i + β j . (4)
The main advantage of implementing both of the above alternative models is that we can distinguish between departures from the neutral model of unknown origin (using Eq. 4) and departures due to local adaptation caused by a particular environmental factor (using Eq. 3).

Material and Methods

Implementation of the statistical model

Our method, summarised in Fig. 1, uses two types of data: (i) the allele counts a for each locus in each population sample, and (ii) observed values E of an environmental variable (one value per population), which are transformed into environmental differentiation using an appropriate function. Indeed, our model aims at associating genetic distance (i.e. the F ij ST ) with an environmental distance. Note that measuring an environmental distance requires to define a reference. The most natural reference would be the average of the environmental values, but this would not be always the case (see the example of adaptation to altitude in humans presented below). Also, it is strongly advised to standardise the environmental values by dividing by the standard deviation, in order to avoid effect size issues regarding the inference of the parameter g. As stated in the previous section, there are three different models:

M1 Neutral model: β j , M2 Local adaptation model with environmental differentiation E j : β j + g i E j , M3 Locus-specific model: α i + β j .
Note that in our framework, the focal model being tested against the two others is M2. Thus, power and error rates (FPR and FDR) are computed for model M2. Model M3 can be considered as a "nuisance model" whose role is to reduce the overall false positive rate by explaining the inflation of the variance in F ST due to locus-specific effects other than selection driven by the focal environmental factor. Hence, the statistical significance of the parameter α i is not of interest for BayeScEnv: only the significant values of g i are considered. All three models were implemented using an RJMCMC algorithm [START_REF] Green | Reversible jump Markov chain Monte Carlo computation and Bayesian model determination[END_REF]. In order to propose relevant values for new parameters during the jumps, the RJMCMC is preceded by pilot runs. These are aimed at both calibrating the MCMC proposals to reach efficient acceptance rates, and approximating the posterior distribution of parameters, as proposed by [START_REF] Brooks | Markov chain Monte Carlo method and its application[END_REF] and already implemented in BayeScan [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. Our code is based on the source code of BayeScan 2.1 and is written in C++. The source and binaries are available at https://github.com/devillemereuil/bayescenv. Our prior belief in the three models is described by two parameters: the probability π of moving away from the neutral model and the preference p for M3 against M2 as alternative models. We can calculate the prior probability for each model as:

P (M1) = 1 -π, P (M2) = π(1 -p), P (M3) = πp.
(5)

The mathematical details of the transition between models can be found in the Supplementary Material. Pilot studies showed that using values of p above 0.5 yielded extremely conservative results (note that setting p = 1 would mean that model M3 is always favoured over M2, in which case the power of the method is zero, yielding no positives whatsoever).

We used a uniform Dirichlet prior for the allele frequencies f i ∼ Dir(1, . . . , 1). The priors for the hyperparameters α and β, were Normal with mean -1 and variance 1 (note that the results of our method will be especially sensitive to the prior mean of α, but our pilot studies showed that -1 was a good default). Since under a local adaptation scenario the parameter g is only expected to be positive, it was assigned a uniform prior between 0 and 10. Our method outputs posterior error probabilities and q-values, which are test statistics related to the False Discovery Rate (FDR) [START_REF] Storey | A direct approach to false discovery rates[END_REF][START_REF] Käll | Posterior Error Probabilities and False Discovery Rates: Two Sides of the Same Coin[END_REF]. Contrary to the commonly used False Positive Rate (FPR), which is the probability of declaring a locus as positive given that it is actually neutral, the FDR is the proportion of the positive results that are in fact false positives, and is more appropriate for multiple testing [START_REF] Käll | Posterior Error Probabilities and False Discovery Rates: Two Sides of the Same Coin[END_REF]. See the Supplementary Information (SI) for more details.

Simulation analysis

We performed a simulation study to evaluate the performance of our method and compare it with that of BayeScan [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. We modelled 16 populations each with 500 individuals genotyped at 5,000 loci, among which one (monogenic scenario) or 50 (polygenic scenario) were under selection. We modelled three kinds of population structure: (i) a classical island model (IM), (ii) a one-dimension stepping-stone (SS) model and (iii) a hierarchically structured (HS) model. The genome was composed of 5,000 bi-allelic SNPs spread along 10 chromosomes. The loci under selection due to an environmental variable E (see Fig. S2 and Eq. S7 and S8), one for the monogenic case and 50 for the polygenic case, were randomly distributed across the genome. Since all markers were independently initialised, our simulations yielded negligible linkage disequilibrium. Consequently, we considered as true positives only the loci subject to selection. For the IM and SS scenarios, we directly initialised all 16 populations. For the HS scenario, we initialised the ancestral population, which, following successive and temporally spaced-out fission events, gave rise to 2, 4, . . . , 16 populations. This hierarchical structure is reinforced by preferential migration between related populations. More details regarding migration and population history are available in the SI. This model is very close to that used by [START_REF] De Villemereuil | Genome scan methods against more complex models: when and how much should we trust them?[END_REF]. It should be particularly difficult for our method, because all populations are equally differentiated (i.e. the β j parameters are expected to be roughly the same across populations), but a phylo-geographic covariance exists between related populations, which is not explicitly accounted for by our probabilistic model. More information regarding the environmental gradient and the fitness function are available in the SI, but, briefly, a polygenic multiplicative model was used with a selection strength of 0.02 (0.1 for the monogenic case). The simulations were performed using the SimuPOP Python library [START_REF] Peng | simuPOP: a forward-time population genetics simulation environment[END_REF] and the scripts are available online in the data section. Our simulated datasets were analysed using our C++ code and version 2.1 of BayeScan [START_REF] Foll | A Genome-Scan Method to Identify Selected Loci Appropriate for Both Dominant and Codominant Markers: A Bayesian Perspective[END_REF]. We generated 100 datasets for each scenario and computed the realised FDR, FPR and power yielded by BayeScan and our new environmental method (BayeScEnv). For the latter, we also compared several parametrisations using a prior probability π of jumping away from the neutral model of 0.1 (equivalent to the default prior odds used by BayeScan, which is 10) or 0.5, as well as a preference for the locus-specific model p of 0.5 (environmental and locus-specific models are equiprobable) or 0 (the locus-specific model is forbidden and only the environmental model is tested against the neutral one).

We supplemented these scenarios with a heterogeneous mutation rate case, based on the IM scenario above, where most of the genome had a high mutation rate of 0.05, whereas 50 loci had a low mutation rate of 10 -7 . The result was an overall low F ST of 0.05 for the whole genome, and of 0.10 for the low mutating loci.

HGDP SNP data analysis

In order to test our new method against a real dataset, we focused on 26 Asian populations from the Human Genome Diversity Panel (HGDP) SNP Genotyping data. This data set consists of 660,918 SNP markers genotyped using Illumina 650Y arrays. After cleaning the dataset from mitochondrial and sex-linked markers, we removed all markers with minor allele frequency below 5%. This left us with a total of 446,117 SNPs. For all populations, we obtained the following environmental variables from the BIOCLIM database: mean annual temperature, precipitation, and altitudinal data. We ran separate BayeScEnv analysis for each variable and compared the results with BayeScan (which doesn't use environmental variables). After standardisation of the environmental variables, we computed environmental differentiation from the mean for temperature and precipitation, and from the sea level for elevation. Gene ontology enrichment tests for the detected genes were performed using the "SNP mode" of the Gowinda software [START_REF] Kofler | Gowinda: unbiased analysis of gene set enrichment for genome-wide association studies[END_REF]. The prior odds for BayeScan was 10 for this analysis. BayeScEnv prior parameters for this analysis were π = 0.1 and p = 0.5.

Results

Simulation results

By definition, a threshold value of α used to decide whether q-values are significant or not is expected to yield an FDR of α on the long run, when the model is robust and priors are calibrated. Recall that in BayeScEnv all q-value tests below were performed on the parameter g to test for local adaptation. In the case of BayeScan, on the other hand, the q-values correspond to parameter α.

As shown in Fig. 2, BayeScan was less well calibrated, yielding higher FDRs than BayeScEnv under all scenarios and for both monogenic and polygenic selection. Additionally, for BayeScEnv, the implementation using π = 0.1 was fairly well calibrated (i.e. the curve is close the grey line in Fig. 2) under the IM scenario (for both monogenic and polygenic versions) and under the polygenic version of the HS scenario. This implementation was much more conservative than the one using π = 0.5. For π = 0.1 and p = 0, the FDRs were closer to those yielded by BayeScan, but still lower.

The higher FDR for BayeScan and BayeScEnv with π = 0.5 or p = 0 was mainly driven by a higher FPR rather than a lack of power (Fig. 3, see also Fig. S3 in the SI). Notably though, BayeScan had a quite high power, higher than that of BayeScEnv. Note, however, that BayeScEnv with p = 0 had, as BayeScan, a maximal power in the monogenic scenarios, and was almost as powerful as BayeScan in the polygenic scenarios. Yet its FDR was lower (sometimes much lower) than that of BayeScan. This indicates that the incorporation of environmental data helps to reduce the error rate both with or without the inclusion of spurious locus-specific effects (α i ). More details regarding the FPR results are available in the Supplementary Information (Fig. S3).

Another traditional way to apprehend the compromise between power and false positives is the so-called Receiver Operating Characteristics (ROC) curve, plotting power against FPR (Fig. 4). In these plots, the curve that is "more to the left" is preferred because this means it offers higher power for a lower FPR. Fig. 4 shows that BayeScEnv with π = 0.1 and p = 0 performed best under the IM and HS scenarios, whereas BayeScEnv with π = 0.1 and p = 0.5 performed better under the "harder" SS scenario. Overall, although BayeScan has higher power to detect local adaptation, it is still too liberal when deciding that a locus is under selection for the scenarios we investigated.

The heterogeneous mutation scenario lead to a dramatically high false positive rate for the low mutating loci in the case of Bayescan (62%). BayeScEnv, on the other hand, yielded a much lower false positive rate for these loci (4.9%). Of course, because the higher differentiation due to low mutation rate can be seemingly distributed according to the environmental variable, higher false positive rates will always be expected in such a scenario. Nevertheless, BayeScEnv is an improvement over Bayescan in that regard.

Analysis of human data from Asia

The results of the human dataset analysis (Table 1) show a dramatic discrepancy between the two methods. Whereas BayeScan yields a very large number (66,316) of markers considered as significant at the 5% threshold, many fewer markers (154 to 2728) are considered significant by BayeScEnv. Gene Ontology (GO) enrichment tests identified many significant terms (Table 1). Note, however, that in the altitude and temperature analyses they correspond to a small number of genes (11 and 20 respectively, see Table 1). The number of genes is larger for the precipitation analysis ( 359) and even larger for the analysis using BayeScan (5628).

Regarding the altitude, significant biological processes included the fatty acid metabolism (e.g. SCARB1), skin pigmentation (e.g. MLANA, SLC24A5), kidney activity (e.g. SLC12A1) and oxido-reductase activity (e.g. NOS1AP). Regarding the temperature, significant biological process included cardiac muscle activity (e.g. SLC8A1) and development (e.g. NRG1, FOXP1), fatty acid metabolism (e.g. FADS1, FADS2) and response to hypoxia (e.g. SLC8A1, SERPINA1). For the precipitation analysis with BayeScEnv, as well as the BayeScan analysis, the number of significant terms was too large for hand-picked examples to be feasible.

The significance results (q-values) are displayed as a Manhattan plot in Fig. 5, along with the above mentioned genes for the altitude and temperature analyses (Fig. 5, A andB). Other regions of the genome also include outlier loci but they correspond to non-coding regions, or are close to genes associated to GO terms that were not significant, or to proteins without a known function (e.g. C9orf91, which was the most significant gene in the temperature analysis). Pattern of linkage disequilibrium was visible, which sometimes strongly supported some candidate genes (Fig. 5, A, SLC12A1 and SLC24A5). Finally, comparing BayeScEnv (Fig. 5, A, B andC) and BayeScan analyses (Fig. 5,D), we see that BayeScan yielded too many significant markers for a Manhattan plot to be a useful display of the results. An interesting pattern is that BayeScan yielded far more outlier markers with maximal certainty (e.g. posterior probability of one) than BayeScEnv. For the present dataset, 22,516 markers had a posterior probability of one, whereas the maximal posterior probability yielded by BayeScEnv was 0.9998. Finally, almost all loci detected using BayeScEnv were also found when using BayeScan (between 98% for altitude to 100% for the two other variables).

Discussion

Features and performance of the method

The method we introduce in this paper, BayeScEnv, has several desirable features. First, just as BayeScan, it is a model-based method. This means that the null model can be understood in terms of a process of neutral evolution. One can thus predict what the method is able to fit or not. Second, we explicitly model a process of local adaptation caused by an environmental variable. Third, in order to render the model more robust, we account for locus-specific effects unrelated to the environmental variable under consideration. These departures can be due to another process of local adaptation (i.e. caused by unknown environmental variables), to large differences in mutation rates across loci, to background selection [START_REF] Charlesworth | Background Selection 20 Years on: The Wilhelmine E. Key 2012 Invitational Lecture[END_REF] or complex spatial effects, such as allele surfing [START_REF] Edmonds | Mutations arising in the wave front of an expanding population[END_REF] and hierarchical population structure [START_REF] Excoffier | Detecting loci under selection in a hierarchically structured population[END_REF]. Our simulation results show that when compared to BayeScan, BayeScEnv has a better control of its false discovery rate under various scenarios (Fig. 2), yielding fewer, but more reliable candidate markers. Obviously, this has a cost in terms of absolute power (Fig. 3), but BayeScEnv still performs better than BayeScan in terms of the investigated compromises between true and false positives (i.e. FDR and ROC, Fig. 2 &4).

Besides, the parametrisation of BayeScEnv allows for a fine and intuitive control of the false positive rate and power. For example, setting p to 0 increases both power and false positive rate, whereas setting p = 0.5 will allow for a more conservative test. This is because with p = 0, that is when the locus-specific effect model (M3) is excluded, the local adaptation model (M2) will absorb much of the signal in the data, yielding a higher probability of detecting true positives, but also a higher sensitivity to false positives. Our simulation results show that, if the species under study has moderate to large dispersal abilities (c.f. hierarchical structure or island model), the former parametrisation will be more appropriate, whereas for species with low dispersal abilities Figure 5: Manhattan plot of the q-values for the human dataset when using BayeScEnv with altitude (A), temperature (B), precipitations (C) or when using BayeScan (D). For altitude and temperature (A and B), genes mentioned in the text are displayed using black lines and genes associated with a significant GO term using grey lines. Top "stripes" for BayeScan (D) are artefacts due to finite number of iterations in RJMCMC (e.g. 0, 1, 2, 3... iterations outside of the non-neutral model), corresponding to determined posterior probabilities when divided by the total number of iterations.

(c.f. stepping-stone model) the latter should be preferred. Thus, being able to choose the right parametrisation only requires limited knowledge about the dispersal abilities of the species.

We note that BayeScan was recently extended to consider species with hierarchical population structure (BayeScan3, [START_REF] Foll | Widespread Signals of Convergent Adaptation to High Altitude in Asia and America[END_REF]. With BayeScan3 it is now possible to study widely distributed species covering several continents or geographic regions. It is also possible to better focus on local adaptation by considering groups that include pairs of populations inhabiting different environments such as low and high altitude habitats. Thus, BayeScan3, allows for the consideration of categorical environmental variables. Our new approach on the other hand, allows the study of local adaptation related to continuous environmental variables in species with a more restricted range.

How to quantify 'environmental differentiation' ?

To model local adaptation, we compute an "environmental differentiation" in terms of the distance (absolute value) to a reference value. Although this reference can conveniently be chosen as the average of the environmental values across the sampled populations, other kinds of reference may be biologically more relevant. For example, in our analysis of the effect of elevation in humans, it seems appropriate to use sea level as the reference. Indeed, given the kind of environmental variables elevation is a proxy for (e.g. partial pressure of oxygen, temperature, solar radiation, etc.), for most systems we would consider the sea level as a neutral environment rather than the differentiated one.

Another way to account for environmental differentiation is to use Principal Component Analysis (PCA), providing one of the axes to BayeScEnv as a description of the distance between environments. Despite this practice being an elegant way to summarise environmental distance between populations, it also has the drawback of making it more difficult to identify the "causal" variable.

Note that the environmental variables must be standardised so as to avoid scale inconsistencies between g and α and β. If we choose the average environmental value as reference, then standardisation involves meancentring and rescaling to have unit variance. However, if we choose another reference, then standardisation only involves rescaling to have unit variance.

Finally, the software implementation of our method only accepts one environmental variable at the time as including more than one variable would considerably slow the algorithm down, and render the biological interpretation of g quite tedious. Also, when using several correlated variables, it is important to realise that statistically distinguishing between the relative selective roles of each one would require many populations.

Comparison with other environmental association methods

There are several genome-scan approaches that incorporate environmental information, such as Bayenv [START_REF] Coop | Using Environmental Correlations to Identify Loci Underlying Local Adaptation[END_REF], LFMM [START_REF] Frichot | Testing for Associations between Loci and Environmental Gradients Using Latent Factor Mixed Models[END_REF] and gINLAnd [START_REF] Guillot | Detecting correlation between allele frequencies and environmental variables as a signature of selection. A fast computational approach for genome-wide studies[END_REF]. These methods perform a regression between allele frequencies and environmental values. Yet non-equilibrium situations combined with complex spatial structuring can lead to spatial correlations in allele frequencies, which in turn can lead to high false positive rates. To minimise this problem, the above methods take into account allele frequency correlations across populations while performing the regression.

BayeScEnv, on the other hand, assumes that all populations are independent, exchanging genes only through the migrant pool. However, it includes a locus-specific effect unrelated to the environmental variable that helps to take into account locus-specific spatial effects due to deviations from the underlying demographic model. The fact that this approach works is illustrated by our simulation study, which showed that BayeScEnv was fairly robust to isolation-by-distance and a hierarchically structured scenario. Moreover, the analyses of simulated datasets from [START_REF] De Villemereuil | Genome scan methods against more complex models: when and how much should we trust them?[END_REF], available in the SI, show that even under very complex scenarios, BayeScEnv can compete with other environmental association methods. In particular, most of these scenarios assume an environmental selective gradient confounded with population structure, which is particularly hard for genome scan methods [START_REF] Frichot | Detecting adaptive evolution based on association with ecological gradients: Orientation matters! Heredity[END_REF]: the results show that, in that case, BayeScEnv suffer from low power, but not from an excess of false positives. When compared with the other methods (including Bayenv and LFMM), BayeScEnv typically yields a medium FDR for most scenarios, and is less scenario-sensitive than Bayenv and LFMM. Nevertheless, we note that BayeScEnv is best suited for species with medium to high dispersal abilities such as marine species and anemophilous plants.

Another point that distinguishes BayeScEnv from these methods is that it does not assume any particular functional form for the relationship between environmental values and allele frequencies. While existing association methods all assume a clinal pattern, BayeScEnv only assumes that genetic differentiation increase exponentially with environmental differentiation. This allows for a more diverse family of relationships between allele frequencies and the environment.

Finally, BayeScEnv is one of the very few methods to study gene-environment associations that can be used with dominant data (but see also [START_REF] Guillot | Detecting correlation between allele frequencies and environmental variables as a signature of selection. A fast computational approach for genome-wide studies[END_REF].

Data analysis

When confronted with real datasets, BayeScEnv typically returned fewer significant markers than BayeScan. This is explained both by the focus on searching for outliers linked to a specific environmental factor and by the lower false positive rate of our approach. When applied to the human dataset, BayeScEnv identified several genomic regions that are enriched for gene ontology terms relevant to potential local adaptation to altitude or temperature. We emphasise that this study was not meant to exhaustively and rigorously investigate local adaptation in Asian human populations. However, our results tend to demonstrate that the candidates yielded by BayeScEnv have a biological interpretation. For example, skin pigmentation and cardiac activity could clearly be involved in responses to increased solar radiation and depleted oxygen availability at high elevation.

Much of the ontologies linked to temperature were potentially confounded with adaptation to altitude, such as the response to hypoxia and cardiac muscle activity. Also, fatty acid metabolism was associated to both altitude and temperature. Of course, the biological functions described here do not account for all the signals yielded by BayeScEnv (see Fig. 5, A andB). Other genomic significant regions include genes with less obvious biological function regarding local adaptation, non-coding regions and proteins without a known function. Finally, the analysis using the precipitation variable yielded too many significant markers for a detailed analysis of the biological functions involved. This may not necessarily be due to a confounding effect of the spatial structure (the human Asian populations being structured mainly from West to East, while the Eastern climate is characterised by strong precipitations during the monsoon), since precipitation may behave as a surrogate for several environmental variables.

Conclusion

The main improvement introduced by our new method, BayeScEnv, over existing F ST -based genome-scan approaches is the possibility of focusing on the detection of outlier loci linked to genomic regions involved in local adaptation and better distinguishing between the signal of positive selection and that of other locusspecific processes such as mutation (see the heterogeneous mutation rate scenario in the Results) and background selection. Although it does not explicitly model complex spatial effects, the consideration of two different locusspecific effects make it more robust to potential deviations from the migrant pool model. This is reflected in its much lower false discovery rate when compared to BayeScan.

Our new formulation also allows for an improved control of the true/false positives compromise through the parameter p, which describes our preference for the model that includes a locus-specific effect unrelated to the environmental factor over the model that includes environmental effects. Although we recommend using p = 0.5, lower values (including 0) could be used if population structure is weak or maximising power is more important than reducing the false positive rate.

With this new method, there are now three alternative formulations of genome-scan methods based on the F model. BayeScan detects a wide range of locus-specific effects (including background selection). Although its false discovery rate is higher than that of the two extensions, it is able to detect regions of the genome subject to purifying selection. The hierarchical version of this original formulation, BayeScan3, allows the study of local adaptation due to categorical environmental factors. Finally, our new method, BayeScEnv, is more appropriate to detect genomic regions under the influence of selective pressures exerted by continuous environmental variables. Thus, all three methods are complementary and jointly cover scenarios applicable to a wide range of species

Figure 1 :

 1 Figure 1: Directed Acyclic Graph (DAG) of the model. Squared nodes denote know quantities (E for environmental data, and A for genetic marker data). Circled nodes denote unknown parameters. Plain arrows stand for deterministic relationships, and dashed arrows stand for stochastic relationships.

Figure 2 :

 2 Figure 2: False Discovery Rate (FDR) against significance threshold α for three scenarios (IM: Island model, SS: Stepping-Stone model and HS: Hierarchically Structured model) and monogenic/polygenic selection. The grey line is the expected identity relationship between the FDR and α. The models tested are BayeScan (blue dashed), and BayeScEnv (orange dotted, green dot-dashed and solid red) with different probabilities π of jumping away from the neutral model (M1) and different preferences p for the locus-specific model (M3). Note that p = 0 means the environmental model (M2) is tested against the neutral one only.

Figure 3 :

 3 Figure 3: Power against significance threshold α for three scenarios (IM: Island model, SS: Stepping-Stone model and HS: Hierarchically Structured model) and monogenic/polygenic selection. The models tested are BayeScan (blue dashed), and BayeScEnv (orange dotted, green dot-dashed and solid red) with different probabilities π of jumping away from the neutral model (M1) and different preferences p for the locus-specific model (M3). Note that p = 0 means the environmental model (M2) is tested against the neutral one only.

Figure 4 :

 4 Figure 4: Power against False Positive Rate (FPR), a.k.a. ROC curve, for three scenarios (IM: Island model, SS: Stepping-Stone model and HS: Hierarchically Structured model) and monogenic/polygenic selection. The models tested are BayeScan (blue dashed), and BayeScEnv (orange dotted, green dot-dashed and solid red) with different probabilities π of jumping away from the neutral model (M1) and different preferences p for the locus-specific model (M3). Note that p = 0 means the environmental model (M2) is tested against the neutral one only.

Table 1 :

 1 Results from BayeScan and BayeScEnv on the human dataset. FDR significance threshold was set to 5%. The total number of tested markers was 446,117.

	Method	Variable	Nr of significant SNPs	Nr of significant GO terms	Nr of genes associated with a significant GO term
		altitude	154	32	11
	BayeScEnv	temperature	170	103	20
		precipitation	2728	439	359
	BayeScan	-	66,316	469	5628

). Note that p = 0 means the environmental model (M2) is tested against the neutral one only.

Acknowledgement

We thank M. Foll for providing the source code of BayeScan and for clarifying several issues related to the code, J. Renaud for his help on getting the average altitude out of the HGDP latitude/longitude data, S. Schoville for the BIOCLIM data, E. Bazin for his help on the HGDP data analysis. PdV was supported by a doctoral studentship from the French Ministère de la Recherche et de l'Enseignement Supérieur. OEG was supported by the Marine Alliance for Science and Technology for Scotland (MASTS).

Data Accessibility

The Python code used to simulate data is available online in the Supplementary Information. The software and its source code are available online at GitHub: http://github.com/devillemereuil/bayescenv. The HGDP dataset is available at http://www.hagsc.org/hgdp/files.html. The BIOCLIM database is available at http://worldclim.org/bioclim.

Author contributions

PdV and OEG designed the statistical model. PdV modified the C++ code and performed the simulation and data analysis. PdV and OEG wrote the article.


Lourdes Monterrubio Ibáñez
email: loumonte@ucm.es

Women's Epistolary Cinema. Exploring Female Alterities: Epistolary Films and Epistolary Essay Films

Keywords: women's cinema, epistolary film, essay film, alterity, cinematic enunciation

This article aims to analyse female authorship in the materialisations of contemporary epistolary cinema, focusing on epistolary films and epistolary essay films. The works of various filmmakers are essential to understand the evolution of this enunciation device and the exploration of female alterities materialised through it. Women filmmakers' epistolary practices delve into the exploration of intimate space, authorial vindication, epistolary materiality, intersubjectivity and cinematic thinking to create diverse experiences of female alterity, developing this postmodern paradigm inherent in the epistolary device. Since Chantal Akerman started the practice of the epistolary film with News from Home (1977), other women filmmakers have developed this cinematic form. The reading of a personal correspondence allows the exploration of female intimate alterities -Measures of Distance (1988), Punto impropio (2015), A Minha Avó Trelotótó (2018). Besides, the epistolary film is fictionalised, displacing it to the intellectual space -From Hetty to Nancy (1997), Endless Dreams and Water Between (2009). Other people's real correspondence is also instrumentalised to create their recreations and representations, vindicating female alterities both socially and personally -Letter #69 (2016), The Dreamed Ones (2016). Finally, women filmmakers addressed the cinematic form of the essay film -Letters from Panduranga (2015), Correspôndencias (2016).

Introduction

This article aims to analyse how women filmmakers explore the possibilities of alterity in epistolary cinema-epistolary films and epistolary essay films-regarding female identity and subjectivity. It offers an itinerary along a wide-ranging corpus whose analyses will trace the evolution of the epistolary device as well as the relevance of these films both from the point of view of cinematic language and female identity. Women's epistolary cinema starts from three key epistolary works by three francophone filmmakers who, in the space of three years, offer three crucial works in the evolution of this enunciative device and use it to embody a female discourse: L'une chante, l'autre pas (Agnès Varda, 1977) through the correspondence inside a narrative in which the filmmaker places herself as an intermediary narrator; Aurélia Steiner (Marguerite Duras, 1979) using the letter-film in which the author becomes a fictional performer; News from Home (Chantal Akerman, 1977) creating a new form, the epistolary film, in which the filmmaker is the documentary protagonist. The three films are the starting point of a deep relationship between female authorship and epistolary cinema, which proliferates in contemporary space (Lourdes Monterrubio Ibáñez 2019) through its different possibilities: letter-film, filmic correspondence, epistolary film and epistolary essay film.

With the advent of postmodernity, the concept of alterity becomes hegemonic, as many authors note, pointing out the relevance of otherness in identity. Julia Kristeva explores how "disturbing, strangeness is within us: we are our own strangers, we are divided" (1988,268). Zygmunt Bauman analyses it through the concept of strangeness, understanding it as "the existential and mental ambivalence" (1991,95) universalised in Postmodernity. For his part, Marc Augé uses the concept of intimate alterity to describe the "necessity at the very heart of individuality, prohibiting at the same time to dissociate the question of collective identity from that of individual identity" (1992,(29)(30). Paul Ricoeur establishes three modalities: "proper alterity, alterity of the other, alterity of conscience " (1990, 410), through which he describes and studies the complexity of this "ontology of alterity" (373), allowing us to understand the dialectics between ipseity and otherness. The idiosyncrasy of the epistolary device lies in offering a unique space for expressing and exploring that "existential and mental ambivalence", that "intimate alterity", that "alterity of conscience" of the addresser in relation to the addressee. It then becomes an ideal tool in the cinematic field to explore the experience of alterity, embodying this paradigm shift in filmic creation. Besides intimacy, self-expression, the border between private and public spheres and, of course, the digital revolution as reasons for the proliferation of epistolary enunciation in contemporary cinema, I argue that the necessity to explore the alterity experience is the nuclear reason for the proliferation of the epistolary device and also of the multiplicity of its forms, since it becomes a powerful ontological instrument to this purpose. The three films mentioned express, reflect and vindicate female subjectivity thanks to the experience of alterity, and other women filmmakers have been able to continue its exploration. This article will focus on the evolution of the epistolary film and the epistolary essay film that starts with News from Home.

The first consequence of the prominence of alterity regarding the epistolary device is the relevance gained by the epistolary addressee, which causes the evolution from the letter-film to the epistolary film. While the letter-film of modern cinema was focused on the subjective expression of the addresser, the importance of alterity makes the epistolary act include the presence of the addressee, as Letter to Jane (Jean Luc Godard and Jean-Pierre Gorin, 1972) already anticipated. First, the letter-film is converted into an epistolary film by replacing the writing of a single letter with the reading of a set of them.

A film is essential to enable this evolution: Akerman's News from Home (1977) becomes the first epistolary film, by constructing its enunciation through Akerman's reading of the letters from her mother. Thus, the epistolary film finally reaches its literary model, and the film is enunciated through a series of letters (Monterrubio Ibáñez 2018, 284-292). Some years later, Sans soleil (Chris Marker, 1983) transforms the epistolary writing of Lettre de Sibérie (Marker, 1958) into the reading that the addressee (an unknown woman) performs of Krasna's missives. Akerman's film, besides starting the exploration of the epistolary film, developed from her real and intimate correspondence, delves into the generational gap between mother and daughter and provides an artistic experience of great relevance to feminist analysis [START_REF] Longfellow | Love letters to the mother: The work of Chantal Akerman[END_REF][START_REF] Mcfadden | Gendered frames, embodied cameras: Varda, Akerman, Cabrera, Calle and Maïwenn[END_REF][START_REF] Margulies | Nothing happens. Chantal Akerman's hiperrealist every day[END_REF][START_REF] Barker | The feminine side of New York: travelogue, autobiography and architecture in 'News from home[END_REF]). The constant concern for the daughter and the insistent request for letters become a kind of family ambient sound, which is not heeded: "a mother's murmur that comes from far away, from the mother tongue precisely, to worry about an absent body [. . .] This voice of a mother in search of her lost daughter disperses, weakens, persists in New York" (José Michel Bulher and Yves Laplace 1977, 54). Thus, this epistolary material is related to the Lacanian notion of llanguage, as indicated by Daniele [START_REF] Dubroux | Il n'y aurait plus qu'une seule image[END_REF], defined as the structure of the unconscious that goes beyond the communicative notion of language to include the specific characteristics of each individual, in relation to family learning and its idiosyncrasies (Jacques Lacan 1998, 139). The epistolary writing represents the preservation of memory for the mother and, therefore, of the maternal-filial bond: "Do not forget us. Write", which is close to the pathological identification: "I live at the rhythm of your letters." The film offers a reflection on the abyss that surrounds the experience of maternal-filial alterity: "News from Home is a film about emptiness, anguish . . . A deep hiatus, something impassable, it exists between these two worlds, New York and Brussels family life" (Francoise Maupin 1977, 109). I will analyse how this notion about family idiosyncrasies and female subjectivity and alterity is explored by different filmmakers in different and fruitful ways following the path open by Akerman. This article addresses the most notable works made by women filmmakers classified into four practices: epistolary films that use the filmmakers' real and personal correspondence; those constructed as epistolary fictionalisations based on documentary image; the interpretation and/or recreation of other people's correspondence; and finally, the materialisation of epistolary essay films. All of them explore the alterity concept, creating a common, shared space that connects them and overcomes their different cultural and mediatic contexts, providing a female cinematic experience of alterity and the power of this filmic practice.

Intimate alterities

Ten years after Akerman's film, Mona Hatoum continues this epistolary experience in Distance (1988), using the same crucial element, the letters sent by her mother; in this case, those caused by the filmmaker getting stranded in London because of the Lebanese civil war. While Akerman used the correspondence to deepen the generational gap between mother and daughter, Hatoum instead explores the depth of the mother-daughter bond despite the distance. Furthermore, the filmmaker introduces a new element: the materiality of the written letter.

Measures of

The short film begins with a succession by crossfading of five detail shots, in which we discern a body, and to which the image of epistolary writing, the weaving handwriting of Arabic on the paper, is superimposed. From the sound image, the conversation between the two women arises. It provides an image of the emotional bond, of the intimacy between mother and daughter, sifted by the distance evidenced by the letters, as we realise later. Then, Hatoum's voice-over emerges, beginning with the reading of a letter from her mother, but translated into English: "My dear Mona. The apple of my eyes. How I miss you and long to feast my eyes on your beautiful face that brightens up my days." In this way, the specific stratification of audiovisual epistolary writing materialises, in which both images express distance: between the photographic images of the encounter and that of the letter; between the sound of the conversation and that of Hatoum's reading in the language of exile. Like Akerman, Hatoum uses the mother's epistolarity: five missives that start with "My dear Mona" and through which the addresser is going to express her emotions regarding the daughter's exile and also her reflections on the women's reality in her culture. We listen to the animated talk of mother and daughter in the background, without their dialogue being translated, configuring an emotional landscape of the bond. The Lacanian llanguage referred to in Akerman's film takes on an opposite meaning here, a kind of rumour of the home as a refuge.

The first letter reveals the origin of the images we observe: the nude portrait of the mother's body from a photo shoot in the absence of the father, and from whom it must be hidden, thus generating the epistolary film in the space of transgression. As Hamid Naficy notes in his indispensable work about the bond between filmic epistolarity and exile: "Hatoum's transgression is in line with what Derrida has called the 'postcard structure' itself, one that raises questions about what is public or private, inside or outside, real or fictional" (2001,120). Besides, epistolary materiality is then associated with the haptic camera defined by Laura Marks:

It is the skin of the mother, as well as the indexical trace of her voice on tape, that gradually activate the sense of her mother's presence as well as the painful finality of her absence […] a muffling quality that seems to want to fill in the gap by appealing to the memory of touch (2000,(112)(113).

Faced with the fragmentation of the images during the first two letters, the third offers the complete portrait of the mother, while her epistolary words address her reflections on sexuality (Figure 1). Thus, the epistolary alterity, the maternal figure, is revealed thanks to the filmic device. The fourth missive continues with the camera moving away from the mother's body, until we contemplate a general shot that is then superimposed on another detail shot before disappearing, thus embodying again the idea of the epistolary stratification made possible by the audiovisual device. The epistolary film, caused by exile, generates a gradual identity portrait of maternal alterity that also faces the reality of absence, since reading the last letter on the black screen and without the sound image of the conversation. This absence of visual image also shows the possibilities of the audio-visual letter compared to the literary one: not only its visual materialisation but also its possibilities of stratification, both in the visual image and in the sound image.

Albertina Carri moves the epistolary film to the video installation space with

Punto impropio (2016), which is constructed from the letters that the filmmaker's mother, disappeared under the Argentine military dictatorship, writes to her three daughters during the months of captivity, when Carri was four years old. Three projections are shown on the floor of a dark room: "Two horizontal projections and a square projection placed in the middle of the other two [. . .] The two rectangular projections (horizontal) form my mother's name ANA MARÍA, the square projection is a point in the middle of her two names" (Albertina Carri 2016, 165). That point, a circular screen, gives way to the projection of images of the letters through a microscopic view, turning them into an unrecognisable abstract geography of the surface of the paper and the ink inscribed on it, where the handwriting disappears to become strangehood. Over these images, Carri's voice-over reads the mother's letters, pronouncing the dots, the commas, the line changes, as if it were a school dictation. Thus, through the two epistolary forms (visual image and sound image) the experience of trauma materialises, the vertigo of the impossibility of apprehending a maternal message at the age of four. The need for the passage of time in order to decipher it makes its reading an already apocryphal text, showing the abyss of absence of almost 40 years. The texts are divided into three blocks, separated by two brief inserts from her previous autofictional film, Los rubios (2003): the narration that the filmmaker's character (played by Analía Couceyro) provided of the parent's kidnapping.

In other words, the epistolary film shows the need to return to her own experience, stripped of the autofictional device of the previous work. While Los rubios distanced itself through autofiction, Punto impropio approaches the topic through the epistolary experience until rendering it abstract. Furthermore, both images are manipulated to cause a sensation of saturation and of sensory dizziness. The microscopic visual image focuses and unfocuses, moves across the surface of the paper and rotates, as if it were the entire screen that was spinning, also changing its sense, contributing to the perception of the impossibility of apprehension. In addition to the filmmaker's voice, the sound image instrumentalises a musical melody that appears and disappears, and that at different times becomes another ingredient of sensory discomfort. This modulation on which the work is built is revealed in minute 10 of the footage. During the reading of the fourth letter, addressed to the three daughters, the music disappears first, and the voice softens, becomes a kind of murmur that turns it into a new materialisation of Lacan's llanguage, regarding and revealing once again the identity-alterity relevance of the mother-daughter bond. Only when the voice becomes a faint echo, does the handwriting reveals itself on screen; the microscopic magnification disappears and the mother's writing becomes accessible to the human eye, but upside down; never completely legible (Figure 2). This decalage between the intelligibility of the epistolary voice and the epistolary image is a lucid metaphor for the trauma that this correspondence contains. From that moment on, the handwriting and the voice get closer and farther throughout the work, evidencing the daughter's determination to decode the mother's messages. That process could finally be successful when intelligible handwriting and voice coincide during the most terrifying content: "If the letters reach someone who wants to harm us, they kill us. And this is literal, they shoot us, so go find them personally."

Figure 2. Punto impropio [START_REF] Carri | Albertina Carri. Operación fracaso y el sonido recobrado[END_REF]. Courtesy of the filmmaker.

The epistolary content, the mother's constant attempt to care for her daughters in the distance covers all possible spaces, from the purely biological to the emotional and intellectual. The need to educate them becomes Ana María Caruso's literary work, also as a feminist vindication: "Those letters are the book that Ana María Caruso could not write [. . .] Punto impropio runs through my mother's non-work and the power that the treatise Ana María wrote in epistolary format-that non-book-has on my voice" (Albertina Carri 2015, 15). It is possible to experience this female alterity of the absent mother through the film also due to the author's life reality, who is older than her mother when she was murdered and who also already knows the experience of motherhood. It is a vital moment where personal experience is vindicated with greater force as a social and political experience: "Letters function as a place to always return to in the face of horror, like a trace [. . .] I think there is an immense political tool there" (Pilar Altilio 2020).

While Akerman and Hatoum explore maternal alterity, Catarina Ruivo addresses her grandmother Julia in O Minha Avó Trelotótó (2018). The work is built from the spaces inhabited by the protagonist, which now trace her absence. The different characters from her daily life reproduce the scenes and actions they shared with her in front of the present absent space she occupied. This anonymous absence will be endowed with identity through her correspondence. Julia herself, in a past audiovisual document, goes through a family photo album that becomes the structural axis of the film, stating her different life stages. Born in Luso, a pharmacist by profession, she married Zé Antonio, and they moved to Mozambique in 1946. After having four children, working as a teacher and moving around the country, her husband died in 1957. This is the period mainly narrated by the missives, which are completed with the account of the mourning, her relationship with a new partner, Alexandre, and finally the correspondence with Ruivo herself. Thus, the biographical narrative is delegated in her correspondence, in the letters written by Julia, mainly, but also some addressed to her or belonging to other characters. Julia's missives, enunciated through the voice-over of Rita Durão, who voices the grandmother, will generate various epistolary expressions, one of them of particular relevance due to its innovation.

The first two letters, from Zé Antonio (voiced by António Pedro Figueiredo) to Julia when they were still dating, generate a first device: the first epistolary text is enunciated on a B/W photograph of both at that time; the second gives way to the moving image of that same place in the present. Next, the third text already offers the new device: in a present colour image, a B/W silhouette of Julia is inserted, as a cut out, belonging to a past image. In this way, the filmmaker continues to experiment with the expressive possibilities of absence. The total absence represented in the present time is now followed by this new figuration between the present space and the past image. It is necessary to point out the choice of the screen format: the 4:3 used homogenises the whole of the work (only some moving images of Julia keep their original format) and emphasises the idea of the aforementioned collage-images as audiovisual postcards that remediate this epistolary object turning it into an artistic expression. It is necessary to note the relationship of this new device with Varda's installation La Grande Carte postale ou Souvenir de Noirmoutier (2006), also generated from the idea of collage, proving also the evolution of the device from L'une chante, l'autre pas (Dominique Bluher 2019). This innovative epistolary device is also used as an expressive element to relate the death of the husband. His silhouette, in the middle of the road, moves away through a tracking shot, unique in the entire film, without any text. Among Ruivo's collage-images, three of them exchange the current moving image for pictorial images. In the most relevant of them, a photograph of Julia is inserted into Edward Hopper's Compartment C, Car 293 (1938) (Figure 3), while we listen to the letter that Alberto, her assistant and friend in the Mozambique years, writes to her on the first anniversary of her husband's death. Julia, as we will see in the outcome of the film, thus achieves the immortality she demands of her granddaughter.

Figure 3. O Minha Avó Trelotótó (Catarina Ruivo, 2018). Courtesy of the filmmaker.

The bond shown with her mother and later with her daughter culminates in her relationship with the filmmaker. The collage-images, in this case one of Julia on the beach, give way to the moving images of Julia recorded by Ruivo, images from the personal archive that now acquire the status of film creation, thus fulfilling the grandmother's desire, enunciated in a truly beautiful letter that shows the bond the film generates: "And you are not here to revive me, to make me feel the miracle of resurrection that you always brought me [. . .] Come on . . . Don't abandon me!" Once again, the epistolary creation of women filmmakers generates new expressions of this device in order to deepen the experience of female alterity, in this case, the grandmother-granddaughter relationship.

Fictionalisation of the epistolary device

The epistolary film also evolves towards a fictionalisation that is generated from the doc- In this way, a first confrontation occurs between the powerful images of the Icelandic scenery (Figure 4) and the mundane account of the anecdotes of this particular expedition: from the dire state of Hetty and Masie's tent, the comical clothing of the group or the criticism of young women, to the tedium produced by the visited landscape: The documentary image also mixes images of the country's powerful landscapes with others dedicated to its most mundane day-to-day life: the daily care of a flock of sheep or the loading and unloading of boats. All these elements embody Hetty's gaze, that of a comic, ironic and satirical female subjectivity that once again abandons stereotypes to vindicate its uniqueness. Thus, the film continues to explore some of the epistolary elements used in Lettre de Sibérie through its fictionalisation: the irony of subjective perception and the questioning of objectivity associated with observational documentary.

In Endless Dreams and Water Between (2009), Renée Green generates a fictional epistolary narrative through the voice-overs of four characters, while the visual image is again of a documentary nature. The fictional character of Aria Phoenix, who lives in Mallorca, sends a written letter to three women to propose an epistolary exchange which should become a space for thinking and reflection on the texts they read, and based on a circumstance common to all of them: to inhabit an island or peninsula. The idea arises from a vivid dream in which Aria founds The September Institute, a space dedicated to this insular thinking: "thinking from the islands we inhabit." Its three addressees: Raya (San Francisco), Lyn (Manhattan) and Mar (Mallorca) respond to the proposal with their first letter writing exercise. In this way, the film is built on six epistolary texts: Aria's proposal and a second letter, the responses of the three recipients and Aria's response to them. Therefore, the fictional characters belong exclusively to the sound image, while the visual image shows water landscapes (Figure 5), the islands where they live, and different archive images inserted in relation to the epistolary contents. Thus, the film does not intend to create an audiovisual epistolary enunciation but, on the contrary, it becomes a reflection on literary epistolary writing as a source of thinking and, more importantly, as an engine of intersubjectivity among these four female characters:

Ideally, I would like us to explore writing letters. This is something that has become nearly extinct and I'd like to attempt reviving this art of writing actual letters [. . .] These letters can be sent via e-mail, although I'd like to experiment with sending them by post, so that it is possible to have something tangible we have touched. This practice of instrumentalising the epistolary activity of female artists, again influencing the exploration of female alterity, will be repeated in two other later works.

The film thus portraits a female intellectual intersubjectivity that is also supported by the reference to Laura Riding's literary creation. After the first epistolary delivery of all of them, Aria is then in a position to establish the postulates of the September Institute and its future activity: "3. Sending transmissions from dispersed islands, linking worlds, time, and space. 4.We continue the ongoing movement of combination people." As Lisa Le Feuvre notes, the film "interrogates how imagination and negotiation of our place in the world collide and corrupt, charging projections, fabulations, and dreams with the complexities of the present" (2010,17). Therefore, the film is not constructed as an essay film that produces cinematic thinking, but as an audiovisual space that favours the absorption of epistolary female intellectual intersubjectivity and encourages the spectator's reflection. In this regard, it is necessary to point out that this film belongs to a larger museum installation developing some aspects of what the film proposes, expanding the possibilities of this spectator's reflection.

Representation and recreation of others' correspondence

As mentioned above, some filmmakers create the epistolary film starting from others' correspondence. Letter #69 (Hsin-I Lin, 2016) is an epistolary short film created from the 68 letters that Shi Shui-huan, a 29-year-old woman, wrote from prison, during the 19 months that she was detained in Taipei as a victim of the Taiwanese White Terror, before being executed in the summer of 1956. The filmmaker then creates an epistolary film that aims to convey the silence and oblivion to which the victims of the regime were condemned: in this case, the 201 victims buried in the Liuzhangli Mass Grave, forgotten for decades. To do this, the epistolary texts are manipulated through a new and innovative procedure that delves into the possibilities of stratification of audiovisual epistolarity.

First, the filmmaker's reading of the letters is reproduced in reverse, making their enunciation an act of denunciation about the silencing to which the victims were subjected:

"the reverse playback of the director reading Shi Shui-Huan's letters, serving as an audible but incomprehensible discourse" (Matteo Boscarlo 2016). While Akerman instrumentalises the unintelligibility of the epistolary text as an expression of the intimate conflict, Hsin-I Lin uses it to denounce the historical trauma. Secondly, the epistolary texts are written on an analogue film, shown on the screen, which is not intelligible either, this time as a metaphor for forgetfulness produced by historical time. Finally, they are also transcribed on the current digital image, a space in which its reading is finally possible. The visual image, meanwhile, offers a kind of sensory recreation in relation to their content: "The scene is set in an abandoned Japanese-style building in Taiwan and a prison scene in a human rights park" [START_REF] Boscarlo | Letter #69[END_REF]. At the beginning of the film, the voices of different women, relatives of the protagonist, narrate her arrest through their voice-overs, while we listen to the sound of the film projection and the unintelligible enunciation of the letters. The visual image shows us the materiality of an analogue film and the epistolary text, also illegible on it (Figure 6). This hybridisation of elements Carri's films, now transferred to the recreation of the situation of enunciation. On the epistolary texts, the visual image oscillates between the interior of these recreation spaces and the exterior of the mass grave. After the third and fourth letters, two poems are introduced, copied by hand by the addresser herself. From the fifth missive, it jumps to the last one, #68, since #69 was never written. On the black screen we only hear the sound of the execution that prevented its writing. After this epistolary enunciation of six letters and the non-realisation of #69, the sound image resumes its reverse reproduction, its intelligibility, a metaphor for oblivion. Like the prologue, the epilogue denounces the ostracism to which the mass grave was relegated: "The Liuzhangli Graves lay here covered by grass, unclaimed, victims of political strife with no voice with which to defend themselves." Once again, it is the female subjectivity that is explored through the experience of alterity that the epistolary legacy provides, in this case associated with the vindication of historical memory. The film begins with the recitation of the first epistolary texts, through a shot-countershot of the close-ups of both characters. Thus, the variations between off-and on-screen voice, between recitation and listening, between writing and reading, offer a first and subtle experience of the epistolary fact from which its different facets will be explored. The recording will be punctuated by brief breaks, up to seven, which will allow us to observe how the epistolary reading generates the evolution of the relationship between the performers; from the distance between the strangers to the proximity of the shared emotional experience through epistolary correspondence. After the first break, the correspondence continues as the listening that the characters enact of their own performance of the following two texts. The epistolary experience is thus captured from different angles: the enunciation itself, the listening of the other; the listening of both outside the epistolary dialogue; and later the instrumentalisation of the epistolary text as a voice-over that accompanies the visual image of some of the following breaks, as if the correspondence between Bachmann and Celan absorbed its current situation of enunciation. The first voice-over enunciation, of one of Bachmann's letters, shows both performers during the third break, separated, so that they then start a dialogue about the correspondence, in which they not only try to understand the decisions of the correspondents, but to imagine and project themselves into the situation described in the text. The experience of this epistolary performance/reading expands its space of influence.

The possibilities of this epistolary enunciation continue to evolve and the correspondence gradually becomes a dialogue. A letter from Celan is interrupted on several occasions by one of Bachmann's sentences, which repeatedly asks about a verse of Celan's poem-"Cologne, Am Hof"-also giving its title to the film: "But are we only the dreamed ones?"

The sentence synthesises Bachman's conflict regarding Celan's marriage and the filmmaker evidences her interest about the female side of the relationship, which will be explore throughout the rest of the film. Bachmann's next letter is enunciated through the voice-over while the visual image shows him listening with headphones, showing again that crucial decalage between the epistolary production and its reading, also hybridising that reality of 1957 and the cinematic present. The epistolary texts are then reduced and their alternation makes of them the dialogue, suggested before, that correspondence yearns for. At the same time, the identification between correspondents and performers advances, evidencing the ability of epistolary writing to reveal the deepest spaces of identity and to allow identification. This progression concludes with Bachmann's last letter, while she is ill. For the first and last time in the film, the actress looks into the camera, which embodies a kind of feminist recognition of Bachmann's life experience, who had to face patriarchy both in her creative activity as a writer and in her romantic relationship with Celan, as the letters reveal (Figure 7). Although the film includes both writings, it seems evident that, once again, the female filmmakers engage in an exercise of sisterhood, choosing the point of view of the female character. Once the film concludes with the text on the screen that informs us of the deaths of both, the filmmaker adds a short epilogue that confirms this idea, in which the actress reads a last text by Bachmann, this one non-epistolary-belonging to Malina (1971)-and unrelated to the recording, about Celan's death: "My life is over, for during transport, he drowned in the river. He was my life. I loved him more than my own life."

Figure 7. The Dreamed Ones (Ruth Beckermann, 2016). Courtesy of the filmmaker.

The epistolary essay film

The instrumentalisation of the epistolary device in the space of the essay film has been the latest practice addressed by women filmmakers. Only recently we have found two works that not only immerse themselves in that practice, but whose results place themselves at the avant-garde of the epistolary essay film.

Letters from Panduranga (2015) by Nguyen Trinh Thi is not only generated as a successor of Marker's epistolary essay film, but the filmmaker is able to continue its evolution, delving into the possibilities of the device as an enunciation form (Laura Rascaroli 2017, 154). The link with Marker's epistolary work is made explicit when the film begins and ends with the same words as in Lettre de Sibérie. The film thus encompasses the evolution that occurs between this work and Sans soleil-the latter generates a problematisation of epistolary diegesis that evidences the presence of the essayist as an extradiegetic entity (Monterrubio Ibáñez 2018, 293-308)-as the filmmaker confirms: "I borrowed from Marker his strategies and structures" (Laura Rascaroli, et al. 2019, 24). Nguyen continues Marker's work to advance its possibilities, creating an epistolary dialogue between two anonymous characters that is configured as a split identity-alterity of the essayist, as the author explains: "They are both mostly myself [. . .] my selves of different times and spaces" (Laura Rascaroli 2017, 154).

Therefore, internal dialogue becomes epistolary dialogue that allows identity dialectics and embodies in an exemplary way the postmodern conception of alterity and its gender dimension. The film begins as an epistolary film composed of the letters exchanged between a woman and a man, both developing an audiovisual work in different territories of Vietnam, enunciated through their voice-overs, hers belonging to Nguyen herself. Thus, the film would materialise as a completely coherent diegetic epistolary narrative, until reaching the sixth letter, third of the male character, from which a new enunciative element emerges: the split screen. It shows us a dance scene. Both images duplicate the same action, but the one on the left shows a more closed frame. That is to say, the difference between the two images occurs in the editing, becoming an element of cinematic thinking, revealing the fictional epistolary film as an essay film of the filmmaker's subjectivity. The eighth letter begins with his account of the arrival in Da

Nang and the visit to the Cham Museum. Then, the diegesis of epistolary fiction becomes problematic, as occurred in Sans soleil, as it turns into a dialogue, no longer deferred, that transforms the epistolary device into the materialisation of an internal monologue. It establishes a dialectic relationship between female identity-linked to the filmmaker's first documentary work: personal space, portraiture, proximity-and the male one-the evolution towards the essay film, the notion of History, distance. The dialectics begin in the female visual space to continue with that already shown in the male one-the split screen-, where both voices, both identities, the identity-alterity dialectics inherent to/in the human being meet. On this occasion, the split screen shows the same image, thus resolving the spatial and temporal decalages shown by the previous ones, accepting the filmmaker's identity split to turn this duality into a thinking tool of great relevance, which presents a crucial reflection on the female point of view. The identity conflict has been resolved and therefore the split screen disappears from the film. It is the assumption of that reality that enables both perspectives to materialise in a very fertile way in the following letters, to even reaching the exchange in the twelfth, in which the male character comments on the images made by the female protagonist. Nguyen addresses the gender perspective in the following letter, the thirteenth, in which she portrays two women together, expressing a bond between them that appeals to sisterhood (Figure 8): Azevedo hybridises epistolarity and poeticity, instrumentalising two possibilities of the essay film as analysed by Rascaroli. On the one hand, there is the epistolary essay film, in which epistolarity becomes "a disjunctive narrative form marked by distance and by absence" (2017, 20) which emerges from its interstitial nature. On the other hand, there is the poetic essay film, in which: "[T]he lyrical in the essay film is not subordinate to logical thinking or separate from it [. . .] it is argument and instrument of argumentation" (157). That is, two opposed materials at the service of cinematic thinking: "[E]pistolarity and lyricism as examples of narration and counter-narration, both seen as disjunctive strategies that may be mobilized by the essay film to create a 'form that thinks'" (163).

The film embodies a reflection on the aesthetic experience, instrumentalising all the audio-visual possibilities and creating a poetic-epistolary, sensory-emotional kaleidoscope around creation, exile and absence. Regarding the materialisation of the female essayist's identity, a crucial image arises at the end of the enunciation of Mello Breyner's letter of December 31 1967, in which she tells Sena about the deaths of her brother and her mother, which occurred only a few months apart. The image hybridises the images of trees that traverse the film with that of Azevedo, who reads the text we have so far heard through the voice-over (Figure 9). This hybrid image exemplifies and synthesises the essayistic nature of the work and defines that complex image, kaleidoscopic image, of contemporary cinema. The words Mello Breyner dedicated to her mother through the letter are now assumed by Azevedo, addressed through the cinematic work. The bond with the mother and the pain of her absence join absence imposed by exile and Azevedo identifies herself with Mello Breyner. The filmmaker thus gives her filmic answer, her reflection, to the question a little girl enunciates in the film and that Azevedo shared in her childhood: Where is exile? This question undoubtedly prompts the search proposed by the film and also confirms the identification between the female poet and the filmmaker. Through Mello Breyner's and Sena's epistolary and poetic texts, it is Azevedo's subjectivity and thinking process which materialises in a contemporary essay film, a complex, filmic kaleidoscope, which becomes another avant-garde expression of epistolary essay film.

Conclusion

This itinerary through epistolary films and epistolary essay films by women filmmakers allows us to draw several conclusions. First, the relevance of these women filmmakers in the innovation and evolution of epistolary enunciation is evidenced. Second, how they use it in a truly fruitful way in order to explore not just alterity, a paradigmatic concept of postmodernity inherent in the epistolary device, but also female alterity and its complexity. They explore this intimate, ambivalent and existential consciousness, embodying deep and valuable cinematic experiences of the theoretical concept. Thus, Akerman begins the epistolary film by focusing it on the reception and reading space to explore an intimate alterity, that of the mother. Hatoum and Carri delve into that same experience in both visual perspective and personal experience. Ruivo, for her part, goes back a generation to make her grandmother the female alterity. Therefore, the epistolary film becomes a useful tool for the exploration of intimate female alterities. Its fictionalisation, based on documentary image, displaces the works from the intimate to the intellectual space. Stratman gives voice to a young university student in order to carry out an exercise in comedy, irony, criticism and even satire on many of the stereotypes women must face. Green, for her part, generates an epistolary fiction in which four women create a space of female intellectual intersubjectivity. In addition, women filmmakers resort to correspondence by letter with other women, to once again carry out an exercise in feminist vindication and creative sisterhood. Lin performs an epistolary recreation exercise to get closer to the addresser's experience, that of captivity before execution, and to generate a political and social vindication for historical memory in her country. Beckermann uses the epistolary correspondence of two great writers to create an experience of epistolary reading and identification that, once again, takes sides in order to explore the female alterity of Ingeborg Bachmann as a woman both in the personal sphere-her relationship with Paul Celan-and in the artistic space-her lack of recognition as a writer. Finally, the creation of epistolary essay films again confirms the ability of women filmmakers to be at the avant-garde of this epistolary form. Nguyen embodies her cinematic thinking from an identity split that takes the form of correspondence between a man and a woman. This reflection concludes with the need for women to gain visibility in the intellectual space, as many of the previous works already pointed out. Azevedo, like Beckermann, takes the correspondence of two other great writers to create an essay film on artistic experience and exile, which cinematic thinking is also linked to the identification with female alterity. All these women filmmakers explore the seriality and materiality of the epistolary device and the stratification of its audiovisual modality in order to show female alterities, whose exploration shows an evident progression from the intimate to the public, from the emotional to the intellectual, always as sisterhood experiences and feminist vindications.

Figure 1 .

 1 Figure 1. Measures of Distance (Mona Hatoum, 1988) Courtesy of the filmmaker.

  umentary image and different forms of textual inscription. In From Hetty to Nancy (1997) Deborah Stratman experiments with different possibilities of hybridisation between the documentary image of Iceland and diverse texts, the main one being an epistolary literary work by Louis McNeice, "Hetty to Nancy", belonging to Letters from Iceland (1937), written in collaboration with W.H. Auden during their trip through the country in 1936.In this way, the film is built from the hybridisation of the 16 mm documentary image and the letters Hetty writes to Nancy, also during her tour of the island. A far cry from romantic travel letters, McNeice creates a humorous and ironic account of the journey of four schoolgirls accompanied by Mrs Greenhalge, the expedition leader, and Hetty and Maisie, two young university girls. Stratman selects various fragments of the text, maintaining its structure-the diaristic letters of the 10 days of travel-that are enunciated by a female voice-over that we identify with Hetty, due to her vocal acting of the letters.

  In the centre of Iceland there are only three kinds of scenery -Stones, More Stones, and All Stone. The third type predominated today. The stones are the wrong size, the wrong shape, the wrong colour, and too many of them. They are not big enough to impress and not small enough to negotiate. Absolutely unpicturesque and absolutely non-utilitarian […] It's certainly hard to think how a country gets in a mess like this.

Figure 4 .

 4 Figure 4. From Hetty to Nancy (Deborah Stratman, 1997). Courtesy of the filmmaker.

Figure 5 .

 5 Figure5. Endless Dreams and Water Between (RenéeGreen, 2009).Courtesy of the filmmaker, FAM, and Video Data Bank.

  around the silencing of victims throughout history is confronted with the inserts in digital video, which extend throughout the entire work. They show us the Liuzhangli graves, inscribing the names of the disappeared to which they belong. Next, the arrest report, in October 1954, is also inscribed on the screen, on a very close-up of the eyes of one of the women, and then her hand holding and caressing some embroidery and a watch. With the title over the image, a constant banging is now added to the sound image, which we discovered a few seconds later in the image: the manual hole-punching of the analogue film. The six letters transcribed on the screen accompany the visual image that shows spaces of recreation of the imprisonment, giving prominence to everyday objects that appear in the epistolary content. The presence of a woman implies a vindication of historical memory and enables a sensory recreation, mainly tactile, of what the addresser experienced. The film advances then in the materiality already analysed in Hatoum's and

Figure 6 .

 6 Figure 6. Letter #69 (Hsin-I Lin, 2016). Courtesy of the filmmaker.

I

  'm writing you from the land of the woman. Champa is a matriarchal society[. . .] the men, as usual, end up being the voice. The women here, like everywhere else, are like the background [. . .] They don't talk about the question or their survival[. . .] They are the landscape.

Figure 8 .

 8 Figure 8. Letters from Panduranga (Nguyen Trinh Thi, 2015)Courtesy of the filmmaker

Figure 9 .

 9 Figure 9. Correspondências (2016, Rita Azevedo Gomes). Courtesy of the filmmaker and C.R.I.M. Productions