Aline Migné
email: migne@sb-roscoff.fr

Claire Golléty

Dominique Davoult

Effect of canopy removal on a rocky shore community metabolism and structure

Keywords: Fucus serratus, intertidal, primary productivity, species diversity, in situ experiment

Effect of canopy removal on a rocky shore community metabolism and structure

Aline Migné, Claire Golléty, Dominique

Introduction

Canopy-forming algae are often found in high biomass and abundance on rocky shores and may be responsible for the major part of carbon fluxes in these systems as they represent the dominant biomass and areal cover. For example, the Ascophyllum nodosum canopy was shown to be responsible for more than 75% of the gross primary productivity and respiration of the community of a temperate mid-shore [START_REF] Golléty | Benthic metabolism on a sheltered rocky shore: Role of the canopy in the carbon budget[END_REF]. Canopy-forming algae are also key structural elements that modify the environment and influence the occurrence of other species. The net canopy effect on the structure of intertidal communities results from the interplay of positive and negative influences [START_REF] Beermann | Effects of seaweed canopies and adult barnacles on barnacle recruitment: The interplay of positive and negative influences[END_REF] and depends on the elevation on the shore (Watt and Scrosati 2013b). For example, understory organism recruitment, growth, and survival may be enhanced by algal canopy reducing the physical stress in high rocky intertidal communities, while they may be reduced by algal canopy increasing the consumer pressure in low intertidal communities [START_REF] Bertness | Testing the relative contribution of positive and negative interactions in rocky intertidal communities[END_REF].

Furthermore, the presence of a canopy-forming alga may promote the community stability by dampening the environmental condition oscillations [START_REF] Bulleri | Temporal stability of European rocky shore assemblages: variation across a latitudinal gradient and the role of habitat-formers[END_REF]. Rocky shore canopy-forming algae are susceptible to loss through various natural and anthropogenic stressors on coastal ecosystems and the loss of a single canopy species can lead to cascading effects on other species of the community and have severe consequences on its functioning [START_REF] Schiel | Rivets or bolts? When single species count in the function of temperate rocky reef communities[END_REF].

The community effects of a canopy-forming alga removal have been widely studied in terms of number, composition and abundance of associated species and a large range of responses has been observed [START_REF] Crowe | Large-scale variation in combined impacts of canopy loss and disturbance on community structure and ecosystem functioning[END_REF]). The response depends on complex interactions among species and local abiotic conditions. Even if the replacement by a less competitive but functionally similar species can occur, the removal of a canopy-forming alga may have important effects on the community structure. For example, canopies of Fucus serratus and F. vesiculosus developed after the removal of A. nodosum in a British shore and the balance between grazing limpets and the cover of red algal turf in the understory community changed [START_REF] Jenkins | Long term effects of Ascophyllum nodosum canopy removal on mid shore community structure[END_REF]). The removal of the canopyforming species will have even more important effects on the structure of the community if no replacement occurs. In some mid-intertidal systems of southern New Zealand, Hormosira banksii is the only fucoid able to withstand the high thermal stress, so that its removal was not compensated and led to the loss of almost the entire epifaunal community [START_REF] Lilley | Community effects following the deletion of a habitat-forming alga from rocky marine shores[END_REF]. Less research has considered the potential consequences of the removal of canopy-forming algae on primary productivity. In the absence of functional replacement of the macroalga, however, a severe reduction in primary productivity may be expected [START_REF] Tait | Legacy Effects of Canopy Disturbance on Ecosystem Functioning in Macroalgal Assemblages[END_REF][START_REF] Crowe | Large-scale variation in combined impacts of canopy loss and disturbance on community structure and ecosystem functioning[END_REF]. Another aspect that has been poorly explored is the role that canopy-forming algae can play in the temporal variability of community metabolism [START_REF] Valdivia | Stressed but stable: canopy loss decreased species synchrony and metabolic variability in an intertidal hard-bottom community[END_REF]. The stability of community functional properties may be related to the dominance of large perennial species, with the outcome depending on the dominant species' identity [START_REF] Hillebrand | Consequences of dominance: A review of evenness effects on local and regional ecosystem processes[END_REF]) and on the environmental context [START_REF] Grman | Mechanisms contributing to stability in ecosystem function depend on the environmental context[END_REF].

Previous studies have demonstrated that the response of rocky shore communities to the loss of canopy species can vary dramatically due to variable combinations of abiotic and biotic factors. The functional consequences of changes in the community structure needs to be measured in the field to realistically take into account this combination of factors. The present study examined the effects of the permanent removal of the canopy-forming alga Fucus serratus on a mid-low rocky shore ecosystem both in terms of diversity (number and composition of species) and functioning (primary productivity and respiration). CO 2 fluxes were measured directly in situ, without altering target assemblages, over a period integrating the seasonal variability. The aim of this field experiment was (1) to test whether the loss of the canopy alga would reduce the community primary productivity and respiration level and affect their temporal variation, (2) to determine how the absence of this canopy might modify the composition of the community and its temporal variation and (3) to examine the links between community composition and metabolism.

Materials and methods

Study site

The study site (48° N 43.686', 3° W 59.282')

Experimental design and set-up

The experiment, designed with two treatments (control (C) or canopy removed (CR)) and five replicates, was conducted during an eighteen month period (from February 2006 to August 2007). All manipulations, measurements and observations were performed during emersion times. Ten 0.09 m 2 quadrats with at least 75% Fucus serratus cover were marked with stainless steel screws. At the start of the experiment, all F. serratus were removed with a knife from 5 randomly selected quadrats and from a 50 cm wide band around them. Canopy removal was maintained throughout the experiment, simulating an extended period of canopy loss.

Sampling

Community metabolism was examined by the measurement of CO 2 fluxes at the rock-air interface using benthic chambers. Measurements were performed on each quadrat four, six, nine, twelve and eighteen months after the initial removal of the canopy. The benthic chamber consisted of a transparent Plexiglass dome and a 0.09 m 2 transparent plexiglass base, air-tightly sealed with neutral silicone, for a total volume of 18.9 L. Changes in CO 2 mol fraction (ppm) were measured by an infrared CO 2 gas analyser (LI-COR, LI-800) and recorded every 15 s with a data logger (LI-COR, LI-1400) during 5-20 min incubations as described by [START_REF] Migné | A closedchamber CO 2 -flux method for estimating intertidal primary production and respiration under emersed conditions[END_REF]. CO 2 fluxes were calculated from the slope of CO 2 concentration (μmol CO2 mol air -1

) against time (min). Results were then expressed in carbon units (mmolC m -2 h -1 ) assuming a molar volume of 22.4 L mol -1 at standard temperature and pressure. Measurements were performed under ambient light to assess the rate of benthic community net primary productivity (NPP) and in darkness, by covering the chamber with an opaque polythene sheet, to assess benthic community respiration (Resp). Benthic community gross primary productivity (GPP) was then calculated as the sum of NPP and Resp. Care was taken to perform the measurements under light at saturating irradiance levels. Irradiance was measured at the rock surface as PAR (Photosynthetically Available Radiation) using a LiCor SA-190 quantum sensor. A threshold of PAR of 300 mol m -2 s -1 was chosen based on the average value of 291 mol m -2 s -1 given for the onset of light saturation of coastal macroalgal communities by [START_REF] Middelboe | Highly predictable photosynthetic production in natural macroalgal communities from incoming and absorbed light[END_REF]. Working at saturating irradiance levels enables valid comparisons between treatments and times despite variations in irradiance.

Before the CR treatment was initiated, all macro-epi-benthic specimens were identified to the lowest taxonomic level possible in the field (usually species). The percentage cover of each alga was estimated using an index (1: ]0-25%], 2: ]25-50%], 3: ]50-75%], 4: ]75-100%]) and the solitary animals were counted in all 10 quadrats. This was repeated the following day in the 5 quadrats from which the canopy was removed and three, six, nine, twelve, sixteen and eighteen months later in the 10 quadrats. Biomass was sampled destructively at the end of the experiment, kept separately for the different taxa, and measured as dry weight.

Data analysis

Rate of community metabolism (NPP, Resp and GPP) measured for each treatment was compared at each period of measurement. Furthermore, the temporal variation in community metabolism (GPP and Resp) was assessed by calculating the coefficient of variation (Standard Deviation (SD)/mean) for each quadrat along the survey.

As the number of taxa per quadrat was low, diversity was analysed at the five quadrat scale (0.45 m 2 ; i.e. at each period, the data of the five quadrats of each treatment were pooled) using either univariate or multivariate descriptors. Univariate descriptors included total number of taxa (S) as well as Shannon's diversity index (H, using logarithm to the base 2) and Pielou's evenness (J) calculated for solitary counted animals. Multivariate descriptors corresponded to community composition. Samples were compared using non-metric multidimensional scaling (MDS) based on Bray-Curtis similarities. Both presence-absence and occurrence data (corresponding to the number of quadrats among five in which the taxon was observed) were used to analyse the whole community. Cover data were used to analyse the algal community (Fucus serratus excluded).

Abundance data were used to analyse the solitary counted animal community. Community composition was also analysed at the quadrat scale to estimate its temporal variation using the average Bray-Curtis similarity for each quadrat over time.

Statistical tests

The absence of difference in S, H and J between C and CR quadrats before the canopy was removed was verified using a Student's t-test. A student's t-test was also used to test for a difference between C and CR quadrats in (1) NPP at the different periods of observation, (2) temporal variation of Resp and GPP (assessed by the coefficient of variation over time), (3) temporal variation of community composition (assessed by the Bray-Curtis similarity over time), and (4) algal biomass (other than F. serratus) and per-biomass gross productivity at the end of the experiment. Univariate descriptors of diversity obtained in each treatment along the survey were compared using paired Student's t-test. All these tests were performed after the normality of data was verified (Shapiro test, P > 0.05). The data of per-biomass productivity measured at the end of the experiment were logtransformed to meet the normality assumption. The Welch correction was applied if the homogeneity of variances was not verified (Fisher test, P < 0.05). This was necessary only to test for differences in community net primary productivity after six months of experiment and in perbiomass gross productivity at the end of the experiment. The difference between C and CR treatments in the distribution of taxa among trophic types was tested using a Chi-square test.

Results

Community metabolism

The removal of the Fucus serratus canopy led to a severe decline in both community gross primary productivity (GPP) and community respiration (Resp) throughout the survey. The mean GPP rates were 2 to 19 times lower in the experimental quadrats than in the control ones (Figure 1a), whereas the mean Resp rates were 5 to 25 times lower (Figure 1b). The mean community net primary productivity was reduced in the canopy removed quadrats after nine months until the end of the experiment, but was not significantly different between the two treatments four and six months after the experiment was initiated (t test, t8 = 1.078, P = 0.312 and t4.3 = 0.673, P = 0.536 respectively, Figure 1c).

The removal of the canopy also led to a significant increase in the temporal variation of the GPP (t test, t8 = 5.083, P < 0.001) while it did not affect significantly the temporal variation of the Resp (t test, t8 = 1.481, P = 0.177, Figure 2).

Community structure

As a whole, 67 taxa were observed during the survey: 26 algae (14 of them common to the two treatments, 6 exclusive to the control and the canopy removed treatments respectively) and 41 animals (17 of them common to the two treatments, 14 exclusive to control and 10 to canopy removed treatment). Among exclusive to the C treatment were sessile species mainly epiphytic on Fucus serratus: the algae Ceramium sp. and Polysiphonia sp., the hydroids Dynamena pumila and Laomedea sp., the bryozoan Electra pilosa and the colonial ascidian Botrylloïdes leachi, and a mobile species inhabiting F. serratus fronds, the isopod Dynamene bidentata. Among exclusive to the CR treatment were primary space holders (that could have benefitted from the absence of the dominant species): the algae Himanthalia elongata, Mastocarpus stellatus and Lithophyllum incrustans, the sea anemone Actinia equina and the gastropod Patella vulgata. The distribution of the whole community among trophic types (autotroph, grazer, suspension-feeder and predator) was not significantly different between the two treatments (Chi-square, X3 = 0.852, P = 0.837, Figure 3). Across sampling dates, the mean number of taxa (± SD, n = 7) was 23 ± 5 in the C treatment and 22 ± 4 in the CR treatment, which was not significantly different (Paired t test, t6 = 1.030, P = 0.343).

When the whole community was considered, the non-metric multidimensional scaling did not evidence a clear separation between the two treatments using presence/absence data (Figure 4a) but did separate the two treatments using occurrence data (except for the sample CR0, taken just after the removal of the canopy, which was grouped with the C samples, Figure 4b). When considering the algal community only (using cover data without Fucus serratus), the two treatments were not separated either (Figure 4c). In contrast, a clear effect of canopy removal was shown on the community structure of counted animals (Figure 4d).

A total of 29 solitary animals were counted during the survey, 12 of them common to the two treatments, 9 and 8 exclusive to the control and the canopy removed treatments respectively.

The mean (± SD) number of animal taxa was the same in the two treatments (9 ± 2, n = 7) but the number of individuals was higher (Paired t test, t6 = 13.314, P < 0.001) and diversity and evenness lower (Paired t test, t6 = 4.003 and 4.757 respectively, P < 0.01) in the control (Figure 5). The community was dominated by grazing gastropods, particularly Gibbula pennanti which density (± SD, n = 7) averaged 312 ± 76 ind m -2 and accounted for 71% of the total density in the C quadrats while it averaged 44 ± 19 ind m -2 and accounted for 50% of the total density in the CR quadrats.

The removal of the canopy also altered the temporal variation of the entire community structure (Figure 6). Species fluctuation was increased, as shown by the significant decrease in average Bray-Curtis similarity for each replicate quadrat over time, when considering the presence/absence data for the whole community (t test, t8 = 4.073, P < 0.01). Fluctuations in the abundance of individual species within the counted animal community were also increased, as the average Bray-Curtis similarity was significantly lower in CR than in C treatment (t test, t8 = 2.434, P < 0.05). There was, however, no significant difference in average Bray-Curtis similarity for each replicate quadrat over time considering the cover data for the algal community (Fucus serratus excluded, t test, t8 = 0.700, P = 0.504).

Ephemeral algae (Ulva) settled in spring. In May, that is three months after the experiment was initiated, it covered more than 75% of the surface area in CR quadrats while it was absent from C quadrats (Figure 7). The following year, the development was less important and similar in the two treatments (between 25 and 50% cover in June).

At the end of the experiment, both algal and animal biomasses were greatly higher in C than CR quadrats (Table 1). The biomass of algae without Fucus serratus, however, did not differ significantly between treatments (t test, t8 = 0.084, P = 0.935).

Discussion

This field experiment confirmed that the loss of a canopy alga can reduce dramatically the community primary productivity, community respiration and community biomass. As the canopy was suspected to be responsible for the major part of the community metabolism of such rocky shores [START_REF] Golléty | Benthic metabolism on a sheltered rocky shore: Role of the canopy in the carbon budget[END_REF]), the severe decrease in both gross primary productivity and respiration observed in the canopy removal treatment was expected. As observed in the preliminary work of [START_REF] Hawkins | Preliminary canopy removal experiments in algal dominated communities low on the shore and in the shallow subtidal on the Isle of Man[END_REF], however, the removal of Fucus serratus allowed the development of ephemeral green algae. Such species are characterized by a higher productivity (on a per-biomass basis) than perennial ones [START_REF] Littler | Primary productivity of marine algal functional-form groups from southwestern North America[END_REF] and their blooming should lead to relatively high per area productivity. Indeed, the cover of opportunistic green algae limited the decrease in productivity three and six months after the removal of the canopy such that the net productivity of the community was not affected by the treatment initially. Nevertheless, after nine months of experiment, the net productivity of the community was drastically reduced in the absence of the canopy and this was still observed after twelve and eighteen months. The dominant large brown alga of this shore then appeared to be irreplaceable as a contributor to the community metabolism, as also shown for the same species on two other rocky shores of northern Europe [START_REF] Crowe | Large-scale variation in combined impacts of canopy loss and disturbance on community structure and ecosystem functioning[END_REF]). The per-biomass community gross productivity measured at the end of the experiment, however, was not significantly different in the presence or absence of the canopy (86.02 ± 98.86 and 131.83 ± 78.52 μmolC g DW -1 h -1 respectively, t test, t4.8 = 1.515, P = 0.192). This showed that Fucus serratus had a major role in the community primary productivity due to its high biomass but not due to a specifically high productivity, in contrast to the dominant fucoids of southern New Zealand mid and low shores [START_REF] Tait | Legacy Effects of Canopy Disturbance on Ecosystem Functioning in Macroalgal Assemblages[END_REF]. Furthermore, the total biomass of other algae at the end of the experiment was not affected by the absence of the canopy. This might result from the balance between positive and negative influences of the canopy on the local environment under emerged and immersed conditions. Canopies reduce desiccation, temperature and light stress in the air at low tide, while they increase light limitation in water to the understory algae at high tide. In contrast, the removal of the canopy greatly decreased the animal biomass, showing an important effect on higher trophic levels.

The removal of the canopy alga led to an increase in temporal variation of gross primary productivity, which could be explained by the increased blooming of ephemeral green algae during the first year of experiment. Nevertheless, the temporal variation of respiration, a process reflecting the resource use by the whole community, was not affected by the canopy removal: a similar seasonal trend was observed for the two treatments (Figure 1b). This shows the predominant role of seasonally variable parameters (such as temperature) in the control of respiration of both canopy and other species, leading to synchronous variation in metabolic activity. An evidence of the control of respiration rate by temperature for both total and understory communities has already been given

for another fucoid stand of the same area [START_REF] Golléty | Benthic metabolism on a sheltered rocky shore: Role of the canopy in the carbon budget[END_REF]. In this previous study, measurement of the understory respiration rate was only performed just after the canopy was removed. The present result, obtained with an extended period of canopy loss, shows that the seasonal variation of temperature was not sufficiently dampened by the canopy to modify the seasonal trend of the understory community metabolism. The canopy did not then enhance the stability of this community aggregate property. This result is in accordance with the study of [START_REF] Bulleri | Temporal stability of European rocky shore assemblages: variation across a latitudinal gradient and the role of habitat-formers[END_REF], which showed that Fucus serratus had a weak effect on the temporal variability of the sessile species cover (used as a proxy for biomass) in North Atlantic rocky shores, in contrast to Ascophyllum nodosum (a mid-level species) and to the canopies in Southern Europe.

The canopy removal affected neither the number of species nor their distribution among trophic groups. This may indicate that the environmental stress was not increased in this mid-low shore experiment, which would have led to decreasing the number of species and changing their distribution among trophic groups [START_REF] Scrosati | Species richness and diversity in different functional groups across environmental stress gradients: a model for marine rocky shores[END_REF]. The canopy removal had little effect on the structure of the algal community. The greater cover attained by ephemeral green algae in canopy removal treatment related to control in the first year of the experiment may have resulted from competitive release through canopy absence. The absence of difference between treatments sixteen and eighteen months after the onset of the experiment, however, suggests that interactions with other species in the community were involved. The single canopy removal effect shown in this study was on the associated invertebrates. The species richness of animals did not differ between quadrats with and without Fucus serratus and only few species were clearly confined to quadrats with F.

serratus, but the assemblages differed consistently and the total animal abundance and biomass were greatly reduced in the absence of canopy. The gastropod grazers, living mainly on the F. serratus fronds, were particularly affected. The canopy removal decreased the density of the dominant species, Gibbula pennanti, increasing the evenness (and then the diversity) in the mobile invertebrate community.

Canopies have been shown to affect community differently along the intertidal gradient. In a manipulative experiment, species richness, diversity and composition were affected by the fucoid canopy at the high and mid intertidal zones (richness and diversity being enhanced in the presence of canopy) but not at the low intertidal zone (Watt and Scrosati 2013a). This result was confirmed by a regional-scale study (Watt and Scrosati 2013b). This implied that the canopy effects on the structure of intertidal community were mediated by the environmental stress. The capacity of fucoid canopies to enhance richness and diversity should be related to their ability to improve conditions in stressful environments but limited to high and mid shores. [START_REF] Tait | Legacy Effects of Canopy Disturbance on Ecosystem Functioning in Macroalgal Assemblages[END_REF] showed, however, an obvious change in community composition following the canopy removal at both mid and low shores. At mid-tide level, newly exposed understory algae became desiccated and died off, confirming the environment amelioration by the canopy in this thermally stressed shore. At low-tide level, proportions shifted between species in the assemblage, involving a role of the canopy in the species interactions. In the present study, the canopy was shown to reduce the diversity of mobile invertebrates in the low shore by increasing the dominance of one species.

The greater number of grazers observed in the control compared to the canopy removal treatment is consistent with observations made by [START_REF] Ingolfsson | The invasion of the intertidal canopy-forming alga Fucus serratus L. to southwestern Iceland: Possible community effects[END_REF] in the south-western Iceland.

Comparing community composition where F. serratus is the dominant alga to the adjacent area where it is absent, he found a greater attractiveness to F. serratus than to other species for grazers.

This may be partly explained by the abundance of understory algae, although the grazers considered may also prefer F. serratus to other species. In the present study, since the assemblage of algae did not differ in the absence of F. serratus, the canopy effect on invertebrates might be direct. It may be hypothesized that this direct effect is related to the high canopy biomass and cover that supply food to primary consumers or to its structural complexity that increases secondary-space availability and provides refuge from predation. The absence of canopy effect on algal community (in terms of species richness, composition and biomass) might also result from the interplay between abiotic and biotic influence. Canopy might reduce the stress of aerial exposure but might also increase the grazing pressure by providing space and refuge to grazers. Physical (thermal and desiccation) stressors and herbivores have been shown to have independent, additive effects on seaweed abundance and diversity in an upper-and mid-intertidal rocky shore of California, on a site more benign compared to the North Atlantic [START_REF] Williams | Additive effects of physical stress and herbivores on intertidal seaweed biodiversity[END_REF]. Complementary studies involving experimental manipulations of these two factors would be necessary to test for their combined influence in the mid-low Fucus serratus zone of the North Atlantic coast.

The canopy removal increased the temporal fluctuation of the community species composition but had no effect on the fluctuations in cover of the individual algal species, indicating the absence of compensatory dynamics within the algal community. Asynchronous compensatory dynamics among algal species should have been expected if the environment variability had been increased as a consequence of the canopy removal [START_REF] Valdivia | Stressed but stable: canopy loss decreased species synchrony and metabolic variability in an intertidal hard-bottom community[END_REF]. This might again suggest that the dampening effect of the canopy on environmental variations was weak in this mid-low rocky shore and not sufficient to modify the algae dynamic. Although the changes within the algal community were not affected, the canopy removal increased the temporal variability in the abundances of the individual mobile invertebrate species, which indicates a direct effect of the canopy on higher trophic levels.

This experimental study showed some significant effects of the dominant canopy-forming alga on the structure and the functioning of the rocky-shore community. Not only were the primary productivity and respiration greatly reduced in the absence of the canopy but also the biomass of associated mobile invertebrates. This indicates an important effect of the dominant alga on higher trophic levels of the community, even if neither the number of species nor their distribution among trophic groups was affected. In addition, community gross primary productivity and community structure were shown to be more temporarily variable after the canopy removal. The canopy did not seem to affect the community by dampening the environmental stress but by providing food, habitat or both. Further experimental works would be necessary to disentangle the species interactions involved.

  is in front of the Station Biologique de Roscoff, southwest of the English Channel (Brittany, France), where the extreme high water of spring tide is situated at 9.85 m above Chart Datum [C.D.]. This is a sheltered area of stacked boulder field, characterized from mean low water neap tide (3.25 m above C.D.) to mean low water spring tide (1.15 m above C.D.), by a dense cover of the fucoid Fucus serratus.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 12345 Figure 1: Mean (± SE) gross primary productivity (GPP, a), respiration (Resp, b) and net primary productivity (NPP, c) measured in mmolC m -2 h -1 in control (C) and canopy removed (CR) quadrats, 4 (n = 5), 6 (n = 5), 9 (n = 3), 12 (n = 4 for C and n = 5 for CR) and 18 (n = 5) months after initial removal (corresponding months of measurement indicated above)

Table 1 :

 1 Mean (± SD, n = 5) biomass (g DW m -2 ) of algae and animals in control (C) and canopy removed (CR) quadrats at the end of the experiment

		C	CR
	Algae	3896.37 ± 4218.39	52.43 ± 39.99
	Algae without F. serratus	54.48 ± 36.49	52.43 ± 39.99
	Animals	356.87 ± 263.88	28.18 ± 13.63

Acknowledgments

This experiment was conducted in the framework of the MarBEF responsive mode project BIOFUSE, led by T. Crowe and L. Benedetti-Cecchi. Thanks are due to colleagues and students who helped carry out the field work and particularly to R. Michel (the most famous "siliconeur") and C. Broudin.


Natacha Luximon

Eric J Petit

Thomas Broquet
email: thomas.broquet@sb-roscoff.fr

Performance of individual vs group sampling for inferring dispersal under isolation by distance

Keywords: Dispersal inference, gene flow, individual-based simulations, dispersal kernel, IBD

Models of isolation-by-distance formalize the effects of genetic drift and gene flow in a spatial context where gene dispersal is spatially limited. These models have been used to show that, at an appropriate spatial scale, dispersal parameters can be inferred from the regression of genetic differentiation against geographic distance between sampling locations. This approach is compelling because it is relatively simple and robust, and has rather low sampling requirements. In continuous populations, dispersal can be inferred from isolation-by-distance patterns using either individuals or groups as sampling units. Intrigued by empirical findings where individual samples seemed to provide more power, we used simulations to compare the performances of the two methods in a range of situations with different dispersal distributions. We found that sampling individuals provides more power in a range of dispersal conditions that is narrow but fits many realistic situations. These situations were characterized not only by the general steepness of isolation-bydistance but also by the intrinsic shape of the dispersal kernel. The performances of the two approaches are otherwise similar, suggesting that the choice of a sampling unit is globally less important than other settings such as a study's spatial scale.

Introduction

Genetic data can inform us about dispersal patterns. But that information can be obtained only when a number of biological and methodological conditions are fulfilled. At one end of a methodological continuum, the direct identification of dispersal events (e.g. using population or parentage assignment) can provide detailed and accurate dispersal data. But because of its reliance on intensive sampling, this approach is constrained in terms of study systems, time frame, and study area. At the other end, indirect estimates of migration rates obtained from measurements of spatial genetic structure and demogenetic models depend critically on models' refinement and assumptions [START_REF] Marko | The complex analytical landscape of gene flow inference[END_REF][START_REF] Whitlock | Indirect measures of gene flow and migration : F ST 1/(4Nm+1)[END_REF]. A sustained interest in this field of research has produced a wealth of alternative potential solutions for inferring dispersal (e.g. reviewed in [START_REF] Broquet | Molecular estimation of dispersal for ecology and population genetics[END_REF] and other references therein), but finding a good fit between biological settings and methodological options is rarely obvious.

Inferring dispersal from isolation-by-distance (IBD) patterns is one approach that seems to stand out by its (relatively) wide applicability. The dynamics of genetic variation in populations along a gradient of spatial proximity were first formalized by [START_REF] Wright | Isolation by distance[END_REF], [START_REF] Malécot | Les processus stochastiques en génétique de population[END_REF], and [START_REF] Kimura | The stepping stone model of population structure and the decrease of genetic correlation with distance[END_REF]. These and following IBD theoretical developments have set ground for several inference methods that aim at estimating dispersal from genetic data (reviewed in [START_REF] Guillot | Statistical methods in spatial genetics[END_REF]). We focus here on the method proposed by Rousset (1997Rousset ( , 2000)), which uses a regression of genetic distances on geographic distances among pairs of samples to infer the product Dσ 2 , where D is the effective density and σ 2 is the mean squared parent-offspring distance. If D can be independently estimated then σ 2 gives a synthetic descriptor of dispersal that can be compared across populations or species (e.g. [START_REF] Pinsky | Using isolation by distance and effective density to estimated dispersal scales in anemonefish[END_REF]; see also [START_REF] Vekemans | New insights from fine-scale genetic structure analyses in plant populations[END_REF] using a related approach), and possibly compared with field-based estimates (e.g. Watts et al. 2007). The product Dσ 2 itself is also of interest as it informs us on the increase of differentiation with distance. This approach is not free from drawbacks. Most importantly, the parameter σ is not intuitive (see discussions in [START_REF] Broquet | Molecular estimation of dispersal for ecology and population genetics[END_REF][START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF]Sumner et al. 2001), some preliminary knowledge of dispersal scale is needed to set an appropriate study scale, and data interpretation requires some understanding of the effect of departure from mutation-migration-drift equilibrium.

But the method's robustness or behavior has been assessed in various aspects (e.g. Broquet et al. 2006b;[START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF][START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF][START_REF] Vekemans | New insights from fine-scale genetic structure analyses in plant populations[END_REF]Watts et al. 2007), and it relies on manageable sampling requirements. Accordingly, interpretations of isolation-by-distance patterns are frequent in the literature, including several estimations of the dispersal parameter σ (reviewed in Table S1, supplementary material. See also Fig. 1).

Rousset proposed to calculate distances between individuals in a continuous population (Rousset 2000) or between groups of individuals (either because the population under study is subdivided into discrete units, or because discrete groups of individuals were sampled from an otherwise continuous population; Rousset 1997Rousset , 2000)). Hereafter we will use the words "individual" and "group" to refer to the sampling unit of each approach. The two methods are based on the same theoretical background (detailed in [START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF]) and aim at estimating exactly the same quantity.

Importantly, the two methods should be used at the same spatial scale, considering samples at distances not greater than ca. 0.56𝜎/√2𝜇, where μ is the mutation rate of the loci considered [START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF]. Because the regression method based upon groups can be applied in a continuous population, some empirical case studies compared the results provided by the two methods with the same species in the same population (Broquet et al. 2006a;[START_REF] Suni | Fine-scale genetic structure and dispersal distance in the harvester ant Pogonomyrmex barbatus[END_REF]Watts et al. 2007).

These studies repeatedly found that the group approach has less power, in some cases to the point that only the individual approach could be used to infer σ. The correlation of genetic and geographic distances is tested using Mantel's test, which is not particularly powerful [START_REF] Legendre | Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data[END_REF], and the number of pairwise comparisons is easily two orders of magnitude greater when using individuals as sampling units. The difference in power observed in case studies could thus be due simply to the number of data points, giving an advantage to individuals as sampling units. On the other hand, individual-based genetic distances may suffer from more sampling variance and more variable effect of genetic drift than group-based statistics. Differences in power remain to be investigated and complemented with results for the precision, bias, and coverage of confidence intervals obtained with each approach. The performances of IBD-based dispersal inference have been thoroughly evaluated in simulation studies that used individuals as sampling units [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF][START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF]). However, individual-and group-based sampling schemes have not yet been compared to one another in controlled conditions. Such a comparison could be useful for planning field studies and for interpreting empirical patterns, particularly in situations where samples are not easily collected individually. Such comparisons are also timely because of the growing interest in using pooled samples (mixtures of individuals) that develops in parallel with modern sequencing protocols [START_REF] Davey | Genome-wide genetic marker discovery and genotyping using next-generation sequencing[END_REF][START_REF] Futschik | The Next Generation of Molecular Markers From Massively Parallel Sequencing of Pooled DNA Samples[END_REF][START_REF] Gautier | Estimation of population allele frequencies from nextgeneration sequencing data: pool-versus individual-based genotyping[END_REF].

Our objective is to determine whether there is an advantage in using one or the other method in situations where the two methods could be applied.

Methods

Using IBDSim [START_REF] Leblois | IBDSim: a computer program to simulate genotypic data under isolation by distance[END_REF]) we simulated a continuous population composed by a square grid of 110×110 units with one diploid individual per node. Each individual was characterized by a multilocus genotype made of 10 microsatellites. IBDSim simulates the demography (coalescence and dispersal) backwards in time before adding in mutations. The life-cycle is as follows: i) gamete production and death of adults. ii) gamete mutation following a generalized stepwise model with rate μ=5×10 -4 as described in [START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF] with a maximum number of alleles set to 100 per locus (a value large enough to be uninfluential here). iii) gamete dispersal according to a predefined distribution of dispersal distances (see below). iv) constitution of diploid individuals. v) regulation of the population to n=1 individual per node.

We defined 36 simulation scenarios (Table S1) differing only in dispersal conditions. Dispersal distances followed a truncated Pareto distribution, where the probability of dispersing k steps in each dimension is given by 𝑓 𝑘 = 𝑀 𝑘 𝑛 ⁄ for 𝑘 ≤ 𝑘 𝑚𝑎𝑥 , as discussed by Rousset (2000). We varied M (total dispersal rate in one dimension), n (a parameter that controls the shape of the distribution)

and k max (maximum dispersal distance) to obtain a range of dispersal situations with simulated σ values (𝜎 𝑠𝑖𝑚 2 , range 1.12 -47.01) comparable to that estimated from empirical case studies (𝜎 𝑒𝑠𝑡 2 : we found estimates for 62 plant and animal species, Fig. 1 and Table S1). Simulations thus differed in the values taken by σ 2 (giving the strength of IBD) but also in the nature of the dispersal kernelscharacterized by M, n and k max -that yielded these values.

Dispersal inference under IBD should consider samples at distances smaller than ca.

0.56𝜎/√2𝜇 [START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF], which is approximately equal to 18σ given our mutation rate. The total size of the simulated population (110×110) was large enough to contain the optimal sampling design for any simulation scenario with some extra space to limit edge effects. At grid edges we used "absorbing" boundaries in IBDSim whereby "the probability mass of going outside the lattice is equally shared on all other movements inside the lattice" (as defined by R. Leblois in IBDSim user manual). The total simulated population was kept constant but samples were taken from within a smaller area and defined as a square of side length 13σ (that is, with diagonal ≈18σ, Fig. 2). A different sampling grid was thus potentially associated with each simulation scenario.

To test for IBD and infer σ 2 we randomly sampled 99 individuals and 11 disjoint clusters of 9 individuals from within the defined sampling grid (Fig. 2). These samples were analyzed in Genepop V4.0 [START_REF] Rousset | GENEPOP ' 007: a complete re-implementation of the GENEPOP software for Windows and Linux[END_REF]) using the estimator â for pairwise genetic distances among individuals (Rousset 2000) and F ST /(1-F ST ) for groups (Rousset 1997). The mean genetic distance among pairs of samples and the global F ST are shown in Table S2 andFig was used to infer σ 2 from the relationship 𝑏 = 1/(4𝐷𝜋𝜎 2 ) with D=1. We also recorded approximate 95% confidence intervals calculated using the ABC procedure implemented in Genepop [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF][START_REF] Rousset | GENEPOP ' 007: a complete re-implementation of the GENEPOP software for Windows and Linux[END_REF]Watts et al. 2007). Each simulation was replicated 200 times (a number large enough to capture most of the variance across replicates, data not shown), giving 36×200=7200 simulations overall.

The power of the regression method based upon groups and individuals was calculated for the 36 simulation conditions as the proportion of replicates yielding a significant Mantel test (using 10 000 permutations and a significance threshold α=5%). The relative error was estimated as (𝜎 𝑒𝑠𝑡 2 -𝜎 𝑠𝑖𝑚 2 )/𝜎 𝑠𝑖𝑚 2 for each replicate, and we defined the bias and the precision of σ 2 estimates as the median and the dispersion of the relative error, respectively. Finally, the coverage was defined as the proportion of replicates where 𝜎 𝑠𝑖𝑚 2 was included within the confidence interval of 𝜎 𝑒𝑠𝑡 2 . These statistics were computed using only the replicates where a significant IBD was detected (5045 and 5357 replicates for the group and individual methods), because σ 2 would not be inferred from a dataset otherwise.

We used generalized linear models to test for i) differences in power, bias, and coverage between methods, and ii) the effect of parameters M, n, and k max on the power, bias, and coverage of each method (with adequate transformation of data or binomial error structure when necessary).

We included 𝜎 𝑠𝑖𝑚 2 as an explanatory variable in these models because it is directly linked to the strength of IBD and thus should be a primary determinant of a method's performances. All results reported in the main text are thus independent of the value taken by 𝜎 𝑠𝑖𝑚 2 . To control for the fact that different simulation conditions were associated with different sampling grids (i.e. different spatial scales), we also included the median of the Euclidean distances among pairs of samples as an explanatory variable. Finally, the models were of the form < response ~ 𝜎 𝑠𝑖𝑚 2 + Med.dist + Method > when we compared the two methods (Med. dist is the median of distances among samples) and of the form < response ~ 𝜎 𝑠𝑖𝑚 2 + Med. dist + n × M × k max > when we assessed the effects of simulation parameters, where response was either power, bias, or coverage.

Results

The power of the two methods, measured as the proportion of replicates yielding a significant Mantel test, dropped from 100% to ca. 20% in our two most extreme situations in terms of simulated dispersal (Fig. 3a, 𝜎 𝑠𝑖𝑚 2 =1.12, and Fig. 3i, 𝜎 𝑠𝑖𝑚 2 =47.05). However, the group approach lost power at an earlier stage as the strength of IBD decreased (Figs. 3d-e). Interestingly, this effect was primarily due to the shape parameter n (e.g. Figs. 3a,d,g), which had a significant effect independently of the value taken by 𝜎 𝑠𝑖𝑚 2 (p<0.001). When n was large (meaning that long-distance dispersal was rare, first row in Fig. 3) the two methods performed well, and M and k max took no effect. With low n the effect of k max became critical (last row of Fig. 3) but the two methods were equally affected. When n was intermediate (middle row of Fig. 3) the group approach was more strongly affected than the individual approach by an increase in k max (e.g. in Fig. 3d the power decreased from 100% to 80% for the individual approach vs 60% for the group approach when k max was increased from 10 to 50). These results convey the following information: i) the two methods have comparable power except in a restricted set of conditions, ii) those dispersal conditions where individuals outperformed groups resulted in 𝜎 𝑠𝑖𝑚 2 in [3.89-11.83], a range of values that fits well empirical estimates from real case studies (Fig. 1), including one study where IBD was detected with individuals only (Broquet et al. 2006a), and iii) these conditions are not determined solely by σ 2 but also by the shape of the underlying dispersal kernel (e.g. the range of 𝜎 𝑠𝑖𝑚 2 mentioned above is also spanned by simulations 25-32, and yet with these simulations the two methods have nearly identical power, Fig. 3c&f).

Besides power, we looked at the bias and the precision of σ 2 estimates with the median and the dispersion of the relative error, respectively. We found that the two methods generally underestimated the true σ 2 by a small proportion (Fig. 4) and that this bias was slightly more pronounced with the individual approach (-15% and -9% for individuals and groups overall simulations, p<0.001). This slight underestimation is in agreement with simulation results obtained by [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF][START_REF] Rousset | Genetic structure and selection in subdivided populations[END_REF] when the sampling design was not too far from theoretical optimum (e.g. simulations 1 and 2 in Table 2 of [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF], note that the bias is calculated for the regression slope). In agreement with results for the power, the two methods showed decreasing performance (increasing bias) with decreasing IBD strength (down to ca. -60% with 𝜎 𝑠𝑖𝑚 2 =47.05, Fig. 4i). Irrespective of 𝜎 𝑠𝑖𝑚 2 , the bias also appeared to be influenced by the shape of the dispersal kernel, and particularly by parameter k max (p<0.001). Increasing k max resulted in deeper negative bias whatever the values taken by the other parameters. Surprisingly, the precision of estimates followed an opposite trend (Fig. 4): the dispersion of estimated values around the median was greatest when IBD was strong, and this effect was particularly visible for small values of k max (left box-plot of each panel in figure 4). As a result, the situations where the bias was minor were generally not favorable in terms of precision. This observation is valid for the two methods, which showed no systematic difference in precision. Yet a difference can be noted regarding the replicates producing the worst estimates. Overall simulations with significant IBD, 17 such replicates (out of 10 402) produced estimates with a relative error larger than 150% (Fig. 4). These cases were all characterized by a near-zero slope estimate, yielding large relative errors. Interestingly, only 3 such cases were produced by the individual approach.

Finally, we did not find any difference in coverage between methods (p>0.05): the proportion of replicates where the 95% confidence interval of the estimate (𝜎 𝑒𝑠𝑡 2 ) included the true value (𝜎 𝑠𝑖𝑚 2 ) amounted to 86% using groups and 85% using individuals (Fig. S2). In the specific cases where a difference in coverage was visible the method with the best coverage also appeared to have larger confidence intervals (data not shown). Note that the coverage values reported here for each method independently may be overestimated, because the ABC procedure used to approximate 95% confidence intervals generally underestimates the upper bound for 𝜎 𝑒𝑠𝑡 2 [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF].

Discussion

Our simulations were parameterized so that the product Dσ 2 fits real situations where IBD patterns had been analyzed (Fig. 1 and Table S1). Yet the conditions of dispersal inference varied widely between simulations for the following reason: the number of samples was kept constant across simulations (99 genotypes) while the sampling scale was set with respect to 𝜎 𝑠𝑖𝑚 2 in order to fit the methods' requirements (distance between samples < 0.56𝜎 𝑠𝑖𝑚 √2𝜇 ⁄ ). It means that the density of the sampling effort decreased with increasing 𝜎 𝑠𝑖𝑚 2 , giving us a range of conditions where the inference of dispersal went from being very favored (when 𝜎 𝑠𝑖𝑚 2 is small and IBD is steep with respect to the sampling scale) to very limited (with larger 𝜎 𝑠𝑖𝑚 2 ). This variation allowed us to explore potential differences between the individual-based and group-based methods.

We find that there is only a small region of parameters where individual sampling outperformed group sampling, and this advantage bears upon power only (we found no sizeable differences in accuracy, precision, and coverage between the two approaches). However, we note that intermediate situations, where the power of the individual-based regression approach was greater than that of the group approach, appeared to cover the range of situations most commonly encountered in natural situations, at least in terms of 𝐷𝜎 2 (Fig. 1, exactly half of the reviewed empirical estimates fall in the 𝐷𝜎 2 region where the individual approach can outperform the group approach, depending on dispersal distributions).

Interestingly, the difference in performances between methods is due to particular conditions of 𝜎 𝑠𝑖𝑚 2 but also to the shape of the dispersal kernel (decreasing n significantly affected the difference in power between methods independently of 𝜎 𝑠𝑖𝑚 2 , see Figs. 3a,d,g). Based upon empirical finding for a forest-dwelling mammal, the American marten, we had the intuition that dispersal kernels characterized by a fat tail of long distance events could affect IBD patterns based upon groups more than individuals (Broquet et al. 2006a). But this idea is not supported by theory (Rousset 2000), and our simulation results suggest that although there really is some effect of the shape of the dispersal kernel on the power of the two methods, it is not particularly due to long distance dispersal.

We also found a slightly reduced risk to get extremely biased estimates with the individual approach (considering those few estimates that were off by 150% or more, most came from group sampling).

Furthermore, the accuracy of each method increased with the proportion of simulation replicates where the two methods yielded a significant IBD pattern. This means that when one method yields a significant result but the other one does not then there is a higher risk of bias using either approach.

In other words, with adequate datasets that fulfill the methods' assumptions, the power difference that may favor the individual-based approach occurs in situations where the risk of bias is anyways higher on average.

There are a number of relevant issues that were not considered here, such as the effects of spatial and temporal heterogeneity in population density on the relative performances of each approach (the density was set to 1 individual per node in all our simulations, see [START_REF] Leblois | Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance[END_REF][START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF] for different conditions with individual sampling). Whether or not such factors could interact with our findings is difficult to tackle, even using simplified simulations. Moreover, all our simulations fulfilled one critical assumption of IBD-based inferences (Rousset 1997(Rousset , 2000)):

migration and drift are stable in space and time, and the pattern of increase of differentiation with geographic distance has reached equilibrium. The results presented here do not apply to other situations, which are irrelevant for inferring dispersal from IBD slopes, though the method seems robust to some disequilibrium situations [START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF]). Finally, we did not explore the effect of the number of samples (e.g. the number and the composition of groups). We chose to use rather small groups to get conservative results with the group approach, and because it is difficult to design simulation conditions that harmonize the requirements for sampling scale, useful 𝜎 𝑠𝑖𝑚 2 , and simulation and analysis time. In a pilot study we found nonetheless that increasing the total number of individuals sampled for each method benefited more to the group approach (data not shown).

Our findings suggest that when the methods are properly applied in continuously distributed populations there is only a slight advantage in using individuals as the sampling unit. Other considerations might thus be more important, such as the spatial scaling of IBD studies. As shown by previous work, the study scale should be large enough so that dispersal becomes spatially limited (unlike in the island model, which may apply at a shorter scale, e.g. see [START_REF] Kerth | Colonization and dispersal in a social species, the Bechstein's bat (Myotis bechsteinii)[END_REF], and, more critically, local enough so that the effect of gene flow does not faint out in front of mutation and is not blurred by non-equilibrated patterns (such as signatures of past colonization, e.g. [START_REF] Austin | Controlling for the effects of history and nonequilibrium conditions in gene flow estimates in northern bullfrog (Rana catesbeiana) populations[END_REF]. Hence priority should be given to identifying the right study scale and choose the sampling unit based upon the spatial distribution of individuals (Rousset 2000) and sampling possibilities rather than intrinsic properties of the methods. We emphasize that our conclusions about the detailed effect of dispersal parameters should not be extrapolated without caution to systems more complex than the simulations described here. But one robust result of this study is that in any case the choice of adequate spatial and temporal scales seems much more important than the sampling unit in continuously distributed populations. Empirical values were obtained from a literature survey of significant IBD patterns for animal and plant case studies that investigated two-dimensional spatial genetic structure (the product Dσ 2 has a different scale in 1D studies, Rousset 1997). These values were either taken directly from the papers, or calculated from related statistics, such as Sp [START_REF] Vekemans | New insights from fine-scale genetic structure analyses in plant populations[END_REF]. When more than one value was available for a given species in a specific paper, only one was retained for drawing the histogram. Most empirical values included in this comparison are taken from the review by [START_REF] Vekemans | New insights from fine-scale genetic structure analyses in plant populations[END_REF], completed with results from additional papers reviewed in our Table S1 (supplementary material). Vertical lines show the lower and upper limits of the region in which individual-based analyses can outperform group-based analyses (see results). Note that the x axis is log-scaled for a better visualization of the distributions.

Figure 2 -Principle of the sampling design. The actual simulations used a 110×110 grid, large enough to contain a square of side length 13σ for any of the conditions listed in Table S1. Ninety-nine individuals or 11 groups of 9 individuals were randomly sampled from within this grid to infer σ 2 using isolation-by-distance patterns. between pairs of individuals (white boxes) or groups (grey). Data from 200 replicates per simulation are shown (simulation conditions as in Figure 3). The solid line in each box shows the median of the error distribution, the box shows the 25% and 75% quantiles, and the whiskers show the full range of the errors. In cases where the whiskers extend beyond the plotting region, 1 to 3 replicates (out of 200) had a relative error greater than 1.5 and are not shown here. Table S1: Literature survey of empirical Dσ 2 values estimated from significant IBD patterns for animal and plant case studies that investigated two-dimensional spatial genetic structure (the product Dσ 2 has a different scale in 1D studies, Rousset 1997). These values were either taken directly from the papers, or calculated from related statistics, such as Sp [START_REF] Vekemans | New insights from fine-scale genetic structure analyses in plant populations[END_REF]. When more than one value was available for a given species in a specific paper, only one was retained for drawing the histogram (see footnotes). replicates per simulation are shown (simulation conditions as in Figure S2).

Species

  . S1. The slope (b) of the regression of pairwise genetic distances and ln-transformed geographic distances among samples (individuals or groups)

Figure 1 -

 1 Figure 1 -Comparison of the frequency distribution of empirical (plotted as positive frequencies, in grey) and simulated (represented by negative frequencies, in white) values of the product Dσ 2 .

Figure 3 -

 3 Figure 3 -Power of Mantel test in detecting a correlation between genetic and geographic distances

Figure 4 -

 4 Figure 4 -Relative error in σ 2 estimated from the regression of genetic-vs geographic distances

  Fig. 1

Fig. 3

 3 Fig. 3

  Fig. 4

Fig. S1

 S1 Fig.S1Mean pairwise genetic distance among individuals (â, in black) or groups (F ST /(1-F ST ), in grey) averaged

Table S2 :

 S2 Simulation conditions. The parameters M, n, and k max set the shape of the distribution of dispersal distances in the simulations. The values taken by these parameters result in a range of dispersal conditions characterized by 𝜎 𝑠𝑖𝑚 2 . The genetic structure observed at equilibrium is given by the mean pairwise genetic distance between sampled individuals (a) or groups (F ST /(1-F ST ) and the global F ST averaged over 200 simulation replicates.

	Simulation			M	n	K max	2 𝜎 𝑠𝑖𝑚	a	mean genetic distance F ST /(1-F ST )	F ST
	1			0.4	2.8	Taxon 10	Sampling unit Density 1.12 0.202	Unit	Dσ 2 0.103	Reference 0.093
	Homo sapiens 2			0.4	Mammal 2.8 25	group 1.53	24 0.201	ind/km² 17 0.101	(Rousset 1997) 0.091
	Dipodomys spectabilis 3 Gnypetoscincus queenslandiae 0.4 4 0.4 5 0.4	Mammal 2.8 50 Reptile 2.8 100 2.2 10	individual 1.83 individual 2.01 1.99	0.0002 ind/m² 2.6 0.203 0.103 0.0136 ind/m² 6.7 0.200 0.103 0.159 0.071	0.093 (Rousset 2000) 0.093 (Sumner et al. 2001) 0.066
	Chamaecrista fasciculata 6	0.4	Fabaceae 2.2 25	group 3.89	-0.151	-	10.7 0.064	(Fenster et al. 2003) 0.060
	Ostrinia nubilalis 7			0.4	2.2	Insect	50	group 6.03	-0.151	-	4.9 0.063	(Martel et al. 2003) 0.059
	Crassostrea virginica 8		0.4	Mollusc 2.2 100	group 7.85	0.24 ind/km² 113.7 0.154 0.064	(Rose et al. 2006) 0.060
	Martes americana 9 Coenagrion mercuriale	a	0.4 0.4 0.4	Mammal 1.8 10 Insect 1.8 25 1.8 50	individual 3.08 individual 7.93 15.23	0.46 ind/km² 6.6 0.133 0.050 0.0022 ind/m² 30.7 0.120 0.040 0.115 0.037	0.047 (Broquet et al. 2006) 0.038 (Watts et al. 2007) 0.036
				0.4	1.8	100	group 23.13	0.0023 ind/m² 31.3 0.119 0.037	0.035
	Plethodon cinereus		0.6	Amphibian 2.8 10	group 1.68	2.82 0.101	ind/m² 9.9 0.074	(Cabe et al. 2007) 0.068
	Microtus arvalis			0.6	Mammal 2.8 25	individual 2.30	1000 ind/km² 16.6 0.101 0.074	(Gauffre et al. 2008) 0.068
	Bonasa bonasia Milicia excelsia b Corrallium rubrum	c		0.6 0.6 0.6 0.6	Bird Moraceae (tree) 2.8 50 2.8 100 2.2 10 Cnidaria 2.2 25	individual 2.75 individual 3.02 2.99 group 5.85	5.5 0.104 4.96 ind/km² 12.3 ind/km² 5 0.075 0.104 0.075 0.071 0.051 --8 0.065 0.043	0.069 (Sahlsten et al. 2008) 0.069 (Bizoux et al. 2009) 0.048 (Ledoux et al. 2010) 0.041
	(a) Based upon the data used to compare group-and individual-based approaches. (b) Computed from Table 2 for 0.6 2.2 50 9.08 0.063 0.042 0.040
	population Mindourou. (c) Computed from the slope value given in Fig. 2 for population Catalonia. 0.6 2.2 100 11.83 0.064 0.042	0.040
				0.6	1.8		10	4.63	0.050		0.035	0.034
				0.6	1.8		25	11.95	0.041		0.026	0.025
				0.6	1.8		50	22.99	0.038		0.023	0.022
				0.6	1.8	100	34.98	0.041		0.023	0.023
				0.8	2.8		10	2.24	0.077		0.057	0.054
				0.8	2.8		25	3.08	0.072		0.052	0.049
				0.8	2.8		50	3.68	0.075		0.053	0.050
				0.8	2.8	100	4.03	0.076		0.055	0.052
				0.8	2.2		10	4.00	0.047		0.036	0.034
				0.8	2.2		25	7.83	0.040		0.030	0.029
				0.8	2.2		50	12.16	0.039		0.028	0.027
				0.8	2.2	100	15.84	0.039		0.029	0.028
				0.8	1.8		10	6.20	0.031		0.024	0.023
				0.8	1.8		25	16.02	0.020		0.016	0.016
				0.8	1.8		50	30.86	0.018		0.015	0.015
				0.8	1.8	100	47.05	0.020		0.015	0.014

Acknowledgements

We thank Raphaël Leblois for insightful discussions and comments, and for answering our questions regarding the software IBDSim. We are grateful to Glenn Yannic, Editor O. Gaggiotti and two anonymous reviewers for their constructive comments on the manuscript. We also thank Christophe Caron for his help with using the computer cluster in the biological station of Roscoff. TB was supported by the "Marine Aliens and Climate Change" program funded by AXA Research Funds.

Data accessibility

Three types of data are available on Dryad (entry doi:10.5061/dryad.mq8n5): i) parameter files for each simulation (IBDSim settings), ii) command lines for the batch analysis of simulation outputs in Genepop, and iii) summaries of the main statistics produced by Genepop for all simulations and replicates that we used here to compare the performances of individual-based vs group-based inferences.

Author contributions

N.L. performed the simulations and analyses. E.P. and T.B. designed the research, performed the analyses, and wrote the paper.