Diala Abu Awad
email: diala.abu-awad@inra.fr

Sylvain Billiard

The double edged sword: The demographic consequences of the evolution of self-fertilisation

Phylogenies indicate that the transition from outcrossing to selfing is frequent, with selfing populations being more prone to extinction. The rates of transition to selfing and extinction, acting on different timescales, could explain the observed distributions of extant selfing species among taxa. However, phylogenetic and theoretical studies consider these mechanisms independently, i.e. transitions do not cause extinction. Here, we theoretically explore the demographic consequences of the evolution of self-fertilization. Deleterious mutations and mutations modifying the selfing rate are recurrently introduced and the number of offspring depends on individual fitness, allowing for a demographic feedback. We show that mutational meltdowns can be triggered in populations evolving near strict selfing. Populations having survived the demographic crash are more stable than ancestral outcrossing populations once deleterious mutations are purged. The relatively rapid time-scales in which extinctions occur indicate that during evolutionary transitions the accumulation of deleterious mutations may not be the cause of extinctions observed on longer time scales, which in turn could lead to the underestimation of transition rates from outcrossing to selfing.

Extinction, Inbreeding, Mating Systems, Models/Simulations, Mutations, Population Genetics

Introduction

The transition from predominantly outcrossing to self-fertilising reproductive systems is one of the most commonly observed and well documented of evolutionary transitions [START_REF] Schoen | Evolutionary history of the mating system in Amsinckia (Boraginaceae)[END_REF][START_REF] Goldberg | Species selection maintains self-incompatibility[END_REF][START_REF] Igic | Is self-fertilization an evolutionary dead end?[END_REF][START_REF] Barrett | The demography and population genomics of evolutionary transitions to self-fertilization in plants[END_REF]. The seeming uni-directionality of this evolutionary change [START_REF] Igic | Is self-fertilization an evolutionary dead end?[END_REF] renders the relatively low frequency of predominant selfing in flowering plants (≈ 11% [START_REF] Wright | Evolutionary consequences of self-fertilization in plants[END_REF]) somewhat paradoxical. Indeed, it has long been suggested that self-fertilisation is an evolutionary dead-end [START_REF] Takebayashi | Is self-fertilization an evolutionary dead end? Revisiting an old hypothesis with genetic theories and a macroevolutionary approach[END_REF][START_REF] Igic | Is self-fertilization an evolutionary dead end?[END_REF]. Recent phylogenetic studies on diversification rates of flowering plants have supported this hypothesis. Results show lower net diversification rates of self-fertilising species compared to that of their outcrossing sister taxa due to higher extinction rates [START_REF] Schoen | Evolutionary history of the mating system in Amsinckia (Boraginaceae)[END_REF][START_REF] Goldberg | Species selection maintains self-incompatibility[END_REF][START_REF] Igic | Is self-fertilization an evolutionary dead end?[END_REF]. These phylogenetic results are supported by numerous theoretical investigations regarding the evolution of selfing and the effect of self-fertilization on the viability of populations. The genetic consequences of the evolution of self-fertilisation can be summarized by two main points: 1) The reduction of the effective population size (noted N e , [START_REF] Wright | Evolutionary consequences of self-fertilization in plants[END_REF] due to a reduced genetic diversity, which leads to weaker selection against deleterious mutations and weaker selection for beneficial mutations; and 2) The reduction of effective recombination and the increase of the Hill-Robertson effect (Kamran-Disfani and [START_REF] Kamran-Disfani | Selfing, adaptation and background selection in finite populations[END_REF]. The combined effects of decreased genetic variation (i.e. lower adaptive potential, [START_REF] Glémin | Adaptation and maladaptation in selfing and outcrossing species: new mutations versus standing variation[END_REF] and reduced efficiency of recombination (leading to the accumulation of deleterious mutations, [START_REF] Lynch | Mutational meltdowns in sexual populations[END_REF][START_REF] Abu Awad | The Interaction between Selection, Demography and Selfing and How It Affects Population Viability[END_REF] are expected to, in the long term, lead to the extinction of self-fertilising populations.

However, all these theoretical approaches suppose that the evolution from outcrossing to selfing and the extinction of selfing populations are independent, i.e. transitions from outcrossing to selfing do not affect population viability per se. On the one hand, existing models studying the extinction of self-fertilising populations have done so considering selfing as a fixed parameter and not a variable [START_REF] Lynch | Mutational meltdowns in sexual populations[END_REF][START_REF] Abu Awad | The Interaction between Selection, Demography and Selfing and How It Affects Population Viability[END_REF], while the change in reproductive systems can be relatively fast [START_REF] Barrett | Plant reproductive systems and evolution during biological invasion[END_REF] Accepted Article [START_REF] Shimizu | Evolution of Selfing: Recurrent Patterns in Molecular Adaptation[END_REF], implying that the evolutionary transition and its ecological consequences can occur on the same timescale. On the other hand, works examining the evolution of mating systems showed that, providing that inbreeding depression is sufficiently low and that populations are constantly at their ecological and demographic equilibrium, an outcrossing population will always be invaded by a self-fertilising mutant (due to Fisher's automatic advantage, Fisher 1941;[START_REF] Charlesworth | Inbreeding depression and its evolutionary consequences[END_REF][START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Cheptou | The evolution of self-fertilization in density-regulated populations[END_REF][START_REF] Porcher | Loss of gametophytic self-incompatibility with evolution of inbreeding depression[END_REF]. Any potential feed-back between the genetic and demographic states of populations during the transition from outcrossing to selfing is therefore neglected. This is especially problematic since we know that the evolution of self-fertilisation is accompanied by the purge of deleterious mutations [START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Gervais | Genetic architecture of inbreeding depression and the maintenance of gametophytic self-incompatibility[END_REF], which may have demographic consequences. The question of whether the transition from outcrossing to selfing allows for the necessary demographic and genetic conditions for population extinction arises. If a viable outcrossing population evolves towards a selfing reproductive system is its probability of extinction increased? Or are only initially demographically unstable populations susceptible? It has been proposed that the purge of deleterious mutations can influence population size [START_REF] Abu Awad | The Interaction between Selection, Demography and Selfing and How It Affects Population Viability[END_REF]. However, the speed at which the purge occurs may have different consequences: if it is very efficient then population size will immediately increase with the selfing rate; if it is not populations may suffer a decrease in size due to the introduction of inbred (hence less fit) individuals. Another unanswered question is whether or not initially outcrossing populations could naturally evolve to rates of self-fertilisation high enough to trigger a mutational meltdown [START_REF] Barrett | Understanding plant reproductive diversity[END_REF]). To answer these questions, models considering the joint evolution of self-fertilisation, mutation load and population size are necessary.

Here we propose a model where recurrent deleterious mutations impact individual fitness (i.e. the reproductive rate) and consequently population size. Mutations promoting self-fertilisation are also introduced recurrently at a modifier locus in an initially outcrossing population at mutation-selectiondrift balance. As the genetic architecture and the strength of mutations affecting selfing rates seem to be variable [START_REF] Barrett | Plant reproductive systems and evolution during biological invasion[END_REF], we consider two modes of the evolution of self-fertilisation. We either continuously introduce mutations drawn in a distribution at the modifier locus so that selfing can evolve to any rate between 0 and 1 [START_REF] Cheptou | The evolution of self-fertilization in density-regulated populations[END_REF][START_REF] Epinat | The evolution of assortative mating and selfing with in-and outbreeding depression[END_REF], or we consider the recurrent introduction of

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a single type of modifier with a fixed and strong effect on the selfing rate [START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Gervais | Genetic architecture of inbreeding depression and the maintenance of gametophytic self-incompatibility[END_REF]. We compare the two models for the evolution of self-fertilisation, noting their respective demographic and genetic consequences, such as the mutation load and effective relative census population size thus evaluating the importance of demographic feedback. Finally we explore the importance of demographic parameters such as the reproductive rate and the carrying capacity.

Model

Both the deterministic and simulation models stem from those presented in Abu Awad et al. (2014). We model a population of hermaphroditic individuals of varying size N t , given by

N t = N t-1 R t-1 (1)
with R t the absolute fitness defined as

R t = r 1- N t K 0 W t , (2)
where r 0 is the intrinsic reproductive rate, reproduction is assumed densitydependent (K is the carrying capacity) and the relative fitness W t at generation t is assumed density-independent [START_REF] Chevin | When do adaptive plasticity and genetic evolution prevent extinction of a density-regulated population?[END_REF]. For an equilibrium relative fitness W det (i.e. at mutation-selection balance) and in the absence of demographic and genetic stochasticity, the deterministic population size N det is

N det = K 1 + Ln(W det ) Ln(r 0 ) . ( 3
)
A population with a relative fitness equal to or below W det ≤ 1 r 0 is not viable as N det ≤ 0.

An approximation of the mean relative fitness W det at mutation-selection balance in a large population with an infinite number of selected loci can be obtained for a given set of demographic and genetic parameters (the haploid mutation rate U , the coefficient of selection s and the dominance h, and the self-fertilisation rate α) and taking into account the effects of linkage disequilibrium (Equation (11) from Roze (2015)):

W det = (1 + I 2 )Exp -U 4h + α(1 -4h) 2h + α(1 -2h) (1 + I 1 ) + 2α 2 -α I 2 (4)
Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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with

I 1 = 2U (1-h)(1-2h) 2+α 2-α T , I 2 = U 2 (1-2h) 2 T and T = 2α(1-α) (4-α ) [2h+α(1-2h)] 2 .
Similarly, we use Roze's (2015) approximation for inbreeding depression with linkage disequilibrium (Equation ( 14) in Roze 2015) to evaluate for which genetic parameters self-fertilisation could evolve:

δ det = 1 -1 + I 2 4 Exp -U 1 -2h 2h + α(1 -2h) (1 + I 1 ) + 2α 2 -α I 2 . (5)

Simulation Model

In order to follow both the evolution of the selfing rate and its demographic consequences, we used an individual-centred model version of the deterministic model presented previously written in C++ and available on Dryad. We consider a population with diploid hermaphroditic individuals and discrete non-overlapping generations, with a variable population size and a stable environment. The life cycle is as follows: mutation, selection, meiosis and reproduction. At a given time t, population size N t is given by

N t = N t-1 i=1 X i t-1 (6)
where X i t is the number of viable offspring an individual i at time t contributes via the female function to the next generation. X i t is sampled from a Poisson distribution with mean

R i t = W i t r 1- N t K 0
(the individual reproductive rate), where W i t is the individual's relative fitness. Fitness is multiplicative and depends on the number of homozygous (n ho ) and heterozygous (n he ) deleterious mutations, with a coefficient of selection s and dominance h, carried by an individual i given by

W i = (1 -s) n ho (1 -hs) n he . ( 7
)
The genetic properties of this model are modelled as in [START_REF] Roze | Diploidy, Population Structure, and the Evolution of Recombination[END_REF] and Abu Awad et al. (2014). We consider that each individual is represented by two homologous chromosomes of length 2D with a potentially infinite number of loci. The map length is considered to be D from the centre of the chromosome to the edge, hence representing a chromosome with a defined centromere. Near the centromere, we have included a modifier locus that affects the rate of self-fertilization as well as a neutral locus linked to Comment citer ce document : Abu Awad, D., Billiard, S. (2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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the modifier. There are also two neutral loci integrated within the chromosome (at positions -D 2 and D 2 ) that recombine. Recombination occurs during gamete production and is considered to be uniform along the chromosome. New individuals are a combination of two gametes, either from two different individuals via outcrossing, or the same individual via selfing.

The number of new deleterious mutations occurring per chromosome per generation, is sampled from a Poisson distribution with mean U , where 2U is the genomic mutation rate. Their position on the chromosome is sampled from a uniform distribution in [-D, D]. For simplicity we first consider that all deleterious mutations have the same coefficient of selection s and dominance h. In order to evaluate the effect of the variance in mutational effects on fitness, certain parameter sets were run using a modified version of the script provided in Roze (2015), in which the coefficient of selection is drawn from a log-normal distribution (with mean µ and variance σ 2 and density function φ

(s) = exp[-(Log(s) -µ) 2 /(2σ) 2 ]/(sσ √ 2π
), truncated at s = 1 (an approximation of Fisher's geometric landscape model). We assume that the heterozygous effect η is constant, making s and h negatively correlated (i.e very deleterious mutations are recessive). The distribution of the dominance coefficients (h = η/s) is given by ψ(h) = (η/h 2 )φ(η/h). Self-fertilisation of an ovule produced by individual i occurs with probability α i t and is given by

α i t = α 0 W i t α 0 W i t + (1 -α 0 ) j =i W j t Nt-1 , ( 8
)
where α 0 is the proportion of an individual's male gametes that are available for self-fertilization. The probability of self-fertilization depends on the individual's relative fitness W i t compared to the average relative fitness of the other possible fathers in the population ( j =i

W i t
Nt-1 ). The lower an individual's relative fitness as a father, the lower the proportion of offspring produced via selfing. The proportion of an individual's offspring produced by selffertilization is sampled from a binomial distribution with parameters α i t and X i t . When α 0 = 0 the population is strictly outcrossing and the population is automatically considered non-viable if N t < 2. When outcrossing occurs, a father, say individual j, is randomly chosen among all possible individuals, except the focal individual to be sired. It successfully sires the focal individual with probability W j . A father is drawn until fertilization is successful, hence there is no limitation in the availability of male gametes.

Comment citer ce document : Abu Awad, D., Billiard, S. (2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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We explore two modes of transition from outcrossing to a self-fertilising reproductive regime by introducing one of two types of modifiers: 1) The rate of selfing of a new allele introduced at the modifier locus via mutation is drawn from a uniform distribution in [α 0d, α 0 + d], i.e. centred around the self-fertilisation rate α 0 (Equation ( 8)) of the mutant's parent, i,e. the new allele inducing a change in the selfing rate α 0 of mean 0 and variance d 2 3 . In this mode of transition, the rate of self-fertilisation can evolve anywhere between 0 and 1 until it reaches an Evolutionary Stable Strategy (ESS); and 2) In order to estimate the effect of the selfing rate induced by mutations at the modifier locus an allele resulting in a fixed selfing rate α m is introduced recurrently, with no back mutations, thus only increasing the selfing rate. In both models, alleles at the modifiers locus are co-dominant.

Initial conditions, measured variables and parameters run

Populations start at size K, with no deleterious mutations and monomorphic neutral loci. Deleterious and neutral mutations are then introduced and simulations are run until the population reaches mutation-selection-drift balance or goes extinct. Mutation-selection-drift balance is assumed to be reached when mean relative fitness W t over one thousand generations varies by less than 1 per cent compared to the average W t of the previous thousand generations. Once the equilibrium is reached, mutations are introduced at the modifier locus. Simulations are then run until population extinction or, once a new equilibrium is reached (the selfing rate and fitness become stable), for at least a further 100 thousand generations. So as to determine the genetic and demographic properties (e.g. the probability of extinction) of fully outcrossing populations, as well as to evaluate consequences of the selfing rate versus the consequences of the transition from outcrossing to a given selfing rate, simulations in which no mutations are introduced at the selfing modifier locus are also run for 150 thousand generations.

Population size, mean fitness (using Equation ( 7)), inbreeding depression, effective population size and the effective rate of self-fertilisation are measured each generation. The mean and standard deviation of all these variables are estimated (conditioned on survival of the population) over one thousand independent replicates for each parameter set. Inbreeding depression δ t is estimated by generating one selfed and one outcrossed offspring from a sample of 200 individuals. If the population size N t is smaller than 200 then the entire population is sampled. In order to estimate the effective

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Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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population size N e , as we consider that the neutral loci follow an infinite allele model, we use the expression for the expected mean frequency of heterozygotes H e using the infinite alleles model in a population of effective size N e (Gale, 1990, p. 325) :

H e = 4µN e 1 + 4µN e , ( 9
)
where µ is the mutation rate at the locus considered. From our simulations, we can calculate H e at each neutral locus using

H e = 1 - na i=1 p 2 i , (10)
(with na the number of alleles segregating at the neutral locus and p i the frequency of allele i in the population at that locus). We also measure the diversity at the neutral locus linked to the modifier to asses the contribution of the recurrent introduction of mutations at the modifier of the self-fertilisation rate on the observed N e . We ran simulations for intrinsic reproductive rates r 0 = 2, 4 and 10, with a haploid genomic rate U between 0.1 and 0.3 for r 0 = 2 (as for higher values of U all populations go extinct) and U between 0.1 and 0.6 for the other values of r 0 . Mutations in simulations run with fixed values of s and h were either mildly deleterious or very deleterious (coefficient of selection s = 0.02 and 0.2), and with either completely recessive with h = 0 or moderately recessive (h = 0.1 and 0.2). In simulations where the coefficient of selection of new mutations is sampled from a log-normal distribution, as in Roze (2015) the mean and variance of the distribution are ≈ -3.316 and 0.8 respectively, resulting in a mean coefficient of selection s = 0.05 and h = 0.25 (the mean of the product sh is therefore η ≈ 0.00659). The recombination rate D is set at 10, as D over 10 has very little effect on the results (Roze, 2012), even though selective interference is expected when there is selfing (Roze, 2015). The mutation at the neutral loci is set at 10 -3 . At the modifier locus, two mutation rates are simulated, 10 -3 and 10 -5 . For the evolution of self-fertilisation to an ESS (mutations are drawn from a uniform distribution [α 0d, α 0 + d]), simulations were run with new alleles introduced at the modifier locus having an effect range d of 0.01, 0.1, 0.5 and 0.9 (giving means around the initial selfing rate of 0 and variances 3.10 -4 , 3.10 -3 , 0.08 and 0.27 respectively). When selfing evolves due to a single type of mutant allele Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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at the modifier locus with selfing rate α m , simulations are run for different α m = 0.1, 0.3, 0.6, 0.9, 0.95 and 0.99. Simulations without the evolution of selfing are run for fully outcrossing populations (α 0 = 0) and values α 0 set at the same values as those used for α m .

Results

Our goal is to investigate the demographic consequences of the evolution of self-fertilisation under different scenarios. First, we explore the expected demographic and genetic properties of populations without the evolution of self-fertilisation, notably population size (which directly reflects population fitness, see Equations ( 3) and ( 6)) and inbreeding depression. We compare simulation results with analytical expectations detailed in the previous section and from previous theoretical works (Roze, 2015). We then allow the evolution of self-fertilisation using two approaches: 1) Self-fertilisation is allowed to evolve freely until it reaches an Evolutionary Stable Strategy (ESS) and 2) A modifier with a large fixed effect is introduced recurrently into the population and can even go to fixation. Finally we touch on the evolution of the effective population size during and after the transition from an outcrossing to a self-fertilising reproductive system and discuss the effects of the demographic parameters (the intrinsic reproductive rate r 0 and the carrying capacity K) on population persistence. We briefly summarise the results obtained from simulations for different parameter sets in Table 1, taking into account the initial (before the evolution of selfing) and final (after the evolution of selfing) states of populations depending on the genetic and demographic parameters. Initial outcrossing populations are either stable or unstable: Stable populations are those which are not expected to go extinct in a relatively short time frame as all simulations result in viable populations for at least 150 thousand generations. Unstable populations are those susceptible to extinction due to demographic and genetic stochasticity within a relatively short time frame (at least one out of one thousand simulations resulted in extinction).

Fixed self-fertilisation rates

In Figure 1 we show that the expected inbreeding depression and population size at mutation-selection equilibrium for populations with fixed rates Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

of self-fertilisation are well predicted by the analytical terms in Equations ( 3), ( 4) and ( 5). When mutations are completely recessive (h = 0, see Figure 1a), inbreeding depression is much higher than 0.5 and self-fertilisation is not expected to evolve in such populations. With partially recessive mutations, inbreeding depression can be low enough to allow the evolution of selfing, provided the deleterious mutation rate is small enough (U ≤ 0.2 for h = 0.1 and U ≤ 0.5 for h = 0.2). For levels of inbreeding depression slightly higher than 0.5, the purging provoked by the recurrent introduction of selfing modifiers, as well as the consequences of genetic drift in small populations, could facilitate the evolution of self-fertilisation.

In Figure 1b, we show that population size increases with the selfing rate (as deleterious mutations are better purged) and decreases with the deleterious mutation rate U . If the deleterious mutation rate is too high, or the reproductive rate too low, populations may be non-viable (the expected population size at equilibrium N det is negative). From Figure 1b, one can expect that population size should increase as the mean selfing rate increases during the transition from outcrossing to selfing because of purging, but only if the demographic effects of purging are negligible, which, as we show below, is not always the case. However, even if the effects of purging are negligible, if the coefficient of selection is too small (i.e. s = 0.02), populations that evolve to very high selfing rates are expected to go extinct as all simulations run for a selfing rate α ≥ 0.98 and s = 0.02 resulted in extinction (even for low deleterious mutation rates and high intrinsic reproductive rates).

Evolution of selfing rates to the ESS

We investigate the ESS of the selfing rate by introducing mutations at a selfing modifier locus (that can either increase or decrease the selfing rate) in an initially fully outcrossing population. The effects of these mutations are drawn from a uniform distribution centred around the modifier's current selfing rate. New alleles introduced at the modifier locus can therefore either decrease or increase the self-fertilisation rate. We follow the evolution of self-fertilisation until we either reach an ESS (defined as the stabilisation of both the self-fertilisation rate and population fitness) or the population goes to extinction.

In populations where self-fertilisation evolves (δ is sufficiently low, i.e. U is not too high and h > 0, see Figure 1), the observed rate of self-fertilisation is not far from the expected ESS of selfing rate α = 1 (the mean observed

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selfing rate ᾱ ≈ 0.98, Figure 2). The coefficient of selection s influences the time needed for populations to purge their deleterious load and reach the ESS, as well as the viability of populations once the ESS value of selfing is reached (Figure 2a). In the first phase, population size (hence fitness) increases and inbreeding depression decreases with the selfing rate. Once the ESS of the selfing rate is attained, populations either remain viable, or, if the coefficient of selection is small (i.e s = 0.02), deleterious mutations accumulate (Supplementary Figure ??), leading to extinction (bottom frame of Figure 2a). Extinction occurs relatively fast once the ESS of the selfing rate is reached, with the average time to extinction being situated between 2000 and 40000 generations depending on the parameter set considered (for the parameter set shown in Figure 2, extinction occurs within 2500 generations for s = 0.02). As expected from the simulations run with a fixed selfing rate α 0 = 0.99 (Figure 1b), eventually all populations in which deleterious mutations have a small coefficient of selection go extinct after the evolution of high selfing rates. This remains true for simulations run with a very small effect range of mutations at the selfing modifier locus (d = 0.01) and also in the case of a coefficient of selection of deleterious mutations sampled from a distribution, with mean s = 0.05 and h = 0.25 (even for low deleterious mutation rates and high intrinsic reproductive rates, Supplementary Figure ??). Decreasing the mutation rate at the modifier locus (µ = 10 -5 , Supplementary Figure ??) increases the time necessary for populations to evolve selfing rates high enough to trigger the accumulation of deleterious mutations, but has no effect on the probability of extinction (i.e. all populations go extinct). Once again, when high selfing rates evolve, time to extinction is relatively short.

In Figure 2b we examine how the change of the selfing rate affects population genetics in comparison to expectations from population genetics models. More specifically we follow the changes in mean population fitness and inbreeding depression conditioned on survival change, not as a function of time, but of the mean selfing rate ᾱt . When compared to the expected relationship between the rate of self-fertilisation and these two variables (fitness and inbreeding depression) under the model with infinite loci and linkage disequilibrium (Equations ( 4) and ( 5)), we find that as the rate of self-fertilisation increases, the genetic properties of populations are well predicted by the analytical expressions from Equations ( 4) and (5) (represented by the line with the black contour in Figure 2b), except for s = 0.02 where fitness plunges at high selfing rates.

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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Despite the recurrent introduction of mutations at the selfing modifier locus that could decrease the selfing rate, these do not go to fixation, hence implying that the evolution to high selfing rates is irreversible. The same patterns are observed for mutations of a larger range of effects at the modifier (greater values of d, Supplementary Figure ??), the main differences being a faster evolution to the ESS and, for mildly deleterious mutations (i.e s = 0.02), shorter times to extinction due to the accumulation of deleterious mutations once at the ESS or extinction due to the demographic consequences of the purging of deleterious alleles (discussed below).

Modifiers with large fixed effect

In the previous section, self-fertilisation was allowed to evolve freely and continuously towards the ESS. However, as it is possible that selfing can evolve from a single effect mutation, we also explore the consequences of introducing recurrent mutations of a strong effect at the selfing modifier locus. The consequences of the introduction of such mutations depends on the demographic state of the initial outcrossing population, as different parameter sets can lead to either stable or unstable populations (Table 1). We define the former as populations that are part of a parameter set for which all simulations result in viable populations in the observed time frame and the latter are populations that are part of a parameter set in which at least one population out of the 1000 simulated goes extinct before 150 thousand generations due to demographic stochasticity (and not parameter sets for which all populations go extinct).

As predicted in Figure 1b, population size at equilibrium is higher once the alleles increasing the selfing rate are fixed at the modifier locus due to a lower mutational load (hence higher population fitness) than in the initial ouctrossing population. In simulations run with s = 0.02 population size does not immediately increase as the selfing rate increases, but there is an initial dip (resp. peak) in population size (resp. inbreeding depression, see Figure 3). This leads to an initial deviation from analytical expectations regarding the relationship between self-fertilisation and the genetic properties of populations that is accentuated by the mutants' selfing rate α m (Figure 3b). This pattern (dip and peak of fitness) is not observed for s = 0.2 (Supplementary Figure ??).

The dip in population size is due to the demographic consequences of the purge: as individuals self-fertilise, they produce a portion of non-viable off-Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

spring carrying deleterious mutations at the homozygous state. As the selfing rate increases, this portion of non-viable offspring increases, further decreasing the reproductive rate and hence population size, until the mutations have been purged and the population is at mutation-selection equilibrium, after which populations go to their equilibrium size. A temporary increase of inbreeding depression could be explained by two phenomena: the purging of deleterious mutations and the potentially independent origins of selfing lineages. The latter hypothesis seems to contribute little to this observation, as the amplitude of the peak in the level of inbreeding depression is not greatly affected by the mutation rates at the modifier locus and results indicate that selfing lineages probably originate from a single self-fertilising ancestor (Supplementary Figure ??). Under the first hypothesis purging has a tendency to eliminate inbred lineages that become highly homozygous for deleterious alleles, while conserving those with higher heterozygosity than initially present in the population. A consequence of this increased heterozygosity is an increase in inbreeding depression and a higher short-term diversity, as confirmed by the observed evolution of neutral genetic diversity (see section below).

During the purging phase, unstable populations can go extinct (Figure 3c) before the fixation of the self-fertilising allele at the modifier locus. The higher the selfing rate of the mutant α m , the stronger the initial dip in population size and the higher the extinction rate in a relatively short time frame (in less than 500 generations, see Figure 3c). The mutation rate at the modifier locus has no effect on the amplitude of the dip in population size, nor on the proportion of populations that go extinct during the purging phase (Supplementary Figure ??). Roughly, there are two outcomes: populations suffering less drastic bottlenecks tend to recover and reach the new equilibrium size, whereas those with smaller sizes go to extinction. Once the new equilibrium has been reached, contrary to their unstable initial state, populations become stable, with no extinctions observed for at least 150 thousand generations (populations run with α 0 = α m are also stable on the long-term). The transition towards higher selfing rates has thus two contradictory effects: it decreases the survival rate of unstable populations on the short term, however populations that survive the demographic consequences of the purge go on to be stable on the long term, resulting in an evolutionary rescue. If however after this initial fixation of a self-fertilising modifier is followed by an evolution of self-fertilisation to the ESS (with smaller modifier effects), we should expect that these populations would go to inevitable extinction

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Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

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(as shown in the previous section). Indeed, when the range of the effects of the selfing modifier are large (d > 0.1), we also observe the dip in population size and in some cases extinction as for modifiers with a fixed effect (Supplementary Figure ??).

Effective population size and lineage selection

In Figure 4, we follow the changes in effective population size relative to demographic size (N e /N ) using the recombinant neutral loci. With selfing modifiers of a fixed effect and mildly deleterious mutations (s = 0.02) we can observe three phases in the changes of the ratio N e /N (Figure 4): An initial peak followed by a rapid dip and finally a slow increase to the new equilibrium ratio (lower than that observed in the initial outcrossing population). These phases are accentuated by the amplitude of the effect of the alleles introduced at the selfing modifier locus (the range d in the case of continuous evolution, and α m of the fixed effect mutations). If self-fertilisation evolves continuously with small mutations at the modifier locus, this peak is never observed and increasing self-fertilisation leads to an almost linear decrease of the Ne N ratio (Supplementary Figure ??).

The initial peak of N e /N corresponds to the dip in population size and peak in inbreeding depression (see Figure 3c). This implies that the demographic consequences of the purge occur at a faster pace than the decrease in genetic variability. This indicates that this peak phase is in large part due to the purge of homozygous deleterious mutations, initially leaving an excess of heterozygous individuals (thus increasing inbreeding depression, Figure 3). As population size recovers, the ratio Ne N decreases to below its initial value, once again because of the differences in time scales necessary for demographic and genetic equilibria, then increases slowly to its new equilibrium value. New equilibrium population size is therefore reached before that of neutral diversity, as expected from works exploring the time necessary for the recovery of neutral diversity after the re-establishment of a large population size following a demographic bottleneck [START_REF] Tajima | The effect of change in population size on dna polymorphism[END_REF]. Indeed this pattern is not observed when the purge is not accompanied by a demographic bottleneck (i.e. for low values of d and for s = 0.2, Supplementary Figure ??).

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

Demographic parameters and their consequences

Extinctions during the transition from outcrossing to self-fertilisation occur only in initially unstable populations (see Table 1). In order to verify whether these extinctions are a consequence of small population size, simulations for the same genetic parameters and similar initial population sizes of outcrossing populations (i.e higher reproductive rates and lower carrying capacities) were run. Figure 5 shows that, in spite of the dip in population size due to the demographic consequences of the purge, no populations go extinct when the reproductive rate is higher. Population size per se is therefore not a deciding factor in the persistence probability of a population during a mating system transition. This implies that extinction is a consequence of the transition from outcrossing to a selfing reproductive system coupled with small reproductive rates.

Discussion

Models on the evolution of self-fertilisation have so far not taken into account the potential consequences of transition from outcrossing to selfing on population demography as well as any feedback between population size and selection. We first discuss to what extent demographic feedback can affect the evolution of self-fertilisation. Then we examine the mechanisms through which self-fertilisation can lead to population extinction both on the short and long-term. Third, we compare our results to existing empirical data on the evolution of self-fertilisation.

Final states are unchanged by demographic feedback in viable populations

The equilibrium states (i.e. mutation-selection-drift balance) of viable populations that have successfully evolved from an outcrossing to a self-fertilising reproductive system agree with the expected equilibria of self-fertilising populations as in previous models without demographic feedback (Figures 2b and3b, [START_REF] Lande | The evolution of self-fertilization and inbreeding depression in plants .1. genetic models[END_REF][START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Kamran-Disfani | Selfing, adaptation and background selection in finite populations[END_REF]Roze, 2015). As expected, in order for self-fertilisation to evolve, inbreeding depression must be low enough and the purging of deleterious mutations must be possible. Selection can either facilitate the purge

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

of deleterious mutations, and (in the case of the continuous evolution of selfing) populations evolve very high rates of self-fertilisation (≈ 1), or deleterious mutations cannot be purged and the population remains outcrossing [START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Gervais | Genetic architecture of inbreeding depression and the maintenance of gametophytic self-incompatibility[END_REF].

We generally find that if the rate of self-fertilisation were to evolve continuously with small enough mutational steps, the continuous evolution of selfing results in a smooth and continuous change of the genetic and demographic variables and analytical theory provides relatively good predictions of how the genetic variables evolve with the change of self-fertilisation (except for small s when high selfing leads to extinction Figure 2b). In this case, the rate of selfing at a time t can be used to predict population fitness (hence size) as well as the level of inbreeding depression (Figure 3). However, for mildly deleterious mutations (s = 0.02) and modifiers of stronger effects on the selfing rate (be it the continuous evolution to the ESS or mutation to a fixed rate of self-fertilisation, with parameter α m ), there is an initial increase (resp. decrease) in inbreeding depression (resp. fitness and size, see Figure 3) before the population reaches its equilibrium state.

The initial increase of inbreeding depression is not observed when selfing evolves slowly as the purge occurs at the same speed as the change in the level of inbreeding. However, this phenomenon is intuitive as the selection against individuals homozygous for deleterious alleles increases the population's heterozygosity, thus resulting in higher inbreeding depression. High inbreeding depression in selfing populations may therefore be an indicator of a recent shift in the reproductive regime. This is further accentuated by the potential existence of several selfing lineages with different mutational backgrounds, which increases the variability between individuals. Independent appearances of alleles promoting selfing rate have been documented in natural populations [START_REF] Shimizu | Evolution of Selfing: Recurrent Patterns in Molecular Adaptation[END_REF], such phenomena during the transition from outcrossing are therefore plausible. A snowball effect could also be in play, with one allele increasing in frequency, triggering the purge, hence allowing the increase in frequency of any other alleles segregating at the modifier locus (see Supplementary Figure ??b).

Towards evolutionary suicide

As suggested both by theoretical and empirical works [START_REF] Takebayashi | Is self-fertilization an evolutionary dead end? Revisiting an old hypothesis with genetic theories and a macroevolutionary approach[END_REF][START_REF] Wright | Evolutionary consequences of self-fertilization in plants[END_REF], self-fertilisation can be an evolutionary deadend. Theoretical works have pointed to the accumulation of mildly delete-Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

rious mutations in populations with high selfing rates being responsible for population extinction [START_REF] Lynch | Mutational meltdowns in sexual populations[END_REF][START_REF] Abu Awad | The Interaction between Selection, Demography and Selfing and How It Affects Population Viability[END_REF], which seems to be the case even when the effects of deleterious mutations are sampled from a distribution (Supplementary Figure 2b). However, these results depend greatly on the properties of new deleterious mutations, requiring them to have, on average, small selective coefficients, which is supported by empirical estimations of the distribution of mutational effects on fitness [START_REF] Agrawal | Inferences about the distribution of dominance drawn from yeast gene knockout data[END_REF][START_REF] Keightley | Rates and Fitness Consequences of New Mutations in Humans[END_REF]. Here we show that high rates of self-fertilisation are not only an evolutionary dead-end but a mechanism for evolutionary suicide. For this, three conditions must be fulfilled: 1) Ancestral outcrossing populations must be viable, 2) The evolution from outcrossing to selfing must be possible (inbreeding depression in the initial population must be low enough) and 3) The equilibrium rates of self-fertilisation attained must be high enough to trigger a mutational melt-down. Figure 2 shows that all these conditions can indeed be fulfilled. Though it has also previously been shown that interspecific interactions can cause evolutionary suicide of selfing populations [START_REF] Lepers | How does pollination mutualism affect the evolution of prior self-fertilization? A model[END_REF] due to feedback mechanisms between demography and genetics, our work is the first to explicitly show that even without such complex interactions initially stable populations continuously evolving from outcrossing to very high self-fertilisation rates can go to extinction.

Purging: the up and the down side

For mating systems to evolve to strict selfing, deleterious mutations must be purged, and when this is possible the final state of populations is either longterm stability or relatively rapid extinction due to either the demographic consequences of the purge or, when selfing rates are very high, a mutational meltdown is triggered. Though purging is often considered to be a positive mechanism in the evolution of selfing, especially since it is expected to decrease inbreeding depression [START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF][START_REF] Frankham | Inbreeding and extinction: Effects of purging[END_REF], any potential demographic consequences of expressing deleterious mutations during purging through inbreeding can be important and be the cause of population extinction as shown empirically in Drosophila melanogaster [START_REF] Frankham | Inbreeding and extinction: Effects of purging[END_REF]. The strength of the purge depends not only on the properties of deleterious mutations but also on the strength of mutations modifying the selfing rate: The smaller the effect of deleterious mutations and the higher the selfing rate of individuals carrying mutations at the self-

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

ing modifier locus, the stronger the strength of the purge, and, despite the important accompanying decrease in inbreeding depression, the greater the probability of extinction during the transition (see Figure 3c). [START_REF] Wright | The Long-Term Benefits of Self-Rejection[END_REF] have suggested that the high extinction rates observed in populations that have recently transitioned to a self-fertilising reproductive system could be due to the unfavourable demographic properties of such populations and not the reproductive system as such. Our results support this hypothesis, as in unstable populations the introduction of mutations at the modifier locus precipitates the extinction of populations that are already at a high risk of extinction because of demographic stochasticity. On the other hand, populations surviving this purge, are then stable, in which case the evolution of self-fertilisation can be quantified as a mechanism of evolutionary rescue (Figure 3c). However, this remains true provided populations do not evolve to extremely high rates of self-fertilisation, triggering a mutational meltdown in a relatively short time compared to the initially outcrossing populations.

Population bottlenecks are commonly accompanied with a decrease in neutral genetic diversity (or effective population size N e , [START_REF] Frankham | Introduction to Conservation Genetics[END_REF]. The decrease in population size brought on by the purge of mildly deleterious mutations (s = 0.02) is associated with an increased Ne N ratio. When it is small, this ratio is often viewed as a signal for population vulnerability in conservation biology [START_REF] Frankham | Genetics in conservation management: Revised recommendations for the 50/500 rules, Red List criteria and population viability analyses[END_REF], but as pointed out by [START_REF] Palstra | Effective/census population size ratio estimation: a compendium and appraisal[END_REF], an Ne N ratio higher than 1 can be associated with a population with non-constant size. Indeed, the high Ne N ratio from our simulations is associated with the decline in population size during the purging phase. The peak in Ne N indicates that population size declines at a different scale than the neutral genetic diversity. Counter-intuitively, a recent transition to selfing, or the increasing frequency of a self-fertilising genotype (Figure 4 and Supplementary Figure ??), will result in a high Ne N and in some cases may in fact be a signal of demographic vulnerability due to decreasing population size.

The demographic and genetic consequences of the transition from outcrossing to selfing may be reduced if we were to take into account the consequences of sib-mating on the frequencies and states of segregating deleterious mutations, as suggested by Porcher and Lande (2016). However, taking sibmating into account would require a spatially structured model and would be applicable only to species in which dispersion is limited.

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

Implications for macro-evolution

Self-fertilisation has been considered an evolutionary dead-end for at least half a century [START_REF] Stebbins | Self fertilization and population variability in the higher plants[END_REF]. This has been supported by empirical works, for instance in the Solonaceae, where self-fertilising species have been shown to have higher extinction rates than their self-incompatible sister species [START_REF] Goldberg | Species selection maintains self-incompatibility[END_REF]. Higher extinction rates have been attributed to two major phenomena: 1) The lack of adaptive potential due to lower standing variation in selfing species Glémin and Ronfort 2013) and 2) The accumulation of deleterious mutations, leading to the mutational meltdown [START_REF] Lynch | Mutational meltdowns in sexual populations[END_REF][START_REF] Abu Awad | The Interaction between Selection, Demography and Selfing and How It Affects Population Viability[END_REF]. Our results support that the transition from an outcrossing to a selfing reproductive system is associated with higher extinction rates due to the accumulation of deleterious mutations. Also, due to the feedback between population size and selection, populations can become vulnerable during the transition from outcrossing, further increasing the probability of extinction. However, the evolution of self-fertilisation is a mechanism that can increase population viability as it is expected to increase population mean fitness, hence population size. This should render populations less susceptible to extinction, all the more so in the presence of ecological perturbations [START_REF] Thomann | Flowering plants under global pollinator decline[END_REF].

The rapidity with which extinction occurs due to the consequences of deleterious mutations leads us to conclude that the extinctions observed on the time scales on which phylogenies are based may not be due to mutational meltdowns but to a lack of adaptive potential as would be expected from the very small effective population sizes N e of selfing populations (Figure 4 and Supplementary Figure ??, Stebbins 1957;[START_REF] Takebayashi | Is self-fertilization an evolutionary dead end? Revisiting an old hypothesis with genetic theories and a macroevolutionary approach[END_REF][START_REF] Glémin | Adaptation and maladaptation in selfing and outcrossing species: new mutations versus standing variation[END_REF]. Contemporary selfing species are therefore most probably those that have survived the initial purging process and which possess genetic mechanisms that allow the avoidance of long-term fitness decline as suggested by Wright et al. (2008) (i.e. in our model if deleterious mutations were to have stronger coefficients of selection, then a low effective population size would not result in triggering a mutational meltdown, Supplementary Figure ??b). However our results have implications for the transition rates used in works on plant phylogenies [START_REF] Goldberg | Species selection maintains self-incompatibility[END_REF][START_REF] Goldberg | Tempo and mode in plant breeding system evolution[END_REF], which may indeed be underestimated as such short lived transitions would not be easily detected.

Finally, we find that the populations most robust to the transition from outcrossing to selfing are, for a same initial population size, those with a Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

higher reproductive rate (Figure 5). This implies that selfing may be associated with high reproductive rates relative to those observed in outcrossing sister species and/or populations. r-strategies have indeed been observed in natural populations, with for instance Arabidopsis thaliana having reproductive rates that are several orders of magnitude larger than outcrossing sister taxa [START_REF] Van Daele | A comparative study of seed yield parameters in arabidopsis thaliana mutants and transgenics[END_REF] and self-fertilisation being associated with an annual life history [START_REF] Morgan | The evolution of selffertilization in perennials[END_REF]. Our results therefore support that if the selfing lineages currently observed generally follow r-strategies, it may be because of lineage selection: i.e. lineages have a higher probability of surviving the transition from outcrossing to selfing when their reproductive output is high.

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

Wright, S. I., R. W. Ness, J. P. Foxe, and S. C. H. [START_REF] Barrett | Plant reproductive systems and evolution during biological invasion[END_REF]. Genomic consequences of outcrossing and selfing in plants. Int J Plant Sci 169:105-118. 3), replacing W eq with W det from Equation (4). r 0 = 4, K = 10000, s = 0.02, h = 0.2.

Tables

Figure 2:

The demographic and genetic consequences of the evolution of self-fertilisation to an ESS for mildly (s = 0.02, grey lines) and strongly (s = 0.2, black lines) deleterious mutations in stable populations with r 0 = 4, K = 10000, U = 0.4, h = 0.2, with a range of the effect of mutations at the modifier set at d = 0.1 and the mutation rate at the modifier µ = 10 -3 using results from 1000 simulations run for each parameter set. a) From top to bottom: Changes with time in the mean selfing rate, the mean population size, inbreeding depression over all simulations run conditioned on survival, and the percentage of surviving populations, i.e. simulations that have not (yet) resulted in extinction at a given time. b) The change in mean fitness and inbreeding depression during the evolution of self-fertilisation over all the simulations run and conditioned on survival. The line with the black contour represents analytical expectations using Equations (4) and (5).

Comment citer ce document : Abu Awad, D., Billiard, S. ( 2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Accepted Article

Figure 3: The mean demographic and genetic consequences of the evolution of self-fertilisation (over 1000 independent simulations) with modifiers of strong effect in stable (r 0 = 4, sub-figures a,b) and unstable (r 0 = 2, subfigures c,d) populations with parameter values K = 10000, U = 0.3, h = 0.2, s = 0.02 and µ = 10 -3 . a) Changes with time in the mean selfing rate, mean population size and inbreeding depression over all simulations run conditioned on survival, as well as the percentage of viable populations, during the evolution of self-fertilisation. α m = 0.3, 0.6 and 0.9 shown respectively by black, dark grey and grey lines. b) The change in mean fitness and inbreeding depression during the evolution of self-fertilisation over all the simulations run and conditioned on survival. The line with the black contour represents analytical expectations using Equations ( 4) and ( 5). c) Same as a) but for unstable populations. The dotted line represents the percentage of surviving populations over 1000 simulations in which self-fertilisation does not evolve (α = 0). d) Same as b) but with unstable populations.

  Comment citer ce document : Abu Awad, D., Billiard, S. (2017). The double edged sword: the demographic consequences of the evolution of self-fertilisation. Evolution, 71 (5), 1178-1190. , DOI : 10.1111/evo.13222

Figure 1 :

 1 Figure1: Genetic and demographic properties of populations without the evolution of self-fertilisation. a) Observed mean inbreeding depression over all the simulations run (1000) and conditioned on survival (points) in completely outcrossing populations (α = 0) as a function of the haploid mutation rate (U ) different coefficients of dominance (h = 0, 0.1 and 0.2). Deleterious mutations have coefficients of selection s = 0.02 (circles) or s = 0.2 (squares), and r 0 = 10, K = 10000. Lines represent analytical expectations from Equation (5). b) Mean population size over all the simulations run and conditioned on survival as a function of the self-fertilisation rate. The points are simulation results and the full grey lines the deterministic expectations from Equation (3), replacing W eq with W det from Equation (4). r 0 = 4, K = 10000, s = 0.02, h = 0.2.

Figure 4 :

 4 Figure 4:The mean change in the selfing rate and effective population size relative to demographic size with time over all simulations run (1000 independent runs) and conditioned on survival for α m = 0.3 (black line) and 0.6 (grey line). r 0 = 2, K = 10000, U = 0.3, h = 0.2, s = 0.02 and µ = 10 -3 . The dotted lines represent the theoretical expectation of the ratio N e /N = (2α)/2, where α the selfing rate is replaced by α t in our simulations, therefore taking into account the changing selfing rate with time.

Figure 5 :

 5 Figure5: Effect of demographic parameters during the evolution of self-fertilisation (with α m = 0.6) on population size and extinction. In grey r 0 = 2 and K = 10000, in black r 0 = 4 and K = 2350, giving the same initial outcrossing population sizes. U = 0.3, h = 0.2, s = 0.02 and µ = 10 -3 . Means obtained from 1000 independent simulations per parameter set and conditioned on survival.

Figures

  Figures

This article is protected by copyright. All rights reserved.

Acknowledgements

We would like to thank Denis Roze for many helpful discussions. Numerical results presented in this paper were carried out using France Grille, CNRS and on the Biomed virtual organization of the European Grid Infrastructure (http://www.egi.eu) via DIRAC (http://diracgrid.org). We thank the technical staff of the European Grid Infrastructure and the supporting National Grid Initiatives for providing the technical support and infrastructure. This work was supported by the French Agence Nationale de la Recherche ANR-11-BSV7-013-03 and benefited from the support of the Chair Modlisation Mathmatique et Biodiversit of Veolia Environnement -cole Polytechnique -Musum National dHistoire Naturelle -Fondation X.


Christophe Dubois

Marion Tharrey

Nicole Darmon
email: nicole.darmon@inra.fr

Christophe Dubois1

Marion Tharrey1

Nicole Darmon1

Identifying foods with good

Keywords: food, food budget, food prices, good nutritional quality and price, intervention research

INTRODUCTION

Studies suggest that the cost of food helps explain social inequalities in nutrition [START_REF] James | Socioeconomic determinants of health. The contribution of nutrition to inequalities in health[END_REF][START_REF] Aggarwal | Does diet cost mediate the relation between socioeconomic position and diet quality?[END_REF][START_REF] Darmon | The contribution of food prices and diet cost to socioeconomic disparities in diet quality: a systematic review and analysis[END_REF] , partly due to the direct relationship between diet quality and diet cost (4;5) . Energy-dense nutrientpoor foods are often the cheapest sources of calories [START_REF] Maillot | Nutrient-Dense Food Groups Have High Energy Costs: An Econometric Approach to Nutrient Profiling[END_REF] , making it more difficult for a person with a very limited budget to get a balanced diet (7;8) . However, healthy eating at low cost is achievable by making nutritionally optimal choices that target affordable nutrient-rich foods (9- 13) . Diet modelling approaches on French data showed that it is possible to get a balanced food basket with a modest budget of at least €3.50 per day per person (8;14) on condition that foods with good nutritional quality for price (NQP)-assessed as the relationship between nutrient profile and average national price-are selected [START_REF] Maillot | Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming[END_REF] . In short, getting a balanced diet on a small budget is difficult but not impossible, but is it realistic, and how do we translate theory into practice? To find out, the Opticourses intervention (www.opticourses.fr) was launched in 2012 in the northern neighbourhoods of Marseille (France) following two pilot actions conducted in 2010 and 2011. Within the framework of a multi-partner, territorial-community participative approach, the Opticourses project features supply-side and demand-side strands, both aimed at increasing purchases of good-NQP foods by financially struggling households.

The demand side of the intervention involved workshops on diet and budget attended on a voluntary basis by local inhabitants responsible for their household's food purchases [START_REF] Marty | Higher nutritional quality at no additional cost among low-income households: insights from food purchases of "positive deviants[END_REF] . The supply side was based on a social marketing intervention that aimed to make good-NQP foods accessible, visible and attractive in shops in the target neighbourhoods [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] .

Consistent with the existing literature, early exploration of the factors driving food purchases in the Opticourses population revealed that price was a major concern [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] , and that participants expressed a strong desire to know "the good price" for foods. This popular notion refered to an affordable price given a low food budget, within the range of market prices [START_REF] Lee | Monitoring the price and affordability of foods and diets globally[END_REF] . The research team thus made it its goal to operationalize this popular notion by co-constructing an educational tool called the 'Good Price Booklet', designed to help participants make sound combined nutritional and budgetary choices at the time of purchase.

The aim of this article is to describe the methodology used to produce the Good Price Booklet and to provide quantitative and qualitative assessments of its applicability, perception and use by the target public.

Comment citer ce document : Dubois, C., Tharrey, M., Darmon

MATERIAL AND METHODS

Study design and population

Details and characteristics of the "Opticourses" nutrition intervention (2012-2014) have been described elsewhere [START_REF] Marty | Higher nutritional quality at no additional cost among low-income households: insights from food purchases of "positive deviants[END_REF] . Participants facing financial problems and willing to participate in the "Demand" strand of the intervention were asked to provide a detailed record of foods entering their household over a 1-mo period. In-depth interviews were also conducted to understand the factors driving food purchases in this population [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] .

Methodology to create the Good Price Booklet

Food composition and price databases

The INCA2 food composition previous study [START_REF] Bocquier | Socio-economic characteristics, living conditions and diet quality are associated with food insecurity in France[END_REF] : one column for added sugars and one column for average national prices (calculated on the basis of purchases made by the 2006 Kantar consumer panel). The food composition table gives nutritional values for foods as consumed, and average national prices are expressed in € for 100g as consumed. However, here we needed to determine the price of foods as purchased, as this is the only relevant information to communicate to participants.

We therefore used correction coefficients enabling us to move from price of food consumed to price of purchase (e.g. the average price of 100g of cooked pasta was multiplied by a coefficient of 3 to obtain the average price of 100g of raw pasta).

SAIN and LIM calculations

SAIN and LIM are indicators that estimate foods' positive and negative aspects, respectively [START_REF] Darmon | Nutrient profiles discriminate between foods according to their contribution to nutritionally adequate diets: a validation study using linear programming and the SAIN,LIM system[END_REF] . SAIN estimates the adequacy, for 100kcal of food, for recommended daily intake (RDI) of protein, vitamin C, fibre, calcium and iron. LIM estimates the average excess, for 100g of food, of sodium, saturated fatty acids and added simple sugars. The SAIN/LIM ratio give a single indicator of nutritional quality: the higher the ratio of a food, the better its nutritional quality [START_REF] Maillot | Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming[END_REF] . In the specific case of a food having a LIM of less than

Definition of foods with good nutritional quality

The next stage of the analysis was carried out on a reduced composition table covering all the foods of the INCA2 table including fortified foods and foods described as "generic" (e.g.

"non-specified fruit" or "non-specified cheese") but excluding ready-made meals (due to their huge variability in composition), alcoholic beverages and zero-calorie beverages. Foods whose SAIN/LIM ratio was higher than the median calculated in this reduced table were considered to be of good nutritional quality

Determination of the good prices for foods of good nutritional quality

Each food of good nutritional quality was then attributed a good price, defined as the price below which the food can be considered as relatively inexpensive. To determine this price, two variables were used: the average national price of the food as purchased, and its "limit price" defined as equal to the value of the first price tertile of the group to which it belongs.

For each food, the average national price was then compared against the limit price, and the following rule was applied: when average national price was below limit price, then average national price was selected as the good price; if not, limit price was chosen instead.

Selection and grouping of foods of good nutritional quality and price for the Good Price Booklet

Based on the calculations described above, a list of foods with good nutritional quality and price was established to be communicated to workshop participants in the form of an educational tool called the 'Good Price Booklet'. To avoid communicating prices that were unrealistic as too low with regard to marketplace reality, it was decided to present only those foods whose average national price was no more than 2.5 times higher than the limit price.

The ratio of 2.5 was chosen because it is the average ratio observed between the price of "brand-name" foods and the price of the cheapest foods sold under the same name (9;10) .

The list of foods was appraised by an expert to avoid potential repetitions in the composition table (e.g. baked potato and boiled or steamed potato) and to group together similar foods under a single designation in accordance with their purchased form (e.g. potato). In that case, the good price indicated in the booklet was the average of good prices of the different foods that have been grouped together.

The selected foods were classified according to supermarket shelves. For some foods, booklet price was calculated by unit as sold in stores (e.g. for one grapefruit or one lettuce).

Assessment

Quantitative assessement of the in-booklet prices

Opticourses participants (n=91) were asked to collect all food-purchase receipts for their household over a 1-mo period. Purchase-receipt protocol training and data collection were previously described by Marty et al. [START_REF] Marty | Higher nutritional quality at no additional cost among low-income households: insights from food purchases of "positive deviants[END_REF] . For each food item, information from receipts (i.e.

date of purchase, corresponding INCA2 food name and code, quantity and price) were entered into a food purchases database. The validity of the food prices listed in the booklet was assessed by quantifying the percentage of purchases bought at a price lower than in-booklet price, by supermarket shelf category, and for the whole food list.

Qualitative assessment of the Good Price Booklet

As part of the effort to evaluate the Opticourses intervention, 19 semi-structured interviews were conducted with participants after the workshops by an external evaluator. The interview guide contained questions on the tools used during the workshops, in particular the Good Price Booklet.

Comment citer ce document : Dubois, C., Tharrey, M., Darmon

RESULTS

Opticourses households: descriptive characteristics

Sociodemographic characteristics of the Opticourses households are given in Table 1.

Average household size was 3.41 (range: 1-8) including 2 children on average (range: 0-6).

Almost half of the households (48.2%) were in a precarious financial situation, and one third (36.5%) declared severe financial difficulties. Each household shopped an average of 5 different stores while collecting receipts, and price was reported as the most important determinant of food purchases.

List of foods featuring in the Good Price Booklet

The different stages in the process of identifying the foods with good nutritional quality and price are summarized in Figure 1. The reduced INCA2 table with ready-made meals and alcoholic and zero-calorie beverages pre-eliminated contained 1,054 foods. The median SAIN/LIM ratio was then calculated on this reduced table, and foods with a SAIN/LIM ratio lower than this median were discarded, resulting in a list of 527 foods of high nutritional quality. Then foods with an average national price 2.5 times greater than their limit price were eliminated (mostly expensive foods such as shellfish, game meat, berries or nuts). Among the remaining foods (n=404), similar items were then grouped together under the same designation, resulting in 153 foods classified according to supermarket shelf. Table 2 presents the list of foods with good nutritional quality and price selected and included in the booklet.

For example, for generic foods, the in-booklet price is €1.94/kg for fresh vegetables, €2.42/kg for tinned or frozen vegetables, €1.80/kg for fresh fruits, €2.35/kg for pasta and rice, €4.34/kg for legumes, €2.07/kg for dairy products, and €9.56/kg for meat and fish (Table 2).

Creation of the Good Price Booklet

The Good Price Booklet was created in collaboration with a graphic designer (Figure 2). This educational tool is presented in the form of a small brochure in payment-card format. It was distributed to participants during the Opticourses intervention workshops to help them spot foods and their corresponding good price when shopping for groceries.

The flyleaf of the booklet carries the slogan "Good for my health and good for my wallet". widely-established health benefits [START_REF] Estruch | Primary prevention of cardiovascular disease with a Mediterranean diet[END_REF] , even though they were not strictly foods of good nutritional quality and price (olive oil has a SAIN/LIM ratio lower than the median of the SAIN/LIM table median and walnuts have an average price over 2.5 times higher than the limit price of their group). Therefore, for these two foods, the booklet did not give a price but instead stated "Although expensive, moderate consumption is good for your health". It was not possible to include foods specific to certain culinary cultures in the booklet (e.g. plantain, sorghum, etc.,) as average national prices in mainland France are often high. It was noted at the end of the booklet that "Traditional basic foods from your culture are usually of good nutritional quality, and you probably know where to buy them at a good price".

Quantitative assessment of the relevance of in-booklet price

Several trials were conducted and compared to test the suitability of the proposed method. It emerged that the choice of the median SAIN:LIM ratio to identify food of good nutritional quality in the table, and the choice of the price tertile of each group to estimate in-booklet prices was the most suitable method to have a sufficient number of foods in each group as well as a realistic price value with regard to prices observed on supermarket shelves. The tool was tested by the team and workshop participants. During the Opticourses intervention, 2386 purchases of foods with good nutritional quality and price were registered, of which 67.1%

were bought at a price lower than the in-booklet price (Table 3). When separately analyzing foods as categorized by supermarket shelf, over half of the purchases made were below prices displayed in the booklet, except for processed meats (46.5%), breads (8.3%) and oils & fats (25.3%). Note however that the booklet only counted a few foods in these 3 categories (due to their relatively low nutritional quality), resulting in few related purchases. None of the breakfast cereals listed in the booklet were purchased by the participants, and so we could not assess the relevance of the in-booklet price for this category. Percentages of purchases below prices displayed in the booklet were higher for foods for which the booklet prices were based on average national price rather than on limit price (i.e. up to 2.5 times cheaper than the average national price), suggesting that it was easier to find the former than the latter.

Applicability of the Good Price Booklet within the framework of the Opticourses intervention

One of the workshop's aims was to share experiences for buying food at lower prices.

Participants exchanged useful tips, with some of them knowing where to buy at unbeatable prices (flea markets, stock clearance stores, the fish market at the end of the morning, etc.). These discussions gave contributors the opportunity to highlight several strategies as substitutions between different food groups (e.g. purchasing less meat and more vegetables), intra-group substitutions (e.g. purchasing cheaper meats of higher nutritional quality), or 'price hunting' (e.g. for a given food, preferring low-cost foods over their brand-name equivalents). Thanks to the Good Price Booklet, the notion of "Good Price" was no longer theoretical. As the Good Price Booklet was designed to be easily transportable in a handbag, it can be used directly in purchase situations: if the price displayed in the shop is below the booklet price for a given food, it is a bargain!

Qualitative assessment of the Good Price Booklet

All the participants appreciated the quality of the discussions during the workshops. This was facilitated by the insight it gave into participants' concerns about the relationship between nutritional quality and food budget. The Good Price Booklet was praised by all the participants interviewed (with the exception of one person with reading difficulties), as well as by professionals. The tool, co-constructed with the workshop participants, was greatly appreciated and continues to be used more than a month after the workshops. Verbatim accounts recorded during interviews one month after the workshops include, for example:

"I

DISCUSSION

The Good Price Booklet, designed to help recognize foods with good nutritional quality and price when grocery shopping, resulted from a co-construction using the desire of people with financial difficulties to have information on "the good price" for foods, and the theoretical work of the research team on the notion of foods with a good NQP [START_REF] Maillot | Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming[END_REF] .

Two indicators-SAIN and LIM-were used to appreciate the nutritional quality of foods based on a limited number of nutrients (5 qualifying nutrients and 3 disqualifying nutrients).

This selection reflected a balance between the need to include nutrients that are of importance to public health and nutrient markers of other essential nutrients (21) . When implemented, the SAIN,LIM system was found to adequately discriminate foods according to their contribution to nutritionally-adequate diets [START_REF] Darmon | Nutrient profiles discriminate between foods according to their contribution to nutritionally adequate diets: a validation study using linear programming and the SAIN,LIM system[END_REF][START_REF] Maillot | Quantifying the contribution of foods with unfavourable nutrient profiles to nutritionally adequate diets[END_REF] . Several studies show that price is a major criterion in terms of food choices, and this is particularly true for people with a limited budget (23;24) .

Managing a small food budget effectively requires a sound understanding of food choices. It is true that the foods we are advised to consume more of to protect our health, such as fruit, vegetable and fish, are more expensive sources of calories, whereas carbohydrates and highfat and high-sugar foods are cheap sources of calories [START_REF] Darmon | The contribution of food prices and diet cost to socioeconomic disparities in diet quality: a systematic review and analysis[END_REF] . Nevertheless, while studies on the cost of a balanced diet unequivocally show that it is more difficult to get a balanced diet with a small budget (7;25) , they also show that it is not impossible on condition that food groups and good-NQP foods are chosen [START_REF] Maillot | Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming[END_REF] . The nutritional quality of foods correlates positively with food prices (expressed in €/100kcal based on average national prices) [START_REF] Darmon | A nutrient density standard for vegetables and fruits: nutrients per calorie and nutrients per unit cost[END_REF] . This indicates that price structure is generally negative for nutritional balance, because the most expensive foods are often the most nutrient-dense. However, there is strong dispersion around this correlation line, which shows the existence of foods with higher NQP than others: for the same price, one can find foods of high and lower nutritional quality. In particular, legumes, vegetable oils, wholemeal cereal products, milk, plain yoghurt, eggs, poultry and some seafood (e.g. tinned sardines) have a higher NQP "in absolute terms". Conversely, other animal products and most fruits and vegetables (with exceptions, such as carrots, orange juice, etc.) emerge as too expensive to have a good NQP (6;11;12) . Giving priority to foods with a good NQP "in absolute terms" makes it possible to create a nutritionally optimal diet for €3.50 per day [START_REF] Maillot | Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming[END_REF] .

Many studies have jointly addressed the notions of diet cost and diet quality [START_REF] Darmon | The contribution of food prices and diet cost to socioeconomic disparities in diet quality: a systematic review and analysis[END_REF] . Some have found that healthy eating does not necessarily cost more when foods with higher nutritional quality for their price are selected (8;12) . Above all, they highhlight that achieving higher- 11 quality diets does not entail major changes in habitual dietary patterns but rather optimal choices in each food group (e.g. by preferring low-cost foods to their brand-name equivalent, or canned products to fresh ones) (9;10) . However, any effort to encourage a balanced diet for underprivileged populations mainly by promoting foods with good NQP "in absolute terms" is potentially contentious: not only because many of them are rarely consumed and therefore not socially acceptable for everyone (as is the case for tinned sardines and giblets, for example) [START_REF] Maillot | Are the lowest-cost healthful food plans culturally and socially acceptable?[END_REF] but also because, given the variability of prices, it is highly theoretical to claim categorically that a food has higher nutritional quality for its price in absolute terms. In this regard, during the Opticourses workshops, the theoretical list of foods with good NQP "in absolute terms" quickly proved ill-adapted to the reality in the field. For example, participants challenged the relevance of the list because peppers were not included. The average national price of bell pepper is too high for it to qualify as a food with good NQP "in absolute terms", but the fact is that many participants managed to find this highly nutritious food far cheaper than the average national price. Basing their work on these observations and discussions over food prices, the research team was able to develop the notion of a food's good price.

The Good Price Booklet was produced in a dynamic two-way interaction between research and fieldwork. Co-construction is recognized as a factor for success in actions to promote health (28;29) . When they are developed in interaction with the public for which they are designed, educational tools have a better chance of being adapted to people's real situation and thus getting used. This is the case for the Good Price Booklet, since the qualitative assessment showed that the tool was appropriated by participants who knew how to use it.

Most participants appreciated the tool and continued to use it more than a month after the interventions, thus demonstrating that the tool meets participants' expectation to find foods of good nutritional quality at an affordable price relative to their food budget. Considering the socieconomically disadvantged situation of the study population, these results suggest that prices displayed in the booklet may remain appropriate for any other population, notwithstanding the fact that'good price' is a budget-dependent concept. Scaling up effective implementation of this education tools requires adapting the methodology to the target population. The booklet must notably integrate specific food patterns and dietary habits which may vary according to population or country considered. In particular, the Opticourses intervention targeted a financially-struggling population with diverse cultural backgrounds, which may have resulted in specific dietary habits. Booklet prices must also be adapted to domestic food prices and currency. This tool has several limitations. First, it uses average national prices dating from 2006, well before the Opticourses intervention began. It would be desirable to frequently update the inbooklet prices. However, collecting robust average national prices of foods is still a challenge [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] . In France, average national prices were estimated by researchers to be matched with consumption data from the two national dietary surveys, i.e. INCA1 (1998-99) and INCA2 (2006-07). Furthermore, previous analyses carried out as part of the Opticourses intervention showed that participants purchased food at prices significantly lower than the 2006 average national prices [START_REF] Marty | Higher nutritional quality at no additional cost among low-income households: insights from food purchases of "positive deviants[END_REF] , which thus remain relevant within the framework of our intervention. Second, national prices may not directly reflect local prices which are influenced by many factors such as local markets or policies [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] . Third, exposure to food contaminants, a growing health concern [START_REF] Hussain | Food Contamination: Major Challenges of the Future[END_REF] , is not captured by the SAIN,LIM calculation. Fourth, the definition of good nutritional quality in this study-based on the median of foods' SAIN/LIM ratios-is relative and depends on the number and type of foods included in the table. If the composition table contained more fruit and vegetables, for example, then the value of the median SAIN/LIM ratio would increase and thus modify the foods of good nutritional quality selected. Groups of foods high in fat and/or sugar would be less represented. An analysis based on the medians of the SAIN/LIM ratio of each group would allow for the selection of more foods in certain groups, but this choice was rejected here as since median values were hugely disparate depending on the group, some foods with high nutritional quality would be eliminated (e.g. certain fruits and vegetables) while others with lower nutritional quality would be selected (e.g. foods high in fats and sugars) due to the differences in nutritional quality of the groups to which they belong. To overcome these problems, one solution would be to adopt a non-relative definition of nutritional quality, such as its classification within the SAIN,LIM nutrient profiling system, which depends exclusively on the nutritional composition of each food, independent of the food group to which it belongs [START_REF] Darmon | Nutrient profiles discriminate between foods according to their contribution to nutritionally adequate diets: a validation study using linear programming and the SAIN,LIM system[END_REF] . A final limitation concerns the methodology used to produce the booklet's prices, which could itself be considered arbitrary. However, several trials were conducted to test the realism of the findings obtained by means of the method adopted, and they confirmed the possibility of finding the foods presented in the booklet at a price cheaper than listed. The method developed here needs to be validated more thoroughly to assess the sensitivity of results to spatial and temporal variation in food databases and average national prices. Various actors (departmental health education committees, family allowance offices, health insurance companies, dieticians, social workers, etc.) require adapted tools to address the issue of shopping and eating healthily on a low budget. The Opticourses Good Price Booklet enables them to move from theory to practice on purchasing food for a balanced diet on a low budget, and is an example of an educational tool produced through co-construction. The transferability of the Opticourses approach is currently being studied as part of a broader project in France. This will provide an opportunity to test the acceptability and benefits of Opticourses protocols and tools in different contexts in terms of target populations, organizations, areas, etc.

Health logos, nutritional information and even subsidies can give rise to unwanted effects and may be liable to increase social inequalities with regard to nutrition [START_REF] Darmon | Food price policies improve diet quality while increasing socioeconomic inequalities in nutrition[END_REF] . A positive nutritional logo exclusively indicating foods with a good NQP (by making them available, visible and attractive in shops) was found to direct purchases towards these foods [START_REF] Gamburzew | In-store marketing of inexpensive foods with good nutritional quality in disadvantaged neighborhoods: increased awareness, understanding, and purchasing[END_REF] and would be a concrete way to help consumers identify foods that enable them to reconcile nutrition and budget when they shop for food. Further research is now needed to investigate the effect on nutritional status of a positive logo scheme promoting good-NQP foods.

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  Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282 12

  Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282

	13

Table 1 .

 1 , N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282 Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Sociodemographic characteristics of Opticourses households (n=91)

	Mean (SD)

Public Health Nutrition, 20

(17)

, 3051-3059. , DOI : 10.1017/S1368980017002282 17 Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282 18

Table 2 .

 2 List of foods with good nutritional quality presented in the booklet with their 'good price' (€/kg or €/article)

			GOOD			GOOD
	SHELF	FOOD	PRICE	SHELF	FOOD	PRICE
			(€/kg)			(€/kg)
	VEGETABLES		GRAINS
		Aubergine	1.76		Wheat	2.35
		Avocado	0.44*		Couscous	2.15
		Beetroot	2.06		Pasta	2.09
		Chard	1.99		Wholemeal pasta	2.35
		Broccoli	2.18		Polenta/cornmeal	2.25
		Carrot	1.12		Rice	2.31
		Celery/celeriac	1.70		Wholemeal rice	2.35
		Mushroom	1.70	POTATO
		Cabbage a	1.74		Potato	1.28
		Cucumber	0.49*		Dried mashed potato	1.66
		Courgette	1.78		Potato gnocchi	2.35
		Chicory	1.81	LEGUMES
		Spinach	1.74		Dry kidney/white beans	5.19
		Corn on the cob	0.40*		Dry lentils	3.85
		Turnip	1.47		Dry split peas	3.48
		Onion	2.07		Dry chickpeas	4.83
		Leek	1.70	TINNED VEGETABLES
		Pepper	2.06		Carrots	2.42
		Pumpkin	1.70		Celery/celeriac	2.42
		Radish (bunch)	0.72*		Mushrooms	2.42
		Lettuce b	0.86*		Sauerkraut without garnish	2.42
		Tomato	2.18		Green beans	2.42
	FRUITS				Diced mixed veg.	2.19
		Apricot	2.18		Sweetcorn	2.42
		Pineapple	1.89*		Peas with or without carrots	2.42
		Banana	1.39		Ratatouille	2.42
		Lemon	2.18	TINNED TOMATOES
		Clementine/mandarin	1.70		Tomato concentrate	1.77
		Dried fruit c	3.90		Tomato sauce	3.01
		Kiwi	0.16*		Tomatoes	1.89
		Melon	1.70*	TINNED LEGUMES
		Plum	2.18		Kidney/white beans	2.67
		Nectarine/peach	2.18		Lentils	1.79
		Walnut d	-		Chickpeas	1.97
		Orange	1.23	TINNED FISH
		Grapefruit	0.64*		Cod liver	9.56
		Watermelon	0.73		Mackerel	8.74
		Pear	2.06		Sardine	7.94

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Darmon

, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282 Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282 21

Table 3 .

 3 Proportion, by supermarket-shelf category, of purchases of the booklet's foods bought by Opticourses participants at a price below the booklet's price * Not purchased by Opticourses participants

		Median (IQR) price, (€/kg)	Total, N	Price below the booklet's price, N	Price below the booklet's price, %
	Vegetables (fresh or frozen) 1.5 (1.0-2.0)	425	263	61.9%
	Fruit	1.5 (1.0-2.0)	373	219	58.7%
	Fish (fresh or frozen)	5.9 (4.0-12.0)	11	6	54.5%
	Meat (fresh or frozen)	6.8 (4.0-8.8)	163	93	57.1%
	Processed meat	9.8 (7.4-13.3)	28	13	46.4%
	Eggs	1.9 (1.9-2.8)	130	97	74.6%
	Dairy	0.9 (0.6-1.5)	319	276	86.5%
	Bread	3.8 (2.5-4.5)	12	1	8.3%
	Grains	1.2 (0.8-2.0)	209	164	78.5%
	Potato	1.0 (0.6-1.7)	126	84	66.7%
	Legumes	2.0 (1.3-2.7)	37	27	73.0%
	Tinned vegetables	2.2 (1.7-2.8)	87	51	58.6%
	Tinned tomatoes	1.6 (0.6-2.1)	100	73	73.0%
	Tinned legumes	1.8 (1.2-2.7)	27	18	66.7%
	Tinned fish	7.4 (5.8-9.2)	39	24	61.5%
	Soup	1.4 (1.0-2.0)	6	4	66.7%
	Juice	0.9 (0.7-1.1)	141	116	82.3%
	Oils & fats	1.5 (1.4-1.6)	95	24	25.3%
	Breakfast cereals*	-	-	-	-
	Sweet products	2.5 (1.8-4.6)	9	5	55.6%
	Frozen potato	1.1 (0.8-1.4)	49	42	85.7%

Flowchart showing how foods were selected for the Good Price Booklet Figure 2. Good Price Booklet distributed during Opticourses* workshops

  Note: *photo credits: Cédric Dubois Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282INCA2 table of the composition of foods (n=1,343)Elimination of foods whose average national price is 2.5 times higher than the limit price (except for olive oil and walnuts)Foods of good nutritional quality and price (n=404)

	Elimination of ready-made meals, alcoholic
	beverages and zero-calorie beverages
	Reduced INCA2 table of the composition of foods (n=1,054)
	Elimination of foods with a
	SAIN/LIM ratio < median
	Calculation of limit price for each food
	Foods of good nutritional quality (n=527)
	Grouping together similar foods under a
	single designation
	Dividing into categories depending on
	supermarket shelves
	Good Price Booklet (n=153)

Comment citer ce document : Dubois, C., Tharrey, M., Darmon, N. (2017). Identifying foods with good nutritional quality and price for the Opticourses intervention research project. Public Health Nutrition, 20 (17), 3051-3059. , DOI : 10.1017/S1368980017002282

Hind Gaigi (project leader), Malu-Séverine After two innovative actions funded by the ARS-PACA in 2010 and 2011, Opticourses received funding for 2 years from the Institut National du Cancer (INCa), and since September 2014 has been funded by the ARS-PACA to study its transferability on a regional scale. The funding organizations had no role in the design, analysis or writing of this article. The protocol of the Opticourses education intervention was reviewed by the Comité de Protection des Personnes Sud-Méditerranée which stated that no institutional review board approval was necessary for this research.

data analyses. CD and MT analyzed data, performed statistical analysis and wrote the first draft of the manuscript. All

Comment citer ce document : Dubois, C., Tharrey, M., Darmon