Toinon Vigier
email: toinon.vigier@univ-nantes.fr

Yoann Baveye
email: yoann.baveye@univ-nantes.fr

Josselin Rousseau
email: josselin.rousseau@univ-nantes.fr

Patrick Le Callet
email: patrick.lecallet@univ-nantes.fr

Visual Attention as a dimension of QoE: Subtitles in UHD videos

With the ever-growing availability of multimedia content produced, broadcast and consumed worldwide, subtitling is becoming an essential service to quickly share understandable content. Simultaneously, the increased resolution of the ultra high definition (UHD) standard comes with wider screens and new viewing conditions. Services as the display of subtitles thus require adaptation to better fit the new induced viewing visual angle. This paper aims at evaluating quality of experience of subtitled movies in UHD to propose guidelines for the appearance of subtitles. From an eye-tracking experiment conducted on 68 observers and 30 video sequences, viewing behavior and visual saliency are analyzed with and without subtitles and for different subtitle styles. Various metrics based on eye-tracking data, such as the Reading Index for Dynamic Texts (RIDT), are computed to objectively measure the ease of reading and subtitle disturbance. The results mainly show that doubling the visual angle of subtitles from HD to UHD guarantees subtitle readability without compromising the enjoyment of the video content.

I. INTRODUCTION

Nowadays, more and more multimedia content is produced, broadcast and consumed worldwide. Therefore, subtitling is an essential service to quickly share understandable content worldwide. For instance, in non-English speaking countries, popular movies and TV series are often available in original language with subtitles long before the dubbed version. It is thus required to take into account style settings of subtitles according to display and device in quality of experience. More specifically, the question of subtitle style and size is raised out with the emergence of ultra high definition television (UHD TV) to replace the current high definition television (HD TV) system. Indeed, UHD TV standard defines new video technologies such as increasing resolution from HD (1920 × 1080) to 4K (3840 × 2160) or 8K (7680 × 4320). Thus, the emergence of UHD potentially provides a better immersion of the user thanks to a wider visual angle with appropriate larger screens [START_REF] Bt | Parameter values for ultra-high definition television systems for production and international programme exchange[END_REF]. These new viewing conditions must be evaluated in terms of quality of experience of multimedia systems and services such as subtitling in video. In order to accurately measure and quantify viewing behavior and reading of subtitles in videos, visual attention analyses from eye-tracking experiments can be carried out. Several studies were conducted to evaluate speed and ease of reading of subtitles. Most of them were often focused on the impact on subtitle reading of subtitle speed (e.g. [START_REF] Jensema | Viewer Reaction to Different Captioned Television Speeds[END_REF], [START_REF] Rayner | Eye Movements and Visual Encoding During Scene Perception[END_REF]), style [START_REF] Szarkowska | Harnessing the Potential of Eye-Tracking for Media Accessibility[END_REF], language soundtrack (e.g. [START_REF] Ross | Eye movements while viewing narrated, captioned, and silent videos[END_REF], [START_REF] Kruger | Attention distribution and cognitive load in a subtitled academic lecture: L1 vs . L2[END_REF]) and personal characteristics of observers such as language, disability, or frequency of subtitle usage (e.g. [START_REF] Diao | The effect of written text on comprehension of spoken english as a foreign language[END_REF], [START_REF] Szarkowska | Harnessing the Potential of Eye-Tracking for Media Accessibility[END_REF], [START_REF] Kruger | Attention distribution and cognitive load in a subtitled academic lecture: L1 vs . L2[END_REF]). Some recommendations have been published by TV channels (e.g. [8], [START_REF]Subtitling Guidelines for foreign-language programmes[END_REF]) and some style characteristics have been harmonized:

• Subtitles are displayed on two lines of text;

• Suitable fonts are from the sans-serif typeface, such as Helvetica, Arial or Verdana; • Characters are approximately between 30 and 40 per line of text. The current increase of the size of TV screens question these recommendations, in particular subtitle size and placement (e.g. [START_REF] Brown | Dynamic subtitles: the user experience[END_REF], [START_REF] Park | Automatic Subtitles Localization through Speaker Identification in Multimedia System[END_REF]). For example, Brown et al. proposed a dynamic subtitle placement in which subtitles are positioned to minimize the distance from the area of interest to subtitles [START_REF] Brown | Dynamic subtitles: the user experience[END_REF]. Only a few research studies are focused on subtitle size. Lee et al. evaluated the preferred subtitle font size according to viewing distance [START_REF] Lee | Screen luminance, subtitle, and viewing angle on viewing distance of liquid crystal display high-definition television[END_REF]. They deduced an optimal viewing angle for subtitles around 0.7°. However, results cannot be directly used in Latin script since this study was done in Chinese.

Based on this review, there is a need for studies on subtitle appearance and size in UHD viewing conditions. In this paper, an experiment is described in order to evaluate subtitle readability, reading comfort and intrusion of subtitles thanks to eye-tracking measures. The final objective is to provide guidelines on subtitle insertion in UHD. The paper is organized as follow. Section II presents the experiment design while Section III lists the data and metrics used to analyze the results discussed in Section IV. Finally, conclusion and future work end the paper in Section V.

II. EXPERIMENTAL DESIGN

A. Stimuli selection

The stimuli used in this experiment are based on 30 Source Video Sequences (SRCs) in English extracted from seven professional Hollywood movies. The 30 segments have been manually extracted in order to select semantically coherent video excerpts containing at least one subtitle composed of two lines of text. The SRCs last 30 seconds which seems long enough for observers to make sense of the subtitled video sequences. For each SRC, corresponding raw Blu-ray subtitles, written in French, have also been extracted. Thus, issues about timing, synchronization, translation or cuts are avoided and not studied in this work. For all SRCs, subtitles are arbitrarily positioned at 8.3% (= 1/12 × H video ) from the bottom of the video. The font of all subtitles is Arial and subtitles are written in white with a black outline around the text. The sequences are originally extracted at HD resolution (1,920 × 1,080) and upscaled at UHD resolution (3,840 × 2,160) using Lanczos-3 algorithm [START_REF] Duchon | Lanczos filtering in one and two dimensions[END_REF], since it is one of the best upsampling algorithm in term of preference of experience [START_REF] Li | Comparing upscaling algorithms from hd to ultra hd by evaluating preference of experience[END_REF]. The 30 SRCs are split in three groups. The distributions of the SRCs inside each group are comparable to each other in terms of spatial and temporal information (SI, TI as described in ITU-T P.910 [START_REF]Subjective video quality assessment methods for multimedia applications[END_REF]), total number of text characters in the SRC and number of subtitles displayed on two lines in the SRC (Figure 1). Thus, 30 SRCs divided in three SRC groups, denoted SRCG1, SRCG2 and SRCG3, are evaluated in this experiment. In average, the subtitles corresponding to these 30 SRCs are composed of 30 characters per subtitle (6.5 words) and are displayed onscreen for 2.63 seconds at a rate of 148 words per minute. Subtitles are displayed on 62% of the video frames and 48% of them are displayed on two lines.

B. Hypothetical reference circuit

A Hypothetical Reference Circuit (HRC) is a particular set of processing operations. In this experiment, three factors are used to generate six HRCs: the resolution of the SRC (HD/UHD), the size of subtitles, and the maximum number of lines used to display subtitles. The six HRCs are listed in Table I and illustrated in Figure 2. As stated in Section I, no standard settings exist for the display of media subtitles. The characteristics of the subtitles for HD videos used in HRC2 are based on the mean of the characteristics of the subtitles used in this work, extracted from commercial DVDs. Thus, the font size of text characters in HRC2 corresponds to a vertical viewing angle of 1.03°for one line of text in subtitles. For HRC4 and HRC6 composed of UHD videos, the vertical viewing angle for one line of text is unchanged. Consequently, for both HRCs, the vertical ratio for one line of text in term of screen height is half the size of the one in HRC2 (in HD). For HRC5, also composed of UHD videos, the font size of text characters in subtitles is twice the size of text characters in previously mentioned HRCs to preserve the vertical ratio for one line of text in term of screen height compared to HRC2 (in HD). Because UHD screens are wider than HD screens, the display of subtitles on one line only is also tested in HRC6. Finally, sequences without subtitles are inserted in the test in HRC1 (HD) and HRC3 (UHD), in order to compare the impact of subtitles on visual attention.

C. Experimental setup

The 4K display used in the experiment is a Panasonic TX-L65WT600E with a 65-inch screen size. In this study, we decided to set the viewing distance for UHD videos to 1.5H (126cm), with H the height of the screened video, as recommended in ITU-R BT.1769 [START_REF]Parameter values for an expanded hierarchy of lsdi image formats for production and international programme exchange[END_REF]. The viewing distance was set to 3H for HD videos. Both viewing distances are strictly the same because HD videos were shown at the center of the 4K display as illustrated in Figure 3. The soundtrack of the videos sequences was played using external speakers and the volume was set at a comfortable level. The test environment is set as a standard test condition according to ITU-R BT.710 [START_REF]Subjective assessment methods for image quality in high-definition television[END_REF]. Because of the wider viewing angle in UHD, observers may move their head and eye-tracking systems may not be 1 The values are computed considering a mean number of 35 text characters per line of text when subtitles are displayed using a maximum of two lines of text and 70 characters otherwise (HRC 6). accurate enough at the borders of the screen. Therefore, we developed and used a new eye-tracking setup, named Eye Head Tracking (EHT), which is a combination of the mobile SMI eye-tracking glasses and the OptiTrack ARENA head-tracker. Gaze data are recorded at a frequency of 30Hz in binocular mode [START_REF] Vigier | A new hd and uhd video eye tracking dataset[END_REF].

D. Experimental protocol

Observers are split in three groups with a similar distribution of age, gender and subtitle viewing experience. We restrict the number of occurrences of the same SRC for the same observer to two. During the experiment, each group of observers watches Processed Video Sequences (PVS) composed of the videos from the SRC groups treated with the HRCs indicated in Table II. In this table, "1" stands for the first group of observers, "2" stands for the second group of observers and "3" stands for the third group of observers. SRCG1, SRCG2 and SRCG3 refer to the three groups of SRCs mentioned in Section II-A. Thus, each observer watches 60 PVS during this experiment. For a given observer, the PVS corresponding to his assigned group of observers were selected. The 10 PVS generated using the same HRC were displayed consecutively in a random order. The order of the six groups of 10 PVS corresponding to the six HRCs was displayed randomly. Before each group of 10 PVS generated using a given HRC, the same two 30 seconds long training video sequences treated using the considered HRC were displayed in order to accustom observers to the new subtitles parameters. Thus, recorded data is less sensitive to the adaptation delay and enables the evaluation of the reading easiness. The PVS were separated by two seconds breaks during which a black frame was displayed. For example, a participant assigned to the first group of observers could have watched the following sequence of PVS: the two test videos treated with HRC4, then the 10 SRCs in SRCG1 treated with HRC4 displayed in a random order, then the two test videos treated with HRC6, then the 10 SRCs in SRCG3 treated with HRC6 also displayed in a random order, etc. Before the experimental session, participants had to sign a consent form and instructions were given. The experiment started after the calibration of the eye-tracking system. Eyetracking data was recorded in free-viewing conditions. To avoid visual fatigue, the viewers were asked to take a five minutes HRC1 HRC2 HRC3 HRC4 HRC5 HRC6

SRCG1 1 2 3 1 2 3 SRCG2 3 1 2 3 1 2 SRCG3 2 3 1 2 3 1
break after half of the test samples. The total duration of the test was approximately 45 minutes.

E. Participants

68 remunerated viewers participated in this subjective experiment (46 female and 22 male), aged between 19 and 51 (mean= 23.16 ± 5.34SD). 65 participants are French, while the remaining three participants are Moroccan, Greek, and Russian. Participants had different educational backgrounds. Participants also assessed their English language proficiency level and the frequency of subtitled movies viewing (Figure 4). All are non-expert in subjective experiment, image processing or 4K related fields. All participants have either normal or corrected-to-normal visual acuity. Correct visual acuity was assured prior to this experiment. For near vision test, a Parinaud chart was used (French equivalent of Jaeger chart) while for the far vision test, a Monoyer chart was used. Testing both may seem particularly useful for such a subjective experiments with subtitles and UHD videos as the viewing distance is only 1.5H. Ishihara color plates were used to test color vision. All of the 68 viewers passed the pre-experiment vision check.

III. DATA AND METRICS

In this section, data and metrics, calculated from raw gaze data and used for the analysis of results are presented.

A. Fixations and saccades

Fixation points and saccades reflect reading behavior and can be used to evaluate the ease of reading [START_REF] Kruger | Subtitles on the moving image: an overview of eye tracking studies[END_REF]. They are extracted from the raw gaze data following the method explained in [START_REF]User Manual -Tobii Studio[END_REF]. However, because duration of fixations and length of saccades can be shorter when viewers read subtitles, different parameters were chosen to better fit with this experiment. The fixation velocity maximum threshold is set at 20°/s. The minimum time between separate fixations is set at 55 ms and the minimum visual angle between separate fixations is set at 0.33°. Finally, the minimum fixation duration is set at 50 ms. Extracted fixations and saccades are illustrated in Figure 5.

B. Subtitle area-based metrics

For each frame with subtitles, the subtitle area is defined as a box with dimensions equal to the size of the current subtitle with a raised outer border of 2°in visual angle. From raw gaze data, the number of fixations per word and the time spent in the subtitle area is computed for each subtitle and each observer. Then, for each video, the reading duration is defined as the percentage of the time spent in the subtitle area over the video, when the subtitles are displayed. The length of the saccades and the number of backward saccades in the subtitle area are also computed. A backward saccade is defined as an horizontal saccade oriented in the opposite direction of reading. The metrics mentioned in this section are averaged for each video. These values are used for statistical analyses.

C. RIDT

To evaluate the ease of reading, the Reading Index for Dynamic Texts (RIDT) is computed, representing the degree to which each subtitle is read or, in other words, the quantification of reading [START_REF] Kruger | Subtitles and Eye Tracking: Reading and Performance[END_REF]. For video v, with participant p viewing subtitle s, the RIDT vps is defined as:

RIDT vps = number of unique fixations for p in s number of standard words in s × average forward saccade length for p in s standard word length for v

In the following, RIDT v , which is the mean of RIDT vps over all observers and all subtitles for each video, are used for statistical tests. Moreover, RIDT values mentioned in Section IV represent the mean of RIDT v over all the videos for the HRCs.

D. Saliency metrics

To evaluate the intrusion of subtitles in videos, visual saliency for the different HRCs is compared. Fixation density UHD

H 1 HD H 2 α 1 α 1 = 2 × α 2 ≈ 60 • α 2 1 . 5 × H 1 3 × H 2 Fig. 3.
Viewing distance for UHD and HD videos.

maps are calculated, for each frame, on fixations with a bidimensional gaussian function with σ = 1°as recommended in [START_REF] Meur | Methods for comparing scanpaths and saliency maps: strengths and weaknesses[END_REF]. In order to compare saliency only for the original video content without subtitles, fixation density maps are cropped to discard the bottom of the frame corresponding to a height of 469 pixels in UHD. The fixation density maps of HRCs with and without subtitles (separately in HD and UHD) are then compared by calculating Pearson's correlation coefficient (Cp) and Kullback-Leibler divergence (KLD) as recommended in [START_REF] Meur | Methods for comparing scanpaths and saliency maps: strengths and weaknesses[END_REF]. The continuous fixation density maps are aggregated per video, thresholded and processed as a binary classifier to keep the top 2%, 5% and 10% salient pixels of the thresholded maps, labeled as fixated. For a given threshold, the binary maps with and without subtitles are compared to compute the precision, accuracy and Matthews correlation coefficient (MCC) from the confusion matrices. In this context, the precision corresponds to the percentage of the pixels labeled as fixated without subtitles also classified as fixated in the map with subtitles (for a given HRC). The accuracy and the MCC represent the similarity between binary maps with and without subtitles.

IV. RESULTS AND DISCUSSION

In this section, the results are discussed based on the nonparametric Kruskal-Wallis test and Tukey's multiple comparison test, which are used to determine which distribution is significantly different from the others.

A. Impact of subtitle display on reading behavior

The Tukey's test revealed that the reading duration for HRC5 is not significantly different from the one for HRC4 (p = 0.099) and HRC6 (p = 0.677). Thus the size of the subtitles do not influence the reading duration significantly. However, the Tukey's test also revealed that observers read subtitles displayed on one line (HRC6) significantly faster (p < .01) than subtitles displayed on two lines (HRC4). Indeed, the observers spend 29.2% of the time in the subtitle area for HRC4 while this value equals 27.5% for HRC6. It may be due to the fact that the absence of line break for HRC6, thus reducing the amount of backward saccades occurring in the subtitle area.

The RIDT is significantly different for the four HRCs with subtitles (χ 2 (3) = 282.3; p < .001). Actually, the Tukey's test revealed that significantly higher RIDT values are obtained for the two HRCs with the highest vertical ratio in terms of screen height (0.68 for HRC2 and 0.66 for HRC5). RIDT values for HRC4 and HRC6 are respectively 0.64 and 0.54. Thus, for subtitles displayed on UHD screens, keeping the same vertical ratio as the one on HD screen while doubling the height of the subtitles seems the best solution to maintain the ease of reading. However, the length of the saccades for subtitles displayed with a vertical viewing angle of 2.05°(HRC5) is almost twice the lengths of the saccades for the subtitles of the other HRCs. It seems consistent with that fact that saccades span the same amount of characters [START_REF] Sereno | Measuring word recognition in reading: eye movements and event-related potentials[END_REF]. However, the impact of the amplitude of the saccades over the eye fatigue is uncertain and have to be studied in the future. Contrary to the other HRCs, displaying subtitles on one line of text (HRC6) reduces the RIDT for long subtitles (composed of more than the mean of the number of characters of all subtitles, i.e., 30 characters) compared to short subtitles (χ 2 (1) = 20.03; p < .001). Indeed, compared with HRC4, the average length of the saccades in the subtitle area is moderately longer for HRC6 (231.06px ± 73.62SD for HRC4 and 284.67px ± 104.33SD for HRC6) while the number of fixations in the subtitle area per word is roughly the same (0.63 for HRC4 and 0.60 for HRC6). This result extends the standardized use of two lines of text to display subtitles for UHD.

To summarize, displaying subtitles on one line of text for UHD screens (HRC6) is the worst solution in term of ease of read, in particular for long subtitles. The HRC5, preserving the vertical ratio of subtitles in UHD in term of screen height compared to HD, is the optimal HRC to facilitate subtitle reading. However, the subtitle intelligibility cannot be directly inferred from the measures used in this analysis. Further work is required to address this limitation.

B. Impact of subtitle display on visual saliency

In this section, saliency metrics (see Section III-D) are used to evaluate the intrusion of subtitles in videos. Both HRC5 and HRC6 are significantly closer to HRC3 than HRC4 in terms of Cp (p < .001) and KLD (p < .001). This tendency is also confirmed by the precision, accuracy and MCC metrics based on the confusion matrix from thresholded binary maps. Respective mean values are indicated in Table III. For all these metrics, the HRC5, which corresponds to the same vertical ratio of subtitles as in HD, seems the least disruptive HRC in term of saliency. However, these metrics mainly evaluate similarities between visual saliency with and without subtitles. Other assessment methodologies are needed to study the subjective experience of the video content (intelligibility, immersiveness, etc.).

C. Other results

Beyond the different HRCS, subjective characteristics also influence the way viewers read subtitles. The time before the first fixation in the subtitle area is significantly different (p < .001) from HD (0.35 sec for HRC2) to UHD (close to 0.48 sec for HRCs 4 to 6), whereas there is no significant difference between UHD HRCs. This result shows that the subtitle placement is questionable for wider screens as mentioned in Section I. However, this slight augmentation of duration of the visual path between the video region of interest and the subtitle is not so annoying because observers tend to enter in the subtitle area only once and read entirely the subtitles before going back to video content. Indeed, the average number of visits in the subtitle area equals 1.28 for all HRCs. It can also be noted that observers with an upper-intermediate or bilingual English language proficiency level obtain, in average, a significantly smaller RIDT score compared to the other viewers (χ 2 (1) = 74.48; p < .001). It can be explained by the fact they do not need to read the subtitles entirely to understand the storyline of the videos but at most likely looking keywords and/or are visually attracted by the apparition of subtitles [START_REF] Kruger | Subtitles on the moving image: an overview of eye tracking studies[END_REF].

V. CONCLUSION

In this paper, an experiment has been described in order to evaluate subtitle appearance in UHD viewing conditions using eye-tracking measures. The analyses of the reading comfort and intrusion of subtitles allowed us to propose guidelines for the appearance of subtitles in UHD. First, it is not recommended to display long subtitles using one line of text only. Second, vertical visual angle of subtitles can be conserved from HD to UHD, but doubling this angle is preferred to maximize the ease of reading and minimize the disturbance of subtitles. This applies even more that in standard European living rooms, the median distance between TV screens and observers is 2.63 m for a median screen height of 49 cm, namely a median viewing distance of 5.5H [START_REF] Noland | A survey ok UK television viewing conditions[END_REF], far superior from the experimental viewing conditions. To confirm these findings, future work is needed to investigate more varied subtitle sizes and style characteristics in UHD to define the optimal subtitle appearance. However, currently available metrics from eye-tracking data are not sufficient to appropriately evaluate subtitle disturbance, visual fatigue, understanding of the storyline and quality of experience. To address these limitations, this study could be extended by combining visual attention with subjective selfassessments.

Fig. 1 .

 1 Fig. 1. Groups generated for the 30 SRCs based on their (a) video frame characteristics (SI/TI) and (b) subtitle-based characteristics (total number of text characters and number of subtitles displayed on two lines).

Fig. 2 .

 2 Fig. 2. Illustration of the six HRCs using a screenshot from Alice in Wonderland, Copyright the Walt Disney company, 2010.

Fig. 4 .

 4 Fig.4. Repartition of the participants' answers to the questions asked after the experiment to measure their English language proficiency level and the frequency of subtitled movies viewing.

Fig. 5 .

 5 Fig. 5. Fixation points and saccades extracted from the raw gaze data. Red lines the saccades in the subtitle area.

TABLE I .

 I THE HYPOTHETICAL REFERENCE CIRCUIT FOR THE SUBJECTIVE EXPERIMENT

	HRC	Viewing	Presence of	Font	Maximum	Vertical	Vertical ratio	Average	Average
		distance	subtitles	size	number	viewing angle	for one line	horizontal	horizontal
				(px)	of lines	for one line	(% screen	viewing angle	ratio of total
						(°)	height)	of total	subtitle area
								subtitle area 1	(% screen
								(°)	width)
	1	3H (HD)	No	-	-	-	-	-	-
	2	3H (HD)	Yes	58	2	1.03°10.7%	20.7°61.7%
	3	1.5H (UHD)	No	-	-	-	-	-	-
	4	1.5H (UHD)	Yes	58	2	1.03°5.37%	20.7°30.8%
	5	1.5H (UHD)	Yes	116	2	2.05°10.7%	40.2°61.7%
	6	1.5H (UHD)	Yes	58	1	1.03°5.37%	40.2°61.7%

TABLE III .

 III SIMILARITY COEFFICIENTS BETWEEN UHD FIXATION DENSITY MAPS WITH AND WITHOUT SUBTITLES

		Cp	KLD		Precision			Accuracy			MCC
				2%	5%	10%	2%	5%	10%	2%	5%	10%
	HRC4	0.568	3.188	0.63	0.72	0.76	0.99	0.97	0.95	0.62	0.70	0.74
	HRC5	0.601	2.720	0.65	0.75	0.79	0.99	0.98	0.96	0.65	0.74	0.76
	HRC6	0.591	2.773	0.64	0.73	0.78	0.99	0.97	0.96	0.64	0.72	0.76

978-1-5090-0354-9/16/$31.00 ©2016 IEEE

ACKNOWLEDGMENT

This work is part of the UltraHD-4U project financed by the DGCIS through the European CATRENE program CAT111.


Amélie Fargevieille
email: afargevieille@gmail.com

ORCID Arnaud Grégoire

Doris Gomez

Claire Doutrelant

Evolution of female colors in birds: the role of female cost of reproduction and paternal care

Keywords:

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Males in many animal species display conspicuous ornaments and armaments and a large body of evolutionary research has aimed to understand the factors at the origin of this variation [START_REF] Andersson | Sexual Selection[END_REF]. Females in many animal species also display conspicuous traits and in the past twenty years, research focusing on the evolution and variation in female ornaments has increased [START_REF] Amundsen | Why are female birds ornamented?[END_REF][START_REF] Harrison | Evolution of an ornament, the dewlap, in females of the lizard genus Anolis[END_REF][START_REF] Nordeide | Female ornaments revisited -are they correlated with offspring quality?[END_REF][START_REF] Odom | Female song is widespread and ancestral in songbirds[END_REF][START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Riebel | New insights from female bird song: towards an integrated approach to studying male and female communication roles[END_REF][START_REF] Doutrelant | Evolution of female coloration: What have we learned from birds in general and blue tits in particular[END_REF].

Owing to the paradigm that inter-and intra-sexual selection is typically stronger on males [START_REF] Bateman | Intra-Sexual Selection in Drosophila-Melanogaster[END_REF][START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF]; but see [START_REF] Hoquet | Bateman (1948): rise and fall of a paradigm?[END_REF], female ornamentation was historically considered as a genetic by-product of male ornamentation with natural selection (e.g. predation) leading to more cryptic phenotypes in females. Nowadays, there is a general agreement that natural, sexual and social selection also impact female ornamentation, and that studies need to understand how these complex arrays of forces interact and explain the observed variability [START_REF] Kraaijeveld | The evolution of mutual ornamentation[END_REF][START_REF] Clutton-Brock | Sexual selection in females[END_REF][START_REF] Tobias | The evolution of female ornaments and weaponry: social selection, sexual selection and ecological competition[END_REF][START_REF] Hare | Sexual selection and its evolutionary consequences in female animals[END_REF][START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF][START_REF] Doutrelant | Evolution of female coloration: What have we learned from birds in general and blue tits in particular[END_REF].

Comparative studies have been a powerful tool to investigate the multiple drivers of female ornamentation. Overall most of the comparative studies focused on the selective forces driving the evolution of sexual dichromatism, which expresses the effect of sexual and natural selection acting on both sexes [START_REF] Johnson | Different modes of evolution in males and females generate dichromatism in fairy-wrens (Maluridae)[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF]Shultz & Burns, 2017). These studies clearly outlined three factors explaining the evolution of female ornamentation: predation, female competition, and selection acting on males. Increase of predation risk, migration and intense sexual selection on males are usually associated with lower coloration in females compared to males [START_REF] Martin | Sexual Dichromatism in Birds: Importance of Nest Predation and Nest Location for Females Versus Males[END_REF][START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF] whereas higher female competition for access to reproduction in cooperative breeding species is associated with lower sexual dichromatism [START_REF] Rubenstein | Reproductive skew and selection on female ornamentation in social species[END_REF][START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF]. To go further in understanding the variation in female ornamentation at the interspecific level, it is important to keep focusing on female ornamentation and to test the effect of female-related forces -i.e. intensity of selective pressures and constraints specifically acting on females [START_REF] Rosvall | How research on female vertebrates contributes to an expanded challenge hypothesis[END_REF][START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF][START_REF] Doutrelant | Evolution of female coloration: What have we learned from birds in general and blue tits in particular[END_REF].

Egg production, as a female-specific cost of reproduction is a factor expected by theoretical models to influence female ornamentation [START_REF] Fitzpatrick | Ornaments or Offspring -Costs to Reproductive Success Restrict Sexual Selection Processes[END_REF]. While predation risk has been well-studied as a cost of reproduction limiting the evolution of female ornaments (e.g.; [START_REF] Martin | Sexual Dichromatism in Birds: Importance of Nest Predation and Nest Location for Females Versus Males[END_REF][START_REF] Soler | Evolution of sexual dichromatism in relation to nesting habits in European passerines: a test of Wallace's hypothesis[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF][START_REF] Matysiokova | Broad-scale variation in sexual dichromatism in songbirds is not explained by sex differences in exposure to predators during incubation[END_REF][START_REF] Cain | Conspicuous Plumage Does Not Increase Predation Risk: A Continent-Wide Test Using Model Songbirds[END_REF], the consequences of investing more in the production of eggs remain overlooked by comparative studies. Theoretically, females paying higher reproductive costs are predicted to invest less in signaling [START_REF] Chenoweth | Can non-directional male mating preferences facilitate honest female ornamentation?[END_REF]. This trade-off was shown experimentally in blue tits where females forced to lay more eggs during one breeding season produced less developed color ornaments in the consecutive molt [START_REF] Doutrelant | Female plumage coloration is sensitive to the cost of reproduction. An experiment in blue tits[END_REF]. At the interspecific level, this trade off was verified in the Hirundinidae family for a morphological trait, with female tail fork depth decreasing with increasing egg size [START_REF] Hasegawa | Egg size decreases with increasing female tail fork depth in family Hirundinidae[END_REF]. In another study, females from tropical passerine species -typically associated with smaller clutch size than temperate species -were found to be more colorful [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF]. But yearlong territoriality and lifelong pairs are also more widespread in tropical species, and may also explain the evolution of female coloration through intrasexual selection and male mate choice. Thus, whether variation in female reproductive costs constrains the evolution of female coloration still needs attention.

Paternal care is by contrast a factor supposed to influence two female-related forces promoting the evolution of female ornaments. Theoretical models predict the more time a male invests in parental care, the choosier he is expected to be [START_REF] Kokko | Why is mutual mate choice not the norm? Operational sex ratios, sex roles and the evolution of sexually dimorphic and monomorphic signalling[END_REF], enabling the evolution of female ornaments through intersexual selection. In addition, paternal care can also be indirectly related to the evolution of female ornaments through intrasexual selection if females compete for access to paternal care [START_REF] Lyu | The evolution of postpairing male mate choice[END_REF]. At the interspecific level, the effect of paternal care has been rarely tested specifically, with mixed results across studies. Absence of paternal care was related to species with duller female upper part coloration in one study [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF]. In another study, paternal care was more widespread in more colorful monochromatic species, but with no change in female brightness and color [START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF]. Last, male participation to nestbuilding was associated with more intense female coloration (estimated by human eye) in a comparative analysis on 178 Western Palearctic passerines [START_REF] Soler | Conspicuousness of passerine females is associated with the nest-building behaviour of males[END_REF]. In these three studies, paternal care was estimated as a binary index (presence/absence) while paternal investment can vary both within the stages of reproduction and across bird species. Thus, a necessary step to help clarifying the role of paternal investment in reproduction on the evolution of female ornament is to quantify variation in male investment across different stages of paternal care (from incubation to fledgling). Finally, it is important to estimate the effect of the interaction between costs of reproduction and paternal care, because the cost of female reproduction may reduce the expected expression of female coloration in species with high paternal care.

Here, we carried out phylogenetic comparative analyses to test whether interspecific variation in paternal care interacts with female reproductive costs to explain some of the variation in female coloration. We controlled for male coloration to account for genetic correlation between males and females. Excluding female coloration from the models is a common approach when working on the evolution of male ornamentation. Using this approach assumes that all coloration is potentially adaptive, which seems unrealistic for both sexes [START_REF] Price | Sexual selection, selection load and quantitative genetics of zebra finch bill colour[END_REF]. Here, we chose a conservative perspective, and we studied female coloration while controlling for male coloration. Yet, for the sake of comparison with the literature, we presented the results of analyses that excluded male coloration in ESM and discussed both results.

We worked on passerine bird species from the temperate Northern hemisphere. The amount of paternal care during different stages of reproduction (incubation, chick rearing and post fledgling) is better described, thus more quantifiable for these species than for non-temperate ones. Likewise, information on female reproductive costs -egg size and volume -is also better described in temperate species, with temperate species also presenting more variability in reproductive costs compared to tropical ones. We measured the whole-body plumage of females and males with a spectrometer. Bird eye physiology allows many species of birds to see ultra-violet and to discriminate colors differently from human [START_REF] Vorobyev | Coloured oil droplets enhance colour discrimination[END_REF]. We therefore used avian visual perception models so that our color metrics reflect coloration as perceived by birds in their avian color space (Stoddard & Prum, 2008;Renoult et al., 2017). We predicted that paternal care should enhance female conspicuous plumage coloration and female reproductive costs should constrain it, with possible interactions between these two factors [START_REF] Fitzpatrick | Ornaments or Offspring -Costs to Reproductive Success Restrict Sexual Selection Processes[END_REF]Kokko andJohnstone 2002, Chenoweth et al. 2006).

Material & Methods

We studied 133 Northern temperate passerine species (complete list in Table S1) for which we had enough information on paternal care and cost of reproduction. Because evolutionary lability in female color traits was historically detected in Icteridaes and Thraupidaes (Icteridaes: [START_REF] Irwin | The Evolution of Plumage Dichromatism in the New-World Blackbirds -Social Selection on Female Brightness[END_REF]Thraupidaes: Burns, 1998), we included species belonging to 17 families phylogenetically close to Icteridaes and Thraupidaes (Fig. S1). All selected species breed on the mainland to avoid some confounding effects of insularity syndrome (Doutrelant et al., 2016).

Response variables -Color analyses

We measured with a spectrophotometer (details in ESM) well preserved stuffed specimens of adults with breeding plumage. These specimens belong to the collections at the National Museum of Natural History in Paris and were selected by AF and DG. Spectrometry is a precise and objective method that is strongly recommended when the human visual system differs from that of the natural signal receivers [START_REF] Odeen | Evolution of ultraviolet vision in the largest avian radiationthe passerines[END_REF]. Previous analyses have shown that spectrometric estimates of plumage coloration are similar for well-preserved specimens and freshly collected specimens [START_REF] Doucet | Do museum specimens accurately represent wild birds? A case study of carotenoid, melanin, and structural colours in long-tailed manakins Chiroxiphia linearis[END_REF]. To estimate coloration across the whole body in both males and females we measured the same twenty-one topographical zones on each specimen (Fig. S2).

We selected one male (except for one species for which two males were selected) and one female from each species/subspecies, focusing on the best-preserved birds (see details in ESM and Table S1), a method which is similar to the common practice in recent comparative analyses of working on 'typical' specimens from bookplates or photos [START_REF] Rubenstein | Reproductive skew and selection on female ornamentation in social species[END_REF][START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Negro | Melanin-based sexual dichromatism in the Western Palearctic avifauna implies darker males and lighter females[END_REF][START_REF] Soler | Conspicuousness of passerine females is associated with the nest-building behaviour of males[END_REF], Merwin et al 2020, Delhey et al 2021), while gaining more precision, specifically by assessing ultraviolet part of coloration and integrating avian vision instead of human vision.

We analyzed the spectral data using the R (R Core Team, 2022) package pavo (Maia et al., 2019).

We used both equal illuminance across wavelengths and the blue tit visual system (Stoddard & Prum, 2008) to reconstruct how colors would be perceived by birds and more specifically by conspecifics.

For each male and female of each species, we quantified three coloration metrics to encompass different aspects of coloration (Renoult et al., 2017): (i) mean brightness as an achromatic metric of coloration, (ii) mean chromaticity as an index of the intensity of coloration, and (iii) color volume as an index of the diversity of colors (see details in ESM and, Table S2 for correlation between these metrics). Male and female color volumes were log transformed to fit a normal distribution. The values of the coloration metrics were standardized to have a mean of zero and a variance of one.

Explanatory variables.

Values for life-history traits were determined using the literature (Cramp & Simmons, 2009;Rodewald, 2015).

Egg production. We used clutch volume (mm 3 ; egg volume*clutch size) to estimate reproductive costs associated with female initial investment in reproduction (referred as "egg production") [START_REF] Watson | Reassessing Breeding Investment in Birds: Class-Wide Analysis of Clutch Volume Reveals a Single Outlying Family[END_REF]. This allowed us to account for both egg production strategies: large clutch sizes or large eggs. We only used mean clutch size when median clutch size (a more common statistic) was not available. Egg volume (mm 3 ) was calculated using Hoyt's formula [START_REF] Hoyt | Practical Methods of Estimating Volume and Fresh Weight of Bird Eggs[END_REF]: egg volume=0.509*(egg length)*(egg width)². Since we used closely related songbird species, we assumed there was no bias due to the potential asymmetry in egg shape [START_REF] Hoyt | Practical Methods of Estimating Volume and Fresh Weight of Bird Eggs[END_REF].

Paternal care. In songbirds, male investment can vary continuously from a lack of paternal care to equal share of duties with females. In some species, male's contribution relates only to postfledgling care whereas in other species, males also share incubation duty with females. To account for this variation of investment in parental care, we characterized paternal care during three main reproductive stages: incubation, chick rearing (i.e., brooding and feeding), and post-fledgling. We used the method developed by [START_REF] Webb | Who cares? Quantifying the evolution of division of parental effort[END_REF] to quantify the relative male contribution during each stage (P x male in (1)) and then to define the relative male contribution to total parental care (P T male in (2)). P T male , P I male , P R male , and P F male in (2) refer to the relative contribution made by males to (T) total parental care, (I) incubation, (R) chick rearing, and (F) post-fledging, respectively. The variables t T , t I , t R , and t F refer to the duration (in days) of these same periods, where t T =t I +t R +t F (see ESM for details).

We based our scoring on quantitative estimates of contributions when available in [START_REF] Webb | Who cares? Quantifying the evolution of division of parental effort[END_REF]. Otherwise, we estimated them as followed: when only descriptions were provided, we applied a standardized scoring procedure based on the use of adverbs and other qualifiers (rarely, often, female-only, etc.; details in Table S3). Median activity duration was used when mean activity duration was not available. When possible, we employed information corresponding to the subspecies selected for plumage measurement; otherwise, we used information corresponding to main subspecies. AF assigned scores. To control for bias in assigning scores, the list of species with adverbs and qualifiers used in the literature was provided to all co-authors who were asked

(1) (2)
∑ male contribution at stage "X" P X male = ∑ male contribution at stage "X" + ∑ female contribution at stage "X" P T male = P I male * t I + P R male * t R + P F male * t F t T to assign a score to each species based on the qualifiers. There was a high correlation among coauthors in the way of assigning scores (>0.82). The scoring performed by AF was kept for analyses.

For all species in the dataset, the total female contribution to parental care was equal to or higher than the total male contribution. There were no species with male-only parental care; we thus avoided rare cases of reverse sexual selection, which have already received significant attention [START_REF] Edward | The evolution and significance of male mate choice[END_REF].

Controlled covariates. Our analyses also included additional factors likely to affect the evolution of female coloration. Controlled covariates corresponding to life-history traits were determined using the literature (Cramp & Simmons, 2009;Rodewald, 2015).

Male coloration: genetic correlation and constraints on male coloration is predicted to affect female coloration. We used a conservative approach and included male coloration (corresponding color metric) as a covariable in our analysis to quantify this correlation.

Nest characteristics: nest height and openness were related to color evolution [START_REF] Soler | Evolution of sexual dichromatism in relation to nesting habits in European passerines: a test of Wallace's hypothesis[END_REF] by increasing vulnerability to predation during nest attendance. We used an index of nest characteristics, combining nest openness and nest height, to control its effect on female coloration in our analysis. We assigned a score from 0 to 2 to both nest position and openness, for each species (details in Table S4). We then summed the two scores to an overall score ranging from 0 to 4, with 0 characterizing the lowest level of vulnerability and 4 the highest level of vulnerability of nest characteristics.

Female body size: Since female body size can influence egg production [START_REF] Bennett | Ecological basis of mating system diversity[END_REF] as well as plumage coloration [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF], we also included in our analyses mean female body mass for each species and log transformed the values to fit a normal distribution.

Migration: migratory behavior has also been shown to affect color evolution (Friedman et al., 2009;[START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF]Delhey et al., 2021;[START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF]. Three levels were defined for this variable: strictly resident, partially migrant and strictly migrant.

Breeding period duration (in days): Breeding period duration was also added as a covariable because it may influence reproductive investment and thus plumage coloration [START_REF] Bokony | Melanin-based black plumage coloration is related to reproductive investment in cardueline finches[END_REF]. It was calculated by multiplying the amount of time needed to produce a single brood by the mean number of broods per breeding season. This value was log transformed to fit a normal distribution.

Phylogenetic comparative methods

We carried out phylogenetic generalized least squares (PGLS) [START_REF] Grafen | The Phylogenetic Regression[END_REF] using the R packages phytools [START_REF] Revell | phytools: Phylogenetic Tools for Comparative Biology (and Other Things)[END_REF] and phylolm [START_REF] Ho | A linear-time algorithm for Gaussian and non-Gaussian trait evolution models[END_REF]. PGLS analyses make it possible to run a model and estimate the phylogenetic signal in the model residuals at the same time [START_REF] Revell | Phylogenetic signal and linear regression on species data[END_REF]. To account for potential phylogenetic relationships among the species in our dataset [START_REF] Felsenstein | Phylogenies and the Comparative Method[END_REF], we extracted 500 random phylogenetic trees (available file "phylogenies.tre" in dryad repository) with Hackett backbones from the birdtree.org website [START_REF] Jetz | The global diversity of birds in space and time[END_REF] using the R package ape [START_REF] Paradis | ape: Analyses of Phylogenetics and Evolution[END_REF].

For each of the three color metrics, we ran a linear model including our two predictors of interest (paternal care and egg production), allowing their interaction, and the five covariates defined above. All the predictors and covariates tested in our analysis are presented in Figure 1 and their values were similarly standardized. We tested for multicollinearity among them using the R package yhat [START_REF] Nimon | yhat: Interpreting Regression Effects[END_REF]. Apart from a strong correlation between female body mass and egg production (r=0.683), multicollinearity was low (r<0.07).

For each color metric set as the variable to explain, we ran PGLS analyses on the models using each of the 500 phylogenetic trees and simultaneously estimated Pagel's lambda for tree (Table 1). To include uncertainty [START_REF] Paradis | Analysis of Macroevolution with Phylogenies -6.1 Phylogenetic Comparative Methods[END_REF][START_REF] Garamszegi | Multimodel-Inference in Comparative Analyses[END_REF] within the songbird phylogeny, we used a model-averaging procedure [START_REF] Garamszegi | Multimodel-Inference in Comparative Analyses[END_REF]) that was based on the AIC weights associated with each tree and calculated the estimate values and 95%

confidence intervals for all the predictors in the models accounting for phylogenetic uncertainty [START_REF] Garamszegi | Multimodel-Inference in Comparative Analyses[END_REF] based on 500 phylogenetic trees.

Results

The three female color metrics were strongly associated (all estimates ~0.7) with their corresponding male color metrics (Figure 1, Table 1). More colored females were found in species with more colored males.

Female brightness and female chromaticity were slightly correlated to paternal care (brightness: 0.14 [0.03; 0.26] 95% CI, chromaticity: 0.13 [0.002; 0.26] 95% CI) independently of egg production (Figure 1a, Figure 2, Table 1). Species with more paternal care had brighter females and higher female chromaticity. The interaction between paternal care and egg production was in addition marginally associated with female chromaticity (-0.14 [-0.26; -0.02] 95% CI), Figure 1b, Table 1). At low egg production, female chromaticity increased when paternal care increased.

When paternal care was relatively high, female chromaticity decreased when egg production increased (Figure 3). We found no effect of paternal care or egg production on female color volume (Figure 1c, Table 1).

Among the covariates, only migratory behavior was correlated with chromaticity. Females from strictly resident species had less intense coloration than partially migrant and migrant species (-0.43 [-0.83; -0.03] 95% CI) (Figure 1 and Table 1).

Discussion

This study aimed at determining whether female cost of reproduction and paternal care explained part of the evolution of female ornaments. The results suggest modest but detectable male-independent associations between these two factors and two proxies of female coloration.

Female brightness slightly covaries with paternal care, and female intensity of coloration (chromaticity) is associated with paternal care and the interaction between the two factors. In addition, our results confirm strong coevolution between male and female coloration, which represents a major source of variation for the coloration of both sexes.

In two former very large-scale comparative analyses, presence/absence of paternal care during nestling stage tested in association with other proxies of male sexual or natural selection, was associated with female coloration, once positively and once negatively [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF]. In one smaller scale comparative analysis, the presence/absence of paternal care during incubation was in addition positively associated with female coloration [START_REF] Soler | Conspicuousness of passerine females is associated with the nest-building behaviour of males[END_REF]). Our analysis, also conducted at a small scale but using a continuous index of paternal care, encompassing incubation to post-fledging care, suggests that interspecific variation in time invested by males in parental care is associated to both female brightness and female chromaticity.

In the Northern temperate passerine birds included in our study, paternal care is slightly positively related to female brightness (Figure 2). A positive association may result from the action of two non-exclusive forces: through male mate choice as males are predicted to be choosier when they invest more in paternal behaviors [START_REF] Kokko | Why is mutual mate choice not the norm? Operational sex ratios, sex roles and the evolution of sexually dimorphic and monomorphic signalling[END_REF], and through intra-sexual competition where females compete to access paternal care [START_REF] Tobias | The evolution of female ornaments and weaponry: social selection, sexual selection and ecological competition[END_REF][START_REF] Cain | Mates of Competitive Females: The Relationships between Female Aggression, Mate Quality, and Parental Care[END_REF]. For female chromaticity, our study suggests in addition a small but detectable role of female investment in egg production. In species with low egg production, the chromaticity of female coloration increases with paternal care, but in species with the highest male investment, the chromaticity of female coloration decreases when investment in egg production increases (Figure 3). This interaction suggests a threshold beyond which the cost of reproduction in females could no longer favor the positive coevolution of female coloration and male investment in parental care.

The colors of ornaments, i.e. their chromaticity, are often costly to produce [START_REF] Mcgraw | Mechanics of Carotenoid-Based Coloration[END_REF], and a trade-off between female investment in offspring and female investment in costly ornaments is predicted to limit the evolution of female coloration at some point [START_REF] Fitzpatrick | Ornaments or Offspring -Costs to Reproductive Success Restrict Sexual Selection Processes[END_REF][START_REF] Chenoweth | Can non-directional male mating preferences facilitate honest female ornamentation?[END_REF]. This trade-off can even lead female traits to become non-functional [START_REF] Nordeide | Female ornaments revisited -are they correlated with offspring quality?[END_REF]. Nonetheless, most of the species included in our study have some form of paternal care, and only few species have large egg production, (Figure 3). Therefore, to confirm the detected trade-off between investing in eggs or color intensity, future comparative analyses may include more species with low or no paternal care and high level of female investment in eggs.

We found no association between female brightness and egg production. This suggests that the production of achromatic ornamentation may be less costly and thus less constrained by the cost of egg production than color intensity. In an experiment in blue tits, an increase in reproductive costs in females changed the chromatic component (hue) of the blue crown but did not affect brightness of the same patch [START_REF] Doutrelant | Female plumage coloration is sensitive to the cost of reproduction. An experiment in blue tits[END_REF]. Experiments aimed at relating the effect of reproductive costs on both achromatic and chromatic components of coloration are needed to confirm this suggestion.

Color volume was not associated with any of our tested variables. Color volume relates to the diversity of coloration (Stoddard & Prum, 2008), and it is sometimes thought that greater volume indicates more diverse mechanisms of color production. The fact that paternal care and female investment in reproduction does not affect this diversity of coloration in females when controlling for male coloration may suggest diversity of coloration in females is not under strong intra-and intersexual selection in females and its evolution may be related to other selective forces. To date, comparative analyses found an association between color volume and sex, documenting higher diversity of colors in males than females [START_REF] Delhey | The colour of an avifauna: A quantitative analysis of the colour of Australian birds[END_REF]Shultz & Burns, 2017), and males from sexually dichromatic species to be more colorful than males from less dichromatic species [START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF]. Additionally, they found for each sex an association between color volume or colorfulness and type of habitats (Shultz & Burns, 2017;[START_REF] Cooney | Latitudinal gradients in avian colourfulness[END_REF], or between color volume and the number of sympatric species from the same family (Doutrelant et al., 2016). Thus, habitat selection and interspecific competition may be the main factors associated with the evolution of color volume, with stronger selection in males than females.

For our three proxies of coloration, male coloration was the factor explaining most of the variation in female coloration. This result was also found in several former comparative studies (e.g. [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF]e.g. Delhey 2015;Shultz and Burns 2017;[START_REF] Cooney | Sexual selection predicts the rate and direction of colour divergence in a large avian radiation[END_REF]). This strong phenotypic correlation is potentially in favor of the prevailing role of genetic correlation [START_REF] Lande | Sexual Dimorphism, Sexual Selection, and Adaptation in Polygenic Characters[END_REF] i.e. shared genetic architecture, in the level of expression of color traits in females. For instance, the coloration of the red bill of zebra finches is strongly correlated between fathers and daughters [START_REF] Price | Sexual selection, selection load and quantitative genetics of zebra finch bill colour[END_REF]. However, phenotypic correlation may also be the result of other colorcorrelated factors such as shared diets [START_REF] Amundsen | Female Coloration: Review of Functional and Nonfunctional Hypotheses[END_REF] as well as shared natural, social, and sexual selective pressures acting on both sexes (Shultz & Burns, 2017). It could also be the result of divergent types of selection in males and females that select for similar ornamentation in both sexes, for instance social selection for females and sexual selection for males [START_REF] Tobias | The evolution of female ornaments and weaponry: social selection, sexual selection and ecological competition[END_REF]. So the part of variance explained by the phenotypic correlation in our models can also overestimate the importance of genetic correlation. Female coloration may be driven by femalespecific selective pressure even in species sharing similar colors, with different forces leading to similar colorations [START_REF] Amundsen | Female Coloration: Review of Functional and Nonfunctional Hypotheses[END_REF][START_REF] Enbody | Production of plumage ornaments among males and females of two closely related tropical passerine bird species[END_REF].

By including male coloration in our analyses, we have statistically "corrected" for correlated plumage similarities between sexes and the effect of genetic correlation, but we have also drastically reduced our ability to detect the real importance of selective pressures. When removing male corresponding color metric from our models (See Table S5), we found that estimates for egg production were much bigger in relation to female brightness (0.435 [0.063;0.806] 95% CI), suggesting we potentially underestimated the effect of female investment on female coloration.

Estimate values remained similar for paternal care and the interaction between paternal care and egg production (See Table S5). So female reproductive costs may drive the evolution of female coloration (constraining chromaticity and favoring brightness) as a higher level than what we find with our conservative approach including male coloration in the statistical model. Yet, we think it is better to retain the conclusion of the model controlling for male coloration, to include the acknowledged effect of genetic correlation.

We assumed that species showing higher values of brightness and chromaticity could be seen as more ornamented/conspicuous This is reasonable for conspicuous carotenoid and structural colors (red, blue, yellow, blue, violet), but works poorly for dark to black ornaments [START_REF] Marcondes | Fifty shades of brown: Macroevolution of plumage brightness in the Furnariida, a large clade of drab Neotropical passerines[END_REF]. If males produce black ornaments and females not, female brightness and chromaticity will be higher than male brightness and chromaticity but in fact female would appear duller. But only three species of our data set correspond to males with large amount of black coloration (using a method adapted from [START_REF] Osorio | Detection of Fruit and the Selection of Primate Visual Pigments for Color Vision[END_REF] that defines black as a coloration that produces less than 0.05 percentage reflectance of the white standard at each photoreceptors), so it unlikely affected our results.

Regarding ecological factors included as covariate in our study, we found a correlation between migratory behavior and intensity of coloration. In accordance with previous work [START_REF] Dale | The effects of life history and sexual selection on male and female plumage colouration[END_REF][START_REF] Dunn | Natural and sexual selection act on different axes of variation in avian plumage color[END_REF], females from strictly resident species were less likely to have intense colors (chromaticity metric). Unlike Cooney et al (2022), we did not find a correlation between migratory behavior and female color volume, which may be a consequence of our dataset, restricted to species breeding in northern temperate areas. We did not find any correlation between female color metrics and nest characteristics. Different studies had found that birds breeding in higher and more open nests have less conspicuous females [START_REF] Martin | Sexual Dichromatism in Birds: Importance of Nest Predation and Nest Location for Females Versus Males[END_REF][START_REF] Soler | Evolution of sexual dichromatism in relation to nesting habits in European passerines: a test of Wallace's hypothesis[END_REF], but other recent studies failed to find a correlation between predation risk or nest openness and plumage conspicuousness [START_REF] Matysiokova | Broad-scale variation in sexual dichromatism in songbirds is not explained by sex differences in exposure to predators during incubation[END_REF][START_REF] Cain | Conspicuous Plumage Does Not Increase Predation Risk: A Continent-Wide Test Using Model Songbirds[END_REF][START_REF] Simpson | Natural and sexual selection shape the evolution of colour and conspicuousness in North American wood-warblers (Parulidae)[END_REF]. This lack of consistency among studies can be explained by the difficulty to build adequate metrics to estimate predation risk. It can also be related to variation in the quantification of coloration (human vision, color from bookplates, spectrometry) or to the decision of treating males and females together or separately.

To conclude, our work confirms the strong covariation between male and female coloration. In addition, it reveals a moderate association between paternal care and female coloration when female costs are reduced, either with lower cost of egg production, or lower cost of producing female ornament. These costs are likely important to consider and should be incorporated when testing other potential factors that drives the evolution of female ornamentation (such as female ). The number of measurements is the total number of color measurements carried out by spectrometry on the bird, where *3 indicates that the measurements were replicated three times to test repeatability. (1) Two male specimens of Myadestes townsendi were used; measurements were carried out on the second specimen in zones that were stained on the first specimen (except for the stain on its abdomen, the first specimen was in better condition than the second specimen).

SI-11

2/ Coloration measurement

Spectrometry: A single person (AF) performed all the spectrometric measurements, using a Jaz spectrometer (Ocean Optics, Dunedin FL, USA) with a Jaz light source covering a spectral range of 300 nm to 700 nm and a 200 µm optical probe (FCR-7UV200-2-45-ME, Avantes, Apledoorn, NL) whose tip contained a 45° quartz window, which guaranteed a constant distance between the light and the sample and highly repeatable measurements. Reflectance was calculated in relative terms, via comparison with a black and a white reference (WS1, Ocean Optics, Dunedin FL, USA).

Before measuring the whole plumage, we first characterized zone coloration for each bird (see Figure S2). When a bird had distinct color patches or a patch was composed of different colors (up to four) in any of the 21 zones, we measured each color. Although the preliminary assessment of distinct patches or colors was carried out with the naked eye (and thus affected by human visual bias), we doublechecked the assessment by examining the spectrometric spectra [START_REF] Gomez | Influence of ambient light on the evolution of colour signals: comparative analysis of a Neotropical rainforest bird community[END_REF]Stoddard & Prum, 2008;Doutrelant et al., 2016). Ultimately, number of measurements ranged from 22 to 45 depending on the species (details in Table S1); the mean number of measurements per bird was 33.

Within species, measurements number was the same for both sexes, even if one sex displayed fewer colors (Shultz & Burns, 2017). For some specimens we repeated all measurements three times to test measurement repeatability (details in Table S1).

For specimens in which we tested repeatability, we calculated the mean spectra per patch after controlling for concordance in spectral shape among the replicates.

SI-12

Figure 1 :

 1 Figure 1: Forest plots for a) brightness, b) chromaticity, and c) color volume in females, representing the mean estimates and their

Figure 2 :

 2 Figure 2: Relationship between paternal care and mean female plumage brightness. The black crosses are the raw values for each

Figure 3 :

 3 Figure 3: Depiction of the two-way interaction between paternal care and egg production and its effect on interspecific variation in

Figure 1 :

 1 Figure 1: Forest plots for a) brightness, b) chromaticity, and c) color volume in females, representing the mean estimates and their

Figure 2 :

 2 Figure 2: Relationship between paternal care and mean female plumage brightness. The black crosses are the raw values for each

Figure 3 :

 3 Figure 3: Depiction of the two-way interaction between paternal care and egg production and its effect on interspecific variation in

Figure S2 :

 S2 Figure S2: Topography of a house sparrow (Passer domesticus). In this study, we started characterizing coloration in 22 zones (abbreviations for zone names in brackets). The lore zone (LO) was initially included but then later removed because it was poorly preserved in a large number of specimens. Consequently, only 21 zones were used in the final analyses.

Table and Figure legends Table 1 :

 andlegends1 Estimated values from the PGLS analyses. Variables are sorted in the same order as in Figure 1. 95% confidence intervals (displayed in brackets) include phylogenetic uncertainty. Estimates with confidence intervals not overlapping zero are represented in bold (except for Pagel's Lambda values).

Table 1 :

 1 Estimated values from the PGLS analyses. Variables are sorted in the same order as in Figure 1. 95% confidence intervals (displayed in brackets) include phylogenetic uncertainty. Estimates with confidence intervals not overlapping zero are represented in bold (except for Pagel's Lambda values).

	Estimates with confidence intervals

Table S1 :

 S1 Bird species/subspecies/families included in the analyses. The scientific names are those used by birdtree.org. The collection point is where the bird was collected (nearest town/city (state), country; the list of country abbreviations is at the bottom of the table

Journal of Evolutionary Biology

Acknowledgments.

We thank the National Museum of Natural History in Paris, especially Patrick Boussès and Jérôme Fuchs who gave us access to the bird collection and facilitated the use of the specimens selected. We thank Maria del Rey Granado for her help with recording spectrometric measures.

We last thank Marianne Elias and Benoît Nabholz for help with phylogenetic comparative methods, Tim Janicke and anonymous reviewers for insightful comments on the manuscript, and Jessica Pearce and Kaitlyn Murphy for English language editing and comments. Funding was provided by the CNRS, the University of Montpellier, the French National Research Agency (CD: ANR 09-JCJC-0050-0) and the regional government of Languedoc Roussillon (Chercheur-es d'Avenir grant to CD).

Data archival: Data sets are deposited in the Dryad Digital Repository (URL: https://doi.org/10.5061/dryad.9s4mw6mkh)

territoriality). Paternal care is associated with both female brightness and chromaticity showing the importance of considering this factor in further analyses. More generally, this study shows the importance of testing factors related to female-specific forces of selection and costs, to understand and determine the array of factors leading to the evolution of female ornaments.

Supplementary information

SI-9

Figure S1. Phylogenetic tree representing the major families of Passerines from the Northern Hemisphere. Highlighted families correspond to the 17 families included in the analyses and show they are more closely related to each other than to the other families represented on the tree. The species of tanagers included in our analyses were formerly identified as "Thraupidaes" but are now included in the sister-family of Cardinalidae. Therefore, we did not included "Thraupidaes" in the phylogenetic tree.

SI-13

Visual model: colors are points in the avian tetrahedron color space, and plumage is a cloud of points.

The center of the color space is where all the cones receive equal stimulation, and a color is thus perceived as achromatic (Maia et al., 2019). A color is perceived as more intense or vivid as its distance from the center of the color space increases. Mean plumage brightness was the mean relative reflectance over the entire spectral range (300 nm to 700 nm) and corresponded to the number of photons caught by double cones (Stoddard & Prum, 2008). We calculated mean plumage chromaticity based on the mean distance from the center of the color space. We calculated color volume as the convex hull that included all the points in a plumage cloud. Different colors differentially stimulate the four cones responsible for color detection, which leads to point dispersal and increased color volume (Renoult et al., 2017). Hence, color volume expresses color diversity in bird plumage. We also calculated the mean distance between all color pairs (Stoddard & Prum, 2008) as a metric of mean within-plumage contrast. This mean distance was highly correlated with color volume (see Table S2), so we omitted it from later analyses. Few males, little information on male incubation duration Female more than male 0.7 1 Female leaves first 1 0.5 Post-fledging period Male may cover eggs briefly 0.2 1 Male observed incubating 0.5 1 Male provides more supplies 1 0.7 One observation of male feeding 0.1 1 Male with small harem; male if fledgling in territory 0.1 1 Very rare situation Miscellaneous "Several weeks" was estimated to be 21 days. When information on activity or duration was missing for a species, we used the median value for the whole data set.

SI-14

Table S5: Estimated values from the PGLS analyses when excluding corresponding male coloration from the models. Variables are sorted in the same order as in Figure 1 (excluding male coloration). 95% confidence intervals (displayed in brackets) include phylogenetic uncertainty. Estimates with confidence intervals not overlapping zero are represented in bold (except for Pagel's Lambda values).

Estimates with confidence intervals


Asbathou Biyalou-Sama
email: asbathou.biyalousama.etu@univ-lille.fr

Matthieu Allon
email: matthieu.allon@axellience.com

Cédric Dumoulin
email: cedric.dumoulin@univ-lille.fr

Emmanuel Renaux
email: emmanuel.renaux@imt-lille-douai.fr

Towards an MDE approach of Digital Twin for Software Applications

Keywords: Digital Twin, MDE, Software Application

Digital Twin (DT) refers to a digital representation of a physical entity and its functions, behaviors and rules. Digital Twin (DT) technology, originally, emerges from manufacturing and aerospace sectors. With the advancement of Industry 4.0 and IoT, DT is applied in other domains like cyber-physical systems (CPS), building, and health. This scattering of the DT technology results in a lack of clear and concise definition of what is exactly a DT.In this context, we want to explore what could be a DT for Software Applications (SA)

. This paper describes the approach that we will follow to identify what could be a DT for Software Applications. On the basis of the features (of a DT) identified in the other domains, we propose ways to define a DT for Software Applications. In a first approach, we propose to use structural and behavioral UML diagrams to instrument the application (by defining software probes), and we visualize the results in a "dashboard". This gives us the "monitoring" features of the DT. From this approach, we want to explore the other features (simulation, prediction, optimization…) that will allow us to propose a more complete digital twin.

I. INTRODUCTION

Digital twins (DT) have found wide application in areas such as cyber physical systems (CPS) buildings, Iot, health ... A DT is composed of a physical part (the CPS, a building ...) and its digital counterpart (the twin). In these different domains, the digital twin allows, among other things, to monitor the physical part, to perform simulations on the digital part, or to interact on the physical part.

As we observed these DTs, we wondered ourselves what a DT of a software application might look like and what such a DT might be used for... By Software Application (SA), we mean an application realized in an Object Oriented Language and for which we can obtain representations, even partial, in the form of UML diagrams.

In the absence of a formal definition for DTs, we have identified different points characterizing a DT. We then tried to transpose these characteristics to the domain of SA. One of the difficulties encountered is that in our case, the 'physical' part of the DT is itself already digital. Despite this difficulty, we propose a first MDE approach in which we describe our DT with the help of three models: a model partially representing the application and in which we can place 'sensors', a model to describe how the data from the sensors are transformed, and a model to describe how to visualize the results. Thereafter, in order to follow the MDE process, we will automatically generate the code corresponding to the DT described in these models.

To quickly validate our approach, and to be able to experiment around the definition of a DT for SA, we propose a framework allowing "to build programmatically" (i.e. without automatic code generation) the DT conform to the models. This short paper presents the state of progress of our thinking and our future investigations, which, we hope, will allow us to experiment around the notion of DT for SA. These experimentations and the developed tools will allow us, in the future, to propose a more precise definition of a DT for SA.

Section 2 describes the characteristics we have retained when studying DTs in different areas. In section 3, we cite references on which we have based our work. In Section 4, we detail our proposed DT for SA. Section 5 describes the implementation of the framework for the experimentations. In section 6, we describe the challenges that we have identified and that need to be solved in order to complete the definition of a DT for SA. Finally, we conclude and discuss the perspectives in section 7.

II. DIGITAL TWINS : DEFINITION THROUGH DOMAINS AND MAIN USAGES

In CPS, the digital twins consist of a set of models that represent the physical system. These models are digital representations of the physical system. They are able to capture real data from the system [START_REF] Vrabič | Digital twins: Understanding the added value of integrated models for through-life engineering services[END_REF]. Digital Twins also offer a set of microservices that exploit the data from the system [START_REF] Lim | A state-of-the-art survey of Digital Twin: techniques, engineering product lifecycle management and business innovation perspectives[END_REF], [START_REF] Boje | Towards a semantic Construction Digital Twin: Directions for future research[END_REF]. These microservices provide, among other things, data visualization or system simulation. The Building Information Model (BIM) is considered as the digital twin for building [START_REF] Kaewunruen | Digital Twin for Sustainability Evaluation of Railway Station Buildings[END_REF]. It is a numeric plan where some values, such as temperature, may change over time. This plan is updated with data gathered from sensors placed on the real building. BIM is used to visualize the information and the behavior of various building components.

The study of these two domains highlights some common characteristics of digital twins:  Digital representations: whether in CPS or in buildings, digital twins are primarily digital representations integrating various functions of the physical system.

 Data visualization: one of the main purposes of digital twins is to be able to trace and visualize what is happening in the physical system. For example, BIM makes it possible to visualize real information coming from the building.

 Data gathering: Digital twins gather data from the physical system using sensors.

 Data processing: data retrieved by the sensors are raw data. A processing and filtering phase is often necessary to obtain information more relevant for humans.

The digital twins are designed to serve different purposes. The literature reviews in [START_REF] Boje | Towards a semantic Construction Digital Twin: Directions for future research[END_REF], [START_REF] Liu | Review of digital twin about concepts, technologies, and industrial applications[END_REF], [START_REF] Lu | Digital Twindriven smart manufacturing: Connotation, reference model, applications and research issues[END_REF] provide a list of these most frequent aims:

 Monitoring: this is the data visualization part.

 Simulation and prediction: simulate the real system is a purpose present in almost all digital twins. According to [START_REF] Boschert | Digital Twin-The Simulation Aspect[END_REF], digital twins are the next generation of simulation techniques. Simulation allows to observe the behaviors and the reactions of CPS or buildings in different scenarios.

 Optimization: a digital twin can also be used to optimize various resources of a system.

III. EXISTING CONCEPTUAL METHODS AND PROPOSED

ARCHITECTURES

We have studied several approaches for DT. We would like to cite the following two:

Reference [START_REF] Kirchhof | Model-driven digital twin construction: synthesizing the integration of cyber-physical systems with their information systems[END_REF] proposes to design digital twins for CPS using some dedicated tools: UML/P class diagrams for the Digital Twin Information System, MontiArc models for the physical system. A dedicated language is used to make the interconnection between the two systems. The implementations are generated from the different models.

Reference [START_REF] Caporuscio | Architectural Concerns for Digital Twin of the Organization[END_REF] proposes an approach for designing DT of organizations. It proposes to integrate the different entities of an organization, i.e. processes, people, etc., while also proposing different diagrams.

In terms of the architecture of a digital twin, [START_REF] Lim | A state-of-the-art survey of Digital Twin: techniques, engineering product lifecycle management and business innovation perspectives[END_REF] proposes a four layers architecture: communication, data representation, data computation and microservices. We use parts of this architecture as a start for our work.

These papers show that DT can be designed with an MDE approach, but they do not answer our question « what could be a DT of a SA »?

IV. OUR PROPOSAL : TOWARDS AN MDE APPROACH OF DT FOR SOFTWARE APPLICATIONS

In section 2, we have identified some common characteristics of DTs: digital representations, data visualization, data gathering and data processing. Now we propose the equivalent of these concepts for SA. We also introduce the models used to define a DT for a SA.

A. Equivalent concepts 1) Digital representation of software

In CPS and buildings, the digital representation is used to observe various characteristics of the system, either structural or behavioral. In software engineering, UML is used to describe these later characteristics. We use UML and its diagrams to describe the structural part (class diagram) and the behavioral part (activity diagram, collaboration diagram...). We do not describe the whole application, but only the parts that the user wants to observe. To obtain these diagrams and the UML model, we plan to use some reverse engineering tools.

2) Data visualization: monitoring

Data visualization is done in different formats depending on the target applications or the various domains. This can be textual presentation, graphic components or 3D visualization. In our context, we propose the concept of viewers to display data according to the user observation needs. Viewers are not responsible for processing or interpreting the data. The only operations performed are related to the display of data.

3) Data gathering

In CPS or buildings, physical sensors are used to gather real data such as temperature, position of a robot… At the SA level, we propose to capture data related to the system (temperature, memory usage, CPU speed…) and also application-related data (values of variables or instances, number of instances, values of method parameters, exceptions thrown…). These data are captured in the application using « software probes » that are placed in the code.

4) Data processing

For data processing purpose, we propose the concept of operation boxes. They will be in charge of processing the raw data from the system: filtering, interpretation, extraction of information based on business rules.

B. Concept modeling

The modeling of a DT for a SA is done through the use of the previous concepts in three models (Figure 1-a) that we are going to describe.

1) Probe Model

The probe model (Figure 1-a left) is used to describe both the digital representation of the SA and the placement of software probes within that SA. This model is a partial digital representation, which can be structural or behavioral, of the application. We propose to use UML diagrams to represent the probe models. The probes can be placed on different elements of the SA, such as variables, classes, properties, activities... In a first approach, we focus on placing probes on methods, in order to capture the input and output parameter values, as well as the system data.

2) Data manipulation and connection model

The data processing and connection model (figure 1-a center) allows both to describe the operation boxes and to connect these boxes to each other, as well as to probes and viewers. This model reuses the probes described in the probe model and the viewers described in the visualization model.

It models the flow of data, from probes to viewers through the various processing boxes.

3) Visualization model

This model (Figure 1-a right) allows the user to describe the set of viewers he wants to use to observe his digital twin. The user has the possibility to use simple viewers like text, image, etc. or to compose them in order to build viewers that are more complex. This model describes the data displayed by the digital twin.

V. TECHNICAL IMPLEMENTATION OF OUR APPROACH

To validate our approach, we develop a prototype. Its architecture (Figure 1-b) is inspired by the three models: application and probes model, data processing model and visualization model. We add communication between the different parts. The prototype implements the metamodels for the three models, as well as a framework allowing to build a DT for a SA. Proposing a framework to build DT is important, as highlighted in [START_REF] Bordeleau | Towards Model-Driven Digital Twin Engineering: Current Opportunities and Future Challenges[END_REF]. To be complete, we test our framework on a real SA.

A. Metamodels

For the probe model, we use UML and its diagrams. The probes are designed using stereotypes that can be positioned on any UML element. The metamodels for data processing models and visualization models are realized with EMF, and the corresponding diagrams with Sirius.

B. Model to framework transformations

The code generation of the DT will be possible from the templates. This will be done later, when the models and the framework are stabilized.

C. Framework

The framework provides the basic building block to build DTs. The assembly and configuration of the building blocks will later be generated from the models. The framework uses existing technologies (figure 1-b): Kibana for viewers, a web server (in Spring) to implement the data processing blocks, RabbitMQ to communicate between probes and processing blocks, http requests to communicate between processing blocks and Kibana logstash and ElasticSearch).

The notion of software probe is realized thanks to "Spring interceptors". This allows placing probes on method calls without touching existing code of the application to observe. The downside is that we are currently limited to applications developed with Spring. Other technologies are available to implement probes and will be studied later.

D. Targeted software application

To test the framework, we use a real software application that is in production. It is a web application developed in Spring and React allowing "computer science project proposals" for students in Masters.

VI. CHALLENGES

We have identified several challenges.

A. What data to display?

The first challenge we identified was "what data could be visualized using the DT, and in which forms"? There is of course the basic data such as values of arguments, of variables or instances, CPU time, temperature, memory usage, etc. These data are immediately accessible, and their visualization is straightforward. It is also possible to combine data in order to obtain and display more complex data such as the one related to business processes, execution of activities... We could thus visualize the percentage of users in the different steps of a business process, some statistics on errors, withdrawals, paths followed... Still by combining data, we can find new data that can hardly be accessible today: for example, we can combine the CPU temperature with the number of user instances in order to check the correct functioning of the processor, or to improve the energy consumption.

B. Improve the prototype

Our second challenge consists in improving the prototype of our approach. To achieve this we need to improve our framework to make it easier to use and to integrate into different types of applications: server, desktop... We need to complete the concepts used in our metamodels, allow the automatic generation of the DT code, and also propose to build the probe model by reversing the real application. We also need to explore other mechanisms for probes to observe other types of software applications.

C. Simulation and optimization

Our current proposal does not allow any simulation. This is our third challenge: what can we propose to perform software application simulation?

In an answer that we propose, we divide the software application into "interconnected blocks". Each block takes input and output data, and performs processing on these data. For example, blocks are classes, components, methods, packages... Our current DT proposal allows monitoring and recording the inputs and outputs of these blocks. We can then consider different scenarios as in the following examples:  We modify the behavior of a block and we reinject the recorded data in order to study the new implementation. This is close to unit tests, but here we work on "real" data. Changing the behavior can be done by providing new code, or by using a language to describe the output data in terms of inputs, such as OCL.

 The behavior of a block can also be simulated and modified by replacing the block with a mock. A mock allows to specify output data according to input data. A generic implementation is to record pairs of {input data, output data}, and then provide the output data based on the submitted inputs. With the help of our DT, we can record the inputs and outputs, and thus automatically create a mock of a block. Of course, the number of pairs of {inputs, outputs} we can record is limited.

 Going even further, we can imagine putting an Artificial Intelligence (AI) in the block, and instructing this AI using the input and output data. Once this "AI block" is instructed, we can replace the original block and observe the behavior of the rest of the blocks. Here we do not have the memory limit anymore, but we have to find out how to change the behavior of the block. One possible approach is to instruct the block with modified data.

If we know how to decompose the application into blocks, and reinject modified blocks, we can then perform simulations. We can also study the performance of the blocks in order to optimize the system.

D. Interaction with the application

Another challenge is to propose solutions to enable our DT to interact with the application. For example, the DT would allow changing configuration variables in order to adapt the SA to a new context.

E. Define a DT for a SA

Our last challenge will be to provide a more precise definition of what a DT for an SA is, and what it can bring.

VII. CONCLUSION & PERSPECTIVES

We are at the beginning of our work, and we have a real question we want to answer: what a DT of a software application might look like and what such a DT might be used for. To answer this question, we propose to experiment around the definition of a DT. The study of DTs in other domains allows us to suggest ways to define a DT for a SA. The DT is defined using three models describing the part of the application to be observed and the probes used to gather data, the data transformation, and finally the data visualization. A prototype using this approach is currently under implementation.

Our next work will be to search and deepen the solutions for the identified challenges. The framework will allow us to explore and test these solutions. The first aim of this short paper is to expose the ideas we want to develop and implement to be able to define what is a DT for a SA. The second aim is to initiate discussions.

Figure 1 :

 1 Figure 1: (a) Conceptual approach (b) Technical implementation