Leonor R Rodrigues

Mario Torralba Sáez

João Alpedrinha

Sophie Lefèvre

Muriel Brengues

Sara Magalhães

Alison B Duncan

Consequences of population structure for sex allocation and sexual conflict

Keywords: local mate competition, hard and soft selection, experimental evolution, budding dispersal, scale of competition, Tetranychus urticae

Both sex allocation and sexual conflict can be modulated by spatial structure. However, how the interplay between the type of dispersal and the scale of competition simultaneously affects these traits in sub-divided populations is rarely considered.

We investigated sex allocation and sexual conflict evolution in meta-populations of the spider mite Tetranychus urticae evolving under budding (pairing females from the same patch) or random (pairing females from different patches) dispersal and either local (fixed sampling from each subpopulation) or global (sampling as a function of subpopulation productivity) competition.

Females evolving under budding dispersal produced less female-biased offspring sex ratios than those from the random dispersal selection regimes, contradicting theoretical predictions. In contrast, the scale of competition did not strongly affect sex allocation. Offspring sex ratio and female fecundity were unaffected by the number of mates, but female fecundity was highest when their mates evolved under budding dispersal, suggesting these males inflict less harm than those evolving under random dispersal. This work highlights that population structure can impact the evolution of sex allocation and sexual conflict. Moreover, selection on either trait may reciprocally affect the evolution of the other, for example via effects on fecundity.

Introduction

Many organisms exist in structured populations, sub-divided into patches, that are linked and shaped by demographic factors such as dispersal. The frequency and type of dispersal can determine whether interactions are more likely to occur among related or unrelated individuals [START_REF] Hamilton | The genetical evolution of social behaviour[END_REF][START_REF] Bulmer | Sex ratio theory in geographically structured populations[END_REF][START_REF] Queller | Does population viscosity promote kin selection?[END_REF][START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF][START_REF] Courteau | Optimal sex ratios in structured populations[END_REF][START_REF] West | Sex Allocation[END_REF]. For instance, if dispersal is limited, such that only some individuals disperse, the probability of interactions among genetically related individuals in a patch increases compared to populations in which all individuals disperse [START_REF] Taylor | Altruism in viscous populations -an inclusive fitness model[END_REF][START_REF] Wilson | Can altruism evolve in purely viscous populations?[END_REF][START_REF] Taylor | Evolutionary stable strategy sex ratios when correlates of relatedness can be assessed[END_REF][START_REF] Hamilton | The genetical evolution of social behaviour[END_REF]. However, if individuals disperse in groups from the same patch (i.e., if there is budding dispersal), interactions among genetically related individuals can be maintained, even if dispersal rates are high [START_REF] Gardner | Budding dispersal and the sex ratio[END_REF][START_REF] Gardner | Demography, altruism, and the benefits of budding[END_REF][START_REF] Lehmann | Population demography and the evolution of helping behaviors[END_REF][START_REF] Lehmann | How life history and demography promote or inhibit the evolution of helping behaviours[END_REF][START_REF] Aviles | Interdemic selection and the sex ratio: A social spider perspective[END_REF].

Dispersal frequency and timing also influence the scale of competition. For example, high dispersal, and dispersal occurring prior to the competitive interaction, leads to global competition, in which individuals compete with equal probability with others in the population (West et al., 2002a[START_REF] Griffin | Cooperation and competition in pathogenic bacteria[END_REF][START_REF] Taylor | Altruism in viscous populations -an inclusive fitness model[END_REF]. In contrast, limited dispersal, and/or dispersal occurring after the competitive interaction, is associated with local competition (i.e., competition within the natal patch) (West et al., 2002a[START_REF] Griffin | Cooperation and competition in pathogenic bacteria[END_REF][START_REF] Taylor | Altruism in viscous populations -an inclusive fitness model[END_REF][START_REF] Frank | Foundations of social evolution[END_REF][START_REF] Wilson | Can altruism evolve in purely viscous populations?[END_REF]. Therefore, the type, frequency and timing of dispersal can have a significant impact on the scale at which competitive interactions occur.

In turn, both relatedness and the scale of competition can affect sex allocation -the differential investment into male and female offspring. Indeed, in subdivided populations, sex allocation theory predicts an offspring sex-bias towards the sex for which local competition between kin is less intense [START_REF] Wilson | Can altruism evolve in purely viscous populations?[END_REF][START_REF] Hamilton | Extraordinary sex ratios[END_REF][START_REF] Charnov | The Theory of Sex Allocation[END_REF]. For example, more female-biased offspring sex ratios are predicted when males compete locally on their natal patch for mates, and mated females disperse and compete globally for new patches [START_REF] Hamilton | Extraordinary sex ratios[END_REF][START_REF] Taylor | Intra-sex and intersex sibling interactions as sex ratio determinants[END_REF][START_REF] Herre | Sex ratio adjustment in fig wasps[END_REF]. If there is budding dispersal, relatedness among the offspring of foundresses increases, exacerbating local competition between related males for mates, thus selecting for even more female-biased sex ratios [START_REF] Gardner | Budding dispersal and the sex ratio[END_REF][START_REF] Aviles | Interdemic selection and the sex ratio: A social spider perspective[END_REF]. However, if the proportion of individuals dispersing is limited, and females compete locally for resources, competition becomes intense for both sexes and selection favours a more balanced offspring sex ratio (Table S1; [START_REF] Courteau | Optimal sex ratios in structured populations[END_REF][START_REF] Taylor | Evolutionary stable strategy sex ratios when correlates of relatedness can be assessed[END_REF][START_REF] Frank | Hierarchical selection theory and sex ratios. II. On applying the theory, and a test with fig wasps[END_REF][START_REF] Herre | Sex ratio adjustment in fig wasps[END_REF][START_REF] Bulmer | Sex ratio theory in geographically structured populations[END_REF][START_REF] Frank | The genetic value of sons and daughters[END_REF]. A few empirical studies to date have investigated the consequences of budding dispersal [START_REF] Kummerli | Limited dispersal, budding dispersal, and cooperation: an experimental study[END_REF], or disentangled the relative effects of the scale of competition and relatedness [START_REF] Griffin | Cooperation and competition in pathogenic bacteria[END_REF] on the evolution of kin-selected behaviours, but none have disentangled the effect of these two factors on sex allocation.

Population structure is also predicted to impact the evolution of sexual conflict, i.e., asymmetric reproductive interests between mating partners [START_REF] Pizzari | Inclusive fitness and sexual conflict: How population structure can modulate the battle of the sexes[END_REF][START_REF] Bourke | The kin structure of sexual interactions[END_REF][START_REF] Faria | Kin discrimination and demography modulate patterns of sexual conflict[END_REF]. Competition for mates between males often involves strategies that are harmful to females reducing their survival and reproductive output [START_REF] Arnqvist | Sexual Conflict[END_REF][START_REF] Parker | Sexual conflict over mating and fertilization: an overview[END_REF][START_REF] Wigby | Female resistance to male harm evolves in response to manipulation of sexual conflict[END_REF][START_REF] Crudgington | Experimental removal and elevation of sexual selection: does sexual selection generate manipulative males and resistant females?[END_REF]. However, under global competition, when interactions occur among kin, reduced harming behaviour in males is expected to be selected for, as harm reduces patch productivity [START_REF] Pizzari | Inclusive fitness and sexual conflict: How population structure can modulate the battle of the sexes[END_REF][START_REF] Pizzari | The sociobiology of sex: inclusive fitness consequences of inter-sexual interactions[END_REF][START_REF] Rankin | Kin selection and the evolution of sexual conflict[END_REF].

A number of empirical studies are compatible with this prediction [START_REF] Lukasiewicz | Kin selection promotes female productivity and cooperation between the sexes[END_REF][START_REF] Carazo | Within-group male relatedness reduces harm to females in Drosophila[END_REF][START_REF] Hollis | No evidence that within-group male relatedness reduces harm to females in Drosophila[END_REF][START_REF] Page | Male relatedness and familiarity are required to modulate male-induced harm to females in Drosophila[END_REF], but see [START_REF] Chippindale | Does kin selection moderate sexual conflict in Drosophila?[END_REF].

For instance, in the fruit fly Drosophila melanogaster, females repeatedly exposed to related, as opposed to unrelated, males presented a higher lifetime reproductive success [START_REF] Carazo | Within-group male relatedness reduces harm to females in Drosophila[END_REF].

The evolution of sexual conflict may also depend on the frequency [START_REF] Eldakar | Eight criticisms not to make about group selection[END_REF] and type of dispersal [START_REF] Faria | Kin discrimination and demography modulate patterns of sexual conflict[END_REF]. Because random dispersal reduces relatedness among competitors, it is predicted to increase the intensity of sexual conflict [START_REF] Faria | Sex-biased dispersal, kin selection and the evolution of sexual conflict[END_REF][START_REF] Rankin | Kin selection and the evolution of sexual conflict[END_REF]. This may be alleviated by budding dispersal, which maintains interactions among kin, reducing sexual conflict and harm inflicted to females, hence increasing their fecundity [START_REF] Faria | Kin discrimination and demography modulate patterns of sexual conflict[END_REF].

Although population structure is predicted to affect sex allocation and sexual conflict [START_REF] Bourke | The kin structure of sexual interactions[END_REF], no study to date has disentangled how the type of dispersal and the scale of competition impacts the evolution of both within the same set-up. This is at odds with the fact that evolution under different population structures may simultaneously impact sex allocation and sexual conflict in a non-independent manner, highlighting the need to integrate studies on these traits [START_REF] Chapman | Sexual conflict and sex allocation[END_REF][START_REF] Schärer | Sex allocation and sexual conflict in simultaneously hermaphroditic animals[END_REF]. For instance, changes in sex allocation may result in the production of more or fewer individuals of each sex, which impacts sexual conflict.

At the same time, sexual conflict may impact the number of offspring produced [START_REF] Carazo | Within-group male relatedness reduces harm to females in Drosophila[END_REF][START_REF] Lukasiewicz | Kin selection promotes female productivity and cooperation between the sexes[END_REF], which may in turn influence sex allocation [START_REF] Stubblefield | Local mate competition with variable fecundity: dependence of offspring sex ratios on information utilization and mode of male production[END_REF]. This is supported by studies showing that multiple mating can impede optimal sex allocation in the parasitoid wasp Nasonia vitripennis [START_REF] Boulton | Local mate competition modifies the costs of mating in a mostly monandrous parasitoid wasp[END_REF][START_REF] Boulton | A sex allocation cost to polyandry in a parasitoid wasp[END_REF].

Here, we uncover the effects of the type of dispersal and the scale of competition on the evolution of sex allocation and sexual conflict in the spider mite Tetranychus urticae. Previous work in this species has shown the evolution of sex allocation, and conflict between the sexes over the optimal offspring sex-ratio, in populations evolving under panmixy or local mate competition [START_REF] Macke | Experimental evolution of reduced sex ratio adjustment under local mate competition[END_REF][START_REF] Macke | Local mate competition mediates sexual conflict over sex ratio in a haplodiploid spider mite[END_REF]. In addition, it is known that in this species only the sperm from the first copulation fertilises a female's eggs [START_REF] Rodrigues | Costs and benefits of multiple mating in a species with first-male sperm precedence[END_REF]. Still, multiple mating is common in this species, imposing costs in females by reducing the proportion of daughters as well as female fecundity [START_REF] Rodrigues | Costs and benefits of multiple mating in a species with first-male sperm precedence[END_REF][START_REF] Macke | Mating modifies female life history in a haplodiploid spider mite[END_REF]. This reduction in female reproductive output is thought to be a consequence of strong competition among males and, thus, evidence of male harm due to sexual conflict [START_REF] Rodrigues | Costs and benefits of multiple mating in a species with first-male sperm precedence[END_REF].

In a fully crossed design, using experimental evolution, we placed replicate populations of T. urticae in 4 selection regimes with either local or global competition, and random versus budding dispersal. This design enabled us to follow evolution of both sex ratio and sexual conflict under different population structures. We expect sex allocation evolution under global competition to be towards more female biased offspring sex ratios than under local competition, due to reduced competition between related females locally in the patch. Furthermore, global competition, when coupled with budding dispersal, should produce the most female biased offspring sex ratios (see Table S1 for precise predictions for sex allocation under our different selection regimes). In contrast, as there is no mixing under local competition with budding dispersal, we do not expect selection to occur in this treatment.

Sexual conflict should also evolve differently in the different selection regimes. We predict that female harm inflicted by males, expressed as reduced fecundity, will be diminished when males evolve under budding dispersal, where interactions occur among kin.

Material and Methods

Biological model

The two-spotted spider mite, T. urticae Koch (Acari: Tetranychidae), is a generalist herbivore with a host range of over 1100 plant species [START_REF] Migeon | Spider Mites Web: A Comprehensive Database for the Tetranychidae[END_REF][START_REF] Helle | Spider Mites: Their Biology, Natural Enemies and Control[END_REF]. T. urticae has an arrhenotokous haplodiploid life cycle (~14 days egg -adult at 20-25˚C): sons develop from unfertilised, haploid eggs and daughters from fertilised, diploid eggs. In this species, females are the dispersing sex, whereas males generally remain on their natal patch with mating occurring before female dispersal [START_REF] Kennedy | Dispersal. In: Spider mites[END_REF][START_REF] Mitchell | Growth and population dynamics of a spider mite (Tetranychus urticae K., Acarina: Tetranychidae)[END_REF]. We report tertiary sex ratios (adult males divided by the total number of adult offspring) as males and females can only be distinguished as adults using microscopy: males are smaller than females and possess a pointed abdomen.

Population origins

In 2013, 10 different T. urticae populations were collected and separately maintained on bean plants at 25 ± 2°C, with a 16h light: 8h dark cycle at the University of Lisbon. These populations comprised seven populations from Portugal (Lou, DC, AMP, DF, CH, COL and RF), two from Spain (Albe and Alro) and one from France (FR) [START_REF] Zélé | Endosymbiont diversity and prevalence in herbivorous spider mite populations in South-Western Europe[END_REF]. All populations were treated with antibiotics to ensure that they were free of bacterial endosymbionts, known to be sex ratio distorters [START_REF] Breeuwer | Wolbachia and cytoplasmic incompatibility in the spider mites Tetranychus urticae and T. turkestani[END_REF]. The sex ratio of each individual population ranges from 0.22 to 0.40 [START_REF] Zélé | Endosymbiont diversity in natural populations of Tetranychus mites is rapidly lost under laboratory conditions[END_REF]. In November 2015, more than 50 females from each of the 10 populations were transferred to the University of Montpellier and mixed to form a genetically diverse population to seed the experiment (hereafter called the 'ancestral population'). This newly mixed population was maintained on 12 whole bean plants (variety: Pongo) in a plastic box (395 mm length x 335 mm width x 323 mm height) at 25˚C with a 16h light: 8h dark cycle. Each week, old plants were removed and replaced with young, un-infested plants. All bean plants used to maintain mite populations and for all experiments described below were grown from seeds in an isolated, herbivore-free room at 23 ± 1°C with a photoperiod of 12h light: 12h dark at the University of Montpellier.

Fourteen days before starting the experiment, 10 independent groups of 40 females were haphazardly sampled from the ancestral population and put on a patch (10-15 bean leaves placed together) on water-saturated cotton wool to lay eggs. This allowed maternal effects to be equalised and ensured that females seeding the experiment were of the same age. Two weeks later, when mites of the following generation had reached adulthood, all 10 groups were mixed, and the newly emerged mated adult females were haphazardly assigned to the different selection regimes.

Establishment and maintenance of selection regimes

The impact of different types of dispersal (budding versus random) and scales of competition (local versus global) on the evolution of sex allocation and sexual conflict in T. urticae was investigated using a fully crossed experimental design (Figure 1): 1) global competition, budding dispersal ('Global Budding', GB), 2) global competition, random dispersal ('Global Random', GR), 3) local competition, budding dispersal ('Local Budding', LB) and 4) local competition, random dispersal ('Local Random', LR). Each regime was replicated three times (GB-1, GB-2, GB-3, GR-1, GR-2, GR-3, LB-1, LB-2, LB-3, LR-1, LR-2 and LR-3).

For each replicate population, each generation comprised a total of 96 mated adult females, being assigned in pairs to 48 bean leaf patches (4 cm 2 each, corresponding to a very mild infestation level, thus low competition) placed on water-saturated cotton wool in a plastic box (255 mm length females from each of the 48 patches (squares) were transferred in pairs to a new patch for the next generation (Gx+1). In 'Local Random', an equal number of females (2 -4; the number was adjusted each generation to account for mortality) from each patch were pooled together on a large common leaf patch ('mixing patch', rectangle), from which females were subsequently haphazardly transferred in pairs to 48 new patches. In 'Global Budding', the number of adult females per patch was counted before each transfer to calculate fecundity relative to that of the other 47 patches in the replicate. Each patch contributed with a number of female pairs, to the following generation, proportional to its relative fecundity. In 'Global Random' all 48 patches were placed on a 'mixing patch' onto which females could disperse for ~4 hours, after which adult females were haphazardly transferred in pairs to 48 new patches for the next generation. Related females within a treatment are denoted as the same shade of grey.

x 183 mm width x 77 mm height). Mating occurred on the natal patch among the offspring of the 2 females, before mated daughters dispersed. A single male is capable of fertilising up to 15 females in a single day [START_REF] Krainacker | Reproductive limits and heterogeneity of male two-spotted spider mites[END_REF], hence the number of males available to fertilise all females on a patch was not limiting. All replicates from all regimes were maintained in the same conditions, the only difference being how populations were mixed and transferred to new patches at each generation (Figure 1). Note that such variation in population structure inherently affects the effective population size and thus the degree of inbreeding in populations.

In the budding dispersal regimes, females were always transferred with another female Under global competition, relative patch productivity (the total number of daughters produced compared to that of the other patches within the replicate) determined the number of female adult offspring transferred to the next generation: in the 'Global Random' regime, all 48 patches were placed on a 'mixing patch' onto which adult females dispersed (patches with more female offspring having a higher representation on the 'mixing patch') before being transferred in pairs;

in the 'Global Budding' regime, the number of adult females on each patch was counted to calculate relative fecundity (i.e. dividing the number of females per patch by the total number of females across the 48 patches), so that patches with the most offspring contributed more pairs of females to the next generation.

Due to the time taken for each transfer, transfers from one generation to the next were done over 1, 2 or 3 days. When done over more than one day, at least one replicate population from each regime was transferred on the same day. All replicates were maintained in a climate chamber at 25 ± 2°C, with a photoperiod of 16h light: 8h dark. During the selection experiment, all replicates in the 'Local Budding' regime were lost after generation 14, and 1 replicate in the 'Global Budding' regime was lost at generation 22 (GB-3). These lines were lost because females on the different patches did not produce any offspring, or only male offspring, leading to extinction of lines. In total, 33 generations of selection were performed.

Responses to selection 1. Sex allocation during experimental evolution

The sex allocation of females was measured directly in the replicate populations of each selection regime at generations 12, 17, 20 and 31. This was done by counting the number of males and females per patch within each experimental replicate prior to the following transfer. Thus, sex ratio comprised the combined output of the two females per patch.

Sex allocation in a common environment

In this assay, all regimes were each exposed to a common environment for 1 generation to equilibrate maternal effects before measuring the offspring sex-ratios of females that mated randomly with males from their selection regime (Figure S1). For this, at generation 31, 96 mated daughters were haphazardly chosen from the 48 patches within each selection regime and placed on a large leaf patch (~200cm 2 ) where they laid eggs together. Fourteen days later, the offspring on these patches emerged as adults and mated amongst themselves (Generation 31 + 1). Ninetysix mated female offspring from each mixing patch were then haphazardly chosen to measure their offspring sex-ratio; 48 were placed individually on 2cm 2 patches, and another 48 placed in pairs on 4 cm 2 patches. Females were allowed to lay eggs for 7 days on these new patches, before being killed. After 2 weeks, once offspring had emerged as adults, the number of daughters and sons on each patch was counted. This experiment was set up over three days, with one replicate per regime being treated each day.

Sex allocation in response to patch fecundity

Measures of offspring sex ratio on patches concern the sex allocation of two females on that patch.

While this is informative, it may obscure responses to selection, especially if offspring sex ratio differs between females, for instance, if a focal female's sex allocation changes in response to her own fecundity only, or also to that of her patch mate [START_REF] Stubblefield | Local mate competition with variable fecundity: dependence of offspring sex ratios on information utilization and mode of male production[END_REF]. To test this hypothesis, we measured the fecundity and sex allocation of single females from our selection regimes in response to the presence of eggs laid by sterile females on the same patch [START_REF] Osouli | Gamma irradiation used on adult Tetranychus urticae Koch as a quarantine treatment[END_REF]. Because the eggs of the sterilised females do not hatch, we can distinguish the offspring of the focal female (adult individuals) from that of the sterilised one (unhatched eggs) within a single patch.

This experiment was implemented after 33 generations of selection. As for the preceding experiment, individuals within each replicate population were subject to a common environment.

However, in this experiment it was over two generations (generation 33 + 2; Figure S1). At the same time, females from the ancestral population were placed in a common environment for 2 generations, as done with females from the selection regimes (Figure S1) to generate sterile females. To sterilise these females, they were exposed to 100 Gy, at a dose of 2.7 Gy minute -1 , using a Xstrahl XenX pre-clinical irradiator at the Institute of Cancer Research, Montpellier (IRCM). Preliminary studies revealed that this dose of X-ray irradiation is sufficient to sterilise females, that lay eggs that do not hatch (see Table S2).

Single adult females from the different selection regimes were placed on individual leaf patches with one sterile female and allowed to lay eggs for 5 days. Both females were then killed and patch fecundity, the total number of eggs per patch (laid by the sterile and the fertile female, coming from the ancestral population and from one of the selection regimes, respectively) was measured. Nine days later the adult offspring of fertile females were counted, and the offspring sex ratio measured. A total of 48 leaf patches (4 cm 2 ) were set up per replicate population.

Sexual conflict

The impact of mating with males evolved under the 'Global Budding' and 'Global Random' selection regimes on the fecundity of females from the ancestral population was compared in a separate assay. Females were collected from the different selection regimes at generation 33 and spent two further generations in a common environment before the experiment (G33 + 2, as above;

Figure S1). The females from the ancestral population experienced one generation in a common environment, being placed in 2 boxes, each containing 100 females on a large 'mixing patch'.

Thirteen days later, 240 immature, virgin females (i.e., daughters) were isolated on 4 cm 2 individual leaf patches later used to measure the degree of sexual conflict.

To obtain males from each selection regime, on days 10 and 11 of the second generation in the common environment (G33 + 2), 30 immature, juvenile females were isolated from each replicate population and each placed on a 4cm 2 leaf patch. These virgin females emerged as adults and laid eggs for six days. Because spider mites are haplodiploid, only male progeny emerged from these eggs. Due to female mortality or failure to lay eggs, the total number of patches containing virgin males from each line varied from 17 to 28 (GB-1 = 28, GB-2 = 17, GR-1 = 21, GR-2 = 21 and GR-3 = 21). On day 1 of the experiment, males from the different patches within each replicate population were mixed on a large leaf patch so they could be haphazardly distributed across treatments (see below).

The 240 immature, virgin females (i.e. daughters) were taken from the ancestral population and kept isolated for 2 days on their individual patches. Subsequently, the eggs laid by these females were removed and patches were assigned to males from either the 'Global Random' or 'Global Budding' selection regime, and to a 'single' or 'double' mate treatment (N=30 per treatment). In all treatments, males from the selection regimes were placed with the virgin females for 5 hours on day 1 of the experiment. Twenty-four hours later (day 2), in patches assigned to the double mating treatment, a second male was placed on the patch and left for 5 hours. This mating period was chosen to take into account the time females were together with their mates each generation prior to their transfer to new patches. In both treatments, females were left to lay eggs and on day 6 of the experiment, female mortality was checked and alive females were removed from the patches. The total number of eggs per patch was counted and, 8 days later, offspring sexratio was measured.

Statistical analysis

All analyses were carried out using the R statistical package (v. 3.0.3) and JMP13. We used Generalised Linear Mixed Models (GLMMs, package glmmTMB; [START_REF] Brooks | Balances Speed and Flexibility among Packages for Zero-Inflated Generalized Linear Mixed Modeling[END_REF] with a betabinomial error structure and logit link function, and quasi-poisson or negative binomial error structures and log link function, to analyse the effect of selection regime on sex ratio and mean offspring production, respectively. Maximal models were simplified by sequentially eliminating non-significant terms (p < 0.05) from the highest-to the simplest-order interaction, with the highest p-value to establish a minimal model [START_REF] Crawley | The R Book[END_REF]. The significance of the explanatory variables in the minimal models was established using chi-squared tests [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF]. A posteriori contrasts with Bonferroni corrections were done to interpret the effect of selection regime when significant (glht, multcomp package; [START_REF] Hothorn | Simultaneous inference in general parametric models[END_REF]. Details of all models are given in Table S3.

Sex allocation during experimental evolution

To analyse the impact of the selection regime on offspring sex ratio, generation (12, 17, 20 and 31) and selection regime (GB, GR and LR) were included in the model as fixed factors, as well as their interaction. Generation was analysed as a covariate and was log transformed to improve the fit of the model. Experimental replicate (GB-1, GB-2, GR-1, GR-2, GR-3, LR-2 and LR-3,) was included as a random factor nested within selection regime, and the day measurements were taken as a random factor nested within generation.

Sex allocation in a common environment

To investigate the effect of selection regime on offspring sex ratio in a common environment, we used a model with selection regime (GB, GR and LR) and the number of females per patch (1 or 2) as fixed factors, as well as their interaction, and replicate population (GR-3, GB-1, GB-2, GR-1,GR-2, LR-2 and LR-3), nested within selection regime as a random factor. This analysis excluded replicate LR-1 due to fewer than 8 patches with more than 3 offspring. For this variable, the best fit model included a parameter to account for zero inflation (ziformula~1; package glmmTMB; [START_REF] Brooks | Balances Speed and Flexibility among Packages for Zero-Inflated Generalized Linear Mixed Modeling[END_REF].

Sex allocation in response to patch fecundity

In a second analysis, using data from the 'Sex allocation in response to patch fecundity' experiment, we investigated whether the sex allocation of the focal female depended on her relative fecundity ('relative patch fecundity': the number of eggs laid by the focal female divided by the total number of eggs laid on the patch) and on the total number of eggs present in the patch ('total patch fecundity'). In this analysis, the selection regime of the focal female (GB, GR and LR), relative (or total) patch fecundity were included in models as fixed factors, as well as their interaction, and experimental replicate (GB-1, GB-2, GR-2, GR-3, LR-2 and LR-3) nested within selection regime was added as a random factor. These analyses only included females alive on day 4 of the experiment and excluded replicates GR-1 and LR-1, due to fewer than 10 patches with more than 3 offspring.

We used data from this experiment to compare observed offspring sex ratios with predicted values from theoretical models (see Supplementary Materials Table S1 for details) using two tailed t-tests in JMP13. Observed offspring sex ratios were mean values for fertile females from each selection regime.

Sexual conflict

To test whether selection regime affected the intensity of sexual conflict and male-male competition, female fecundity and offspring sex-ratio were analysed including the number of mates (one or two mates) and the selection regime of the male ('Global Budding' versus 'Global Random') as discrete, fixed variables in the model, as well as their interaction. Replicate population (GB-1, GB-2, GR-1, GR-2 and GR-3) and box (the container in which several individual replicates were maintained) were included nested within dispersal type as random factors. In the analysis of female fecundity, all individual replicates in which females died before day six were excluded.

Results

Sex allocation during experimental evolution and in a common environment

There was a consistent significant effect of selection regime on sex allocation during the selection experiment and after a generation in a common environment (during selection experiment: X 2 2 = 14.046, p < 0.001; common environment: X 2 2 = 11.845, p = 0.002; Figures 2a and2b, Table S4).

Females from the 'Global Budding' regime produced less female-biased offspring sex ratios than females from the 'Global Random' regime (during selection experiment: Z = -3.741, p < 0.001; the 'Global Budding' regime to produce a less female-biased offspring sex ratio than females from the 'Local Random' regime during the selection experiment (Z=-2.289, p = 0.066), but not after a generation in a common environment (Z=-1.53, p = 0.331 Figures 2a and2b; Table S5). There was no difference in sex allocation between females from the 'Global Random' and 'Local Random' regimes (during selection experiment: Z=1.554, p = 0.361; common environment: Z=-1.597, p = 0.3776; Figures 2a and2b; Table S5). The number of females on a patch did not affect offspring sex ratio (selection regime x number of females per patch: X 2 2 = 4.114, p = 0.128; number of females per patch: X 2 1 = 0.94, p = 0.331; Table S4).

Comparing observed offspring sex-ratios with theoretical predictions

In table S1, we present the theoretical predictions corresponding to the selection regimes in which spider mite populations evolved [START_REF] Herre | Sex ratio adjustment in fig wasps[END_REF][START_REF] Taylor | Local mate competition and the sex ratio[END_REF], Gardner et al., 2009).

Females from the 'Global Random' selection regime produced an offspring sex ratio of 0.19 (± 0.19 SE), that does not differ from the predictions of [START_REF] Taylor | Local mate competition and the sex ratio[END_REF] and of Gardner Specifically, females from the 'Global Budding' selection regime produced a less female-biased offspring sex ratio (mean 0.30 ± 0.03 SE; t = 9.54, df = 55, p < 0.0001), and females from the 'Local Random' regime a more female-biased offspring sex ratio (mean 0.24 ± 0.02 SE; t = 7.99, df = 74, p < 0.0001), than predicted by theory.

Sex allocation in response to patch fecundity

Offspring sex ratios changed according to the selection regime of focal females and their relative patch fecundity (selection regime: X 2 2 = 10.90, p = 0.004; relative patch fecundity: X 2 1 = 6.87, p = 0.009; Figure 3, Table S4). As before, females from the 'Global Budding' regime produced less female-biased offspring sex ratio than females from the 'Global Random' regime (Z=-3.298, p = 0.003; Figure 3, Table S5). The offspring sex ratio of females from the 'Local Random' treatment did not differ from that of the other two selection regimes (Table S5). Across all treatments, females with higher relative patch fecundity produced more female-biased offspring sex-ratios (selection regime x relative patch fecundity: X 2 2 = 2.55, p = 0.28; Figure 3). These results did not change when using total patch fecundity (sum number of eggs laid by the fertile and sterile female on each patch, Figure S2, Tables S4 andS5).

Sexual conflict

Overall, there was no significant effect of mate number (X 2 1=0.024, p = 0.876), male selection regime (X 2 1=0.028, p = 0.867), or their interaction (X 2 1=0.073, p = 0.788) on the offspring sexratio of females from the ancestral population (Figure S3, Table S4). However, the total number of offspring produced was higher when females mated with a male from the 'Global Budding', as opposed to the 'Global Random', selection regime (X 2 1=4.336, p = 0.036; Figure 4, Table S4).

First, inbreeding is affected by dispersal type (with high inbreeding expected for the budding dispersal regime). Inbreeding can select for more female-biased offspring sex ratios [START_REF] Herre | Sex ratio adjustment in fig wasps[END_REF][START_REF] Chung | Evolutionary stable sex ratios with non-facultative male-eggs first sex allocation in fig wasps[END_REF][START_REF] Frank | Hierarchical selection theory and sex ratios. II. On applying the theory, and a test with fig wasps[END_REF]. If coupled with high levels of juvenile mortality this could, in some cases, result in no males in a patch [START_REF] Chung | Evolutionary stable sex ratios with non-facultative male-eggs first sex allocation in fig wasps[END_REF], West et al., 2002b), potentially explaining why all 3 replicates of the 'Local Budding' and 1 replicate of the 'Global Budding' regimes were lost. Moreover, different inbreeding levels may lead to different levels of inbreeding depression among selection regimes, being highest under budding dispersal. Thus, in our surviving selection regimes, the consequences of inbreeding depression may be more pronounced in the 'Global Budding' regime. In haplodiploids like spider mites, inbreeding depression is expressed mainly in female traits [START_REF] Tien | Inbreeding depression and purging in a haplodiploid: genderrelated effects[END_REF]. Therefore, the accrued costs of inbreeding may negate any benefit of female-biased sex ratios in the 'Global Budding' regime in the replicates that survived [START_REF] Greeff | Alternative mating strategies, partial sibmating and split sex ratios in haplodiploid species[END_REF]. As such, there might be selection to augment the production of sons in patches with low fecundity and/or high mortality due to inbreeding depression to ensure female fertilisation [START_REF] Chung | Evolutionary stable sex ratios with non-facultative male-eggs first sex allocation in fig wasps[END_REF], West et al., 2002b). In line with this, females in the 'Global Budding' regime produced fewer offspring that became adult, which might be due to higher offspring mortality or lower fecundity (Figure S4, Table S5). These females also produced slightly more male offspring than those from the 'Global Random' regime (Figure S5a, Table S5).

Another factor that may affect sex allocation is variable clutch size. Indeed, when females with asymmetric fecundities oviposit simultaneously in the same patch, the sons of a more fecund female are subject to more intense competition for mates, as they mostly compete among brothers to mate with sisters, whereas the sons of a less fecund female mostly compete with unrelated males to access unrelated females [START_REF] Stubblefield | Local mate competition with variable fecundity: dependence of offspring sex ratios on information utilization and mode of male production[END_REF]. More fecund females are thus expected to produce more female-biased sex ratios, while less fecund females should produce less femalebiased sex ratios. As a result, the patch sex ratio becomes skewed towards that produced by the more fecund females, i.e. a more female-biased sex ratio [START_REF] Stubblefield | Local mate competition with variable fecundity: dependence of offspring sex ratios on information utilization and mode of male production[END_REF][START_REF] West | Sex Allocation[END_REF].

In addition, theory predicts that this adjustment by females should emerge from a differential investment in daughters, while maintaining a constant production of sons, known as the 'constant male hypothesis' [START_REF] Yamaguchi | Sex ratios of an aphid subject to local mate competition with variable maternal condition[END_REF][START_REF] Frank | Variable sex ratio among colonies of ants[END_REF]. Here, we found that, for all selection regimes, the sex ratio declined as the relative fertility of the focal female increased (the same was observed for total patch fecundity, Figure S2), showing that female fecundity and sex-ratio are not independent traits. Furthermore, although not significantly different from the other regimes, 'Local Random' females generated the steepest slope. Coupled with higher overall fecundity observed in this selection regime (Figure S4, Table S5), this may explain why offspring sex ratios are more female-biased than expected. Finally, although son production is not constant across selection regimes (Figure S5a, Table S4), its variation is much lower than that for the number of daughters produced (Figure S5b). Again, this seems to be in line with an effect of clutch size on sex allocation. Note however that the constant male hypothesis is expected to break down under local competition [START_REF] Rodrigues | Simultaneous failure of two sex-allocation invariants: implications for sex-ratio variation within and between populations[END_REF], a result we do not recapitulate here.

A final possibility for why populations in the 'Local Random' and 'Global Budding' selection regimes do not produce the predicted offspring sex ratios is that they have not reached their evolutionary equilibrium. Another selection experiment found an initial reduction in cooperation under budding dispersal followed by a subsequent increase in this trait value [START_REF] Kummerli | Limited dispersal, budding dispersal, and cooperation: an experimental study[END_REF]. Although our experimental evolution was done over 33 generations, which is a large number for non-microbial organisms, populations may still have been in a transient stage when traits were measured.

Sexual Conflict

Theory predicts that multiple mating with unrelated males causes a greater reduction in female reproductive success than multiple mating with related males [START_REF] Pizzari | Inclusive fitness and sexual conflict: How population structure can modulate the battle of the sexes[END_REF]. More precisely, [START_REF] Faria | Kin discrimination and demography modulate patterns of sexual conflict[END_REF] predict that budding dispersal leads to higher relatedness between males, thus reducing levels of sexual conflict and increasing levels of female fecundity. In accordance with this we found that females mated to males from the 'Global Budding' regime had higher fecundity than those mated to males from the 'Global Random' regime, suggesting that 'Global Budding' males inflicted less harm. This replicates previous findings showing that evolving with kin reduced the level of male harm inflicted to females in bulb mites [START_REF] Lukasiewicz | Kin selection promotes female productivity and cooperation between the sexes[END_REF]. Other studies have shown that a reduction in male harm may be a plastic response to the presence of kin [START_REF] Carazo | Within-group male relatedness reduces harm to females in Drosophila[END_REF][START_REF] Lymbery | Males harm females less when competing with familiar relatives[END_REF]. However, in our experiment, since mating was with unrelated females from the ancestral population, there were no direct cues indicating the presence of kin. In addition, competitor males coming from the same selection regime experienced 2 generations of common garden prior to the experiment which probably reduced relatedness among them. This means that if the response were plastic, then there should be no difference between selection regimes. Thus, reduced harm was most likely an evolved response in our study.

Contrary to expectations [START_REF] Arnqvist | Sexual Conflict[END_REF], we did not find that multiple mating reduced fecundity in either selection regime. Possibly, the differences in harm inflicted by one or two mates over a single, or two successive five-hour periods respectively, might have been insufficient to detect differences in fecundity between the two treatments. Previous studies with spider mites found fecundity costs when females were simultaneously exposed to multiple mates for two consecutive periods of 24 hours with an interval of 24h hours between them [START_REF] Rodrigues | Costs and benefits of multiple mating in a species with first-male sperm precedence[END_REF], or exposed to two mates on multiple occasions during their lifetime [START_REF] Macke | Mating modifies female life history in a haplodiploid spider mite[END_REF].

Here we only tested the effect of the type of dispersal on sexual conflict. However, the outcome of sexual conflict may also change according to the type of population regulation. Indeed, under local competition, increased competition among relatives is predicted to cancel out the benefits of cooperation [START_REF] Queller | Does population viscosity promote kin selection?[END_REF][START_REF] Taylor | Altruism in viscous populations -an inclusive fitness model[END_REF][START_REF] Wilson | Can altruism evolve in purely viscous populations?[END_REF]. This means that sexual conflict might be maintained among related individuals when competition is local [START_REF] Pizzari | Inclusive fitness and sexual conflict: How population structure can modulate the battle of the sexes[END_REF][START_REF] Wild | Sexual conflict in viscous populations: the effect of the timing of dispersal[END_REF]). Yet, despite its general interest, we are not aware of any studies that explicitly test this.

The interplay between sex allocation and sexual conflict

Evolution under different population structures may simultaneously impact sex allocation and sexual conflict in a non-independent manner [START_REF] Chapman | Sexual conflict and sex allocation[END_REF][START_REF] Schärer | Sex allocation and sexual conflict in simultaneously hermaphroditic animals[END_REF]. One possibility is that sexual conflict might impact sex allocation if a reduction in female fecundity prevents the production of optimal offspring sex ratios. Our sexual conflict experiment showed that females from the ancestral population mated to males from the 'Global Random' regime had the lowest fecundity, suggesting that these males inflict more harm. Yet females from the 'Global Random' regime produced offspring sex ratios closest to those predicted by theory (Table S1). In addition, 'Global Random' females, when mated to 'Global Random' males in the sex allocation experiment had higher fecundity (Figure S4, Table S4). This suggests that 'Global Random' females may have evolved mechanisms to overcome male harassment or induced harm, as shown in this [START_REF] Macke | Local mate competition mediates sexual conflict over sex ratio in a haplodiploid spider mite[END_REF] and other [START_REF] Wigby | Female resistance to male harm evolves in response to manipulation of sexual conflict[END_REF][START_REF] Michalczyk | Experimental evolution exposes female and male responses to sexual selection and conflict in Tribolium castaneum[END_REF] systems.

Female resistance to harassment may thus be one trait involved simultaneously in the outcome of sexual conflict and sex allocation.

Conversely, sex allocation may also impact sexual conflict through changes in levels of male-male competition; as the sex ratio becomes more male biased so will the intensity of competition. Indeed, evolving with kin may reduce male harm and be associated with more femalebiased offspring sex ratios [START_REF] Lukasiewicz | Kin selection promotes female productivity and cooperation between the sexes[END_REF]; although the latter was not significantly different from the non-kin evolution treatment). In our sex allocation experiment, sex ratio was the least female-biased in the 'Global Budding' selection regime. However, males from this regime inflicted the least harm to females from the ancestral population (sexual conflict experiment), suggesting sex allocation evolution did not result in stronger sexual conflict.

Conclusions

To date, we are only aware of one study that considers the evolution of both sex allocation and sexual conflict under different population structures [START_REF] Lukasiewicz | Kin selection promotes female productivity and cooperation between the sexes[END_REF]. Although the latter study is a very important step toward integrating responses of both traits, relatedness was the only variable that differed between treatments. Therefore, much remains to be investigated concerning the consequences of populations structure for these traits, which have been found to be nonindependent in a number of systems [START_REF] Macke | Local mate competition mediates sexual conflict over sex ratio in a haplodiploid spider mite[END_REF][START_REF] Boulton | Local mate competition modifies the costs of mating in a mostly monandrous parasitoid wasp[END_REF][START_REF] Boulton | A sex allocation cost to polyandry in a parasitoid wasp[END_REF]. Here, we show that responses to selection on these traits under different population structures mostly depended on the dispersal regime. Clearly, more studies simultaneously investigating the evolution of sex allocation and sexual conflict are needed, as interactions among these traits may account for data not matching theoretical predictions.

SM, a joint grant from the Agence Nationale de la Recherche and the Fundação para a Ciência e a Tecnologia to Isabelle Olivieri and SM (FCT-ANR/BIA-EVF/0013/2012), a PHC-PESSOA grant (38014YC) to ABD and SM, and a SIRIC Montpellier Cancer Grant (INCa_Inserm_DGOS_12553) funded the irradiator. This is ISEM contribution number 2020-310.

Data is archived at Dryad: https://doi.org/10.5061/dryad.w3r2280ph

Figure 1 .

 1 Figure 1. Description of the selection regimes. Four selection regimes were established and maintained for 33 generations, each with three experimental replicates. In 'Local Budding', 2

  from the same patch to form the next generation. In contrast, in the random dispersal regimes, females from different patches were placed together on a 'mixing patch' (10 bean leaves placed together) before being transferred, in haphazardly chosen pairs, to a new patch. Local competition was imposed by letting an equal number of adult females per patch seed the next generation (2 -4 females per patch in 'Local Random'; adjusted each generation to accommodate mortality).

Figure 2 .

 2 Figure 2. Mean offspring sex ratio (± standard error) of females from the 'Global Random' (GR, dark grey), 'Global Budding' (GB, black) and 'Local Random' (LR, light grey) selection regimes across generations. The proportion of male offspring was measured a) during experimental evolution at generations 12, 17, 20 and 31 (experimental replicate means shown for each selection regime) and b) at generation 31 + 1 after one generation in a common environment, in patches with one or two females (means shown for each experimental replicate (different symbols) in each selection regime).

Figure 3 .

 3 Figure 3. Offspring sex ratio as a function of relative patch fecundity per patch in the 'Global Budding' (GB, black), 'Global Random' (GR, dark grey) and 'Local Random' (LR, light grey) selection regimes. Females from the different selection regimes were placed on individual patches (one per patch) with a sterile female from the base population. For each patch, the proportion of offspring produced by the focal female (i.e. from the selection regime) was calculated as the proportion of eggs that hatched and became adult (relative patch fecundity), and her offspring sex-ratio was measured. Each dot represents an individual replicate (i.e., patch from which measurements were taken).

Figure 4 .

 4 Figure 4. Mean fecundity (± standard error) of females from the ancestral population presented with either one or two males from the 'Global Budding' (GB, black) or 'Global Random' (GR, dark grey) selection regimes. Means shown for each experimental replicate (different symbols) in each selection regime at generation 33, after two generations in a common environment.

Acknowledgements

We would like to thank François Rousset and Elsa Noël for helpful discussion about this manuscript. This work was funded by an ERC consolidating grant (COMPCON GA 725419) to

Discussion

Both sex allocation and sexual conflict responded to selection under different population structures. Sex allocation responses were mainly driven by dispersal type (budding vs random), which influences whether interactions occur among kin or unrelated individuals, and not by the scale of competition. Females from the 'Global Budding' regime consistently produced more male-biased offspring sex ratios than those from the 'Global Random' selection regime. We also found that higher relative patch fecundity was associated with more female-biased offspring sexratios across all selection regimes. Finally, when comparing the intensity of sexual conflict, females from the ancestral population mated to males from the 'Global Budding' regime had higher fecundity than those mated to males from the 'Global Random' regime.

Sex Allocation

Females from the 'Global Random' selection regime produced offspring sex ratios consistent with theory [START_REF] Taylor | Local mate competition and the sex ratio[END_REF]. This corroborates previous findings in mites [START_REF] Macke | Experimental evolution of reduced sex ratio adjustment under local mate competition[END_REF] and is consistent with sex ratio observations in other haplodiploid and diploid systems (e.g. [START_REF] Reece | Kin discrimination and sex ratios in a parasitoid wasp[END_REF][START_REF] Reece | Sex ratio adjustment and kin discrimination in malaria parasites[END_REF][START_REF] Herre | Sex ratio adjustment in fig wasps[END_REF]. However, the 'Local Random' and the 'Global Budding' regimes present offspring sex ratios that differ from theoretical predictions, being more and less female-biased than predicted, respectively (see Table S1). The fact that offspring sex ratios in the 'Global Budding' treatment were not as predicted, and that sex ratios in the 'Local Random' and 'Global Random' regimes were equivalent, suggest that other factors, besides the type of dispersal and the scale of competition, may be at play. Below, we highlight potential factors that may account for the observed patterns.


Jill Dill Pasteris
email: pasteris@levee.wustl.edu

Olivier Beyssac
email: olivier.beyssac@upmc.fr

Welcome to Raman Spectroscopy: Successes, Challenges, and Pitfalls

Keywords: Raman spectroscopy, Earth sciences, applications, spectrometers, spectra, minerals

Geoscientists quickly recognized the broad applicability of Raman microprobe spectroscopy to the Earth and planetary sciences, especially after commercially built microprobe instruments became available in the early 1980's. The sensitivity of Raman spectra to even minor (chemical or structural) perturbations within chemical bonds in (even amorphous) solids, liquids, and gases has been applied to the identification, characterization, and differentiation of, e.g., individual minerals, fluid inclusions, glasses, carbonaceous materials, solid solution phases, strain in minerals, and dissolved species in multi-component solutions. The articles in this issue explore how Raman spectroscopy has deepened and broadened our understanding of geological and extraterrestrial materials and processes.

INTRODUCTION

Raman spectroscopy is an analytical technique strongly suited to application in the Earth and planetary sciences, chemistry, materials science, medicine, and industry.

Ongoing improvements in several components of Raman systems (e.g., lasers, computers, detectors, motorized stages, software) have encouraged much innovation in instrumentation [START_REF] Adar | Evolution and revolution of Raman instrumentation--Application of available technologies to spectroscopy and microscopy[END_REF][START_REF] Dubessy | Instrumentation in Raman spectroscopy: Elementary theory and practice[END_REF], both broadening the range of instrumental capabilities (e.g., improved spectral imaging/mapping, field-portable Raman instruments, hybrids such as Raman-atomic force microscope) and targeting of specialized needs (e.g., undersea applications, deployment on Mars) [START_REF] Dubessy | Instrumentation in Raman spectroscopy: Elementary theory and practice[END_REF]Cardell and Guerra 2016;[START_REF] Chou | Application of laser Raman micro-analyses to Earth and planetary materials[END_REF]Beyssac this This article and more generally this issue provide no learner's handbook of Raman spectroscopy, firstly for lack of space, but also because there are many books and articles that address the physics of the Raman effect and how it can be exploited in the context of specific instrumentation and analytical techniques. Instead, we offer here a basic-level overview of "how Raman works" in order to alert readers to which types of samples and questions Raman spectroscopy typically can be applied. Some of the information below will be understood better in the context of individual articles in this issue.

RAMAN EFFECT IN A FEW PARAGRAPHS

Raman spectroscopy deals with a scattering phenomenon in which photons (from a laser) of a single quantum energy are focused/collimated by a lens onto or into a sample. After interaction with the atoms of the sample, most importantly their covalently bonded components, some portion of the resultant back-scattered photons is captured by the same lens, transmitted and dispersed through a spectrometer, then digitized according to wavelength via a detector (Fig. 1). Those photons returning with the same quantum energy as that of the laser (i.e., Rayleigh elastic scattering) are not of interest here, but rather those (only 1 in 10 7 ) that return with quantum energies shifted from that of the laser source (Fig. 1). The amounts of those shifts, recorded as wavenumber values (i.e., Δcm -1 , the "Raman shift" due to inelastic scattering), reflect the energies of the vibrations between bonded atoms within the internal structure/symmetry of the host material. Photons in the ultraviolet (UV) to infrared (IR) range of the electromagnetic spectrum may transfer energy to molecules or crystals as vibrations or electronic transitions depending on their energy [START_REF] Rull | The Raman effect and the vibrational dynamics of molecules and crystalline solids[END_REF]. Figure 2 sketches some interactions that may happen when an incident energetic photon strikes a molecule. In the mid to far infrared domain, the photon energy of incident light is low and may correspond to the difference between two allowed vibrational levels in the molecular unit. The photon is then absorbed and generates a phonon with the same energy [START_REF] Mcmillan | Infrared and Raman spectroscopy[END_REF]. This is the process analyzed by infrared spectroscopy, which is based on light absorption. Visible light cannot be absorbed through phonon excitation, because the photon energy is much greater than the energy difference between the vibrational states of the molecules. Visible light rather is scattered and excites the molecules to virtual energy states with extremely short lifetimes and quasi-immediate relaxation. Most light scattering is essentially elastic, i.e., the molecule ends up in the same vibrational state as before excitation, and the energy of the scattered light is unchanged. This is Rayleigh scattering (Figs. 1,2). But a small fraction of the scattering occurs inelastically. In such cases, after scattering, the molecule resides at a higher (energy loss, Stokes scattering) or lower (energy gain, Anti-Stokes scattering) vibrational state than before excitation. Consequently, the photon energy of the scattered light is either decreased or increased with respect to the exciting photon: this is the Raman effect. Note that this photon energy difference corresponds to the specific energy difference between vibrational states of the molecule, thereby imparting molecular information to the Raman signal [START_REF] Neuville | Advances in Raman spectroscopy applied to Earth and materials sciences[END_REF][START_REF] Mernagh | Using infrared and Raman spectroscopy to analyze gas-solid reactions[END_REF].

Figure 2: Different types of scattering processes and electronic transitions (x-axis) that may be recorded by the photon detector and the relative energies (y-axis) at which they occur. Stokes, anti-Stokes, and Rayleigh scattering (also illustrated in Fig. 1) can be seen.

The spectrum acquired encapsulates a combined chemical-structural characterization of the sample. Individual elements are not measured, but the presence and amounts of specific atoms in a phase will affect the vibrational frequency (heavier atoms causing lower frequencies) of a bond and therefore the specific Raman peak position recorded in the spectrum (Fig. 3). In addition to internal vibrations associated with individual molecular units within a crystal (e.g., CO3 2-, SO4 2- , OH -), external vibrational modes, also called lattice vibrations, may be recorded, even in ionically bonded crystals such as fluorite, CaF2. Lattice vibrations/modes arise because the molecules in a crystal -with their specific spacings, symmetry, and bonding -do not vibrate independently of each other. When the displacements of all the atoms, vibrating about their equilibrium positions, are synchronized, they also create fundamental lattice vibrations (phonons), which can be monitored in Raman spectroscopy. Such lattice vibrations are also unique features of a specific mineral or other crystalline compound (Fig. 4). In summary, Raman spectra are fingerprints of solids and, like powder XRD patterns, permit identification and characterization of the solid material (Fig. 5); they also can be used to identify the molecular species present in a fluid [START_REF] Frezzotti | Raman spectroscopy for fluid inclusion analysis[END_REF]Bodnar and Frezzotti this issue).

CAN'S AND CAN'TS

An enumeration of the Do's and Don'ts in Raman spectroscopy is beyond the scope of this introduction, but a brief explanation of some Can's and Can'ts of Raman For micro-Raman analysis via a confocal optical system, the beam of the exciting laser is commonly focused to a spot diameter in the range of hundreds of nanometers to a few micrometers, making the spatial scales of information complementary to those of the electron probe microanalyzer. The technique usually is non-destructive, but opaque and highly colored samples may heat up destructively and hydrated minerals may dehydrate due to absorption of the incident laser light [START_REF] Nasdala | Raman spectroscopy: Analytical perspectives in mineralogical research[END_REF][START_REF] Fries | Raman spectroscopy and confocal Raman imaging in mineralogy and petrography[END_REF]. Raman is applicable to solids (amorphous to crystalline, mineral or organic), liquids, and gases (Fig. 5). In transparent samples, analyses can be made on targets below the sample surface, e.g., fluid, melt, and mineral inclusions (Bodnar and Frezzotti this issue) or samples in a diamond-anvil cell [START_REF] Mao | Ultra-high-pressure transitions in solid hydrogen[END_REF][START_REF] Dietrich | A new optical cell for in situ Raman spectroscopy, and its application to study sulfur-bearing fluids at elevated pressures and temperatures[END_REF]). Analyses can be made of aqueous components and phases in water, for example, dissolved sulfate and minerals undergoing a reaction. In nanocomposites of organic and inorganic compounds, such as bone, the interwoven phases typically have Raman bands in different parts of the spectrum and thus can be identified individually and without destructive treatment of the sample [START_REF] Pasteris | Bone and tooth mineralization: Why apatite?[END_REF]).

As indicated above, Raman spectroscopy does not identify individual atoms, although identification of the compound itself can reveal much about its chemistry. If the Raman spectral identification is diopside, then the sample clearly is dominated by Ca, Mg, Si, and O. Because it is vibrational frequencies of bonds that are being monitored, anything that affects those bonds will affect their frequency and therefore specific peak positions, e.g., isomorphous ion substitution, site vacancies, other defects (Apopei et al. 2017). Indeed, the Raman spectrum is much more sensitive to changes in or differences between compounds than it is to the identity of the element(s) or the specific molecular environment the change (Fig. 3). Various chemical aspects of solid phases, gases, and aqueous species can be explored and characterized by Raman spectroscopy. Because specific bonded entities interact with the incident photons, the Raman spectrum shows the speciation of the atoms involved, e.g., revealing not just that sulfur is dissolved in the water, but that the dominant aqueous sulfur species is (HSO4) -with lesser concentration of (SO4) 2- [START_REF] Benison | Acid saline fluid inclusions: Examples from modern and Permian extreme lake systems[END_REF][START_REF] Dietrich | A new optical cell for in situ Raman spectroscopy, and its application to study sulfur-bearing fluids at elevated pressures and temperatures[END_REF]. The effect on the vibrational frequency of substituting ions of different mass or isotopes of the same element, but different mass, can be calibrated against independently analyzed reference materials. Mixtures of more than two substituents of different masses are more difficult to interpret. The relative state of hydration, hydroxylation, carbonation, etc. (involving covalently bonded species) of a solid phase also can be determined by Raman (Fig. 3). Although polymorphs have the same chemical composition, their contrasts in structure are revealed by differences in the number of and/or positions of Raman bands (Figs. 4,7).

As for all analytical techniques, Raman spectroscopy has its drawbacks and limitations. As suggested above, not all compounds are Raman active (i.e., produce spectral peaks), and some have much stronger scattering efficiencies than others, e.g., diamond (very strong) vs. nanocrystalline iron oxides (weak). In particular, many natural samples have impurities (e.g., defects, trace elements, organics) that can generate a luminescence signal when excited (Figs. 2,4). This luminescence signal may have various expressions (e.g., broad bands to continuous background, as exhibited by Mn 2+ substitution in calcite, Fig. 4; discrete lines, as exhibited by rareearth elements in Raman-active or -inactive minerals) and may be so intense that the Raman signal becomes subsumed by and often indistinguishable from the luminescence band and/or background (Fig. 4 inset B). Narrow, laser-induced emission lines can be mistaken for Raman bands, thereby causing confusion and possible errors in sample identification. There are also concerns of sample alteration (e.g., melting, oxidation, chemical breakdown) by laser heating [START_REF] Nasdala | Raman spectroscopy: Analytical perspectives in mineralogical research[END_REF] and heat-induced downshifting of Raman bands [START_REF] Bryant | Variability in the Raman spectrum of unpolished growth and fracture surfaces of pyrite due to laser heating and crystal orientation[END_REF].

Aspects of the specific instrument being used, as well as the physics of the Raman effect, put constraints on the type of information retrievable and the specificity of the interpretation of the spectra. The spectrum shows only what the focused laser was able to "sample", especially for highly confocal instruments. In opaque or strongly light-scattering samples (e.g., fine-grained powders), the spectrum will be dominated by the surficial species/phases. The latter two factors make it difficult to readily determine with a Raman microprobe the quantitative ratio of solid phases in a mixture, because it is a scattering signal (Raman) rather than a volume-integrating absorption signal (transmission IR) that is evaluated. In individual, non-isometric crystals, the orientation of the crystal with respect to the plane of polarization of the incoming laser will affect the relative intensities of (some of) the Raman peaks (Fig. 4 inset A), as will inherent strain in the material.

INTERPRETABLE ASPECTS OF A RAMAN SPECTRUM

The standard presentation of a Raman spectrum shows scattering intensity on the vertical axis and wavenumber shift on the horizontal axis (Fig. 1). More specifically:

The intensity data initially are recorded as the number of Raman-scattered photons detected per unit time, the exact values of which depend on multiple sampling and instrumental factors. The vertical axis therefore is typically labeled with "arbitrary units" and indicates the relative peak intensities across a single given spectrum (Fig. 3). The horizontal axis is based on wavenumber, calculated 1/ (where  units are in cm), i.e., "wavenumber, cm -1 ." It is actually the difference in wavenumber values between that of the incoming photons (from the laser) and the scattered photons that is plotted; the units displayed on the x-axis are the absolute wavenumber value of the laser light minus the absolute wavenumber value of the scattered photons, i.e., the socalled Raman shift, in Δcm -1 . There are two major benefits to this mode of presentation: 1) Raman band positions are labeled identically regardless of which laser wavelength is used for excitation, and 2) the Δcm -1 wavenumber values (listed simply as cm -1 , in typical practice) in a Raman spectrum match the cm -1 wavenumber values in the IR spectrum of the same material for those vibrational modes that are both Raman-and IR-active (Fig. 2).

Several distinct characteristics of a Raman spectrum can be examined for chemicalstructural information: number of peaks, peak position, peak shape, and relative peak area (Fig. 3). The number of peaks seen in a Raman spectrum (for solids, typically a smaller number than would be calculated by group theory) indicates the number of Raman-active vibrational modes (i.e., internal molecular modes, crystal field splittings, librations, and lattice /external vibrational modes). Lattice modes/phonons in some cases can be viewed directly in low-wavenumber Raman spectroscopy (Fig. 4). The symmetry of the bonded component as well as that of the over-all structure control the number of peaks, which is larger for the less symmetric structures. The peak position indicates the vibrational frequency of the specific mode within its over-all structure, thereby reflecting the bond's strength and the atomic masses of the bonded atoms. Thus, few-wavenumber offsets between the peak positions obtained on the same instrument for a pure end-member compound and for a geological sample of the same mineral/compound indicate some amount of solid solution present in the geological sample (Fig. 3).

The shape of the "peak" (the as-observed signal, i.e., the recorded "hump" in the raw spectrum) is also revealing. Particularly if the observed peak is asymmetric, it likely comprises two or more underlying Raman bands, but the asymmetry also may reflect very small particle size or a misalignment between the spectrometer and detector.

Such spectra can be better characterized with instruments of higher spectral resolution. With appropriate software, one can deconvolve the peak into separate, spectroscopically recognized bands that are characteristic of specific vibrational modes (Fig. 3,inset A). Even if the peak appears symmetric, its FWHM value (quantified as full band width assessed at half intensity/height maximum) should be examined, as should the FWHM of constituent bands. For several samples of the same compound/mineral, but which formed under different conditions (e.g., temperature, cooling rate, compositional complexity, grain size), the peak widths typically will differ. The narrower the peak, the more atomically well ordered the solid is (Fig 3,inset B). For example, rapid cooling from a high-temperature melt and spontaneous precipitation from a strongly supersaturated solution at low temperature can lead to broader bands than for crystals that formed slowly and in equilibrium with their host melt or solution [START_REF] Maksimuk | Influence of the cooling rate on lowtemperature Raman and infrared-reflection spectra of partially deuterated Κ-(BEDT-TTF)2Cu(N(CN)2)[END_REF]). There are cases in which relative peak heights or areas can be used (especially in conjunction with a set of independently analyzed reference standards) to determine proportions of components within the same phase. In most cases, peak areas (or areas of deconvolved bands) are recommended as more reproducible than heights for quantification, e.g., the amount of carbonate substitution in apatite [ratio of spectral bands for CO3/(CO3 + PO4)] [START_REF] Awonusi | Carbonate assignment and calibration in the Raman spectrum of apatite[END_REF], the degree of crystallinity of graphitic carbon [relative contribution of defect bands] [START_REF] Wopenka | Structural characterization of kerogens to granulitefacies graphite: Applicability of Raman microprobe spectroscopy[END_REF][START_REF] Beyssac | Raman spectra of carbonaceous material in metasediments: A new geothermometer[END_REF], and the molar fractions of CH4, N2, and CO2 in the gas phase of a fluid inclusion [START_REF] Frezzotti | Raman spectroscopy for fluid inclusion analysis[END_REF]. Importantly, quantitative use of spectral data (e.g. FWHM, peak area ratios) from different instruments should be done only after correction for the instrumental response function (Nasdala and Schmidt this issue).

Over the past few decades, several different groups have developed and made available on-line their Raman spectral databases, representing spectra of wellcharacterized minerals. The best known of these is the RRUFF Raman, IR, and XRD database (http://rruff.info/about/about_general.php), which contains over 14,000 high-resolution Raman spectra and their accompanying downloadable data files. The majority of the minerals have been confirmed by XRD and/or chemical analysis. The database is searchable by mineral name and by major elements [START_REF] Lafuente | The power of databases: The RRUFF project[END_REF].

RAMAN HYPERSPECTRAL MAPPING

Over the last decade, a very important methodological development has been Raman hyperspectral mapping, which opened Raman to the imaging of internal microtextures of minerals and mineral assemblages [START_REF] Nasdala | Application of Raman-based images in the Earth sciences[END_REF][START_REF] Fries | Raman spectroscopy and confocal Raman imaging in mineralogy and petrography[END_REF]. Raman mapping consists in plotting in two, or even three, dimensions a spectral parameter extracted from a collection of spectra precisely located on the sample. The experimental principle is very simple: move the sample with constant step in X and Y directions and record a spectrum at each position. Three-dimensional mapping may be done when using transparent samples but is rather challenging to properly process and interpret. In general, data processing will consist in extracting the appropriate information from each spectrum and plotting it in 2D or 3D maps.

Depending on the purpose of the map, this information could be 1) a peak position for strain patterns or compositional variations in minerals, 2) the presence or absence of a representative peak for each mineral/gas for mapping mineral/gas assemblages in a rock or a fluid inclusion, or 3) the FWHM of a selected peak for mapping defects in minerals, among many other possibilities. Please see examples in other articles of this issue. Raman mapping can be very useful to detect and locate a specific feature (e.g., mineral phase, fluid inclusion, organics) in a sample (including powders) and/or to retrieve a very large spectral dataset acquired on a specific sample in order to derive multiple types of statistics.

For a long time, Raman hyperspectral mapping suffered from the very long duration of the spectral acquisition, but recent developments in hardware and, overall, software make possible the generation of maps encompassing thousands of spectra within minutes. Manufacturers of Raman systems have deployed various strategies, such as line-scan mapping, dynamic mapping involving synchronization of sample displacement with data reading on the detector, and dynamic and continuous autofocus, which makes Raman mapping an easy-to-use technique with modern instruments. Importantly, the spatial resolution of Raman mapping is mostly controlled by the sampling step distance and the lateral resolution of the laser spot for each analysis, both of which typically are on the order of a micrometer. Of course, all methodological traps inherent to Raman spectroscopy remain, and there are more specific drawbacks to mapping depending on the instrument used and sample analyzed [START_REF] Nasdala | Application of Raman-based images in the Earth sciences[END_REF]. The relative maturity of the technique now permits most of these problems to be overcome, if the operator is aware and cautious. All the parameter choices made to generate a Raman image have to be clearly specified. This includes not only the data processing (e.g., details on peak-fitting procedure, methodology used for principal-component analysis), but also the link between the scientific information mapped (e.g., mineralogy, strain distribution, mineral or gas composition) and the raw spectral data (e.g., peak identification, FWHM, peak position, or area ratio). Two examples of necessary considerations of such links are the desire to know stress, when Raman spectra reveal strain (Korsakov et al. this issue), and the desire to determine (fluid) pressure, when Raman spectra sensitively monitor density (Bodnar and Frezzotti this issue). Figure 7 illustrates the Raman mapping of aragonite-garnet intergrowths in an impure marble. A similar map of such a mineral assemblage at similar resolution easily could be obtained by techniques based on X-ray spectroscopy, such as SEM-EDX (scanning electron microscopy-energy dispersive X-ray spectroscopy) or EPMA (electron probe microanalysis), but the ability of Raman to distinguish mineral polymorphs is invaluable here. Techniques based on X-ray spectroscopy actually would map Ca-carbonate as a high-Ca phase, but would not distinguish the polymorphs calcite and aragonite. Such distinction is possible by Raman, as by detecting lattice vibrations specific to each mineral structure (Fig. 4). Raman mapping has become so popular that it is now used in virtually all field of Earth sciences as attested by the examples provided throughout the following articles.

IN THIS ISSUE

In the articles in this issue of Elements, our goal is to highlight several of the Earth and Planetary Science fields in which Raman analysis, dominantly via Raman microprobe systems, has had wide-ranging impacts. The selection of topics was difficult, but our intention is to demonstrate a sufficient number and diversity of applications (with their inherent "successes," challenges, and pitfalls) to enlighten readers of Ramanbased studies and to encourage more geoscientists to apply this technique in both well-accepted and new ways. Bodnar and Frezzotti review the application of Raman for studying fluid and melt inclusions. This is truly an historical but still continuously developing field of application, as Raman spectroscopy is one of the very few

  issue). The Raman effect was discovered/demonstrated in 1928 by Chandrasekhara Venkata Raman and Kariamanickham Srinivasa Krishnan (1930 Nobel prize in physics to Raman for this discovery) and has been routinely used in physics and chemistry since the 1950-1960s following mainly the development of laser sources and photon detectors. In Earth sciences, Raman spectroscopy became popular later in the 1980s with the development and commercial availability of Raman microprobes. Since then, as happened with isotope analysis and electron probe microanalysis decades earlier, earth scientists have been quick to pursue new applications of Raman spectroscopy, which in turn has helped to reinvigorate or to open up multiple fields of research, such as fluid-inclusion-based studies, the search for traces of life in the oldest terrestrial rocks or extraterrestrial materials, and mineralogy of the deep Earth by in situ characterization in diamond-anvil cells. Another major early and continuing use has been in gemology for the identification of gems and the mineral and fluid inclusions in them (e.g., for verification of natural origin).

Figure 1 :

 1 Figure 1: Schematic overview of the basic instrumental setup required to take a Raman spectrum. Note that one typically views the Stokes-scattering (red-shifted, i.e.,right-hand) portion of the spectrum.

Figure 3 :

 3 Figure3: Raman spectra of two different synthetic samples of carbonated lead apatite (pyromorphite), differentiated by their amount of (CO 3 ) 2-substitution, 0.2 or 2.7 wt%. Isomorphous substitution (i.e., solid solution) introduces atomic disorder (thus, band broadening; see inset B) and shifts in peak positions. The complex peaks can be deconvolved into separate, recognized spectral band components (5 such bands shown in inset A). The molecular substituent (CO 3 ) 2-can be spectroscopically identified and, based on instrument-specific calibration, quantitatively evaluated for concentration. Samples provided by Claude Yoder.

  are in order, e.g., what kinds of information are obtainable, which samples are most amenable to Raman analysis. Sample preparation is minimal. Polishing is not necessary. No coating on the sample or vacuum chambers are needed.Straightforward Raman identification can be accomplished within seconds. Both crystals and powders of them can be analyzed, but commonly yield differences in their respective signal and background intensities. The caveats typical for techniques using visible light to interact with a sample, however, do pertain. Importantly, the surface state and overall transparency/optical absorption of the sample at the excitation wavelength are key parameters controlling the excitation volume during the analysis.

Figure 4 :

 4 Figure 4: Illustration of Raman spectral differentiation of polymorphs, i.e., CaCO 3 phases aragonite and calcite. Note the very strong similarity of the dominant ν 1 peak positions, but visible differences between the other internal vibrational modes and the very obvious difference in the external vibrational/lattice (phonon) modes of the two carbonate phases. Insets A and B illustrate two other confounding factors for one and the same CaCO 3 grain.The relative intensity ratios among bands within the spectrum of a given, anisotropic grain will change as the grain is rotated with respect to the laser's plane of polarization (inset A). Many natural minerals luminesce under the laser (inset B), decreasing the apparent signal strength of the mineral. Background correction (seen in bottom, main spectrum) is convenient, but masks the effects of luminescence on the recorded band intensities.

Figure 5 :

 5 Figure 5: Simplified sketch showing the peak position for one principal peak of various common rock-forming minerals. Peak positions for major gases (vertical gray bars) and organics are also depicted. This is just a sketch to show how the Raman spectrum contains fingerprint information; proper characterization of solids requires the identification of several peaks in most cases.

Figure 6 :

 6 Figure 6: Raman map of a garnet crystal containing various mineral inclusions: quartz and calcite in the core, fibrous aragonite in the rim. The rock matrix is composed of calcite and graphitic carbon (here in black). The sample comes from Alpine Corsica (France). A -general Raman map of a garnet crystal (scale bar 1 mm, 10 x 11 µm sampling step). B -zoom of the box in A (3.3 x 3.3 µm sampling step). C -Color codes used on the map. Reference spectra used for the map: colored vertical bars indicate the specific peak(s) used to identify each mineral phase. Note that external/lattice vibrations at low Raman shifts were used to distinguish calcite from aragonite. Modified after Chopin et al. (2008).

  techniques allowing in situ characterization of such tiny objects. Nasdala and Schmidt show the versatility and rich information offered by Raman spectroscopy to mineralogy and geochemistry. Korsakov et al. discuss the variety of geological information that can be extracted from rocks, thanks to Raman spectroscopy, to better understand their tectonic and metamorphic history. Steele et al. show how Raman spectroscopy has played and still plays a key role in the emerging interdisciplinary fields of biomineralogy and biogeochemistry. Lastly, Beyssac discusses some new trends in Raman spectroscopy for geoscientists from applications in the laboratory to the exploration of Mars.

ACKNOWLEDGMENTS

The authors wish to thank Lutz Nasdala and an anonymous reviewer for their detailed, insightful comments and Nancy Ross for her helpful editorial handling.

Raman instruments at IMPMC were funded by the city of Paris, Sorbonne Université, and CNRS. JDP thanks John Freeman for numerous spectroscopy discussions over the years and the U.S. Department of Energy and Washington University in St. Louis for the Raman instrument used.