Franc ¸ois Gardes
email: francois.gardes@univ-paris1.fr.

A Method to infer time preference from the value of time

Keywords: Time Allocation, Inter-temporal substitution rate, psychological rate of interest, Opportunity cost of time. JEL: D31, J22

Using a generalization of Becker's time allocation model in order to estimate the shadow price of time, we explore the relationship between the inter-temporal substitution rate and the opportunity cost of time, allowing the endogenization of the time preference from the estimation of the value of time.

Introduction

Actualizing the future supposes the definition of an intertemporal substitution rate (ITSR) which is generally calibrated by reference to the capital market or to an anticipated rate of return for public investments when considering public expenditures. That actualization rate is often fixed at the average long term growth rate of the economy (see the discussion in Sunstein, 2014, pp. 62-63). Independently from this intertemporal rate, households value their disposable time by some opportunity cost of time which influences their decisions for market work and domestic production. A natural idea is that there may exist some relationship between these valuations of present and future time, but it seems that no model exists up to now exploring that link. It can be expected that an exogenous increase of the value of time may accelerate monetary expenses by way of substitution with time use in home production, which could develop the preference for present money over future money, thus increasing the psychological rate of interest. This article explores a relationship between these parameters based on the assumption of a constant household's permanent wealth. Other possible ways to define this relation, either considering the saving and present consumption decisions, or by means of the utility changes attached to postponing some expenditure, are discussed in [START_REF] Gardes | Infering Time Preference from the Value of Time: three models[END_REF].

In order to estimate the opportunity cost of time, I use a home production model (presented in Appendix A) where the consumer combines time with market goods to produce activities that generate utility. Utility maximization implies that the value of time is given by the ratio of the marginal utility of time over the marginal utility of income. Previous papers [START_REF] Gardes | On the Value of Time and Human Life[END_REF][START_REF] Gardes | The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application Using French Micro-Data[END_REF][START_REF] Canelas | Are Time and Money Equally Substitutable for All Commodity Groups in the Households Domestic Production?[END_REF] show that this ratio can be structurally estimated at the individual level provided that data on households' time and monetary expenditures are available.

To overcome the lack of this type of data, I combine, using a statistical matching procedure described in Appendix B, a french survey on household expenditures with a survey on time use made in the same year (2000).

Section 1 describes the estimation of the opportunity cost of time while section 2 presents the relation between the intertemporal rate and the opportunity cost of time. Section 3 applies the model to the french dataset.

I Estimation of the proportion of substituable choresTwo indicators of full income

Two indicators of full income

The usual full income concept y f 0 is the maximum monetary income which could be earned when working during all disposable time T, valued at the market wage rate net of taxes W:

y f 0 = W T +V.
(1)

with V other incomes unrelated to market work (financial revenues, social distribution...).

Another indicator of household's full resources, adding the opportunity cost of domestic production to monetary income from market work and other sources, can be defined, first valuing the time used in home production by the estimated opportunity cost and second, considering that only a part of domestic production could be afforded by market goods and services. The non-substituable component of domestic production (speaking with one's spouse for instance)

would not be added to the full estimate of household's resources. Indicating by π i the proportion of home product i which can be replaced by a market product or service, this indicator of full resources writes:

y f = Wt w +V + ω ∑ π i t i .
(2)

The next section proposes a method to calculate these proportions π i .

Substituable chores

Chores (domestic dayly works) are generally defined as the minimum amount of home production the value of which could be added to the value of the agent's production working on the labor market. Pure leisure activity would for instance be excluded. Home production related to food would be considered as a chore only if it corresponds to the normal amount of food for a typical similar agent, the individual surplus of a given agent being considered as linked to its particular constraints or preferences to be excluded from the chores. But this minimum amount is difficult to estimate, either directly on a survey (choosing for instance the first tercile of the distribution of time use for food among similar individuals) or by estimation of a demand system such as the Linear Expenditures System.

I propose a new method estimating the proportion of time devoted to some home activity which can be considered as a chore, by means of the degree of substitution with market alternative goods or services: the value of chores for a given domestic production (for instance of transport) is the cost to acquire a substitute on the market. The integration of that value in the market production thus proceeds from the possibility to obtain the same final good on the market at a given price which is attributed to that component of the domestic production.

This requires that the elasticity of substitution between market factors of production and time must be large, so that it is possible to produce the same amount of final good with these market factors substituted to time use.

Suppose that the domestic production of some final good i is divided between 'substituable' chores 1 produced under possible substituability with market goods or services (supposed to be governed by a unitary elasticity of substitution between monetary and time inputs, corresponding to a Cobb-Douglas domestic production function: : El t i,1 /ω = 1) and non-substituable chores 2 characterized by a zero elasticity of substitution with market goods (

δ [(t i,1 )/m i ] δ (ω) = 0).
The same division applies to the total time devoted to the home production of the final good:

t i = t i,1 + t i,2
, with t i,1 and t i,2 the times spent in substituable (respectively non-substituable) home work producing the final good i. The elasticity of substitution of the aggregate time t i over the opportunity cost of time ω writes, with m i the expenditure made for market goods and services used producing the final good:

σ i = δ [(ti,1+ti,2)/mi] δ (ω) [(t i,1 + t i,2 )/m i ] /ω = δ [ti,1/mi] δ (ω) (t i,1 /m i )/ω t i,1 (t i,1 + t i,2 ) = σ i,1 t i,1 t i,1 + t i,2 = - t i,1 t i,1 + t i,2 = -π i (3)
The proportion of chores in this domestic activity can then be measured by the absolute value of the elasticity of substitution of the aggregate, the absolute value of which is smaller than one for all activities in our french dataset : 0.36 for food, 0.30 for clothing, 0.66 for leisure activities, 0.30 for All Other activities (see [START_REF] Canelas | Are Time and Money Equally Substitutable for All Commodity Groups in the Households Domestic Production?[END_REF]. The total value of chores v i in each domestic activity will be calculated by means of these elasticities of substitution and added to the monetary value of expenditures made to produce the corresponding final good:

v i = ω i .t i,1 = |σ i |.ω i .t i .
A generalization to the case of multiple components of chores with different elasticities of substitution is straightforward.

The household's full resources are therefore the sum of monetary income and of that component of substituable chores valued by the estimated opportunity cost of the household:

y f = Wt w +V -ω ∑ σ i t i = Wt w +V + ω|σ |(T -t w ) (4)
with σ the weighted average (weighted by the time budget shares) of the elasticities of substitution σ i . The permanent income is estimated at the households' level, then aggregated over the population.

II Relating time preference to the value of time

A natural relation between ρ and ω can be extracted from their complementary relations with the household's saving rate, since the value of time impacts the household's consumption and labor income, while the rate of interest impacts its saving rate. In this first model, the household's time preference determines its saving rate, while the value of time is correlated with its expenditures, so that it could be possible to establish a relationship between them equalizing the values of its household's savings depending on these two variables. The calculus implies a positive relationship between the intertemporal rate and the value of time. This model relies on

the assumption that the decision to save part of income is taken in relation with an interest rate independently from the marginal propensity to consume, which is a heroic hypothesis whence it applies to one agent (while it is more naturally applied to aggregates in the simple keynesian model). Another way to obtain a relation between ρ and ω relies on the maximization of a utility depending both on monetary and time expenditures, but this needs specifying a particular utility and estimating its coefficients 1 .

The more general method we propose relies on the assumption that the ITSR and the opportunity cost of time both influence the present value of the household's permanent full income (equal to the discounted sum of all future full incomes y f 2 ). Following the assumption made in the permanent income theory, the present value of the stream of future full incomes is supposed to remain constant over the household's life cycle, in spite of changes in the opportunity cost of time due to age, family structure or income. This supposes that the inter-temporal rate of substitution varies accordingly to the opportunity cost of time in order to maintain the permanent income constant through the life cycle, in spite of changes in the opportunity cost of time due to age, family structure or income (all being supposed to be anticipated by the household). Therefore, it is possible to calculate the change between two consecutive periods of the intertemporal rate of substitution which corresponds to a change in the opportunity cost of time. The present value of the permanent income stream can be written for the full income flow y f and an ISTR ρ:

v y f = y f t exp (-ρt) dt (5)
The derivative over ω of this integral equals, under usual conditions, the integral of the derivative of the full income y f , which is, with ρ depending on ω:

φ = ∂ y f ∂ ω = W ∂t W ∂ ω + (T -t W ) -ω ∂t W ∂ ω = W ω -1 Etw ω + ∑ |σ i |t i (6)
The integration over time (from 0 to infinity 3 ) of this derivative is equal to zero since permanent full income remains constant:

1 The calculus for these methods are presented in Gardes, 2021b.

2 A model restricted to two periods is presented in Gardes, 2021b. 3 Households are supposed to leave their permanent wealth to their inheritants. Considering the life cycle from birth to age T multiplies the derivative of ρ over ω by the fraction exp(-ρT )-1 ρ exp(-ρT ) T + 1 ρ -1 which is for instance 0.925 for ρ = 5% and T=80 years (corresponding to the average life duration in developed countries) or 0.418 for T=20 (corresponding to an evaluation at age 60 till 80).

6 Documents de travail du Centre d'Economie de la Sorbonne -2021.19

∂ y f t ∂ ω exp (-ρt) dt = φ ρ -y f t 1 ρ 2 ∂ ρ ∂ ω = 0 (7)
Under the assumption that the household's permanent income does not change for corresponding changes of the intertemporal rate and the opportunity cost (dρ, dω), the marginal propensity and the elasticity of the ITSR over the opportunity cost of time are:

∂ ρ ∂ ω = W ω -1 t W Elt W ω + ∑ |σ i |t i Wt W +V + ω ∑ |σ i |t i ρ (8) El ρ ω = (W -ω)t W Elt W ω + ω ∑ |σ i |t i Wt W +V + ω ∑ |σ i |t i (9)
Therefore, the ISTR increases with the opportunity cost of time with an elasticity positive and smaller than 1 whence V ≥ 0, Elt W ω ≤ 1 and W ≥ ω. It may vary between households, which implies different intertemporal rates across the population, and may depend on macroeconomic conditions changing the households' wage rates, their opportunity cost of time, the allocation of time between market work and home production and the elasticity of market work supply.

III Empirical Results

The only parameter which must be estimated in equations ( 11) and ( 12) is the elasticity of market labor over the opportunity cost. Market labor time can be considered as the residual of domestic production time over the total disposable time T (supposed to be exogenous), so that this elasticity can be estimated by means of the elasticities of domestic production times t i over the opportunity cost of time ω. Estimation of that elasticity of the market labor time using the french dataset [START_REF] Gardes | Labor Supply, Consumption and Domestic Production, w.p. CES 2014[END_REF]

IV Conclusion

This paper provides an estimate of the intertemporal substitution rate depending on the value of time experienced by the household. This relation serves as an endogeneisation of the psychological intertemporal rate which is generally supposed to be the same for all households and which is calibrated at an a priori amount which is rarely justified by some reasoning. It gives also a microeconomic explanation of the level of the primary interest rate central to the austrian school (see von Mises, 1949, chapters 18 and 19) and articles by Garrison, Fetter, Herbener, Kirzner and Rothbard in Herbener ed., 2011). The empirical analysis of individual data shows that this psychological rate of interest is positively correlated to the value of time, depends on the elasticity of market labor over the value of time and varies significantly across the population. This relationship between time preference and the value of time have been used in Gardes (2021a) in order to estimate an enlarged GDP including domestic production and to discuss the Austrian trade cycle theory [START_REF] Gardes | An Austrian Trade Cycle model with an Endogenous Value of Time[END_REF] Appendix A: Estimation of the opportunity cost of time7

In order to estimate the shadow price of time, I assume that the consumer combines time with monetary expenditures to produce activities that generate utility in a model where the market working time is valued by the consumer's wage rate while the remaining time (e.g., time allocated to leisure or non-market work) is valued by a shadow price of time that may differ from the wage rate. It is assumed that the consumer's utility function is given by u(z) = ∏ i a i z

γ i i
where a i is a positive parameter and z i is the quantity of the activity i produced by the combination of monetary and time inputs denoted m i and t i , respectively:

z i = b i m α i i t β i
i where m i = x i p i with x i the quantity of the market goods i, p i its monetary price, and b i a positive parameter8 .

Contrary to the complementarity structure of domestic production functions in Becker's model of the allocation of time (1965), the choice of the Cobb-Douglas forms allows the parameters to be identifiable assuming that α i + β i = 1 (no economy of scale in the domestic productions). As we estimate the parameters locally (i.e., for each observation in the dataset), Combining the utility and the production functions allows to write the utility in terms of inputs:

u(m,t) = Π i (a i b γ i i ) ∏ i m α i γ i ∑ α i γ i i ∑ α i γ i ∏ i t β i γ i ∑ β i γ i i ∑ β i γ i (10) = A m ∑ αγ i t ∑ β i γ i (11)
where m and t are geometric weighted means of the monetary and time inputs and A ≡ Π i a i b

γ i i .
In this framework, the consumer is subject to an income constraint, ∑ m i = wt w +V ≡ Y , and to a time constraint, ∑ i t i + t w = T , where V is other income, t w is the time allocated to market work and T total disposable time9 . Utility maximization implies that the shadow price of time, denoted ω, is given by:

ω = ∂ u ∂t ∂t ∂ (∑t i ) ∂ u ∂ m ∂ m ∂Y = m ∑ β i γ i ∂t ∂ (∑t i ) t ∑ α i γ i ∂ m ∂Y (12)
The shadow price of time differs from the market wage rate when, for instance, there exist some market imperfections, transaction costs, and constraints on the labor market or in the home sector. The shadow price of time can be estimated provided that estimates of α i , β i , and γ i are available, which is obtained considering the substitutions between monetary and time expenditures in the production of each final goods and by the substitution of time or money between activities (see details in Gardes 2019). ): marginal propensity (respectively elasticity) of the intertemporal rate of substitution over the value of time using estimates in [START_REF] Canelas | Are Time and Money Equally Substitutable for All Commodity Groups in the Households Domestic Production?[END_REF]. [START_REF] Gronau | Time vs. Goods: the Value of Measuring Production Technologies[END_REF] we obtain similar patterns of what these authors call "relative goods/time intensity" defined as a ratio of good to time inputs relative to total amount of goods and time allocated to the production of final goods. (such as education level and the age of the head, the family demographic structure and location) for all observation units in the FTB survey and these estimations serve to predict the time spent on these activities for the corresponding units in the FES survey.

the

  Cobb-Douglas specifications imply simply constant substitution between time and monetary resources only in the neighborhood of each individual's equilibrium point. As discussed in Gardes (2019), the Cobb-Douglas specification allows identifying a unique shadow price of time for all activities while a more general model based on CES household production functions allows identifying activity-specific shadow prices of time together with an average value of domestic time.

The

  French dataset from INSEE combines at the individual level the monetary and time expenditures into a common, unique goods and services consumption structure by a statistical match of the information contained in two surveys: the Family Expenditure Survey (FES, INSEE BDF 2001) and the Family Time Budget (FTB, INSEE BDT 1999). I define 8 types of activities or time use types compatible with the available data both from FES and BDT: Eating and cooking time (FTB) and food consumption (FES), cleaning and home maintenance and dwelling expenditures (including imputed rent), clothing maintenance and clothing expenditures, education time and education expenditures, health care time and health expenditures, leisure time and leisure expenditures, transport time and transport expenditures, miscellaneous time use and miscellaneous goods and services. Time uses for all selected activities are regressed on households' characteristics using common covariates observed in the two surveys

Table 1

 1 provides an estimate 0.861 for the whole population, with significant changes for different sub-populations, as indicated in Gardes and Margolis, Table1. A direct estimation of the regression between T -∑ti and ρ, reported in

, gives positive but smaller estimates which are more in line with the usual estimations of the elasticity of market work over the wage rate. These estimations are used in the calculus

TABLE 1

 1 Derivative of ρ over ω and Elasticity

		ω	El t W ω	∂ ρ ∂ ω	ω El ρ	ρ5 th (%)	ρ95 th (%)
	Whole Population	6.23	0.281	0.00221	0.246	4.26	5.74
	s.e.	2.02	0.017	0.00197	0.171	-	-
	Singles	5.82	0.093	0.00184	0.184	4.53	5.47
	s.e.	1.56	0.035	0.00145	0.126	-	-
	Couples without children	6.23	0.213	0.00222	0.265	4.14	5.86
	s.e.	2.36	0.027	0.00179	0.148	-	-
	Couples with children	6.62	0.356	0.00279	0.338	3.77	6.23
	s.e.	1.87	0.031	0.00143	0.126	-	-
	Age till 35	6.02	0.413	0.00174	0.194	4.50	5.50
	s.e.	1.73	0.036	0.00329	0.307	-	-
	Age 36-55	6.46	0.268	0.00223	0.250	4.16	5.84
	s.e.	2.30	0.019	0.00157	0.122	-	-
	Age after 56	6.09	0.127	0.00321	0.358	4.04	5.86
	s.e.	1.81	0.065	0.00203	0.182	-	-

Note: Bootstrap standard errors. Direct estimation of El t W ω on the dataset. ρ5 th : estimate of ρ in the fifth quintile of the income distribution.

TABLE 2

 2

			Descriptive statistics
		σ food	σ non-food	El t W	t food	t non-food	t w	W
				ω
	Whole Population	0.620	0.692	0.861	31.0	101.1	56.3	10.13
	s.e.	0.017	0.009	0.0038	13.6	32.4	24.9	15.87
	Singles	0.685	0.741	1.336	18.1	67.6	38.5	9.04
	s.e.	0.047	0.023	0.0116	7.1	15.6	13.3	5.80
	Couples without children	0.558	0.644	1.043	39.1	122.4	59.5	10.92
	s.e.	0.022	0.011	0.0096	13.5	29.7	26.1	22.35
	Couples with children	0.905	1.097	0.590	33.3	106.4	62.5	10.10
	s.e.	0.034	0.017	0.064	8.4	18.9	24.3	13.6
	Age till 35	0.619	0.902	-	21.4	91.3	57.4	7.72
	s.e.	0.063	0.030	-	9.9	28.5	24.3	3.77
	Age 36-55	0.596	0.711	-	29.6	93.0	57.4	10.67
	s.e.	0.023	0.012	-	11.1	27.3	24.5	10.8
	Age after 56	0.764	0.768	-	37.9	115.4	46.8	13.64
	s.e.	0.029	0.014	-	14.23	34.37	26.5	39.88

Note: σ : elasticity of substitution between monetary expenditures and time uses; t:time use per week; t w : market work time; W: household's average wage rate; El t W ω : elasticity of the labor supply over the opportunity cost of time; ∂ ρ ∂ ω (respectively El ρ ω

Documents de travail du Centre d'Economie de la Sorbonne -2021.19

Estimates using the higher elasticities of market work obtained by the indirect method based on domestic work in Gardes and Margolis are not so different.

In this estimation, the domestic times are reduced by a factor |σ i | which measures the component in the domestic activity i which can be substituted to market goods and services as discussed in the previous sub-section. Computed on total domestic times, the corresponding ∂ ρ ∂ ω = 0.00559(0.00237) is doubled.

 6 This can be explained by the different time budget constraints of these households' types. 8 Documents de travail du Centre d'Economie de laSorbonne -2021.19

From Gardes, 2019.

z is assumed to depend on m (rather than x) because the dataset informs only expenditures. This approach yields consistent results when all households face the same prices. 10 Documents de travail du Centre d'Economie de laSorbonne -2021.19

Excluding sleeping time, although, as remarked by[START_REF] Aguiar | Measuring Trends in Leisure: The Allocation of Time over Five Decades[END_REF], sleeping time is in fact a choice variable over which individuals optimize. Sleeping time is generally excluded from domestic and leisure time in the time use literature.11 Documents de travail du Centre d'Economie de laSorbonne -2021.19

of the marginal propensity and the elasticity of ρ over ω 4 On the french dataset, equation ( 11) gives a derivative of ρ over ω equal to 0.00221 for the whole population and an elasticity El ρ ω = 0.246 5 . It can be concluded that the intertemporal rate of substitution ρ increases with the opportunity cost of time ω, with an elasticity which is smaller than one. These parameters change a lot on sub-populations : results in Table 1, in accordance with other studies [START_REF] Gardes | The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application Using French Micro-Data[END_REF](Gardes, , 2020)), show that the opportunity cost of time is greater for households having a more constrained time budget (families with children, middle aged households) and much smaller for singles 6 . The elasticity of market work over the opportunity cost of time diminishes with age and is larger for families with children, while the elasticity of the inter-temporal rate of substitution over the opportunity cost of time increases with age and the presence of children and is one half smaller for singles compared to families with children. This shows that the effect of the value of domestic time over the rate of substitution differs much across the population. The resulting change of the inter-temporal substitution rate due to income (in the cross-section dimension) is a relative increase by one third to two thirds from the 5th centile to the 95th centile of the income distribution (for instance from 3.77% to 6.23% for families with children, which corresponds to a cumulated actualized full income over the life cycle equal to 26.5 times the yearly income for 3.77% and only 16.0 for 6.23%). Therefore, the increase of yearly full income has a proportional positive direct effect on the cumulated income over the life cycle, but also a negative indirect effect through the increase of the inter-temporal substitution rate: for instance, an increase of yearly income (over the whole life cycle) by +10% increases the ISTR supposed at its mean 5%) by 0.114% , which implies a reduced total positive effect +7.7%.

Appendix B: Datasets

In order to dispose of households' monetary expenditures and time uses, I use a French dataset from INSEE which combines at the individual level the monetary and time expenditures into a common, unique goods and services consumption structure by a statistical match of the information contained in two surveys: the Family Expenditure Survey (FES, INSEE BDF 2001) and the Family Time Budget (FTB, INSEE BDT 1999).

The definition of comparable good and time groups of expenditure is a difficult and sometimes arbitrary operation. This rather difficult exercise needs some arbitrary assumptions about the substitution between time use and monetary expenditures (see [START_REF] Gronau | Time vs. Goods: the Value of Measuring Production Technologies[END_REF] for a discussion). The commodity consumption structure does not correspond exactly to what is often used as a standard classification of time uses even if differences can be limited. The reason is that not all time use activities can have a clear work equivalent. This is particularly the case of the leisure time. However, comparing our classification with other similar approaches


Rialy Andriamiseza
email: rialy.andriamiseza@irit.fr

Franck Silvestre
email: franck.silvestre@irit.fr

Jean-François Parmentier
email: jf.parmentier@gmail.com

Julien Broisin
email: julien.broisin@irit.fr

Data-informed Decision-Making in TEFA Processes: An Empirical Study of a Process Derived from Peer-Instruction

Keywords: technology-enhanced formative assessment, learning analytics, peer instruction, decision-making CCS Concepts

When formative assessment involves a large number of learners, Technology-Enhanced Formative Assessments are one of the most popular solutions. However, current TEFA processes lack data-informed decision-making. By analyzing a dataset gathered from a formative assessment tool, we provide evidence about how to improve decision-making in processes that ask learners to answer the same question before and after a confrontation with peers. Our results suggest that learners' understanding increases when the proportion of correct answers before the confrontation is close to 50%, or when learners consistently rate peers' rationales. Furthermore, peer ratings are more consistent when learners' confidence degrees are consistent. These results led us to design a decision-making model whose benefits will be studied in future works.

INTRODUCTION

To address formative assessment challenges and the growing number of students in higher education, Technology-Enhanced Formative Assessment (TEFA) and its interactive response systems emerged.

Such systems implement different processes allowing teachers to conduct formative assessment sequences. Among them, a group of processes, namely the "two-votes-based processes", requires learners to provide an answer before and after a confrontation with peers. However, these various processes lack evidence to help teachers make decisions depending on learners' behavior. In this paper, we address the following research question: Which meaningful information for teachers can be inferred from the analysis of data gathered from a tool implementing a two-votes-based process, to improve decision-making in face-to-face formative assessment sequences? We tackle this question by (i) identifying hypotheses based on literature, and (ii) applying various data mining techniques to evaluate these hypotheses and infer relevant information about decision-making in formative assessment sequences.

RELATED WORKS

Formative assessment

Formative assessment aims to improve learning by providing teachers and students with feedback designed to help them adapt their behavior. In 1998, Black and William defined formative assessment as: "All those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged" [START_REF] Black | Assessment and Classroom Learning[END_REF]. This definition highlights the importance of collecting data in order to make decisions during teaching. However, Ellis emphasized the difficulty of capturing learning interactions in a face-to-face context [START_REF] Ellis | Broadening the scope and increasing the usefulness of learning analytics: The case for assessment analytics[END_REF], especially when the number of learners increases. Collecting and analysing interaction data make learning analytics a relevant field for formative assessment. More precisely, the involvement of technology is needed so as to effectively capture learning interactions and thus help teachers conduct a formative assessment sequence.

Technology-Enhanced Formative Assessment

TEFA is one of the emerging solutions for delivering formative assessment with immediate feedback [START_REF] Michael Spector | Technology enhanced formative assessment for 21st century learning[END_REF]. Since questioning an audience enters in the frame of formative assessment [START_REF] Black | Assessment and Classroom Learning[END_REF], Classroom Response Systems (CRS) are the most commonly used systems supporting TEFA in face-to-face context. A generic formative assessment process of CRS is implemented by web-based platforms such as Poll Everywhere [START_REF] Clark | Enhancing Active Learning: Assessment of Poll Everywhere in the Classroom[END_REF] which simply allows teachers to ask a question, and learners to vote for the correct answer(s). Histograms are then immediately displayed as feedback in order to help teachers and learners engage in a debriefing phase. A richer formative assessment process implemented by ComPAIR [START_REF] Potter | ComPAIR: A new online tool using adaptive comparative judgement to support learning with peer feedback[END_REF] lets teachers ask openended question, while learners provide textual answers. Afterwards, learners engage in a peer review loop. Elaastic [START_REF] Silvestre | Reflexive learning, socio-cognitive conflict and peer-assessment to improve the quality of feedbacks in online tests[END_REF] and myDalite [START_REF] Charles | Harnessing peer instruction in-and out-of class with myDALITE[END_REF] offer even richer processes with even more interactions. Both systems stand on Mazurs' Peer Instruction [START_REF] Catherine | Peer instruction: Ten years of experience and results[END_REF] and implement a two-votes-based process illustrated in Figure 1. More precisely, they ask user to answer an exclusive choice question and to provide a textual justification (also called rationale). However, when it comes to step 3 and 4, Elaastic engages learners in a peer rating phase before they submit their second answers. Even though quantitative studies [START_REF] Mazur | Just-in-time teaching and peer instruction[END_REF][START_REF] Parmentier | How to quantify the efficiency of a pedagogical intervention with a single question[END_REF][START_REF] Tullis | Why does peer instruction benefit student learning?[END_REF] and the ICAP framework [START_REF] Michelene | The ICAP Framework: Linking Cognitive Engagement to Active Learning Outcomes[END_REF] emphasized the benefits of such interactivityrich processes , these 5 phases might not always be the best choice to orchestrate the sequence. Alternative options should be considered by teachers depending on learners' behavior and understanding.. To the best of our knowledge, Mazur's recommendation to skip phases 3 and 4 when less than 30% or more than 70% of learners' first answers are correct [START_REF] Mazur | Just-in-time teaching and peer instruction[END_REF] is the only recommendation that can be found in literature (with few variations [START_REF] Vickrey | Research-Based Implementation of Peer Instruction: A Literature Review[END_REF][START_REF] Lasry | Peer instruction: From Harvard to the two-year college[END_REF][START_REF] Catherine | Peer instruction: Ten years of experience and results[END_REF]). On the basis of a dataset gathered from an authentic usage of Elaastic in higher education from 2015 to 2019, the remaining of the paper explores which information can be used to help teachers driving a FA sequence.

CONTENT OF THE DATASET

With Elaastic, a sequence is characterised by a learning context (i.e. face-to-face, distant or hybrid), learners' answers for the first and second votes, as well as the number of participants. For each answer, the following data are collected: the learner's identifier, the content of the rationale, the score and the selected choice(s) when applicable. If the answer is a first vote, it is characterised by additional data such as the mean level of agreement of peers (self-reported on a 5-items Likert scale) to the rationale, and the confidence degree of the learner who provided the answer (self-reported on a 4-items Likert scale). Questions are described by their statement and their type (e.g. open ended, multiple-or exclusive-choice). Finally, for each evaluation resulting from the confrontation phase, the following data are collected: the rated rationale, the identifier of the rater, and the rate she assigned.

Data Analysis

The whole dataset has been filtered in order to keep only relevant data for our study. First, we only considered choice questions so as to evaluate correctness of answers. In order to classify an answer as right or wrong, we considered answers as incorrect if the score is lower than the maximum score that can be obtained (i.e. 100). Then we removed sequences with less than 10 participants because we wanted to focus on larger settings. Finally, we considered the variables p1 and p2 which are the proportion of learners who answered correctly at the first and second vote respectively. Sequences where p1 = 0 were removed (since there is no rationales for correct answers to convince incorrect peers) as well as sequences where p1 = 1 or p2 = 1 (as they point out questions that were too easy to measure an impact). We finally obtained 104 sequences conducted by 21 teachers where 616 learners provided 1981 answers and performed 4072 peer ratings. Even though this sample doesn't follow a normal distribution, it is large enough to conduct analysis with parametric tests [START_REF] Ghasemi | Normality tests for statistical analysis: a guide for non-statisticians[END_REF].

Benefits of formative assessment sequences increase when the proportion of correct answers is close to 50%

Based on Mazur's statement about the proportion of correct answers [START_REF] Mazur | Just-in-time teaching and peer instruction[END_REF], we make the hypothesis that sequence benefits increase as the distance between p1 and 50% decreases. In order to verify this hypothesis, we measured the effect size between the first and second votes. To this end, we used the estimation of Cohen's effect size d proposed by Parmentier [START_REF] Parmentier | How to quantify the efficiency of a pedagogical intervention with a single question[END_REF] and calculated as follows:

d = 0.6ln p2 1-p2 1-p1 p1
. Based on this estimation, we define sequences as beneficial when d > 0 (which implies that p1 < p2) because it means that students understanding of the topic has been enhanced [START_REF] Tullis | Why does peer instruction benefit student learning?[END_REF]. As suggested by Figure 2, the mean effect size decreases when the distance between p1 and 50% increases. The calculated Pearson correlation between |p1 -0.5| and d is -0.31 with a p-value equal to .001 and a 95% confidence interval equal to [-0.48:-0.13], which supports our hypothesis.

Based on our results, the recommended interval for p1 should be [20%-80%] because when p1's distance from 50% is L@Scale Works-in-Progress L@S'21, June 22-25, 2021, Virtual Event, Germany greater than 30%, the effect size is significantly lower (< 0.2).

1 Recommendations: If there are too few correct answers (p1 < 20%) teachers should provide detailed explanations and restart the sequence, or provide hints before peer interactions. If there are enough correct answers (20% ≤ p1 ≤ 80%), learners can engage in a peer interaction phase. Else (p1 > 80%), teachers can provide brief explanations and end the sequence.

Furthermore, the effect size d serves as a good indicator to determine how well learners understood the topic and how detailed teachers' explanation should be.

2 Recommendation: After the second vote, teachers explanation should be more detailed if the proportion of correct answers did not increase (d ≤ 0).

Benefits of formative assessment sequences increase

when learners consistently rate peers' rationales Double and al. argue that reflecting on peers answers is expected to lead to a higher percentage of correct answers [START_REF] Kit S Double | The impact of peer assessment on academic performance: A meta-analysis of control group studies[END_REF].

Since correct learners are expected to convince incorrect learners, we make the hypothesis that sequence benefits increase alongside peer rating consistency. Consistency of peer ratings ρ peer can be computed by using the correlation between the level of agreement of a learner to a peer's rationale with the correctness of his answer. Since both these variables are latent [START_REF] Everett | An introduction to latent variable models[END_REF], the polychoric correlation is the adequate one [START_REF] Olsson | Maximum likelihood estimation of the polychoric correlation coefficient[END_REF].

In other words, ρ peer indicates if the rationales matching with correct answers are positively evaluated by peers, and if those matching with incorrect answers are negatively evaluated.

Figure 3 shows a plot diagram of the effect size d depending on ρ peer . The calculated Pearson correlation between ρ peer and d is 0.34 with a p-value lower than .002 and a 95% confidence interval equal to [0.14:0.52], which supports our hypothesis. Let us note that ρ peer is not significantly correlated to the distance between p1 and 50% (p-value = 0.25). Consequently, we identified two independent predictors of the benefits of a sequence. When ρ peer < 0, it means that incorrect answers were better rated than correct ones which must be addressed by teachers.

3 Recommendations: If peer ratings are inconsistent (ρ peer < 0), teachers should focus on incorrect rationales during the oral feedback. Else (ρ peer ≥ 0), teachers should focus on correct rationales.

Peer ratings are more consistent when learners' confidence degrees are consistent Back to the first vote, Curtis used confidence of learners to identify misinformed learners [START_REF] Donald A Curtis | Does student confidence on multiple-choice question assessments provide useful information[END_REF]. As a consequence, we make the hypothesis that the consistency of peer ratings increases alongside the consistency of learners' confidence degrees.Confidence consistency ρ con f can be computed by using the polychoric correlation [START_REF] Olsson | Maximum likelihood estimation of the polychoric correlation coefficient[END_REF] between learners confidence degree and correctness of their first answers. Figure 4 is a plot diagram of ρ con f according to ρ peer . The calculated Pearson correlation between ρ con f and ρ peer is 0.38 with a p-value lower than 4e -4, and a 95% confidence interval equal to [0.18:0.55], which supports our hypothesis. This result suggests that the consistency of learner confidence degree is correlated to the consistency of peer's rates. When ρ con f < 0, it means that incorrect answers are more popular than correct answers. Depending on the result of the first vote (p1), this information can determine either the next steps to engage in, or the answers that need to be addressed by teachers.

4 Recommendations: When there are too many correct answers (p1 > 80%), if learners are inconsistently confident (ρ con f < 0), teachers should focus their brief explanations on incorrect rationales. Else (ρ con f ≥ 0), teachers should focus their brief explanations on correct rationales. When there a too few correct answers (p1 < 20%), if learners are inconsistently confident (ρ con f < 0), teachers should provide detailed explanations and restart the sequence. Else (ρ con f ≥ 0), teachers should provide hints before engaging learners in a peer interaction phase.

DISCUSSION AND FUTURE WORKS

Thanks to our findings, we can extend Vickrey's model of two-votes-based processes [START_REF] Vickrey | Research-Based Implementation of Peer Instruction: A Literature Review[END_REF] and propose an orchestration model as shown in Figure 5. Future works will implement and evaluate this experimental model within Elaastic.

L@Scale Works-in-Progress L@S'21, June 22-25, 2021, Virtual Event, Germany

Figure 1 .

 1 Figure 1. The 5 phases of the two-votes-based process.

Figure 2 .

 2 Figure 2. The effect size d depending on p1's distance to 50%.

Figure 3 .

 3 Figure 3. The effect size d depending on consistency of peer ratings ρ peer .

Figure 4 .

 4 Figure 4. The consistency of peer rating ρ peer depending on the confidence consistency ρ con f .

Figure 5 .

 5 Figure 5. A decision-making model of two-votes-based process. White steps are from the original model [19]. Light grey steps are steps that we modified. Dark grey steps are steps that we added. The numbers refer to the corresponding recommendations and bold arrows represent the nominal case.


Jean-Paul Guillet

Ronan Adam

Annick Pénarier

Jérémi Torres

Philippe Nouvel

Laurent Chusseau

Thierry Grosjean

Fadi Baida

Laurent Billot

Daniel Charraut

A New THz Passive Radial Polarizer

A new THz radial polarizer suitable to convert the usual linearly polarized signal from a millimeter or submillimeter source is described. It is based on mode-filtering within a cylindrical waveguide combined with two tapers and a discontinuous phase element. An experimental demonstration is given at ≈ 100 GHz and transposition to higher THz frequencies by scaling is straightforward.

I. INTRODUCTION

As experienced in the optical domain, the generation and use of radially polarized beams should have a significant impact in the evolution of the THz community, especially in the nearfield microscopy and derived techniques as well as in THz plasmonics. At optical frequencies, the management of symmetric fields has strongly improved high numerical aperture focusing [START_REF] Quabis | Focusing light to a tighter spot[END_REF] and near-field optical microscopy and plasmonics [START_REF] Bouhelier | Plasmoncoupled tip-enhanced near-field optical microscopy[END_REF]. All these studies take benefit from the total field symmetry provided by radial polarization, thereby leading, for example, to focused fields with either a strong longitudinal component [START_REF] Quabis | Focusing light to a tighter spot[END_REF], [START_REF] Youngworth | Focusing of high numerical aperture cylindrical-vector beams[END_REF] or a p-polarization state with symmetry of revolution. So far, only a very limited number of systems allow the generation of radially polarized THz beams. All of them are based on the excitation of the mode sustained by metal wires whose electric field distribution is radial around the wire [START_REF] Wang | Metal wires for terahertz wave guiding[END_REF].

We propose in this communication a new concept of passive radial polarizer at THz frequencies. Such a system is aimed at working with continuous waves and it is specially designed for radiating in free space a radially polarized doughnut mode. It has the advantage to be simple and adaptable to any kind of existing THz continuous sources. The principle proposed here is directly derived from the concept of an optical radial polarizer [START_REF] Grosjean | A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations[END_REF].

II. POLARIZER DESIGN

The TEM mode of a coaxial waveguide is in essence radially polarized. However, coaxial waveguides are challenging to built at THz frequencies and the radiation efficiency of the wire mode in free space is questionable [START_REF] Wang | Metal wires for terahertz wave guiding[END_REF]. We consider here a hollow circular waveguide because its TM 01 mode is also radially polarized although it is a high-order mode. Our polarizer design thus rely on the adequate rejection of the fundamental linearly polarized TE 11 mode whose cut-off frequency is lower than that of the desired TM 01 mode. The difficulty with free space propagation is then to couple and decouple efficiently with guided modes. The coupling efficiency between the waveguide modes and an incoming Gaussian beam has been calculated to optimize the power conversion efficiency [START_REF] Grosjean | Generation of radially polarized THz beams using a passive system[END_REF]. Results given in Fig. 1(a) show the calculated coupling efficiency in the two propagating modes TM 01 and TE 21 as a function of the circular input waveguide radius. A linearly polarized input beam fed through a discontinuous phase element is considered as input. An optimum of ≈ 30% appears at a radius of ≈ 10 λ. Next, a taper is used to reduce the waveguide to a dimension small enough so that only the TM 01 mode can propagate. The Fig. 1(b) help us to chose the taper angle θ: provided that θ ≥ 83 • a quasi adiabatic regime is reached and more than 90% of the input TM 01 mode energy is transferred to the smallest guide.

III. POLARIZER REALIZATION & RESULTS

The experimental realization of the radial polarizer was conducted at ≈ 100 GHz and the overall experimental arrangement is given in Fig. 2. At the heart of the polarizer is a hollow circular waveguide of 2.7 mm diameter that supports the simultaneous propagation of both the TE 11 and TM 01 modes. Input is tapered with a circular horn up to an external aperture of diameter ≈ 20 mm. Adiabatic conversion of the freespace propagating mode is ensured by a taper angle less than 10 • with a resulting attenuation ≤ 0.5 dB. For convenience, the output of the waveguide is also tapered but to a limited diameter of ≈ 5 mm well adapted to the near-field probing of the output employed as detection.

Mode selection in the circular waveguide is obtained by help of a halfwave PTFE plate inserted before the input taper.

The plate position can be adjusted manually to cover only half of the taper geometrical acceptance and then creates a null field at center that favors only the TM 01 mode in the circular waveguide. Owing to large enough propagation length of a few wavelengths in the circular waveguide, the output field includes only the TM01 mode with the desired radial polarization.

The polarizer has been realized by micromachining an aluminium rod. Transmission experiments were conducted using an electronic source emitting in free space. Detection involved a Schottky diode coupled to a PTFE pyramidal probe tip of principle similar to Ref. [START_REF] Klein | A metal-dielectric antenna for terahertz near-field imaging[END_REF]. Detection is thus linearly polarized depending of the probe orientation. Probe position is kept close to the ≈ 5 mm diameter polarizer output. Images obtained when the axis of the polarizing probe stage is set parallel and perpendicular to the incoming polarization direction are displayed in Figs. 3(a) and 3(b), respectively. These orientations are indicated by white arrows on each image. A numerical reconstruction of the outgoing beam from Figs. 3(a) and 3(b) is provided in Fig. 3(c).

Two-grain structures jump out in Figs. 3(a) and 3(b). As expected, their directions follow the prescribed axis of the polarizing micro-detection system. The numerical combination of these two orthogonal patterns leads to an annular shape intensity distribution. The null intensity at the beam center evidences that the fundamental TE 11 mode, whose maximum is expected at the center, has been totally rejected by the structure. Moreover, the visibility of the two-spots pattern remains unchanged when the probe axis is rotated (Figs. 3(a) and 3(b)). This is another evidence that all higher modes, except TM 01 , are reflected by the system. These observations validate our concept of THz radial polarizer. Note that the efficiency of this prototype cannot be measured with precision by means of the uncalibrated detection tools that we used.

IV. CONCLUSION

A new THz radial polarizer suitable to convert the usual linearly polarized signal from a millimeter or sub-millimeter source is described and demonstrated at ≈ 100 GHz. Its principle of operation involves an adequate mode filtering in a metallic cylindrical waveguide that supports only TE 11 and TM 01 propagating modes. The correct system operation arises with the selection of the radially polarized TM 01 mode that is ensured by means of a discontinuous phase element placed at the entrance of the system. The built polarizer has shows an operation in excellent agreement with the theoretical design. Doughnut modes are observed at polarizer output with a very high rejection of the fundamental TE 11 mode. Provided that micromechanical machining difficulties can be overcome, the proposed design is straightforwardly scalable to much higher frequencies in the whole THz domain. In the future, this polarizer coupled to an axicon is aimed at generating very small focal spots with enhanced longitudinal electric field for THz near field imaging purposes.

Fig. 1 .

 1 Fig. 1. (a) Coupling efficiency C between a Gaussian beam and the various modes sustained by a cylindrical hollow waveguide of perfect metal, as a function of the waveguide diameter. Half the incoming Gaussian beam crosssection has been phase retarded by π using a discontinuous phase element (see inset). (b) Channeling efficiency of the TM 01 mode as a function of the taper angle θ. The diameters of the large and small waveguides are 7 λ and 0.9 λ, respectively.

Fig. 2 .

 2 Fig. 2. Scheme of the experimental setup.

Fig. 3 .

 3 Fig. 3. Acquisition results of the field distribution transmitted by the prototype over a scan of 7 × 7 mm 2 . (a) and (b) are images acquired for two orthogonal axis of the polarizing detection probe (axis indicated by arrows). (c) Numerical combination of (a) and (b).


Flore Vandier

Maxime Tourte

Cara Doumbe-Kingue

Julien Plancq

Philippe Schaeffer

Phil Oger

Vincent Grossi

Reappraisal of archaeal C20-C25 diether lipid (extended archaeol) origin and use as a biomarker of hypersalinity

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

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*Author for correspondence : Vincent.grossi@uni -l on1.fr

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	i e ai i c i h he a e (He ), He /DCM (1:1, / ), He /e h ace a e (3:1, / ), a d DCM/MeOH e e de d. F i a ce, hi c d ha bee e ed i ig ifica diffe e he P-a e e e be 0.05. he ficia edi e e e a a ed a d e f he -a edi e i hich 2 T f he e e e ia ada i e f c i f 2 a d a i i a d he g h i hi Ha a chaea i ha he abi i he i e hi i id e e ged a d c fe ed i a g h e e a e f Ha a chaea (P-a e = 0.523; Fig. 2B). Thi gge
	a cie (1:1, / ) a e e . The hi d f ac i , hich c ai ed f ee a c h , a i a ed a i e e e ce h i g i h gica e ide ce f high a i i ie a de ec ed e c ed e a i e hich c d ha e a e ed f a h e a i e a a e e , e ked f i cc e ce a g a he a chaea e b a e i id i c ea ed fi e de ec ia e i e a c di i , a d a h ai ai ed. ha e e a e ha e e e ed a ig ifica c he bi he i f 2 d i g
	(Na a icchi e a ., 2017). O he he ha d, e i i a e i h idi e/N,O-bi ( i e h i ) if ace a ide (1:1, / ) a d a a ed b ga -ba ed ab a 3. Re a d Di c i c di i . I a a be e i aged ha he cc e ce f 2 f he de e d he c i i a ai ab e i he i e a e (N= 450). I h d be e ha i ed ha a I a eff di e a g e he c ib i f a . e e e i he he g-e e i f hi c ade (Fig. S1A). I a ec de, h e e , ha
	ch e i i e a e da a a a g a h -a e a a a e e h cc e ce f 2 i Ha a chaea, e ga he ed f ec e (GC-MS) i g a Agi e 6890 ga ch a H e e a e. Beca e he e i ge e i he e e ha e die f c ed he i e a e he i -ab e e a e a i f e ce he i f hi i id i he e b a e f he a chaea gica IPL, i a
	ch a a e e a g a h c e e he ea he g h c di i	ed a Agi e 5975C a a ai ab e f a he died i e (Tab e S1), hei ec e e . C die e ed CL c i i b ai ed af e h d f a ecie i h de c ibed e b a e i id c	d e e e ia i f a i id i i (Fig. 2B).
	i jec ed c i f e ce e ac . Si ce he cc e ce f 2 c d a d e a a ed a HP5-MS ca i a c be a ia i e iga ed (Fig. S1). S i , f (30 0.25 e c ide ed b h IPL a d CL, i h d be bia ed b he T ide if a i e bg ha igh f i a ce e f he af e e i ed
	e a ed 0.25 he i i ed e f da a a ai ab e, a a a d i a NaC c ce a i (Da ) i g he f i g GC e e e a e g a : 60 C he d f 0.5 i , e a ., 2012). He e, e e ia i f e ce f b h a iab e he he e ge ei f he i e a e da a. C d 2 a e ed i 91 f 450 i f e ce f a , e e e e ed da a i g i i i ead f ica b i The c e e f a chaea i id c i i f he ace Ha a chaea a he ai
	e 20 C i -1 130 C he 4 C i -1 300 C he d f 45 i . The e e a e f he he e e ce f 2 i face edi e f a a ic e i e i h di e e i e ha 50 e ce i e f 2 a iced. R ee ed dec ea e i h i c ea i g i -i e e a e (i he a ge ecie , i h 87 ecie be gi g he h ee de f Ha a chaea, i.e., he . U ike he a e , i i e e e he babi i f a da a i be i a d ce f 2. A he a aj i f c e k Ha a chaea a e ab e
	a i i ie , a d ei e iga e i cc e ce i (ha )a chaea ba ed a e e i e -c i jec a g a ed a f ed: 60 C he d f 0.5 i , 200 C i -1 a i e d f G ade e i h a a i i f ca. 41 (Fig. 1B; Tab e S1). A h gh 15-30 C; Fig. S1A a d Tab e S1) hich c a i h e i b e a i ade Ha bac e ia e , Ha fe aca e a d Na ia ba e . The 4 addi i a ecie d ci g 2, ce ai egi f he (e.g., he a ge he egi he e da a i i c ai ) a d h i e a a i i be 100 , he e e ce f 2 i edi e i h a i i f ca. 40
	i e a e 300 C he d f 1 i . T a I C e (TIC) a d Se ec ed I M i i g (SIM) f e be e c ai i bi gica igi a d e ia e a a edi e f h e a i e d i h he highe a i i (ca. 350 , c e i g ab a c e f a i g e Ha a chaea ecie (Ya a chi, 2008). O he h be e de ic he da a e di ib i . Re h ed ha Ha a chaea 100 i i ig i g (Fig. 1B). H e e , 2 ha bee e ed i -ha hi ic
	( a e )e i he i / 130, 131, 426 a d 496 ( ecific f i a ed de i a i e f 1 a d 2; Tei id e a i dica . a a i he ha d, 2 a de ec ed i edi e i h H a e a gi g f 7.5 9.4 (Fig. he i i g 2 g i a a ig ifica highe H (7.45 . 7.30, P-a e = ecie di i c f Ha a chaea (i.e., i -ha hi ic e ha ge ; De R a e a .,
	e a ., 1993) e e ec ded. D e S1B a d Tab e S1), i i g 0.015) a d a i i (200 . 190 1986; G a a d R , 1986; Becke e a ., 2016) a d he i id c he a f 2 a d/ c a d diffe e H c di i f , P-a e = 0.035) ha -d ci g ecie (Fig. d c e i g d c i . La , i i f e
	i h 1 i a a e The ef e, e f c ed e a e , he ab da ce f 2 e a i e 1+2 (R) a de e i ed f c ide ed he cc e ce f 1 a d 2 de hei f ee f [i.e., a c e he a a i Ha a chaea (N= 277; Fig. 2A). C d 2 2B). H e e , a h gh ig ifica , he e diffe e ce a ea ed a he a a a chaea ecie i e cha ac e i ed. The ibi i ha a h e a ge f d ce
	2.1. Sedi e a eak a ea ea ed i id (CL) i h a ide ified i he aj i e a d i id a a i he SIM ch a g a , i h R = 2/(1+ 2) 100. I h d be h ha hi a head ] a d did ake i acc he e ia c -f c e k Na ia ba e (51 f 78 ecie , 16 aj i f e ce f g h H a d/ a i i he bi he i f 2. Thi e he e f 2 be ide Ha a chaea a c ib e he f hi i id bi a ke i
	S face edi e c i g f ed, h e e , ha he b h ea e e 31 i e i h a a i i a gi g f e e ib e, SIM a d TIC ig a 0 ac ica a i i bi a ke i e ic ed e e e a i e e i e , e e di g i e e i g cc e ce f he e die he a i ac a i id (IPL), a f d i i i g bi a . f 22 ge e a), b a e adica e ed i Ha bac e ia e (32 f 90 hi ha 2 a ha e a ed a e i he ( g-e ) ada a i f Ha a chaea H e i e i h c a ed a i i h ca be ed . O he he ha d,
	). h c di i , ecie ) e e i e iga ed f he e e ce f 1 a d 2 a ab e R a e (Tab e S1). a a i (ca. 350 i h a a i i d i ( ) ie ded c ca. 40-50 . Thi i i i e i h he cc e ce f 2 i H e e , c ide i g ha 1 a d 2 IPL a e ike e hibi i i a a head , hei ecie , 14 f 31 ge e a) a d Ha fe aca e (6 f 109 ecie , 2 f 18 a d a i i a ia i . L ki g e c e a hei i a g Ha a chaea ha e bee b e ed i -e e e a i e e i e ch a
	H e e , fe e ce i (Tab e S1). The diffe e i e i c de ake f e i ide hi c ade (e.g., Becke e a ., 2016). The e a he Ca adia P ai ie (P a c e a ., Mi ce e ha e , a a d ca b a e hich a e ed ha e f ed de -h d i a e d i g diage e i a e e ec ed be c e each he , h i i i g ge e a, i.e., Halorubrum a d Halalkaliarchaeum). S ch di i c di ib i f 2 ca ab e f he he i f 2 a e di ib ed i hi di i c g : e c ed e a ie (P d e a ., 2004; Si gh e a ., 2010), f -ich i g (E hahed e a .,
	i 2018) a d he Tibe a P a ea (Wa g e a ., 2020), a e f e id i ei he e f he a k chai i 2 c a ed 1 e F a ce (Ca a g e) a d i a 2.2. Li e a e e a d a i ica a a e The i f 2 did e ia bia e ef ec ed i he R a i ba ed CL a a i . Whe he hi a i be ee he h ee Ha a chaea de he idea ha fac c i g i f e hi ic Ha a chaea ( edia H = 7.2) a d e f a ka i hi ic 2004) hi hic ic bia a (Je e e a ., 2016), gge i g ha e ( e

c e f a i g e Ha a chaea ecie (f he de Ha bac e ia e ) ha e h ha he e a i e i f 2 i c ea e i h i c ea i g e e a e a d a i i (Ya a chi, 2008), hi e i cc e ce i hi a fe Ha a chaea ecie a ea ed C d 1 a d 2 e e de ec ed i 19 a d 10 f he 31 a e a a ed, e ec i e . O he i e id die he i id [e.g., ( ac )c c ic h d a ed1] e e de ec ed be ide 1 a d 2. A g he 19 ake he e 1 a b e ed, 2 a de ec ed i a i e i h a a i i a d ab e 50 , ie di g R a e be ee 1.7 a d 11.3 %, a d a de ec ed i ake i h a a i e e ) di a ed he highe i f 2 (R a e f ca. 11 %), i i a i f 2 e e a b e ed i i e i h a a i i be ee 70 a d 210 (Fig. 1B). The e e 2 a a bi a ke f h e a i e e i e a e i gge ed (Tei id e a ., 1993; Bi ge e a ., 2014), b f he e e e c di i f a i i (Na a icchi e a ., 2017). a e , Methanomassilicoccales l min ensis, Methanolobus tindarius, Methanosarcina barkeri a d Methanosarcina ma ei, e e a d di ib ed i hi -ha hi ic e ha ge (De R a e a ., 1986; G a a d R , 1986; Becke e a ., 2016). d ce d i g h -e acc i a i a i (Ya a chi, 2008; Fig. S1A).


Flore Vandier

Maxime Tourte

Cara Doumbe-Kingue

Julien Plancq

Philippe Schaeffer

Phil Oger

Vincent Grossi
email: vincent.grossi@univ-lyon1.fr

Reappraisal of archaeal C 20 -C 25 diether lipid (extended archaeol) origin and use as a biomarker of hypersalinity

Keywords:

The diether core membrane lipid sesterterpanyl-phytanyl-glycerol (so-called extended archaeol and often abbreviated C 20 -C 25 ) is considered as a hallmark of Haloarchaea, a clade of archaea thriving under extreme high salinities. We here report about extended archaeol occurrence in different saline aquatic settings with salinity ranging from ca. 50 psu (5 % NaCl w/v) to saturation (ca. 350 psu). This demonstrates that this lipid is not restricted to extreme saline environments but suggests a minimum salinity threshold of ca. 50 psu above which C 20 -C 25 is most commonly produced. The proportion of C 20 -C 25 relative to that of archaeol (C 20 -C 20 ) did not appear linearly dependent on the salinity of the site and was potentially also influenced by pH and temperature, preventing its direct use as a quantitative salinity proxy based on the present data set. An extensive literature review of archaeal membrane lipid compositions further highlighted that taxonomy also contributes to the distribution of this lipid in the environment and identifies Natrialbales (one of the three orders of Haloarchaea) as the main source. Statistical analysis showed that, among Haloarchaea, C 20 -C 25 producers display pH and salinity growth optima slightly higher than non-producers and are distributed within two distinct groups, one composed mostly of neutrophiles and one of alkaliphiles. In contrast, the presence of C 20 -C 25 was not correlated to the optimal growth temperature of the strains. This suggests that two confounding parameters, i.e., taxonomy and adaptation to changes in salinity and/or pH, contribute to the distribution of C 20 -C 25 within Haloarchaea.

Introduction

Isoprenoid dialkyl glycerol diether lipids are membrane lipids unique to the Archaea. Archaeol 1 (2,3-di-O-phytanyl-sn-glycerol; Fig. 1A) and its elongated homologue called extended archaeol 2 (2-Osesterterpanyl-3-O-phytanyl-sn-glycerol 2a and its regiosiomer 2-Ophytanyl-3-O-sesterterpanyl-sn-glycerol 2b; Fig. 1A) are the two main types of archaeal diether lipids encountered. While 1 is globally distributed among Archaea (e.g., [START_REF] Tourte | Functionalized membrane domains: An ancestral feature of Archaea?[END_REF], 2 was initially described only in haloalkaliphilic archaea [START_REF] De Rosa | An asymmetric archaebacterial diether lipid from alkaliphilic halophiles[END_REF] before being detected in non-alkaline hypersaline environments [START_REF] Teixidor | Isopranylglycerol diethers in non-alkaline evaporitic environments[END_REF] and later on considered as a hallmark of halophilic Euryarchaeota from the clade Haloarchaea (Dawson et al., 2012 and references therein). However, few exceptions exist outside this clade (e.g., [START_REF] Becker | Unusual butane-and pentanetriol-based tetraether lipids in Methanomassiliicoccus luminyensis, a representative of the seventh order of Methanogens[END_REF]. The extra isoprenoid unit on either one of the alkyl chains in 2 compared to 1 results in an asymmetric lipid that was hypothesized to induce "zip-like" archaeal membranes specifically adapted to high alkalinity and strong osmotic stress [START_REF] De Rosa | An asymmetric archaebacterial diether lipid from alkaliphilic halophiles[END_REF]. The detection of 2 in sedimentary archives has been consequently associated with the presence of Haloarchaea and used as a marker of hypersaline/evaporitic environments [START_REF] Birgel | Hypersaline conditions during deposition of the Calcare di Base revealed from archaeal di-and tetraether inventories[END_REF]. Although relevant to some extent, the distribution of 2 in both Archaea and environmental samples as well as its physiological and adaptive functions still remain incompletely understood. For instance, this compound has been reported in ancient marine sequences showing no lithological evidence of high salinities [START_REF] Natalicchio | An archaeal biomarker record of paleoenvironmental change across the onset of the Messinian salinity crisis in the absence of evaporites (Piedmont Basin, Italy)[END_REF]. On the other hand, preliminary results based on laboratory cultures of a single Haloarchaea species (from the order Halobacteriales) have shown that the relative proportion of 2 increases with increasing temperature and salinity [START_REF] Yamauchi | ESI-MS and GC-MS analyses of C 25 -C 20 isoprenoidal diether originated from halophilic archaea with reference to an indicator for hypersaline environment[END_REF], while its occurrence within a few Haloarchaea species appeared related to taxonomy and optimal NaCl concentration [START_REF] Dawson | Molecular characterization of core lipids from halophilic archaea grown under different salinity conditions[END_REF]. Here, we report the presence of 2 in surface sediments from aquatic environments with diverse salinities, and reinvestigate its occurrence in https://doi.org/10.1016/j.orggeochem.2021.104276 (halo)archaea based on an extensive literature survey to better constrain its biological origin and potential use as a (paleo)environmental indicator.

Material and methods

Sediment samples and lipid analysis

Surface sediments coming from 31 sites with a salinity ranging from 0 practical salinity unit (psu) to saturation (ca. 350 psu) were investigated for the presence of 1 and 2 (Table S1). The different sites include lakes from the Canadian Prairies [START_REF] Plancq | Assessing environmental controls on the distribution of long-chain alkenones in the Canadian Prairies[END_REF] and the Tibetan Plateau [START_REF] Wang | TEX 86 as a potential proxy of lake water pH in the Tibetan Plateau[END_REF], salterns from France (Camargue) and Argentina (Valdes Peninsula) and saline ponds from Guadeloupe [START_REF] Huguet | Archaeal and bacterial tetraether lipids in tropical ponds with contrasting salinity (Guadeloupe, French West Indies): Implications for tetraether-based environmental proxies[END_REF]. Some sediments have been analyzed in previous studies while other were specifically considered for the present work (Table S1). Sediment samples were freeze-dried and extracted ultrasonically [methanol (MeOH) x2, dichloromethane (DCM)/MeOH (1:1, v/v) × 2, DCM × 2] or using an automated solvent extractor [START_REF] Huguet | Archaeal and bacterial tetraether lipids in tropical ponds with contrasting salinity (Guadeloupe, French West Indies): Implications for tetraether-based environmental proxies[END_REF][START_REF] Plancq | Assessing environmental controls on the distribution of long-chain alkenones in the Canadian Prairies[END_REF]. The total lipid extracts were chromatographed over a silica gel column with hexane (Hex), Hex/DCM (1:1, v/v), Hex/ethyl acetate (3:1, v/v), and DCM/MeOH (1:1, v/v) as eluents. The third fraction, which contained free alcohols, was silylated with pyridine/N,O-bis(trimethylsilyl)trifluoroacetamide (1:1, v/v) and analyzed by gas-chromatography -mass spectrometry (GC-MS) using an Agilent 6890 gas chromatograph coupled to an Agilent 5975C mass spectrometer. Compounds were injected on column and separated on a HP5-MS capillary column (30 m × 0.25 mm × 0.25 µm) using the following GC oven temperature program: 60 °C held for 0.5 min, 20 °C min -1 to 130 °C then 4 °C min -1 to 300 °C held for 45 min. The temperature of the on-column injector was programmed as followed: 60 °C held for 0.5 min, 200 °C min -1 to 300 °C held for 1 min. Total Ion Current (TIC) and Selected Ion Monitoring (SIM) of the ions m/z 130, 131, 426 and 496 (specific of silylated derivatives of 1 and 2; [START_REF] Teixidor | Isopranylglycerol diethers in non-alkaline evaporitic environments[END_REF] were recorded. Due to the low amount of 2 and/or compounds coeluting with 1 in some samples, the abundance of 2 relative to 1 + 2 (R) was determined from the peak area measured on the SIM chromatograms, with R = 2/(1 + 2) × 100. It should be noted, however, that when both measurements were possible, SIM and TIC signals yielded comparable R values (Table S1).

Literature survey and statistical analyses

Information on the membrane lipid compositions of all Archaea species reported in the literature was collected (N = 450). To estimate the influence of growth parameters on the production of 2, Haloarchaea (N = 277) were sorted between 2-positive and 2-negative species and their optimal growth conditions (salinity, pH and temperature) were compared using a non-parametric test on medians performed with the Python statistical package, as data were not normally distributed. Medians were considered significantly different when P-values were below 0.05.

Results and discussion

Compounds 1 and 2 were detected in 19 and 10 out of the 31 samples analyzed, respectively. Other isoprenoid diether lipids [e.g., (macro)cyclic or hydroxylated1] were not detected besides 1 and 2. Among the 19 lakes where 1 was observed, 2 was detected in all sites with a salinity around or above 50 psu, yielding R values between 1.7 and 11.3 %, and was not detected in lakes with a salinity lower than 50 psu except in one saline pond from Guadeloupe with a salinity of ca. 41 psu (Fig. 1B; Table S1). Although sediments from hypersaline ponds with the highest salinity (ca. 350 psu, close to saturation level) displayed the highest proportions of 2 (R values of ca. 11 %), similar proportions of 2 were also observed in sites with a salinity between 70 and 210 psu (Fig. 1B). These results support 2 as a biomarker of hypersaline environments as previously suggested [START_REF] Teixidor | Isopranylglycerol diethers in non-alkaline evaporitic environments[END_REF][START_REF] Birgel | Hypersaline conditions during deposition of the Calcare di Base revealed from archaeal di-and tetraether inventories[END_REF], but further show that this biomarker is not restricted to extreme saline environments, extending its use to settings with a salinity down to ca. 40-50 psu. This is in line with the occurrence of 2 in Miocene shales, marls and carbonates which are supposed to have formed under non-extreme conditions of salinity [START_REF] Natalicchio | An archaeal biomarker record of paleoenvironmental change across the onset of the Messinian salinity crisis in the absence of evaporites (Piedmont Basin, Italy)[END_REF]. The proportion of 2 did not appear linearly dependent on salinity (Fig. 1B), preventing the definition of a quantitative salinity proxy given the present data set. It is possible, however, that some uncertainties linked to the ways salinity was measured for the different sites (Table S1) may have obscured such a potential linear relationship between the relative proportion of 2 and salinity. On the other hand, the possibility that a sediment sample reflects different salinity conditions than those at the time of sampling is not likely since only the surficial sediments were analyzed and none of the 'low-salt' sediments in which 2 was detected enclosed evaporites which could have attested from past hypersaline conditions. It may also be envisaged that the occurrence of

U N C O R R E C T E D P R O O F
2 further depends on other environmental parameters such as pH or temperature. Because these limnological parameters were not available for all the studied sites (Table S1), their potential influence on the occurrence of 2 could only be partially investigated (Fig. S1). Still, for the limited set of data available, a potential influence of both variables on the proportion of 2 was noticed. R seemed to decrease with increasing in-situ temperature (in the range 15-30 °C; Fig. S1A and Table S1) which contrasts with previous observations made using laboratory cultures of a single Haloarchaea species [START_REF] Yamauchi | ESI-MS and GC-MS analyses of C 25 -C 20 isoprenoidal diether originated from halophilic archaea with reference to an indicator for hypersaline environment[END_REF]. On the other hand, 2 was detected in sediments with pH values ranging from 7.5 to 9.4 (Fig. S1B and Table S1), pointing towards different pH conditions of production. Lastly, our analyses only considered the occurrence of 1 and 2 under their free forms [i.e., as core lipids (CL) without polar heads] and did not take into account the potential co-occurrence of these diethers as intact polar lipids (IPL), as found in living biomass. However, considering that 1 and 2 IPL are likely to exhibit similar polar heads, their hydrolysis rates during diagenesis are expected to be close to each other, thus limiting potential biases reflected in the R ratio based on CL analysis. Whether or not this ratio can become a quantitative environmental proxy remains to be further investigated. It would be of particular interest to determine if the biosynthesis of 2 scales with salinity (or other environmental parameters) within individual producers, and/or if the relative abundance of archaeal species producing this compound scales with salinity (or other variables).

To further explore potential adaptive functions of 2 towards salinity and other growth parameters, we looked for its occurrence among all the archaeal membrane lipid compositions available in the literature (N = 450). It should be emphasized that all literature data was not homogeneous in the sense that some studies focused on IPL, whereas other studies reported CL compositions obtained after hydrolysis of total lipid extracts. Since our survey considered both IPL and CL, it should not be biased by the heterogeneity of the literature data. Compound 2 was reported in only 91 out of 450 species, with 87 species belonging to the three orders of Haloarchaea, i.e., the Halobacteriales, Haloferacales and Natrialbales. The 4 additional species producing 2, namely, Methanomassilicoccales luminyensis, Methanolobus tindarius, Methanosarcina barkeri and Methanosarcina mazei, were randomly distributed within non-halophilic methanogens (De Rosa et al., 1986a;1986b;[START_REF] Becker | Unusual butane-and pentanetriol-based tetraether lipids in Methanomassiliicoccus luminyensis, a representative of the seventh order of Methanogens[END_REF]. Therefore, we focused our analysis on Haloarchaea (N = 277; Fig. 2A). Compound 2 was identified in the majority of currently known Natrialbales (51 out of 78 species, 16 out of 22 genera), but was more sporadically reported in Halobacteriales (32 out of 90 species, 14 out of 31 genera) and Haloferacales (6 out of 109 species, 2 out of 18 genera, i.e., Halorubrum and Halalkaliarchaeum). Such distinct distributions of 2 between the three Haloarchaea orders support the idea that factors controlling its biosynthesis are dependent on taxonomy [START_REF] Dawson | Molecular characterization of core lipids from halophilic archaea grown under different salinity conditions[END_REF]. Its wide distribution within Natrialbales would indicate that the ability to synthesize this compound is a common and ancestral feature of all the species of this order, while its patchy distribution within Haloferacales and Halobacteriales would suggest that members of these orders have sporadically gained this biosynthetic ability by horizontal gene transfers or spontaneous emergence. Another hypothesis to explain the distribution of 2 within Haloarchaea is that the ability to synthesize this lipid emerged and conferred increased fitness under peculiar environmental conditions, and was thus maintained.

In an effort to disentangle the contribution of taxonomy vs. stress response in the occurrence of 2 in Haloarchaea, we gathered from the literature the in-lab optimal growth conditions of all species with described membrane lipid compositions (Fig. 2B). To identify putative subgroups that might for instance result from the aforementioned influence of taxonomy, we represented our data using violin plots instead of typical box plots. Unlike the latter, violin plots represent the probability of a data point to be in a certain region of the plot (e.g., the larger the region the more data points it contains) and thus better depicts the data set distribution. Results showed that Haloarchaea synthesizing 2 grow optimally at significantly higher pH (7.45 vs. 7.30, P-value = 0.015) and salinity (200 vs. 190 psu, P-value = 0.035) than non-producing species (Fig. 2B). However, although significant, these differences appeared rather small to support a major influence of growth pH and/or salinity on the biosynthesis of 2. This nonetheless hints that 2 may have played a role in the (long-term) adaptation of Haloarchaea to pH and salinity variations. Looking more closely at their optimal growth conditions, species capable of the synthesis of 2 are distributed within two distinct groups: one composed mostly of neutrophilic Haloarchaea (median pH = 7.2) and one of alkaliphilic Haloarchaea, mostly Natrialbales (median pH = 9.2; Fig. 2B). Such a bimodality suggests that two 2. A) Archaeal phylogenetic tree (redrawn from Cui and Dyall-Smith, 2021) and average optimal growth parameters (salinity, pH and temperature) of Haloarchaea. Genera highlighted in red illustrate the presence of 2 in at least one species; genera in bold red are those for which all species were reported to produce 2. B) Distribution of optimal growth parameters among Haloarchaea producing (red) or not (white) extended archaeol 2 (literature data). Violin plots include the medians (white dots), 1st and 3rd quartiles (black box limits), ranges (black whiskers) and probability densities (shape width). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) confounding parameters, i.e., taxonomy and adaptation, might contribute to the distribution of 2 within Haloarchaea. For instance, 2 might support adaptation towards extreme pH in Natrialbales, while it might provide other yet unknown advantage in Haloferacales and Halobacteriales.

U N C O R R E C T E D P R O O F Fig.
Our statistical analysis further showed that the occurrence of 2 is not correlated to the optimal growth temperature of Haloarchaea (Pvalue = 0.523; Fig. 2B). This suggests that temperature have not exerted a significant control on the biosynthesis of 2 during the long-term evolution of this clade (Fig. S1A). It may not preclude, however, that temperature may influence the proportion of this lipid in the membrane of the archaeal producers during short-term acclimatisation [START_REF] Yamauchi | ESI-MS and GC-MS analyses of C 25 -C 20 isoprenoidal diether originated from halophilic archaea with reference to an indicator for hypersaline environment[END_REF]Fig. S1A).

The current set of archaeal lipid compositions further places Haloarchaea as the main producers of 2. As the vast majority of currently known Haloarchaea are unable to thrive at salinity below 100 psu, the presence of 2 in sediments with salinity from ca. 40 to 100 psu is intriguing (Fig. 1B). However, 2 has been reported in non-halophilic species distinct from Haloarchaea (i.e., in non-halophilic methanogens;De Rosa et al., 1986b;[START_REF] Becker | Unusual butane-and pentanetriol-based tetraether lipids in Methanomassiliicoccus luminyensis, a representative of the seventh order of Methanogens[END_REF] and the lipid composition of numerous archaeal species is yet uncharacterized. The possibility that a whole range of producers of 2 besides Haloarchaea may contribute to the pool of this lipid biomarker in environments with contrasted salin-

U N C O R R E C T E D P R O O F
ity thus cannot be ruled out. On the other hand, Haloarchaea have been observed in a variety of sediment habitats that experience various levels of salinity [START_REF] Youssef | Phylogenetic diversities and community structure of members of the extremely halophilic Archaea (Order Halobacteriales) in multiple saline sediment habitats[END_REF] including low or non-extreme saline environments such as estuaries [START_REF] Purdy | Isolation of haloarchaea that grow at low salinities[END_REF][START_REF] Singh | Phylogenetic diversity of archaeal 16S rRNA and ammonia monooxygenase genes from tropical estuarine sediments on the central west coast of India[END_REF], sulfur-rich springs [START_REF] Elshahed | Survey of archaeal diversity reveals an abundance of Halophilic archaea in a low-salt, sulfide-and sulfur-rich spring[END_REF] or thiotrophic microbial mats [START_REF] Jessen | Distribution and composition of thiotrophic mats in the hypoxic zone of the Black Sea (150-170 m water depth, Crimea Margin)[END_REF], suggesting that some (yet undescribed) low salttolerant Haloarchaea might be responsible for the production of 2 in settings with moderate salinity.

In spite of the still fragmented information currently available on the biosynthesis (producers and conditions) of extended archaeol, the present study encourages further investigation of the physiological role, environmental occurrence and potential use as (paleo)environmental indicator of this puzzling lipid. [START_REF] Hou | Variable apparent hydrogen isotopic fractionation between sedimentary n-alkanes and precipitation on the Tibetan Plateau[END_REF][START_REF] Wang | Distribution of GDGTs in lake surface sediments on the Tibetan Plateau and its influencing factors[END_REF][START_REF] Wang | A Directory of Lakes in China[END_REF]

Uncited references

Fig. 1 .

 1 Fig. 1. A) Structures of archaeol 1 and the two possible regioisomers of extended archaeol 2; B) Proportion of 2 relative to 1 in superficial sediments of lakes and ponds with different salinities. The dashed line indicates a possible threshold for the presence of 2 around 40-50 psu. R = 2/(1 + 2) × 100.

Acknowledgments

We thank Mingda Wang for his valuable help in gathering the environmental parameters of the Tibetan lakes, Philippe Cuny for providing the sediments from salterns and Arnauld Vinçon-Laugier and Ingrid Antheaume for help with analyses. We thank two anonymous reviewers for their comments which greatly improved the manuscript. We are grateful to the CNRS Interdisciplinary program MITI 'Adaptation du vivant à l'environnement' (grant Adapthalo 2020-2021 to VG) and the ENS Lyon for their financial support.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.orggeochem.2021.104276.