Naiyin Xu

Michel Fok

Lixin Bai

Zhiguo Zhou

Effectiveness and chemical pest control

come   L'archive ouverte pluridisciplinaire

Effectiveness and chemical pest control of Bt-cotton in the Yangtze River Valley, China . Introduction

In China, genetically modified cotton (GMC) was first marketed in 1997, with varieties integrating Bt genes (Bt-cotton) to control some cotton pests, notably Helicoverpa armigera.

By 2005, it was estimated that Bt-cotton is grown on about 60% of the total Chinese cottongrowing area (ISAAA, 2005), and close to 100% in areas with potentially major bollworm infestations (namely in the Yellow River Valley and Yangtze River Valley).

This acceptance of Bt-cotton could be explained by its cost-effectiveness due to a reduction in pesticide use [START_REF] Huang | Bt cotton benefits, costs and impacts in China[END_REF][START_REF] Huang | Plant biotechnology in China: public investments and impacts on farmers[END_REF][START_REF] Pray | Five years of Bt cotton in China -the benefits continue[END_REF]. Three kinds of Btcotton varieties have been grown: varieties integrating the Monsanto Bt Cry 1Ac gene, varieties with the Chinese Bt gene1 [START_REF] Guo | Insecticidal genes and elements regulating their expression[END_REF], and more recently varieties combining the Chinese Bt gene with the protease inhibitor CpTi gene (Cowpea Trypsin inhibitor). Most varieties currently grown in China have only the Chinese Bt-gene although there was a debate on the illegal use of Monsanto Bt-gene in Chinese varieties [START_REF] Pray | Costs and enforcement of biosafety regulations in India and China[END_REF][START_REF] Zou | Fabr.); picker-suckers are composed of Aphis gossypii, Tetranychus cinnabarinus, Adelphocoris suturalis (Jacovlev), Lygus lucorum (Meyer-Dur) and Bemisia tabaci (Gennadius); pests from soil are composed of Agrotis ypsilon and Trachea tokionis(Butler[END_REF]. The market share of the Monsanto gene varieties has dramatically fallen in recent years (10% in 2005 and presumably less since then). The relative share of GM varieties combining two genes has not yet been estimated.

The Chinese experience is a success story which has nevertheless recently been questioned, at least with respect to the Yellow River Valley, through papers accessible to the international community [START_REF] Cricaas | Outcome from a sino-american research on Bt-cotton in China: long term effectiveness is not positive[END_REF][START_REF] Lang | Seven-Year glitch: Cornell warns that Chinese GM cotton farmers are losing money due to secondary pests[END_REF], but documented much earlier in China [START_REF] Yang | Analysis of the response to the risk associated to Bt-cotton use[END_REF]. It is reported that the level of pest resistance is considered to be insufficient, the reduction in chemical control of bollworms seems to be counter-balanced by an increase in insecticides being applied to control other pests and farmers are also complaining about the substantial increase in Bt-cotton seed prices. This worrisome decline in the profitability of cotton growing likely underlies the Chinese Government's decision to implement a seedsubsidy program in 2007 [START_REF] Liu | Situation and consolidation of the market of national pest resistant cotton seeds[END_REF][START_REF] Wang | Survey analysis of the seed subsidy policy in China (in Chinese)[END_REF][START_REF] Yang | Analysis of the practical modalities in the implementation of the seed subsidy policy in China (in Chinese)[END_REF], hence resuming subsidies, which had been discontinued in 1999, at the time when China was preparing its enter the WTO.

Factors underlying the effectiveness of Bt-cotton in China have not been analysed in detail.

Are the varieties in the market really GMs? Is the gene expression correct? Is chemical control adapted for these varieties? Our paper is a contribution towards answering these questions.

It is not easy to directly address these issues with up to 300 varieties being marketed, in 2005 [START_REF] Lu | Need to further address the issue of cotton quality[END_REF], and very time-consuming to conduct a proper survey of farmers' cultivation practices, notably in the area of pest control, and to identify the varieties they use. Some authors have even underlined the difficulties encountered in identifying farmers' pest control practices through surveys in China (Pemsl et al., 2005a). The present study provides a more indirect methodology based on the results of a network of varietal experiments conducted in the Yangtze River Valley which have provided informative data on the issues addressed.

. Materials and Methods

The varietal experiment network

The Yangtze River Valley varietal experiment network (YRVEN) dates back to 1950 and spans eight provinces, accounting for 35% of the cotton production in China in 2005. It currently assesses and recommends varieties adapted to local conditions through trials conducted at 22 locations (Table 1). The aim is to have varieties recommended for all or at least for several provinces of the network . A database was recently set up to help record and process results of more than 50 years of research. Results of data for the 2000-2006 period are considered in the present paper.

(Table 1: General information on the network trial locations)

The varieties in each trial are proposed by the institutions which have bred them. These generally have already been registered at local level and have been cultivated to some extent by farmers. So, the varietal performances in the network trials are quite indicative of what farmers can actually expect in the field. One variety served as a check in each trial. This was a non-GM variety until 2005, but it was replaced by a GM variety (XiangZa 8) thereafter. Seeds for all varieties tested were provided by the variety owners in quantities sufficient for two series of trials in case they had to be tested in a second year.

The experiment implementation

In all Chinese provinces, there are local research institutes at district and county levels which are mainly involved in implementing adaptive research, such as cultivation practices, crop protection, and plant breeding. The staff of these institutes are also responsible for implementing the YRVEN varietal trials, which were designed to identify varieties adapted to local conditions. Network collaborators were asked to apply local cultivation techniques.

Decisions to apply chemical pest control were only made if required, according to the average pressure observed throughout the trial. With mostly Btcotton, the pest pressure observed was illustrative of the average Bt-trait effectiveness. Once decided, chemical sprays were applied on all varieties, regardless to their individual pest resistance status. Hence, chemical control was directed more to GM varieties and potentially less suitable for non-GM varieties.

In addition to the number and dates of sprays, additional information was required from 2004 to determine the pests targeted at each spray, the particular active ingredient targeted at a specific pest and when it was applied. The number of chemical applied is higher than the number of sprays, as a mixture can be applied in one spray to control several pests. More importantly, it has become possible to identify the date of the first bollworm control treatment.

Monitoring the GM status and bioassays

The GM status of the varieties has been monitored since 2003 by the Biotechnology Research Institute, Beijing, owner of the Chinese Bt gene [START_REF] Xia | The Expression of Bt Toxin Gene Under Different Thermal Treatment (in Chinese)[END_REF] Academy of Agricultural Science. The indoor and outdoor trials involved assays of cotton leaves picked from cotton plants grown in 20 m 2 plots per variety, which were generally sown around April 25. In addition to the varieties included in YRVEN, a pest-sensitive variety was sown to serve as a check in the bioassays.

Leaves were picked near the top of the cotton plants at the 4-5 true leaf seedling stage for the laboratory bioassays, in which six one-day old neonates are placed on two cotton leaves in Petri dishes. Five dishes were used per variety. The number of dead and alive bollworm larvae, and the extent of leaf damage were recorded after 3 and 5 days. All of these data, notably the mortality at days 3 and 5 for all varieties, were compared with the results obtained with the non-Bt check variety, according to the formula:

Adjusted mortality = (treatment mortality -check mortality)/(100-check mortality)×100

In the outdoor bioassays, nylon nets were placed over plots and 40 pairs of bollworm moths were introduced when the cotton plants had reached the squaring stage. The total number of squares and bolls attacked, the extent of their damage, and the number of living larvae were recorded 10 and 14 days later. The number of larvae surviving was compared with the check.

The larvae and moths needed for the bioassays were reared by the Crop Protection Institute at a constant room temperature of 26°C with 16 h of sunlight, from an initial collection of larvae from the field.. After about 30 generations, this population was considered quite sensitive to Bt toxin, although a few individuals had to be introduced into this population in recent years to preserve its vigour.

The names of varieties were coded by the YRVEN head agent, who was the only person who could match the codes and variety names after the analyses or bioassays had been implemented. Two non-GM varieties were integrated in the Bt-protein analysis and bioassays.

.

Results

Features of the tested varieties

The number of varieties submitted every year to the network for regional recommendation has risen to as high as 31 varieties (Table 2). These varieties no longer originate from public research institutions alone, as private companies are playing an increasing role. The principally GM varieties are also almost exclusively hybrids as these have stronger vigour, permit lower plant density and hence reduce labour requirement for the widely adopted technique of transplantation [START_REF] Fok | Technology integration and seed market organization: The case of GM Cotton diffusion in Jiangsu Province (China)[END_REF].

(Table 2: Basic information on the varieties tested in YRVEN)

Great variation and fluctuation in Bt-toxin production

The protein tests were effective for certifying the GM status of the varieties tested in YRVEN.

No Bt-proteins were detected in the two non-GM varieties. The range of Bt-protein production in GM varieties (Figure 1) showed that except three varieties, the protein production was below 800ng/g. For most varieties, the protein production was above the 450ng/g threshold, thus suggesting a high pest resistance potential according to the norm retained in China. There were about 24 cases of production below this threshold (although there were 13 cases of protein production between 400 and 450ng/g), i.e. about 33 % of all tests carried out.

Figure 1: Distribution of varieties according to their Bt-protein production Bt-gene expression is not only an issue between genetic background, as expression has fluctuated considerably for the same genetic backgrounds between years. Indeed, 10 varieties were tested in two subsequent years and their Bt-gene expression was evaluated. In spite of similar seeds from one year to another, Bt-protein production fluctuated substantially for more than 50% of the varieties which were tested in duplicate, revealing a quite substantial protein production gap of more than 200ng/g (about half of the threshold of 450ng/g for resistance effectiveness). We also processed data from the larger Yellow River Valley network in which the varieties tested were also mainly Bt ones but quite different to those submitted to the Yangtze River Valley network. The same protein production fluctuations were observed (Table 3).

(Table 3: Fluctuations in Bt-protein production for the same varieties)

Pest resistance confirmed but not perfect

Bioassay results were obtained for 56 varieties during the 2004-2006 period, and 10 of these were tested for two subsequent years, revealing some fluctuation in Bt-protein production, as mentioned above.

In the indoor bioassays, the observed larval mortality after 3 days was not sufficiently indicative of the mortality induced by Bt-toxin, which would require at least 5 days of monitoring. Varieties classified as pest resistant were resistant, especially at the very young cotton plant stage (4-5 real leaf stage). This was clearly indicated by the mortality observed in the indoor trials 5 days after the larvae were placed on cotton leaves: larval mortality was less than 60 -80% only in 5% and 16% of the varieties tested respectively (Table 4).

The reduction in larval survival noted in the outdoor bioassays (implemented in Nanjing) was not correlated with the Bt-protein production measured (in Beijing) but the outdoor bioassay results were quite consistent with the indoor results, although the correlation between these results was not perfect (coefficient of determination of 33%). There was no reduction in larval survival in the field for around 10% of the GM varieties tested. For 10-20% of the other remaining varieties, the reduction was low (less than 60%). These figures are indicative of some pest-resistance effectiveness whose level is already considered to be below expectation in the Yangtze River Valley.

(Table 4: Bt-protein production and bioassay results)

Relatively frequent chemical control of cotton pests

The number of chemical controls and sprays2 varied substantially between provinces and years. It cannot be considered that chemical control requirements diminished during the 2004-2006 period in any of the provinces considered while no changes were introduced in the spraying practices. Averaged across the 8 provinces, 14.5 insecticide treatments were applied in 8.2 sprays in 2006 (Table 5). Less chemical control was noted in three provinces, two of which (Anhui and Jiangsu) are partially connected to the Yellow River Valley where farmers reduced their chemical sprays to a greater extent after the advent of GM cotton [START_REF] Pray | Five years of Bt cotton in China -the benefits continue[END_REF].

(Table 5: Variation of the numbers of chemical controls and sprays in provinces)

Cotton plants still require up to five sprays against bollworms but with variation between provinces and years (Table 6). In addition to the well known H. armigera and P. gossypiella, the Asian Corn Borer (Ostrinia furnacalis Guenee) is another Lepidopteran pest, which is reported to be a pest of increasing threat in the Yellow River Valley [START_REF] He | Efficacy of transgenic Bt cotton for resistance to the Asian corn borer (Lepidoptera: Crambidae)[END_REF] where maize and cotton crops are grown.

More than two sprays are currently needed to control leaf-eating pests, but this category includes Spodoptera litura that the single gene Cry 1Ac has never controlled. It is reported that this pest no longer feeds only on leaves but attacks also squares and bolls, and whose chronic infestation is now regarded as a worrisome threat to cotton production [START_REF] Guo | Influence of Bt transgenic cotton on larval survival of common cutworm Spodoptera litura[END_REF][START_REF] Li | Prodenia litura (Fabricius): factors of its outbreak and how to control it (in Chinese)[END_REF][START_REF] Li | IPM of Prodenia litura Fabr. -a serious worm in Upland cotton[END_REF][START_REF] Qin | Study on the impact of Spodoptera litura and its control on cotton crop (in Chinese)[END_REF][START_REF] Russell | Durabilité de la culture des cotonniers transgéniques en Chine et en Inde[END_REF].

At all locations, sucking pests require more insecticide sprays than bollworms, as it was pointed out [START_REF] Lang | Seven-Year glitch: Cornell warns that Chinese GM cotton farmers are losing money due to secondary pests[END_REF][START_REF] Yang | Analysis of the response to the risk associated to Bt-cotton use[END_REF] and noted in two surveys carried out in Hebei and Jiangsu, respectively located in the Yellow and Yangtze River Valleys [START_REF] Fok | Technology integration and seed market organization: The case of GM Cotton diffusion in Jiangsu Province (China)[END_REF][START_REF] Fok | Diffusion du coton génétiquement modifié en Chine : leçons sur les facteurs et limites d'un succès[END_REF].

(Table 6: Chemical control patterns according to pest types)

. Discussion

Reality and rationale of the wide diffusion of hybrid varieties

Since the year 2000, Bt and hybrid cultivars have dramatically increased their share among the varieties tested in the Yangtze regional network (Table 2). Bt-varieties increased from 30% in 2000 to 94% in 2006, while hybrid cultivars represented 100% of all the varieties tested in 2006. The dominance of hybrid varieties agrees with the full coverage of cotton area with these varieties in many provinces of the Yangtze River Valley [START_REF] Xu | State and market interaction: cotton variety and seed market development in China[END_REF].

The hybrid cultivars achieve a higher yield resulting from more numerous and heavier bolls compared to non-hybrid cultivars (Table 7). Hybrid and non-hybrid cultivars showed the same average value in terms of Bt-protein production during the 2003-2006 period, suggesting that the Bt gene used in creating hybrids is completely dominant.

Nevertheless Bt-cultivars did not show superiority for any of the criteria considered in the Yangtze River Valley, consistent with previous observations which have pointed out the low specific advantage of pest resistance by Bt-gene in the Yangtze River Valley [START_REF] Xu | Economic analysis of Bt cotton Planting in Jiangsu (in Chinese)[END_REF].

The superiority of varieties which successfully pass through the regional testing, appears to be due mainly to improved lint quality criteria (lint length and "spinning quality"), as well as a slightly higher average yield (Table 7). However, this result is biased as non-hybrid cultivars contribute to the lower mean yield of the group of non-approved varieties. The less influence of yield criteria is illustrative of a situation where quite high yields have been obtained for many years.

(Table 7: Hybrid and GM effects on various recommendation criteria)

Efficacy threshold of Bt-toxin

In China, Bt-varieties are considered effective in pest resistance when the Bt-toxin production exceeds 450ng/g, as in 67% of the varieties tested during the 2003-06 period. The Bt-toxin production seldom exceeds 800ng/g. Since some authors have proposed the efficacy threshold of 1900ng/g of Cry 1Ac toxin, on the basis of research undertaken in India [START_REF] Kranthi | Temporal and intra-plant variability of Cry1Ac expression in Bt-cotton and its influence on the survival of the cotton Bollworm, Helicoverpa armigera (Hübner) (Noctuidae: Lepidoptera)[END_REF], could the low toxin production level being observed in the Yangtze River Valley network impact negatively on the pest resistance?

The low level of Bt-toxin production (relatively to what is reported in other countries for Cry 1Ac) is not specific to the Yangtze River Valley network. The levels we have reported are quite consistent with what has been found in previous studies. The maximum values were less than 600ng/g [START_REF] Xia | The Expression of Bt Toxin Gene Under Different Thermal Treatment (in Chinese)[END_REF]) and all values were below 600ng/g (except one value at 900ng/g) in another study [START_REF] Xia | Bt lnsecticidal Gene and Its Temporal Expression in trangenic cotton plants (in Chinese, English abstract)[END_REF]. When the Bt-toxin production is reported from both the Monsanto and Chinese Bt-gene, the data is similar with at most 700ng/g [START_REF] Wan | Seasonal expression profiles of insecticidal protein and control efficacy against Helicoverpa armigera for Bt cotton in the Yangtze River Valley of China[END_REF], by using the ELISA kit provided by the American firm Agdia (Elkhart, IN). When the Bt-toxin production is controlled at the farmers' level 3 , from cotton plants from seeds of Btvarieties they have held back from previous season or they have bought, Bt-toxin concentrations seldom exceed 1000ng/g and 80% were below 800ng/g (Pemsl et al., 2005a).

With reference to bioassays results, mortality ratios were quite substantial whatever the levels of the Bt-toxin production, this implies that the threshold retained in China does not seem to be too low. Nevertheless, the Bt-toxin production measured (in Beijing) is badly correlated to the results of bioassays (implemented in Nanjing); this observation implies that the figure of Btgene expression in one place is not a sufficiently good indicator of the pest-resistance efficacy in real conditions. This is consistent with the multitude of factors which impact on this efficacy (cf. infra).

The content of Cry1Ac toxin is reported to reach 6000ng/g in India and Australia. In India, depending on the plant parts and the period of analysis, the content has fluctuated from 50 to 5510ng/g [START_REF] Kranthi | Temporal and intra-plant variability of Cry1Ac expression in Bt-cotton and its influence on the survival of the cotton Bollworm, Helicoverpa armigera (Hübner) (Noctuidae: Lepidoptera)[END_REF]. In Australia, a very wide range of Cry 1Ac toxin content has been obtained in various experiments to assess the effects of genetic background, agronomic practices and water or fertility stresses. The toxin concentration ranged from 270 to 6010ng/g, but most figures, even for varieties integrating the single Cry 1Ac gene, ranged from 1000 to 2500ng/g [START_REF] Rochester | Effect of Genotype, Edaphic, Environmental Conditions, and Agronomic Practices on Cry1Ac Protein Expression in Transgenic Cotton[END_REF].

The maximum values of Bt-toxin production measured in China are far much lower than in India and Australia, and their range is also smaller consequently. These lower values cannot be regarded as a factor of lower efficacy against the target pests when the results of bioassays are considered. Thus, the suggestion of an efficacy threshold of 1900 ng/g reported from India [START_REF] Kranthi | Temporal and intra-plant variability of Cry1Ac expression in Bt-cotton and its influence on the survival of the cotton Bollworm, Helicoverpa armigera (Hübner) (Noctuidae: Lepidoptera)[END_REF] cannot be applied to China.

Fluctuating expression of Bt-gene

During our research work, we observed that the expression of the Bt-gene in terms of production of Bt-toxin fluctuated a lot between varieties (Figure 1). This is consistent with the observation that genetic background is a major factor of fluctuation in Australia [START_REF] Rochester | Effect of Genotype, Edaphic, Environmental Conditions, and Agronomic Practices on Cry1Ac Protein Expression in Transgenic Cotton[END_REF]. So far, in China, no systematic study has clarified the influence of genetic background on Bt expression.

Our results also demonstrate that Bt expression can fluctuate between years for a given variety (Table 3) with seeds of similar source and with the Bt-toxin concentration measured by the same laboratory. This result confirms that the expression of the Bt-gene, Cry 1A in our case, is sensitive to climatic factors as well as to agronomic factors [START_REF] Rochester | Effect of Genotype, Edaphic, Environmental Conditions, and Agronomic Practices on Cry1Ac Protein Expression in Transgenic Cotton[END_REF]. This means that the Bt-protein production measured at one location one year cannot accurately reflect pest resistance ability everywhere and at all times.

Factors of lower pest resistance efficacy in the Yangtze River Valley

Our data is essentially related to the Yangtze River Valley, so does not allow comparison and thus confirmation that pest resistance is less than in the Yellow River Valley. However efficacy, although satisfactory, is far from perfect (Table 4) and raises the question whether pest resistance is sub-optimal in the Yangtze area.

One possible factor is the origin of the Bt-gene in the varieties used in the Yangtze River

Valley. Based on studies [START_REF] He | Efficacy of transgenic Bt cotton for resistance to the Asian corn borer (Lepidoptera: Crambidae)[END_REF][START_REF] Wan | Seasonal expression profiles of insecticidal protein and control efficacy against Helicoverpa armigera for Bt cotton in the Yangtze River Valley of China[END_REF], one can argue that the Monsanto Cry 1Ac is superior, and yet it is represented in only 4.7% of the total cotton area in Jiangsu province of the Yangtze River Valley in 2003, as opposed to 76.9% in Hebei Province of the Yellow River Valley [START_REF] Xu | State and market interaction: cotton variety and seed market development in China[END_REF]. This indicates that the Monsanto varieties did not compete well against the Chinese varieties, subsequently making the Monsanto Bt-gene less attractive for integration into new varieties, even illegally 4 as it was observed in 2001 and reported in the Yellow River Valley [START_REF] Pray | Costs and enforcement of biosafety regulations in India and China[END_REF]. The argument of the superiority of the Monsanto Bt-gene is nevertheless flawed, at least in the Yangtze River Valley where the Monsanto varieties did not perform better than the Chinese varieties. Even in the Yellow River Valley, the superiority reported is debatable. Only very slight superiority has been observed for the Monsanto Cry 1Ac gene, in the control of the third generation of the Asian Corn Borer [START_REF] He | Efficacy of transgenic Bt cotton for resistance to the Asian corn borer (Lepidoptera: Crambidae)[END_REF], late in the cotton crop cycle when complementary chemical control is needed. In other research, the expression of the Chinese Bt-gene was more variable along the cotton plant cycle and plant parts [START_REF] Wan | Seasonal expression profiles of insecticidal protein and control efficacy against Helicoverpa armigera for Bt cotton in the Yangtze River Valley of China[END_REF], but there is no difference when considering the case of top leaves till the early boll setting stage, organs and periods which are more crucial for the pest-resistance efficacy.

In China, the unique factor considered is the climate as high temperatures have reduced Btgene expression in experimental conditions [START_REF] Rui | Temporal and spatial dynamics of the resistance of transgenic cotton cultivars to Helicoverpa armigera (Hiibner) (in Chinese)[END_REF][START_REF] Xia | The Expression of Bt Toxin Gene Under Different Thermal Treatment (in Chinese)[END_REF]. In reality, high temperatures might limit the Bt-gene expression but they can hardly explain the efficacy differential observed between the Yellow and the Yangtze River Valleys as temperatures are equally high during the cotton growing months.

Explaining factors have mainly to do with the specificities of the cotton growing techniques in the Yangtze River Valley. One of these factors is the widespread if not exclusive practice of transplantation [START_REF] Fok | Technology integration and seed market organization: The case of GM Cotton diffusion in Jiangsu Province (China)[END_REF]. This technique is quite specific to China and notably to the Yangtze River Valley. Cotton seeds are sown in nursery and plantlets are transplanted when they reach the five-true leave stage. As yet, no research work in China has checked the influence of transplantating on the production of Bt-toxins, although plants are stressed and this could reduce the Bt-toxin production [START_REF] Rochester | Effect of Genotype, Edaphic, Environmental Conditions, and Agronomic Practices on Cry1Ac Protein Expression in Transgenic Cotton[END_REF]., DNA sequencing. Till 2007, the Bt-trait has been tested in Beijing by the research lab run by Prof. Guo Sandui, the owner of the Chinese gene.

The other specific factor in the Yangtze River Valley is the almost exclusive use of hybrid cultivars. Debates are ongoing as to whether the hybrid form of the varieties could induce a reduction in Bt-cotton effectiveness, with the argument put forward that the genetic resistance is derived from just one parent [START_REF] Kranthi | Temporal and intra-plant variability of Cry1Ac expression in Bt-cotton and its influence on the survival of the cotton Bollworm, Helicoverpa armigera (Hübner) (Noctuidae: Lepidoptera)[END_REF]. This is nevertheless not consistent with the fact that Bt-genes are single dominant genes, so no reduction in resistance effectiveness has been observed in hybrid varieties [START_REF] Xiao | Inheritance of Insect Resistance of Transgenic Bt Cotton to Cotton Bollworm (in Chinese)[END_REF]. The dominance might not be complete but this is not the case with the varieties considered, as we have noticed earlier.

The negative impacts on Bt-toxin production from using hybrid cultivars could be indirect ones. The plant vigour of hybrid cultivar has led to reduce plant densities in the Yangtze River

Valley; this is the feature which has made hybrid cultivars so much attractive to farmers who implement transplantation because labour requirement is proportionally reduced. It is observed in Australia that the Bt-toxin production is reduced with low densities [START_REF] Rochester | Effect of Genotype, Edaphic, Environmental Conditions, and Agronomic Practices on Cry1Ac Protein Expression in Transgenic Cotton[END_REF]. If this is true also in China, then the Valley efficacy differential is partly explained.

Another indirect negative factor linked to the use of hybrid cultivars is related to the lack of sufficient purity of hybrid cultivar seed, which is probably due to the constraints on manual hybrid seed production. Workers inevitably miss some flower buds when they implement the stamen elimination so some flowers are not hybridized and the seeds they produce are non-Bt cotton mixed with the hybrid seeds when the seed multiplication plots are harvested. The risk of collecting non-hybridized seeds is increased by rain which prevents access to the fields every day. Flowers which have been self-pollinated during the rainy days should be removed,, but some of them can be missed too. Thus purity of the hybrid seeds is not perfect, notably at commercial scale of their production. This shortfall might not be observed at the stage of regional varietal test because the variety owners will have provided the purest seeds.

Sub-optimal chemical control

Since the pest resistance of Bt-cotton is not total, variable larval survival rates are noted in the field, thus explaining why farmers might spray chemicals as a precaution. This precautionary behaviour implies a still high level of chemical control which has been observed but it was either related to the opportunistic behaviour of the extension staff who could make profit by selling insecticides [START_REF] Huang | Transgenic varieties and productivity of smallholder cotton farmers in China[END_REF] or to the lack of proper technical assistance to cotton growers (Pemsl et al., 2005a). Our results, suggest that the still high use of insecticides must also be due in part to the suboptimal effectiveness of Bt-cotton.

In China, it is generally acknowledged that H. armigera could undergo 4 to 5 generations during the cotton growing cycle and that GM cotton cannot control them all.Generally, the first generation coincides with the cotton plant seedling stage; the next generation appears at the cotton squaring stage; the third generation at cotton flowering; the fourth corresponds to the cotton boll setting stage while the fifth generation is at the beginning of boll opening. Surely GM cotton cannot control H. armigera up to the fourth generation at a period when Bt-gene expression has seriously slowed down [START_REF] Yang | Analysis of the response to the risk associated to Bt-cotton use[END_REF]. In the Yangtze River Valley, chemical control is generally recommended when high infestation levels are observed for the third generation of H. armigera.

In practice, we observed that at all the network experimental sites the first chemical control of H.armigera was always conducted before the H. armigera fourth generation. For the three year period of 2004-2006, 50-60% of the first spray was applied against the second generation and even earlier, particularly in 2005 when 37 of the sprays were directed at the first generation, probably because that year was warmer with possibly lower Bt gene expression.

The continued frequent chemical control against H. armigera could be explained by the fact that farmers still observe bollworms that have survived due to the insufficient genetic pest resistance of the cotton crops. This nevertheless highlights that farms habitually spray whenever bollworms are observed regardless of the infestation levels. Furthermore, so far no information is disseminated to help farmers adjust chemical control to threshold levels according to the bollworm populations.

. Conclusion

This study provides further insight into the effectiveness of GM cotton use in China since the international community has become aware that its sustainability is under threat [START_REF] Lang | Seven-Year glitch: Cornell warns that Chinese GM cotton farmers are losing money due to secondary pests[END_REF].

It addresses this issue of effectiveness in the Yangtze River Valley, one of the two main regions where Bt-cotton is widely used in China. An indirect assessment approach was adopted for this study through processing of data collected within the Yangtze River Valley Varietal Experiment Network.

In this network, the status of all varieties classified as GM, with integration of the Bt-gene, was actually confirmed. However, this does not guarantee that all seeds of the same varieties sold to farmers were necessarily GM, i.e. there is sufficient information on the poor quality of seeds, and even fake GM seeds, sometimes supplied to farmers [START_REF] Liu | Situation and consolidation of the market of national pest resistant cotton seeds[END_REF][START_REF] Zhang | Lack of effectiveness of part of the Bt-cotton varieties in Jinan District (Shandong): Factors and countermeasures[END_REF].

This situation prompted the launching of the quality seed subsidy policy in 2007.

It turned out that the expression of the Cry 1A gene substantially varied between genetic backgrounds and between two subsequent years for a few of these varieties. The efficacy of pest-resistance is confirmed but its level is not perfect, the mortalities of the H. armigera larvae in indoor and furthermore in outdoor bioassays are not always sufficiently high. This is consistent with the acknowledgement that the pest-resistance of Bt-cotton in the Yangtze River

Valley is not so good, notably with reference to the Yellow River Valley. We suggest that this relatively lower efficacy could result from the transplantation technique which induces stresses to the cotton plant growth and development. We believe also that it is an indirect effect of the widespread use of hybrid varieties for which it is quite difficult to achieve pure enough hybrid seeds containing the Bt-gene.

Globally speaking, the Bt-cotton varieties being used cannot totally control bollworms even assistance to farmers) to spray chemicals, regardless of the infestation level, i.e. the habit of total eradication seems to still predominate in the area of pest control. Bollworms seem to be sprayed more often than required and far earlier than necessary, i.e. against H. armigera.

Farmers nevertheless are not to blame. No information is disseminated to farmers to inform on how to adapt chemical control according to infestation thresholds and to the bollworm generation number. This shortfall is unfortunately very likely to prevail in developing countries, hence justifying more attention to the institutional aspect in promoting GM varieties (Pemsl et al., 2005b).

From an economic viewpoint, due to the insufficient and variable pest resistance level of the Bt-cotton varieties released in the Yangtze River Valley, and partly to the lack of tailored complementary chemical control, farmers are paying high prices for Bt-cotton hybrids seeds which are not totally pest resistant while pest control costs are not reduced to the extent they might expect. These two phenomena undermine the cost-effectiveness of cotton production.

An additional reason why chemical protection costs are not decreasing is that alternative pests are becoming an increasing threat due to the pest complex shift.

  early in the growing season in the Yangtze River Valley. Surviving larvae will inevitably be observed, thus prompting farmers (or professional agents in charge of supplying technical Preprint of the article published in Crop Protection 27 (2008) 1269-1276

Table 5 :

 5 Variation of the total numbers of chemical controls and sprays in provinces

		Number of chemical controls		Number of chemical sprays
		2004	2005	2006	2004	2005	2006
	anhui	3.0	8.5	10.5	3.0	7.5	6.5
	henan	12.0	10.0	10.0	10.0	8.0	8.0
	hubei	9.2	14.0	13.4	8.0	9.4	8.6
	hunan	13.3	11.0	12.5	9.0	7.3	7.0
	jiangsu	9.3	9.0	10.3	6.0	7.3	6.7
	jiangxi	10.0	16.0	22.0	7.0	6.0	8.0
	sichuan	18.5	10.0	23.5	8.5	7.5	11.5
	zhejiang	18.0	17.0	13.5	10.0	10.0	9.0
	Average	11.7	11.9	14.5	7.7	7.9	8.2

This gene was constructed in 1992 by the team of Prof. Guo Sandui of the Biotechnology Research Institute, Chinese Academy of Agricultural Sciences. Various papers from this team mention this as being a Cry 1A gene, outcome of a gene synthesis. The first cotton varieties integrating this gene were experimented in 1995.

Each control is based on a particular active ingredient targeted at a specific pest at a specific time, so the number of chemical controls is higher than the number of sprays, as one spray can combine several active ingredients to control several pests.

Analysis was made by the Chinese Academy of Agricultural Sciences in Beijing.

It is quite possible that Monsanto Bt-gene has been illegally used in creating new varieties in the Yellow River Valley, but it is doubtful that this practice has persisted after the application of the Biosecurity Act and of the Plant Variety Protection Act (whose decree of application modalities were issued in 1999). After this implementation, breeders have to contract with the Biocentury Transgene Ltd to use the Chinese Bt-gene carried out by Prof. Guo Sandui's team, the only Bt-gene they can use. To formally register a new Bt-cotton variety, the breeder must provide a transgenic biosecurity certificate for which the Bt gene is identified through

Acknowledgement

The authors sincerely thank the two anonymous reviewers and Dr Maurice Vaissayre of CIRAD for their valuable comments to the intermediary versions of this paper

Variety code

Variety code pertains to one variety and one year. The same variety tested during two years will appears in two distinct codes


MD Jean-Marc Marc Foletti
email: jean-marc.foletti@ap-hm.fr

Valentine Martinez
email: valentine.martinez4@gmail.com

MD Pierre Haen
email: pierre.haen@yahoo.fr

Yves Godio-Raboutet

MD Laurent Guyot
email: laurent.guyot@ap-hm.fr

MD Lionel Thollon
email: lionel.thollon@ifsttar.fr

Foletti Jm

Yves Godio
email: yves.godio@ifsttar.fr

Finite element analysis of the human orbit. Behavior of titanium mesh for orbital floor reconstruction in case of trauma recurrence

Keywords: finite element analysis, maxillofacial, trauma recidivism, orbit, biomechanics

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

Introduction

Titanium mesh implants (TMI) is commonly used for orbital floor fracture reconstruction. These devices have proven their effectiveness: they provide a reliable support for the orbital contents, optional screwing of the TMI to the orbital rim prevents secondary displacement. Their relative stiffness may however become a potential disadvantage in case of recurrent injuries as the implant may become distorted and behave as a penetrating foreign body able to threaten the intra-orbital content (eyeball, nerves, vessels) [START_REF] Foletti | Severe distortion of an orbital titanium mesh implant after recurrent facial trauma: a potential threat to the orbital contents?[END_REF]. Studying the behavior of these implants in case of trauma recurrence may help to minimize their potential dangerousness. Our purpose was to simulate the behavior of a TMI used to reconstruct a fractured orbital floor of a previously validated FEM under the stress of blunt traumas.

Materials and methods

A 3D FEM of a human orbit which had previously been developed and validated by our team [START_REF] Foletti | Development and validation of an optimized finite element model of the human orbit[END_REF] was used in this study. Numerous simulations of blunt traumas of the orbit were run on Hypercrash® version 12.0 ((Altair Engineering, Inc., Detroit, MI, USA) by using a FEM of a metallic cylinder impactor (m=300-400g). The impactors was computed in order to hit the inferior rim of the orbit (acceleration =6-7m.s -1 ). For each test, both the weight and acceleration of the impactors were modulated; we sought to reproduce a blunt trauma equivalent to a straight punch [START_REF] Whiting | Kinematic analysis of human upper extremity movements in boxing[END_REF]. The impacts successively affected an empty orbit, and then an orbit filled with fat and an eyeball. In both cases, the orbital floor was fractured and rebuilt by a simplified TMI (figure 1)

The first step was to model a fracture of the floor of the orbit on our model. Some of the elements of the orbital floor were selected and removed, according to a fracture pattern consistent with those usually encountered in clinical practice: The fracture is anterior, and measures approximately 2.5cm²

The second step was to model a TMI to reconstruct the fracture thus obtained. We duplicated the elements removed in the previous step, and changed their biomechanical characteristics by those of titanium. (Density = 4500 kg / m 3 , Young's modulus E = 114.10 3 MPa, Poisson's ratio ν = 0.34). We also duplicated a zone of elements around the fracture, so that the TMI could rest on the floor of the orbit and not fall into the maxillary sinus at the beginning of the simulations. The geometry of the mesh thus obtained is detailed in figure 2.

The impacts were located on the inferior orbital rim. 21 tests were simulated and included in our study, their characteristics being summarized in table 1

Results

In 90,4% (19/21) of the tests conducted, the TMI, whether free from any bony attachment or screwed to the orbital rim, has tended to move inwardly in the orbit, and / or to deform in a "blowin" motion (figure 3). In 19 % (4/21) a fracture of the inferior orbital rim was associated, allowing the bone-plate complex to move and/or deform. In 39,1% (9/23) the movement and/or deformation of the TMI was allowed by partial or total failure of the osteosynthesis. An associated fracture of the lamina papyracea was encountered in 19 % (4/21) of the tests. The results are detailed in table 1.

Discussion

Our simulations showed that under the stress of blunt orbital traumas, TIM used to reconstruct floor fractures may distort and threaten the orbital content.

Finite element model has proven to be a valuable tool to determine the most convenient location, design and material to use for fracture fixation devices [START_REF] Al-Sukhun | Modelling of orbital deformation using finite-element analysis[END_REF][START_REF] Al-Sukhun | Orbital stress analysis, part V: systematic approach to validate a finite element model of a human orbit[END_REF]. Experimentations on an empty orbit with a simplified titanium plate induced in 80% (12/15) of cases a total or partial rupture of fixation between the plate and the bone eventually with fracture next to the screws. In the 3 cases in which this fixation remained intact, the plate itself showed a vertical displacement of up to 3.65 mm. With a filled orbit (fat and simplified eyeball), the findings were similar, but with lower displacement amplitudes. In this case, no fracture of the orbital rim screwing was found, possibly due to amortization and redistribution of forces by the intraorbital fat [START_REF] Schoemaker | Elasticity, viscosity, and deformation of orbital fat[END_REF]. These results are consistent with our clinical findings [START_REF] Foletti | Severe distortion of an orbital titanium mesh implant after recurrent facial trauma: a potential threat to the orbital contents?[END_REF]: a TMI submitted to a direct trauma is likely to deform the orbit inwardly (in a "blow-in" motion) and to threaten the orbital contents, including the eyeball.

However, several limitations must be pointed out. Even in the tests conducted with a perforated TMI, the shape of our titanium plate was simplified, and didn't faithfully reproduce a 3D TMI. The fixation of the TMI to the bone was also an approximation of a real cortical screwing. Rather than modeling a real screw, we numerically attached the nodes of the plate with those of the bone. Nevertheless, this approximation seems acceptable to us. In 4 of our tests, the bone fractured on contact with the attached nodes, as it sometimes happens in vivo, when a screwed osteosynthesis plate is pulled apart, fracturing the cortical bone next to one or several screws. Partial or total failure of osteosynthesis (i.e. the link between two nodes) occurred in 9 other tests. Kasrai et al [START_REF] Kasrai | A biomechanical analysis of the orbitozygomatic complex in human cadavers: examination of load sharing and failure patterns following fixation with titanium and bioresorbable plating systems[END_REF] demonstrated, in a biomechanical analysis of an orbitozygomatic titanium osteosynthesis in human cadavers, sharing strains at the level of bony buttresses, able to create screwing failures. They also noticed a significant decreases in the force required to induce a fracture following titanium plate fixation, and identified plate deformation as a primary cause of failure under blunt trauma load conditions.

The absence of detailed anatomy of the ethmoid was another limit of our orbit FEM. Ramesh et al [START_REF] Ramesh | Medial Buttressing in Orbital Blowout Fractures[END_REF] proved that ethmoidectomy on post mortem human subject reduces the impact energy necessary to induce orbital fractures and increases the prevalence of the medial wall involvement. In our study, we aimed to reproduce a straight punch to the face, and therefore we favored traumas targeting the inferior orbital rim, consistent with the historical buckling theory of orbital fractures [START_REF] Fort | Etude experimentale sur les fractures de la machoire superieure[END_REF]. In this theory, the fractures of the orbital floor are usually anterior, of a rather small surface, and rarely reach the medial wall. However, a fracture of the medial wall of the orbit occurred in 4 of our tests, 3 of which with a filled orbit. Actual trends are that hydraulic and buckling theories of orbital fracture coexist and may result in similar fracture patterns [START_REF] Ahmad | Buckling and hydraulic mechanisms in orbital blowout fractures: fact or fiction?[END_REF][START_REF] Patel | Biomechanic Factors Associated With Orbital Floor Fractures[END_REF]. Forces transmission through the intraorbital fat may have favored lamina papyracea fractures, according to hydraulic theory. Another hypothesis is that the TMI is stiffer than the bone of the orbital floor, therefore the forces are transmitted more posteriorly into the TMI reconstructed orbit than into the native orbit.

TMI have proved their effectiveness for orbital fractures reconstruction [START_REF] Ellis E 3rd | Assessment of internal orbital reconstructions for pure blowout fractures: cranial bone grafts versus titanium mesh[END_REF], even in complex cases.

Specific complications, such as infections and adherence syndromes are rare [START_REF] Peng | Orbital fracture repair outcomes with preformed titanium mesh implants and comparison to porous polyethylene coated titanium sheets[END_REF][START_REF] Kersey | Orbital adherence with titanium mesh floor: a review of 10 cases[END_REF]. This could explain maxillofacial surgeons' craze for these implants.

In contrast, complications related to TMI in case of traumatic recurrence have been studied very little. Maxillofacial trauma recurrence is anything but anecdotal. Nygaard et al [START_REF] Nygaard | Violent trauma recidivism: Does all violence escalate?[END_REF] demonstrated that recidivism for interpersonal violence results in a significant number of admissions to trauma centers. In their cohort, almost 10% of patients were recidivists. These patients had a higher proportion of blunt assault lesions than non-recidivists. It is crucial that the initial interrogation insists on the past trauma history of patients. In the McCoy's study [START_REF] Mccoy | A novel prospective approach to evaluate trauma recidivism: the concept of the past trauma history[END_REF] the recidivism rate was up to 29.3%. The highest rates were noted in victims of interpersonal violence. Alcohol and drug abuses are both well-documented risk factors of trauma recidivism and are frequently encountered in maxillofacial trauma population [START_REF] Foletti | Screening for psychiatric risk factors in a facial trauma patients. Validating a questionnaire[END_REF]. The removal of osteosynthesis material is usually proposed for most maxillofacial fractures (mandibles, zygoma etc.) after bone consolidation, but not for orbital fractures. The risk of deformation of the material persists long term, theoretically for the patient's lifetime.

In line with already reported clinical observations [START_REF] Foletti | Severe distortion of an orbital titanium mesh implant after recurrent facial trauma: a potential threat to the orbital contents?[END_REF], our finite element analysis tends to demonstrate that, in the event of traumatic recurrence, a TMI may deform, and therefore turn into a potentially threatening penetrating object for the intra-orbital structures. Further studies and improvements to our FEM are required to confirm this conclusion. Taking into account the complications of TMIs in case of traumatic recurrence opens new research perspectives, and could lead to reconsider the indications of these implants. Finite element analysis could also help to modify and to improve the design of TMIs, so as to prevent a blow-in distortion in case of trauma recurrence.

Figure captions

Figure 1 -

 1 Figure 1 -3D view of the finite element model of the human orbit used for blunt trauma tests.

Figure 2 -

 2 Figure 2 -Detailed view of the fracture and the TMI used to rebuild it. Notice that the TMI is

Figure 3 -

 3 Figure 3 -Results of a crash simulation under Hypercrash software. The inferior orbital rim was

Table 1 -

 1 Summary of the characteristics and results of the 21 simulations of blunt trauma performed on a 3D finite element model of the human orbit. The orbit status (empty EO versus filled with fat and the eyeball FO), the orbital floor status (reconstructed by a titanium mesh implant TMI perforated or not), the eventual screwing of the TMI (if present), the impactor's speed and mass are precised for each of the tests.

	Test	Orbit status	Orbital floor status	TMI status	Acceleration (m/s)	weight (g)	results
	1	EO	Simplified TMI	Anterior fixation	6	300	The osteosynthesis resists; the plate is deformed and moves about 1 mm vertically
	2	EO	Simplified TMI	Anterior fixation	6	500	The osteosynthesis resists; fracture close to the screws and mobility of the bone-plate complex upwards (10,7mm) and backwards (9,5mm)
	3	EO	Simplified TMI	Anterior fixation	7	300	Partial failure of the osteosynthesis; mobility of the plate upwards and backwards, with about 10 degrees of sagittal rotation
	4	EO	Simplified TMI	2 points fixation	6	300	The osteosynthesis resists; fracture close to the screws and mobility of the bone-plate complex upwards (3,6mm)
	5	EO	Simplified TMI	2 points fixation	6	500	the osteosynthesis resists ; fracture close to the screws and mobility of the bone-plate complex upwards (9,2mm)
	6	EO	Simplified TMI	2 points fixation	7	300	the osteosynthesis resists ; fracture close to the screws and mobility of the bone-plate complex upwards (>20mm)
	7	EO	Simplified TMI	External fixation	6	300	Partial failure of the osteosynthesis; mobility of the plate upwards (8mm), with about 40 degrees of external sagittal rotation
	8	EO	Simplified TMI	External fixation	6	500	Total failure of the osteosynthesis; mobility of the plate upwards (9mm), with about 25 degrees of external sagittal rotation
	9	EO	Simplified TMI	External fixation	7	300	Total failure of the osteosynthesis; mobility of the plate upwards (10mm) and externally (3mm)
	10	EO	Simplified TMI	Internal fixation	6	300	Total failure of the osteosynthesis; mobility of the plate upwards (4,6mm), with about 15 degrees of internal sagittal rotation
	11	EO	Simplified TMI	Internal fixation	6	500	Total failure of the osteosynthesis; mobility of the plate upwards and backwards (>20mm), with about 10 degrees of internal sagittal rotation
	12	EO	Simplified TMI	Internal fixation	7	300	Total failure of the osteosynthesis; mobility of the plate upwards (10,5mm) and backwards (>20mm), with about 20 degrees of internal sagittal rotation
	13	EO	Simplified TMI / perforated	Anterior fixation	6	300	The osteosynthesis resists; the plate is deformed and moves about 0,8 mm vertically
	14	EO	Simplified TMI / perforated	Anterior fixation	6	500	The osteosynthesis resists; the plate is deformed and moves about 0,95 mm vertically
	15	EO	Simplified TMI / perforated	Anterior fixation	7	300	Partial failure of the osteosynthesis; the plate is deformed and moves upwards (2,65mm); lamina papyracea is fractured
	16	FO fat eyeball	Simplified TMI / perforated	None	6	300	The plate is deformed and moves about 0,34 mm vertically
	17	FO fat eyeball	Simplified TMI / perforated	None	6	500	The plate is deformed and moves about 0,44 mm vertically
	18	FO fat eyeball	Simplified TMI / perforated	None	7	300	The plate is deformed and moves about 1mm vertically; lamina papyracea is fractured


Lagergren Richard Elias

Desper

Olivier Gascuel

Distance-based Phylogeny Reconstruction (Optimal Radius)

Keywords: phylogeny reconstruction, distance methods, performance analysis, robustness, safety radius approach, optimal radius

Problem Definition

A phylogeny is an evolutionary tree tracing the shared history, including common ancestors, of a set of extant taxa. Phylogenies have been historically reconstructed using character-based (parsimony) methods, but in recent years the advent of DNA sequencing, along with the development of large databases of molecular data, has led to more involved methods. Sophisticated techniques such as likelihood and Bayesian methods are used to estimate phylogenies with sound statistical justifications.

However, these statistical techniques suffer from the discrete nature of tree topology space. Since the number of tree topologies increases exponentially as a function of the number of taxa, and each topology requires separate likelihood calculation, it is important to restrict the search space and to design efficient heuristics. Distance methods for phylogeny reconstruction serve this purpose by inferring trees in a fraction of the time required for the more statistically rigorous methods. They allow dealing with thousands of taxa, while the current implementations of statistical approaches are limited to a few hundreds, and distance methods also provide fairly accurate starting trees to be further refined by more sophisticated methods. Moreover, the input of distance methods is the matrix of pairwise evolutionary distances among taxa, which are estimated by maximum likelihood, so that distance methods also have sound statistical justifications.

Mathematically, a phylogenetic tree is a triple ( , , ) T V E l = where V is the set of nodes representing extant taxa and ancestral species, E is the set of edges (branches), and l is a function that assigns positive lengths to each edge in E.

Evolution proceeds through the tree structure as a stochastic process with a finite state space corresponding to the DNA bases or amino acids present in the DNA or protein sequences, respectively.

Any phylogenetic tree T defines a metric T D on its leaf set L(T) : let ( , )

T P u v define the unique path through T from u to v, then the distance from u to v is set to

( , ) ( , ) ( ).
T

T e P u v D u v l e ∈ = ∑
Distance methods for phylogeny reconstruction rely on the observation [START_REF] Zarestkii | Reconstructing a tree from the distances between its leaves[END_REF] that the map

T T D →
is reversible; i.e., a tree T can be reconstructed from its tree metric. While in practice T D is not known, by using models of evolution (e.g. [START_REF] Cantor | Evolution of Protein Molecules[END_REF],

reviewed in [START_REF] Felsenstein | Inferring Phylogenies[END_REF]) one can use molecular sequence data to estimate a distance matrix D that approximates T D . As the amount of sequence data increases, the consistency of the various models of sequence evolution implies that D should converge to T D . Thus for a distance method to be consistent, it is necessary that for any tree T, and for distance matrices D "close enough" to T D , the algorithm will output T.

The present chapter deals with the question of when any distance algorithm for phylogeny reconstruction can be guaranteed to output the correct phylogeny as a function of the divergence between the metric underlying the true phylogeny and the metric estimated from the data. Atteson [START_REF] Atteson | The performance of neighbor-joining methods of phylogenetic reconstruction[END_REF] demonstrated that this consistency can be shown for Neighbor Joining (NJ) [START_REF] Saitou | The Neighbor-joining Method: A New Method for Reconstructing Phylogenetic Trees[END_REF], the most popular distance method, and a number of NJ's variants.

The Neighbor Joining (NJ) algorithm of Saitou and Nei (1987)

NJ is agglomerative: it works by using the input matrix D to identify a pair of taxa , x y L ∈ that are neighbors in T, i.e. there exists a node

u V ∈ such that { } ( , ),( , ) . u x u y E ⊂
The algorithm creates a node c that is connected to x and y, extends the distance matrix to c, and then solves the reduced problem on { }\{ , }.

L c x y ∪

The pair (x,y) is chosen to minimize the following sum:

( ) Elias and Lagergren take a related approach to agglomeration, which does not exhaustively seek the minimum value of ( , )

( , ) (| | 2) ( , ) ( , ) ( , ) .

Safety radius-based performance analysis (Atteson 1999)

Short branches in a phylogeny are difficult to resolve, especially when they are nested deep within a tree, because relatively few mutations occurring on a short branch as opposed to on much longer pendant branches, which hides phylogenetic signal. One is faced with the choice between leaving certain evolutionary relationships unresolved (i.e., having an internal node with degree > 3), or examining when confidence can be had in the resolution of a short internal edge.

A natural formulation [START_REF] Huson | Disk-covering, a fastconverging method for phylogenetic tree reconstruction[END_REF] of this question is: how long must be molecular sequences before one can have confidence in algorithm's ability to reconstruct T accurately? An alternative formulation [START_REF] Atteson | The performance of neighbor-joining methods of phylogenetic reconstruction[END_REF] A will return the tree T.

Key Results

Atteson [START_REF] Atteson | The performance of neighbor-joining methods of phylogenetic reconstruction[END_REF] answered the second question affirmatively, with two theorems.

Theorem 1:

The safety radius of NJ is 1 2 .

Theorem 2: For no distance algorithm A is the safety radius of A greater than 1 2 .

Indeed, given any µ , one can find two different trees 1 2 , T T and a distance matrix

D such that 1 2 ( ) ( ) T T µ µ µ = = and 1 2 / 2 . T T D D D D ∞ ∞ - = = - µ
Since D is equidistant from two distinct tree metrics, no algorithm could assign it to the "closest" tree.

In their presentation of an optimally fast version of the NJ algorithm, Elias and Lagergren updated Atteson's results for the FNJ algorithm. They showed Theorem 3: The safety radius of FNJ is 1 2 .

Elias and Lagergren showed that if D is a distance matrix and T D is a tree metric with

Applications

Phylogeny is a quite active field within evolutionary biology and bioinformatics. As more proteins and DNA sequences become available, the need for fast and accurate phylogeny estimation algorithms is ever increasing as phylogeny not only serves to reconstruct species history but also to decipher genomes. To date, NJ remains one of the most popular algorithms for phylogeny building, and is by far the most popular of the distance methods, with well over 1000 citations per year.

∑

  The soundness of NJ is based on the observation that, if T D D = for a tree T, the value ( , ) D S x y will be minimized for a pair (x,y) that are neighbors in T. A number of papers (reviewed in [8]) have been dedicated to the various interpretations and properties of the D S criterion. n is the number of taxa in the data set. Since a distance matrix only has 2 n entries, many attempts have been made to construct a distance algorithm that would only require 2 ( ) O n computations while retaining the accuracy of NJ. To this end, the best result so far is the Fast Neighbor Joining (FNJ) algorithm of Elias and Lagergren [4]. Most of the computation of NJ is used in the re-calculations of the sums ( , ) D S x y after each agglomeration step. Although each recalculation can be performed in constant time, the number of such pairs is 2 ( ) k Ω when k nodes are left to agglomerate, and thus, summing over k,

D S x y at

  each step, but instead uses a heuristic to maintain a list of candidates of "visible pairs" (x,y) for agglomeration. At the (n-k) th step, when two neighbors are agglomerated from a k-taxa tree to form a (k-1)-taxa tree, FNJ has a list of ( ) O k visible pairs for which ( , ) D S x y is calculated. The pair joined is selected from this list. By trimming the number of pairs considered, Elias and Lagergren achieved an algorithm which requires only 2 ( ) O n computations.

  shortest internal edge of a tree T.The latter formulation leads to a definition: The safety radius of an algorithm A is the greatest value of r with the property that: given any phylogeny T, and any distance matrix D satisfying (

(

  output the same tree (T) as NJ.

  appropriate for distance methods: if D is a distance matrix that approximates a tree metric T D , can one have some confidence in algorithm's ability to reconstruct T given D, based on some measure of the distance

	between D and T D ? For two matrices, 1 D and 2 , D the L ∞ distance between them is
	defined by	1	2	max	,	1	( , )	2	( , ) .

Open Problems

With increasing amounts of sequence data becoming available for an increasing number of species, distance algorithms such as NJ should be useful for quite some time. Currently, the bottleneck in the process of building phylogenies is not the problem of searching topology space, but rather the problem of building distance matrices. The brute force method to build a distance matrix on n taxa from sequences with l positions requires calculations. However, this algorithm only applies to over-simple distance estimators [START_REF] Cantor | Evolution of Protein Molecules[END_REF]. Extending this result to more realistic models would be a great advance.

A number of distance-based tree building algorithms have been analyzed in the safety radius framework. Atteson [START_REF] Atteson | The performance of neighbor-joining methods of phylogenetic reconstruction[END_REF] dealt with a large class of neighbor joininglike algorithms, and Gascuel and McKenzie [7] studied the ultrametric setting where the correct tree T is rooted and all tree leaves are at the same distance from the root.

Such trees are very common; they are called "molecular clock" trees in phylogenetics and "indexed hierarchies" in data analysis. In this setting, the optimal safety radius is equal to 1 (instead of 1 2 ) and a number of standard algorithms (e.g. UPGMA, with time complexity in 2 ( ) O n ) have a safety radius of 1. However, experimental studies (see below) showed that not all algorithms with optimal safety radius achieve the same accuracy, indicating that the safety radius approach should be sharpened to provide better theoretical analysis of method performance.

Experimental Results

Computer simulation is the most standard way to assess algorithm accuracy in phylogenetics. A tree is randomly generated as well as a sequence at tree root, whose evolution is simulated along the tree edges. A reconstruction algorithm is tested using the sequences observed at the tree leaves, thus mimicking the phylogenetic task.

Various measures exist to compare the correct and the inferred trees, and algorithm performance is assessed as the average measure over repeated experiments. Elias and Lagergren [START_REF] Elias | Fast Neighbor Joining[END_REF] showed that FNJ (in