Vsevolod Peysakhovich
email: vsevolod.peysakhovich@isae-supaero.fr

Christophe Hurter
email: christophe.hurter@enac.fr

Intuitive visualization technique to support eye tracking data analysis: A user-study

Keywords: Human-centered computing → Visualization techniques, Information visualization, Scanpath, visualization, flow directional map, Oriented Line Integral Convolution

While fixation distribution is conventionally visualized using heat maps, there is still a lack of a commonly accepted technique to visualize saccade distributions. Inspired by wind maps and the Oriented Line Integral Convolution (OLIC) technique, we visualize saccades by drawing ink droplets which follow the direction indicated by a flow direction map. This direction map is computed using a kernel density estimation technique over the tangent directions to each saccade gaze point. The image is further blended with the corresponding heat map. It results in an animation or a static image showing main directions of the transitions between different areas of interest. We also present results from a web-based user study where naive non-expert users where asked to identify the direction of the flow and simple patterns. The results showed that these visualizations can successfully be used to support visual analysis of the eye-tracking data. It also showed that the use of animation allows to ease the task and to improve the performance.

INTRODUCTION

The first step of the eye tracking data analysis is often the visualization of the raw data [START_REF] Holmqvist | Eye tracking: A comprehensive guide to methods and measures[END_REF]. By observing the generated image, the investigator can verify the distribution of the sampled points and verify the correspondence of the densest, i.e. most viewed, areas to some salient stimulus parts. Fixation distribution is conventionally illustrated using heat maps [Špakov Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. ETVIS '18, June 14-17, 2018, Warsaw, Poland © 2018 Association for Computing Machinery. ACM ISBN 978-1-4503-5787-6/18/06. . . $15.00 https://doi.org/10.1145/3205929.3205939 and [START_REF] Špakov | Visualization of eye gaze data using heat maps[END_REF]. A convolution of a small symmetrical kernel with the data points gives an intuitive representation of the most viewed stimulus areas. The width of the kernel allows taking into account the imprecision of both eye tracking device and the fixational eye movements during which a human eye is never still. The lower is the accuracy of the eye tracker, the larger should be the kernel. However, generating such an intuitive illustration of the transitions (or saccades) between these most fixated areas is less straightforward.

While numerous visualization approaches exist [START_REF] Blascheck | State-of-the-art of visualization for eye tracking data[END_REF], none of them proposes an intuitive visualization technique for scan paths. Commonly used gaze plots depict saccades are as straight lines that connect fixations shown as small circles. This straightforward representation can show if there is a connection between two areas of interest or not. It is an efficient visualization method for small datasets [Goldberg and Helfman 2010b]. Unfortunately, the gaze plots become increasingly cluttered when the number of saccades goes up [START_REF] Sukru Eraslan | Eye tracking scanpath analysis techniques on web pages: A survey, evaluation and comparison[END_REF]. But mostly, an important drawback of this visualization method is that it cannot immediately convey the crucial information of the transitionstheir direction.

Recent works proposed to overcome these drawbacks by visually simplifying the drawing and aggregating transitions according to their directions and spatial proximity [Goldberg and Helfman 2010a; [START_REF] Peysakhovich | Scanpath visualization and comparison using visual aggregation techniques[END_REF][START_REF] Peysakhovich | Attributedriven edge bundling for general graphs with applications in trail analysis[END_REF]. It is based on the mean-shift algorithm [START_REF] Comaniciu | Mean shift: A robust approach toward feature space analysis[END_REF] applied both to the fixation points and the saccades. An accessory product of these visual aggregation techniques is the concept of flow direction maps that allows grasping the locally dominant directions of the eye movements in a vector field. The generated two-dimensional vector data can be visualized in a single image using the Oriented Line Integral Convolution (OLIC) technique [START_REF] Wegenkittl | Animating flow fields: rendering of oriented line integral convolution[END_REF]].

The "holy grail" of the eye tracking data visualization is a method that would intuitively convey the directional information in a similar way the heat map conveys the density information. Inspired by wind maps where the directions are depicted using OLIC technique with temperature maps depicted underneath the wind information, we wanted to verify the intuitiveness of these visualizations applied to the eye tracking data. In this preliminary study, we performed a web-based survey aimed to answer two questions: 1) Without any particular instruction nor training, is it possible to understand the flow direction depicted using the OLIC algorithm? and 2) Based on the eye tracking data, is it possible to identify transitions between different areas of interest from a static image?

The paper is structured as follows: after a brief description of the flow direction maps concept and presenting the pipeline of the visualization, we present the survey design and its results. We then discuss the results and conclude on future possible extensions.

EYE MOVEMENTS FLOW DEFINITION AND VISUALIZATION

The flow direction maps [START_REF] Peysakhovich | Attributedriven edge bundling for general graphs with applications in trail analysis[END_REF]] can be used to determine locally dominant eye movements directions. These maps are constructed similarly to attentional maps using the kernel density estimation technique. At each saccade sample, the radial kernel K(•) is multiplied by the vector component (s j+1 -s j ) -an estimate of the unit tangent vector to the point of a saccade s j . Thus, the map θ (•) is defined by

θ (x) = K(x) * j (s j+1 -s j ) • δ (x -s j ).
The flow direction maps are used to perform saccade bundling and are refined at each step of the iterative process.

The pipeline of the technique is presented on the Figure 1. First, the fixations are extracted from the raw data [START_REF] Andersson | One algorithm to rule them all? An evaluation and discussion of ten eye movement event-detection algorithms[END_REF], and are then clustered together using the mean-shift algorithm [START_REF] Comaniciu | Mean shift: A robust approach toward feature space analysis[END_REF]. At this step, attentional maps are generated using the density maps. Following [START_REF] Peysakhovich | Scanpath visualization and comparison using visual aggregation techniques[END_REF], we used maps with a resolution of 420 × 420 pixels and a kernel width of 31. Thus, a 4 × 4 pixel square on the screen corresponds to one map cell. We used neighborhood width of 40 to compute the gradient to the local densest area. At each iteration, samples are moved according to the gradient. We performed 10 clustering iterations.

Second, the saccades are bundled together using both directional information from the flow direction maps and spatial information from conventional density maps. The procedure is similar to the fixation clustering, except that now the points of the saccades are shifted instead of the fixations. The directional compatibility is computed as a maximum allowed angle between the local direction (as defined by the flow direction map) and the point direction. We performed 20 saccade bundling iterations using the similar settings as for the fixation clustering.

After performing the fixation clustering and saccade bundling, heat map and flow direction map are available. While heat map is a 2D texture and can be displayed directly, the flow direction map is stored in two textures. Therefore, as proposed by [START_REF] Peysakhovich | Scanpath visualization and comparison using visual aggregation techniques[END_REF]], we visualize it in a single 2D image using the Oriented Line Integral Convolution (OLIC) method [START_REF] Cabral | Imaging vector fields using line integral convolution[END_REF][START_REF] Wegenkittl | Animating flow fields: rendering of oriented line integral convolution[END_REF]]. This technique uses a noise texture as an input and visualizes vector fields by drawing ink droplets following the local flow direction. A ramp-like one-dimensional kernel is used to visually accentuate the "tails" of streamlines. By shifting the ramp by one of a few pixels, the textures can be animated.

Eventually, the flow visualization using OLIC technique and the heat map are blended together to obtain a single 2D image containing the information about both fixations and saccades.

WEB-BASED USER-STUDY 3.1 Participants

For the first part of the experiment (direction perception), the participants were 32 volunteers (10 females, age 29.1±4.7), recruited through social networks (LinkedIn, Twitter, Facebook). All participants had no previous experience in visual analytics or visualization domains and were naive relatively to the goal of the experiment. All participants gave their informed consent before starting the survey and were free to stop it any time.

For the second part (pattern perception), the participants were randomly assigned to Group 1 (15 volunteers, 3 females, age 28.3±2.6) and Group 2 (11 volunteers, 2 females, age 30.9±6.8). Group 1 was presented with the static condition (cf. Sec. Survey design), while Group 2 was presented with the animated condition. Five participants aborted the survey after completing the first part of the experiment.

Survey design

The survey was implemented online using browser-based Psy-Toolkit (www.psytoolkit.org; [START_REF] Stoet | PsyToolkit: A software package for programming psychological experiments using Linux[END_REF][START_REF] Stoet | PsyToolkit: A novel web-based method for running online questionnaires and reaction-time experiments[END_REF]). It is a free-to-use toolkit that allows to design and run questionnaire surveys online. The browser-based version of the survey was chosen in order to reduce the survey time and also to verify the feasibility of performing in the further a larger survey involving a big number of participants.

Direction perception. In the first part of the experiment, participants were asked to determine the flow direction for each of the 8 presented stimuli (Fig. 2). The answers were depicted as arrows

• , B) 45 • , C) 90 • , D) 135 • , E) 180 • , F) 225 • , G) 270 • , H) 315 • .
in the corresponding direction with only one answer possible. For each direction, participants were then asked to evaluate the difficulty of the decision on the scale from 1 (very easy) to 5 (very hard). The order of questions was randomized. The data corresponded to uniformed generated vector fields. This part of the study was used to evaluate the understanding of the flow visualization per se, without any real-world meaning.

Pattern perception. In the second part of the experiment, participants were asked to check all transitions of different directions that they could spot using the provided visualizations for the square pattern (Fig. 3) and an observation of the Michelangelo masterpiece (Fig. 4). The eye-tracking data used to generate the visualizations are available in open access (See [START_REF] Peysakhovich | Scanpath visualization and comparison using visual aggregation techniques[END_REF], Supplementary files). In the static condition, the image corresponded to Fig. 3B and Fig. 4B. In the animated condition, we generated another frame using a larger convolution kernel (see [START_REF] Cabral | Imaging vector fields using line integral convolution[END_REF]). The interval between two frames were set to 200 ms. The answers were depicted with arrows connecting the areas of interest (4 corners for the square patterns, two heads and hands connection for the Michelangelo example).

Results

We describe the results of the survey using only descriptive statistics and presenting the mean values ± standard deviation. The claims of style "relatively easy" or "relatively hard" are made relatively to the question scale from 1 (very easy) to 5 (very hard).

Direction perception. In the first part of the experiment, the participants gave their response in about 6.3±2.4 seconds. The accuracy was 87.5±3.7% without any effect of direction. The task was perceived as relatively easy (2.2±1.0). Figure 5 shows the results according to the flow direction.

Pattern perception. In the second part of the experiment, the participants gave their response in about 59.5±11.5 seconds.

Figure 6A shows the number of correct responses for the square pattern and the Michelangelo painting dataset for both static and animated conditions. Figure 6A shows the perceived task difficulty.

In the static condition, 33.3% of the participants gave the correct response for the square pattern, considering it relatively hard (3.7±0.7). In the animated condition, 91% of the participants gave the correct response and considered it relatively easy (1.3±2.5).

For the Michelangelo paining, in static condition, participants identified less often the 5 true transitions compared to the animated condition (see Figure 6A). They considered it quite hard in both static (3.4±0.9) and animated condition (3.5±0.8).

DISCUSSION 4.1 Direction and pattern perception

The results of this preliminary study showed that the direction illustrated by OLIC technique can be easily decoded from a picture without any specific instruction nor training. The participants answered the questions with ease (average 2.2 of the difficulty score) and in just about 6 seconds. The majority of the responses were correct (87.5% accuracy), in few cases the directions being taken by the opposites.

These preliminary results could be possibly further improved by considering different parameter settings, i.e. kernel width used for the OLIC computation, or even different visualization method using more complicated glyphs for the vectors [START_REF] David H Laidlaw | Comparing 2D vector field visualization methods: A user study[END_REF].

The pattern perception task was more demanding for naive non-expert users that are not used to heat maps nor vector field visualization methods. However, we aimed to understand to what extent such visualizations can be used without any notice nor training. Participants considered this task much more difficult than the first part of the experiment (difficulty scores above 3). They took about a minute to explore each illustration before giving their answer. The general response accuracy was quite low. For example, only one-third of the participants guessed that all 4 pairs of transitions were present on the square scanpath illustration (Figure 3B) in the static condition. However, the animation condition largely enhanced the performance. Thus, 91% of the participants correctly identified all transitions of the square pattern and found it very easy (average difficulty score of 1.3). In case of the Michelangelo piece, the animation improved the accuracy but at a cost of task difficulty. The participants still considered it to be quite demanding (average difficulty score of 3.5).

These results show that in some cases the nature of the eye movements data can be successfully understood from a single static image. It also appears clear from the results, that the animation greatly improves the easiness of the analysis and its performance, which is consistent with the literature [START_REF] Chevalier | Animations 25 Years Later: New Roles and Opportunities[END_REF]]. Therefore, it is preferable to visualize the eye movement data in a small animation since it provides useful insights on the flow direction. However, it is limited to electronic devices screens and cannot be printed on a piece of paper. Hence, there is a need for further research on most efficient methods of intuitive illustrations of the eye movements data in a single static image.

Visual-based improvements

This paper reports evidences of particle-based visualization of gaze direction on a static or dynamic map. While these initial results are interesting, the visual design space of such data representation is far more complex. In this section, we discuss possible improvement to support a more efficient data retrieval. Image-based techniques support fast and accurate data representation thanks to advanced rendering and interactive techniques [START_REF] Hurter | Image-Based Visualization: Interactive Multidimensional Data Exploration[END_REF][START_REF] Scheepens | Visualization, selection, and analysis of traffic flows[END_REF]. Since this work relies on previous image-based visual simplification technique [START_REF] Peysakhovich | Attributedriven edge bundling for general graphs with applications in trail analysis[END_REF], image-based technique smoothly apply. As an example, the computer density maps can be used to display fixation points with a shaded 3D map [START_REF] Hurter | Graph bundling by kernel density estimation[END_REF]. One can also take advantage of the computed directional density map to retrieve the flow direction and use a specific color coding to better visually discriminate opposite flow direction. For example, Figure 7 shows the result of a Phong shading using dot product of the flow direction and light source vectors. The use of lighting enhances the reading of the opposite directions.

The investigation of the image-based design space for gaze-based visualization is far beyond the scope of this paper. We rather provide here evidence of visual assets to an image-based technique for this specific data type visualization. Furthermore, image-based technique supports interactions with for instance the fast data filtering and data deformation (i.e. focus plus context technique [Card et al. 1999]). As an example, the MoleView provides can provide filtered information in the center of a lens while showing unfiltered contextual information [START_REF] Hurter | Moleview: An attribute and structure-based semantic lens for large element-based plots[END_REF].

CONCLUSIONS

In this work, we presented a novel visualizing technique that consists of blending the images of the heat map and the visualization of flow direction map for the eye tracking data. We conducted a web-based survey that showed that these visualizations can be successfully used in some cases to analyze the patterns of the eye movements. The results also showed that the animated representation allows to ease the analyses and improve the performance. These preliminary results could be further improved by using an expanded version of the study and comparing more techniques with novice and expert users. It would be also interesting to evaluate the user's workload while performing the task to quantify different visualizations.

Figure 1 :

 1 Figure 1: The pipeline of the flow visualization using the OLIC algorithm and visual aggregation techniques.

Figure 2 :

 2 Figure 2: Flow visualization using the OLIC algorithm for flows of different directions. A) The flow angle is equal to 0• , B) 45 • , C) 90 • , D) 135 • , E) 180 • , F) 225 • , G) 270 • , H) 315 • .

Figure 3 :

 3 Figure 3: A) Raw data and B) its visualization using visual aggregation technique for the square pattern.

Figure 4 :

 4 Figure 4: A) Raw data and B) its visualization using visual aggregation technique for the pattern of an observer of the Michelangelo, The Creation of Adam [public domain].

Figure 5 :

 5 Figure 5: The accuracy (A) and the perceived task difficulty score (B) according the direction.

Figure 6 :

 6 Figure 6: The accuracy (A) and the perceived task difficulty score (B) for square pattern and Michelangelo painting dataset for both static and animated conditions.

Figure 7 :

 7 Figure 7: Enhancing visualization using lighting: pixels intensities are weighted using the dot product of the local flow direction and the light source vector. Examples of square patterns and Michelangelo painting in normal resolution (A and B) and high resolution (C and D).


Demographic parameters of ruminant livestock in the arid and semi-areas of West and Central Africa -A review for the conference "Confronting Drought in Africa's Drylands. Opportunities for Enhancing Resilience" (Agence Française de Développement and World Bank). http://livtools.cirad.fr/guideline

Lesnoff, M. (1) , Julien, L. (1) , 2014. Demographic parameters of ruminant livestock in the arid and semi-areas of West and Central Africa -A review for the conference "Confronting Drought in Africa's Drylands. Opportunities for Enhancing Resilience" (Agence Française de Développement and World Bank). http://livtools.cirad.fr/guideline (1) CIRAD, UMR SELMET, F-34398 Montpellier, France. SELMET, Univ Montpellier, CIRAD, INRA, Montpellier SupAgro, Montpellier, France.

Table of contents

Introduction

This note presents a literature review on demographic parameters of cattle and small ruminant herds in traditional husbandry systems of the dry areas of West and Central Africa. It has been realized for the conference "Confronting Drought in Africa's Drylands. Opportunities for Enhancing Resilience"1 (Agence Française de Développement and World Bank) and the World Bank study "Prospects for livestock-based livelihoods in Africa's drylands" 2 (2016, Chapter 5).

The objective was to provide input parameters for demographic models that were planned to be used in the study to simulate the dynamics of the livestock productions.

The literature review was limited to data reported for areas showing an aridity index (AI) ≤ 0.5, more precisely the arid (A = 0-500 mm rain or "AI1-2-3") and the semi-arid (SA = 500-1000 mm rain or "AI4-5") areas. A and SA of West and Central Africa areas have a monomodal rainy season (July-August or June-September).

The review focused on on-farm studies. Data reported under ranch or experimental conditions, with improved feeding and health conditions, have not been considered. A meta-analyze of the demographic parameters collected in the literature were carried out for A and SA areas. A summary of the mean values taken as reference for the parameters are downloadable at http://livtools.cirad.fr/guideline (See WB Dryland study in section Download).

Material and methods

Collection of demographic parameters

The review followed the general principles described in Lesnoff ([1]). For livestock, many demographic parameters have been described in the literature ([2]- [START_REF] Lesnoff | Calculation of demographic parameters in tropical livestock herds -A discrete time approach with LASER animal-based monitoring data[END_REF]) in relation to factors such as the study objectives, the husbandry systems investigated, the levels of detail used to describe the animal life cycle or the methods used for the field survey or the statistical analyses. Before collecting data from the literature, it is important to define a conceptual model for the parameters (model-based approach) to then facilitate the meta-analysis of the data.

In this note, the definitions of the demographic parameters were based on the herd growth models that split the animal populations by sex and age class. Such "sex-and-age" models have been commonly used for tropical livestock (e.g. for description: [START_REF] Tacher | Notes sur la démographie bovine au Sahel : I. Représentation et projection théorique du troupeau par un modèle mathématique[END_REF], [START_REF] Landais | Un exemple d'utilisation d'une projection démographique pour l'analyse technico-économique d'un essai en milieu paysan : évaluation des pertes dues à la trypanosomose bovine dans la région de Khorogo (Côte d'Ivoire) et comparaison de 2 méthodes de lutte : méthodologie et résultats[END_REF], [START_REF] Upton | Livestock productivity assessment and herd growth models[END_REF], [14]), [START_REF] Lesnoff | Dynamics of a sheep population in a Sahelian area (Ndiagne district in Senegal): A periodic matrix model[END_REF]- [START_REF] Lesnoff | DYNMOD: A spreadsheet interface for demographic projections of tropical livestock populations -User's Manual -v3[END_REF], [START_REF] Lesnoff | Simulating dynamics and productions of tropical livestock populationsmmage: A R package for discrete time matrix models[END_REF]). Their main inputs are the demographic rates which measure the occurrence of the demographic events in the herd during a given period:

 the "natural rates", that refer to the natural performances of the herd, i.e. reproduction and mortality

 the "management rates", that refer to the events directly related to farmer decisions. Management rates are commonly composed of "offtake" (exits of animals from the herd due to slaughtering, sales, gifts, etc.) and "intakes" (entries of animals in the herd due to purchases, gifts, etc.). Intakes are generally integrated in the offtake to define net offtake (i.e. balance between offtake and intake).

The "state variables" of the model describe the state of the herd at a given time:

 the herd size (number of animals)

 the sex-and-age structure (% of animals in the sex-and-age categories)

A difficulty of a literature review is the frequent mixing between the types of demographic events. For instance, in the calculations of the rates, abortions can be mixed or not with parturitions, stillbirths with the deaths of offspring born alive, and natural deaths with the emergency slaughtering. Such mixing can have large effects on the values of the rates that are reported from the studies. One way to circumscribe such problem is to define the rates from a pre-defined animal life cycle.

The animal life cycle used in this review is presented in Figure 1. The derived demographic rates are listed in Table 1. Secondary rates can eventually be derived from these primary rates. Some examples are given in Table 2. For the occurrence rates, i.e. the parturition, mortality or offtake rates, it is important to distinguish between probabilities (p) and hazard rates (h) since they have different interpretations and, for the same intensity of occurrence, can be different ( [START_REF] Lesnoff | Calcul des taux démographiques dans les cheptels de ruminants domestiques tropicaux : approche en temps discret[END_REF], [START_REF] Lesnoff | Calculation of demographic parameters in tropical livestock herds -A discrete time approach with LASER animal-based monitoring data[END_REF]). In this note, h rates were preferred to p rates since they are more flexible for defining age classes in the demographic models ([19]).

Figure 1: Example of animal life cycle used for a sex-and-age herd growth model. Table 1: Demographic rates derived from the animal life cycle of Figure 1. Rates are defined for any time-period and animal category represented in the herd growth model.

Natural rates

Abortion rate

Probability or hazard rate for a female to have an abortion a

Management rates

Offtake rate Probability or hazard rate for an animal to exit the herd as offtake (slaughtering d , sales, loans, gifts, etc.)

Intake rate Probability or hazard rate for an animal to enter the herd as an intake (purchases, loans, gifts, etc.)

a An abortion is a gestation that is not carried out to the end, generating a non-viable offspring.

b Stillbirths are not included in natural mortality.

c Natural deaths refer to all types of death except slaughtering. Emergency slaughtering, due to accidents, diseases, etc. are considered as offtake and not as mortality.

d Within the farm.

Meta-analysis

Principle

A statistical meta-analysis was carried out on the data gathered in the Excel file dryland_west_central_africa_demog.xlsx. The objective was to estimate the averages values of the parameters and the levels of uncertainty affecting these estimates.

It is well known that the demographic parameters show large variations between years. As a simplification, between-years variations can be split to two alternative scenarios: (1) a scenario where variations are quite regular (the common "bad/medium/good" year scenario) and ( 2) a scenario where a major shock (e.g. a drought, an epizooty or a war) creates a strong drop in the parameters. The quantitative effects of shocks on the demographic parameters are strongly lacking in the literature ( [START_REF] Lesnoff | Sensitivity analysis of the recovery dynamics of a cattle population following drought in the Sahel region[END_REF]) and could not be documented in this literature review. Therefore, the estimates calculated from this meta-analysis were assumed to represent the average of the first scenario (between-years variations but no shocks). In the World Bank study, this was referred to the "business as usual scenario" (BAU) assuming in particular the same precipitation pattern for the future (with no shock) as has occurred during the past.

The analysis focused on the natural demographic rates (reproduction and mortality) and the simplified herd structures (proportions of females and adult females in the herds). Offtake have not been considered since offtake rates data are too sparse in the literature, and generally badly reported, to be analyzed in a meta-analysis. Moreover, in the demographic projections carried out for estimating livestock productions, the offtake are often used as adjustment variables to reach an assumed annual population growth rate, given some values of natural rates and herd structure ( [START_REF] Lesnoff | Simulating dynamics and productions of tropical livestock populationsmmage: A R package for discrete time matrix models[END_REF]). The few data on offtake rates that have been collected in the Excel file can eventually be used a posteriori to assess the consistency between the literature and the results of the demographic simulations.

Analysis

The factors documented in the Excel file dryland_west_central_africa_demog.xlsx and accounted for in the statistical tests were  Species (variable species), for small ruminants, with two levels: CA = caprines, OV = ovines  Area (variable area), with two levels: A = arid (AI1-2-3), SA = semi-arid (AI4-5)  Type of survey (variable typsurv2), with two levels: ABM3+ = longitudinal survey (in particular animal monitoring) that have lasted at least three years, OTHER = all other types of surveys (longitudinal survey < 3 years, cross sectional retrospective surveys, etc.)  Age class (variable agecla2)

 For cattle, three levels: JUV = 0 to 1 year, SAD = >1 to 4 years, ADU = > 4 years (in exact ages)  For small ruminants, two levels: JUV/SAD = 0 to 10 months, ADU = > 10 months

These variation factors and their interactions were tested with ANOVA F-tests. Since the small number of data in the sample could generate a lack of statistical power, the p-value used to consider a factor as significant was increased to 0.10 instead of the common p-value of 0.05.

For each parameter, the significant factors and eventual interactions were selected in a final ANOVA model that was used to estimate the average values. In complement to F-tests, the Akaike criterion corrected for small size samples (AICc, [START_REF] Burnham | Model selection and multi-model inference: a practical information-theoretic approach[END_REF]) was used to confirm the adequacy of the final model to represent the data. Within a set of competing predictive statistical models, the model showing the lowest AICc is the best trade-off between bias and variance of the estimates. For simplification of the presentation, AICc results were not detailed in this note.

For cases where factor typsurv2 was significant, the analysis gave a priority to data ABM3+. In the literature, data ABM3+ are much sparser than data OTHER but much more reliable. For cases where factor typsurv2 was not significant, data ABM3+ were gathered to data OTHER to increase the statistical power of the tests and the accuracy of the estimations.

Based on the final selected ANOVA models, a 95% Student's confidence interval (CI) was estimated for each parameter. In the present review, these CI were assumed to represent the uncertainty levels affecting the estimates. For a given parameter, the uncertainty percentage affecting its estimate was defined by pct.u = 100 x (upper limit of the CI -estimate) / estimate.

The uncertainty interval (UI) was defined by

UI = estimate  (1 ± pct.u / 100)
The UI could then be injected in the herd growth model to estimate the uncertainties affecting the herd production outputs.

The analyses were carried out with the free R software ( [START_REF]R: A Language and Environment for Statistical Computing[END_REF]).

Results

Parturition

Cattle

There were no data for the level-combination SA x ABM3+ (Figure 2). Therefore, models area + typsurv2 and area + typsurv2 + area:typsurv2 could not be tested directly.

Figure 2: Empirical averages of the parturition rate for cattle (/100 reproductive female-years).

In a first step, the analysis focused on data from area The factor typsurv2 was significant, which did not allow, in a second step, to gather data ABM3+ and OTHER to test factor area. A priority was given to data ABM3+. For area SA, the final estimate was given by u <-x[x$typsurv2 == "ABM3+", ] fm <-lm(rate ~ 1, data = u) res <-fpredict(fm, data = u, digits = 0) res fit lwr upr pct.u 1 51 38 64 25

A u <-x[x$area == "A", ] fm <-lm(rate ~ typsurv2, data = u) anova(fm) Analysis of Variance
In the table above, column fit is the estimate of the rate based on the final ANOVA model, and columns lwr (for lower) and upr (for upper) are the limits of the 95% Student's confidence interval (CI) of the estimate. Column pct.u represents the uncertainty percentage corresponding to the estimate, calculated by 100  (uprfit) / fit (section 2.1.2).The same notations were used for this entire note.

From above, the average parturition rate for area A was estimated to h = 51/100 reproductive female-years, and the uncertainty interval was estimated to [38,64]/100 reproductive female-years (uncertainty percentage of 25%).

The average parturition rate was not estimable for area SA (there were no data ABM3+). For this note, the SA rate was assumed equal to the rate estimated for area A. This seems consistent with the rates observed for data OTHER of this review (Figure 2), as well as with rates estimated from long-term data collected in sub-humid areas (for instance, in South Senegal, the average calving rate was estimated to 42/100 reproductive female-years over a 10-years animal based monitoring implemented by CIRAD and ISRA).

Small ruminants

From the empirical averages (Figure 3), the main variation factor seemed to be area. Effects of factors species and typsurv2 seemed less obvious.

Figure 3: Empirical averages of the parturition rate for small ruminants (/100 reproductive female-years).

The three factors and their 1-order interactions were tested as follows Only factor area was significant. The final estimates were given by fm <-lm(rate ~ area, data = x) res <-fpredict(fm, data = x, digits = 0) res area fit lwr upr pct.u 1 A 92 86 98 7 2

SA 103 96 111 8

Net prolificacy

Small ruminants

Empirical averages (Figure 4) showed large interactions between factors species, area and typsurv2. The highest differences between averages were observed between areas A and SA for data ABM3+. The three factors and their 1-order interactions were tested as follows

Mortality

Cattle

As for parturition, there are no data for the level-combinations SA x ABM3+, and interactions involving factor area (and subsequently factor area) could not be directly tested. From the empirical averages (Figure 5), factor agecla2 seemed to have the largest effect. Other effects seemed very low. In a first step, the analysis selected data from area A and tested factors agecla2 and typsurv2 Both agecla2 and area were significant, but not their interaction. The final estimates were given by fm <-lm(h_y ~ agecla2 + area, data = u) res <-fpredict(fm, data = u, digits = 0) res agecla2 area fit lwr upr pct.

u <-x[x$area == "A", ] fm <-lm(h_y ~ (agecla2 + typsurv2)^2, data = u) anova(fm) Analysis of Variance

Small ruminants

As for cattle, factor agecla2 seemed to be the main variation factor (Figure 6). However, a large interaction was observed from the empirical averages between factors area and typsurv2: for instance for data ABM3+, the rate increased from area A to area SA but this was the inverse for data OTHER.

Figure 6: Empirical averages of the mortality rate for small ruminants (/100 animal-years).

The four factors and their 1-order interactions were tested by fm <-lm(h_y ~ (agecla2 + species + area + typsurv2)^2, data = x) anova(fm) Analysis of Variance 3.4. Herd structure

Proportion of females in the herd

Cattle

There were no data for the level-combinations SA x ABM3+. As before, interactions involving factor area (and subsequently factor area) could not be directly tested. From the empirical averages (Figure 7), factor agecla2 seemed to have the largest effect. Other effects seemed very low. In a first step, the analysis selected data from area A and tested factor typsurv2 u <-x[x$area == "A", ] fm <-lm(F_tot ~ typsurv2, data = u) anova(fm) Analysis of Variance The non-significancy of typsurv2 allowed to gather data ABM3+ and OTHER to test factor area (without accounting for factor typsurv2), as follows u <-x fm <-lm(F_tot ~ area, data = u) anova(fm) Analysis of Variance Unlike what seemed to indicate Figure 7, factor area appeared to be non-significant (this result may be due to a lack of statistical power). The final estimates were given by fm <-lm(F_tot ~ 1, data = u) res <-fpredict(fm, data = u, digits = 0) res fit lwr upr pct.u 1 68 61 74 9

Small ruminants

From the empirical averages (Figure 8), factors area and typsurv2 seemed to be the main variation factors, but the variations were low in absolute values (average F_tot ranged from 74% to 79%) and showed interactions. The eventual effect of factor species seemed very low. The three factors and their 1-order interactions were tested as follows Interactions observed in Figure 8 appeared to be non-significant, as well all the main effects. The final estimates were given by fm <-lm(F_tot ~ 1, data = x) res <-fpredict(fm, data = x, digits = 0) res fit lwr upr pct.u 1 76 75 77 1

Proportion of reproductive females in the herd

Cattle

As before, there are no data for the level-combinations SA x ABM3+. Empirical average F_A ranged from 35% to 39% (Figure 9). In a first step, the analysis selected data from area A and tested factor typsurv2 Factor area was non-significant. The final estimates were given by fm <-lm(F_A ~ 1, data = u) res <-fpredict(fm, data = u, digits = 0) res fit lwr upr pct.u 1 38 34 42 11

Small ruminants

From the empirical averages (Figure 10), the main variation factor seemed to be area. A slight interaction seemed to occur between factors area and typsurv2. The three factors and their 1-order interactions were tested by Only factor area was significant. The final estimates are given by

Summary tables

Results of the estimates of the average CENV parameters and of the percentages of betweenyears variations are summarized in Table 3 and Erreur ! Source du renvoi introuvable. for natural rates and herd structures respectively.

1 .

 1 Introduction ........................................................................................................................................................................ 2. Material and methods.................................................................................................................................................... 2.1.1. Collection of demographic parameters ............................................................................................. 2.1.2. Meta-analysis .................................................................................................................................................. 3. Results ................................................................................................................................................................................... 3.1. Parturition.................................................................................................................................................................. 3.1.1. Cattle .................................................................................................................................................................... 3.1.2. Small ruminants............................................................................................................................................. 3.2. Net prolificacy .......................................................................................................................................................... 3.2.1. Small ruminants............................................................................................................................................. 3.3. Mortality ..................................................................................................................................................................... 3.3.1. Cattle .................................................................................................................................................................... 3.3.2. Small ruminants........................................................................................................................................... 3.4. Herd structure ....................................................................................................................................................... 3.4.1. Proportion of females in the herd ...................................................................................................... 3.4.2. Proportion of reproductive females in the herd ......................................................................... 4. Summary tables .............................................................................................................................................................. 5. Bibliography ..................................................................................................................................................................... 6. Annex ................................................................................................................................................................................... 6.1. Sources used for the literature review (meta-analysis) ..................................................................

Figure 4 :

 4 Figure 4: Empirical averages of the net prolificacy rate for small ruminants.

Figure 5 :

 5 Figure 5: Empirical averages of the mortality rate for cattle (/100 animal-years).

Figure 7 :

 7 Figure 7: Empirical averages of the percentage of females in the herds (F_tot) for cattle.

Figure 8 :

 8 Figure 8: Empirical averages of the percentage of females in the herds (F_tot) for small ruminants .

Figure 9 :

 9 Figure 9: Empirical averages of the percentage of reproductive females in the herds (F_A) for cattle.

Figure 10 :

 10 Figure 10: Empirical averages of the percentage of reproductive females in the herds (F_A) for small ruminants.

  Several Excel files have been provided to the World Bank study in complement of this note, namely:  dryland_west_central_africa_demog.xlsx, which details the demographic parameters collected in the literature and which describe the context of the study for each data reported: location of the study area, type of the survey carried out, type of parameter considered, literature source, etc.

	 dryland_west_central_africa_weights_milk.xlsx (same as above but for live
	weights and milk production rates)
	 summary_param_dryland_west_central_africa.xlsx; which does a comprehensive
	summary of the average parameters values used as input for the demographic model
	calculating livestock productions.

Table 2 : Examples of secondary demographic rates derived from the basic rates in Table 1.

 2

	Reproductive females
	(1) Abortion	(2) Parturition
	rate	rate
	Abortions	Parturitions
		Births
	 Single
	 Twin		(3) Prolificacy
			rate
	 Triplet
	 etc.
			(4) Stillbirth rate
	Born alive	Stillborn
	 Females	(5) Rate of
		females at
	 Males	birth
	(8) Intake rate
	Intakes
			(6) Mortality	(7) Offtake
			rate	rate
	Survivals	Natural	Offtake
			deaths

a A female is considered as "reproductive" when it is older than a given age.

Table Response

 Response

	: rate
		Df Sum Sq Mean Sq F value Pr(>F)
	typsurv2	1 140.03 140.028 6.2278 0.02389 *
	Residuals 16 359.75 22.484

Table Response

 Response As expected from Figure5, only factor agecla2 was significant. The non-significancy of typsurv2 enabled to gather data ABM3+ and OTHER to test factors agecla2 and area (without accounting for factor typsurv2), as follows

	: h_y
		Df Sum Sq Mean Sq F value	Pr(>F)
	agecla2	2 2959.59 1479.79 29.1430 9.299e-08 ***
	typsurv2	1	0.38	0.38 0.0075	0.9315
	agecla2:typsurv2 2	12.13	6.07 0.1195	0.8878
	Residuals	30 1523.31	50.78
	u <-x
	fm <-lm(h_y ~ (agecla2 + area)^2, data = u)
	anova(fm)
	Analysis of Variance Table
	Response: h_y
		Df Sum Sq Mean Sq F value	Pr(>F)
	agecla2	2 3168.9 1584.44 39.7350 2.062e-10 ***
	area	1 159.0 159.03 3.9882	0.05233 .
	agecla2:area 2 131.2	65.58 1.6445	0.20530
	Residuals	42 1674.8	39.88

Table Response

 Response Only factors agecla2 and area were significant. The final estimates were given by

	fm <-lm(h_y ~ agecla2 + area, data = u)
	res <-fpredict(fm, data = u, digits = 0)
	res
	agecla2 area fit lwr upr pct.u
	1 JUV/SAD	A 25 19 31	24
	2	ADU	A	9	0 18	100
	3 JUV/SAD	SA 33 26 40	21
	4	ADU	SA 17	6 27	59
							A	SA
						CA	CA
					JUV/SAD	ADU
				40
				30
				20
				10			ABM3+
			h_y		JUV/SAD OV	ADU OV	OTHER
							40
							30
							20
							10
					A	SA
						area
		: h_y
				Df Sum Sq Mean Sq F value	Pr(>F)
	agecla2		1 5874.8 5874.8 25.9253 5.412e-06 ***
	species		1	14.0	14.0 0.0620	0.80443
	area			1	68.4	68.4 0.3017	0.58529
	typsurv2		1	526.7	526.7 2.3242	0.13368
	agecla2:species	1	55.0	55.0 0.2428	0.62436
	agecla2:area		1	7.9	7.9 0.0349	0.85256
	agecla2:typsurv2 1	182.5	182.5 0.8052	0.37384
	species:area		1	70.3	70.3 0.3101	0.58009
	species:typsurv2 1	3.8	3.8 0.0166	0.89791
	area:typsurv2	1 1068.0 1068.0 4.7132	0.03471 *
	Residuals		50 11330.3	226.6
	A priority was given to data ABM3+. The analysis selected data ABM3+ and re-tested factors
	agecla2, species and area
	u <-x[x$typsurv2 == "ABM3+", ]
	fm <-lm(h_y ~ (agecla2 + area + species)^2, data = u)
	anova(fm)
	Analysis of Variance Table
	Response: h_y
				Df Sum Sq Mean Sq F value	Pr(>F)
	agecla2		1 1264.31 1264.31 11.4372 0.003322 **
	area			1 356.53 356.53 3.2252 0.089318 .
	species		1	51.22	51.22 0.4633 0.504744
	agecla2:area		1	56.89	56.89 0.5147 0.482329
	agecla2:species 1	51.18	51.18 0.4630 0.504875
	area:species		1	6.50	6.50 0.0588 0.811162
	Residuals		18 1989.78 110.54

Table Response

 Response

	: F_tot
		Df Sum Sq Mean Sq F value Pr(>F)
	typsurv2	1	2.84	2.844 0.0226 0.8841
	Residuals 8 1005.56 125.694

Table Response

 Response

					BO
					68
				F_tot	66	Type survey ABM3+ OTHER
					64
					62
					A	SA
					area
		: F_tot
		Df Sum Sq Mean Sq F value Pr(>F)
	area	1	72.6	72.60 0.6562 0.4368
	Residuals 10 1106.4 110.64

  The non-significancy of typsurv2 enabled to gather data ABM3+ and OTHER to test factor area (without accounting for factor typsurv2), as follows

	u <-x[x$area == "A", ]
	fm <-lm(F_A ~ typsurv2, data = u)
	anova(fm)
	Analysis of Variance Table
	Response: F_A
		Df Sum Sq Mean Sq F value Pr(>F)
	typsurv2	1	14 14.000 0.3818 0.5593
	Residuals 6	220 36.667
	u <-x
	fm <-lm(F_A ~ area, data = u)
	anova(fm)
	Analysis of Variance Table
	Response: F_A
		Df Sum Sq Mean Sq F value Pr(>F)
	area	1	3.6	3.60 0.0941 0.7668
	Residuals 8 306.0	38.25

Table 3 : Summary of the average estimates and percentages of statistical uncertainty affecting the estimates (from literature review over areas A and SA of West-and Central Africa). (a) Natural rates, (b) Simplified herd structure.

 3

	(a)

https://openknowledge.worldbank.org/handle/10986/23576

http://documents.worldbank.org/curated/en/485591478523698174/Prospects-for-livestock-basedlivelihoods-in-Africa-s-drylands