A Palloix
email: alainpalloix@avignon.inra.fr

V Ayme

B Moury

Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies

Keywords: pepper, potato virus Y, polygenic resistance, resistance durability, resistance breakdown, virulence, mutation, selection

The breakdown of plant resistance by pathogen populations is a limit to the genetic control of crop disease. Polygenic resistance is postulated as a durable alternative to defeated major resistance genes. We tested this postulate in the pepper-Potato virus Y interaction.

• The virus was selected for virulence towards monogenic and polygenic host resistance, using serial inoculations in laboratory and in natural epidemic conditions. The frequency of resistance breakdown and the genetic changes in the virus avirulence gene were analysed. • The monogenic resistance due to the pvr2 3 gene was defeated at high frequency when introgressed in a susceptible genetic background whereas it was not when combined to partial resistance quantitative trait loci. The suppression of emergence of virulent mutants due to the genetic background resulted both from a differential selection effect and the necessity for the virus to generate multiple mutations. The virus adaptation to the polygenic resistance required a step-by-step selection with a primary selection for virulence towards the major gene, followed by selection for adaptation to the genetic background. • Polygenic resistance proved more durable than monogenic, but breeding strategies giving priority to major resistance factors may jeopardize the progress in durability expected from polygenic resistance.

Introduction

The breakdown of genetic resistance by plant pathogen populations is a major limit to the genetic control of crop disease. Research efforts increase to propose breeding strategies, resistance gene or cultivar deployment strategies and cultivation methods that aim at controlling the pathogen evolution over time and its adaptation to the resistant cultivars [START_REF] Kiyosawa | Genetics and epidemiological beakdown of plant disease resistance[END_REF][START_REF] Finckh | Cereal variety and species mixtures in practice, with emphasis on disease resistance[END_REF][START_REF] Lindhout | The perspectives of polygenic resistance in breeding for durable disease resistance[END_REF][START_REF] Pink | Strategies using genes for non-durable disease resistance[END_REF]. The evolutionary potential of the pathogen population, when inferred from its population genetic and dynamic characteristics, permits to predict the risk of pathogen evolution towards virulence and of breakdown of resistance or other control methods (McDonald andLinde 2002, Garcia-Arenal and[START_REF] Garcia-Arenal | An analysis of the durability of resistance to plantviruses[END_REF]. However, for a given pathogen, this does not predict if one resistant host genotype will be more rapidly overcome than another. Plant breeders who face a pathogen population have to optimise the plant genotype, by choosing the most promising resistance genes and gene combinations regarding the durability of resistance.

Very few experimental data presently explain why, in a given pathosystem, some resistant cultivars succeed over a long time while others fail rapidly. The fitness penalty associated to virulence acquisition is strongly suspected to be involved in the durability of resistance since it determines the increase in frequency of virulent genotypes and their survival in presence as well as absence of the resistant cultivars [START_REF] Leach | Pathogen fitness penalty as a predictor of durability of disease resistance genes[END_REF]. This was experimentally demonstrated by Vera Cruz et al. (2000) in the Xanthomonas oryzae -rice pathosystem. However, fitness penalty can also be transitory since compensatory mutations may increase the fitness of virulent genotypes on the long term (García-Arenal et al., 2001, Wijngaarden et al., 2005). The number of mutations required for virulence acquisition was another parameter related to resistance durability by [START_REF] Harrison | Virus variation in relation to resistance breaking in plants[END_REF]. He compared the relative durability of resistance in several plant-virus pathosystems and showed that the more mutations are required for virulence, the more durable was the resistance. Indeed the probability of emergence of virulent mutants is directly dependent on the probability of occurrence of these mutations, which may impact resistance durability. Recent experimental data supported the importance of these parameters in the pepper-Potato virus Y interaction. The observed durability of the resistance alleles at the pvr2 locus was related to the number of mutations required for virulence in the virus [START_REF] Ayme | Molecular dissection of the Potato virus Y VPg virulence gene reveals complex adaptations to the pvr2 resistance allelic series in pepper[END_REF]). In addition, for a given pvr2 allele, the emergence of different virulent PVY mutants was proportional to the relative fitness and to the relative rates of the virulence mutations [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF]. Increasing results from several authors consolidate the idea that population genetics and dynamics may deliver new criteria for breeding durable resistance. The most durable resistance genes are those that require multiple mutations from the pathogen for virulence, with mutations causing the highest fitness penalty. Besides these formal analyses, many empirical results suggest higher durability of polygenic resistance relatively to monogenic resistance [START_REF] Parlevliet | Durability of resistance against fungal, bacterial and viral pathogens; present situation[END_REF]. Highly durable polygenic resistance was observed in several pathosystems where monogenic resistance failed (Schurnbursch et al. 2004[START_REF] Chen | Comparative analysis of gennomic locations and race specificities of loci for quantitative resistance to Pyricularia grisea in rice and barley[END_REF][START_REF] Turkensteen | Durable resistance of potatoes against Phytophthora infestans[END_REF]). However, a few analyses showed that pathogen populations may adapt to polygenic resistances, bypassing all or part of the resistance quantitative trait loci (QTLs) (Le Guen et al. 2007). In this case, resistance bypassing was observed a posteriori, i.e. the isolated pathogen populations were assumed to result from the earlier deployment of resistant cultivars, but the dynamics of their evolution could not be observed. Presently, no experiment clearly demonstrates the higher durability of polygenic resistance, nor permits to address the question of the determinism of this durability. Two main hypotheses are currently proposed : i/ the more resistance factors to breakdown, the more virulence mutations are required in the pathogen genome and the less probable their In this paper, we addressed this question by comparing the relative durability of a monogenic and a polygenic resistance in controlled conditions, in a pathosystem that permits to analyse the genetic changes of the pathogen during its adaptation to the resistance. In the pepper -PVY interaction, both the avirulence gene of the virus and the corresponding resistance gene in the plant were isolated, and the point mutations controlling the specificity of the pathotype x cultivar interaction were identified [START_REF] Moury | Mutations in Potato virus Y genome-linked protein determine virulence toward recessive resistances in Capsicum annuum and Lycopersicum hirsutum[END_REF][START_REF] Ruffel | A natural recessive resistance gene against potato virus Y in pepper corresponds to the eukaryotic initiation factor 4 E (eIF4E)[END_REF]. One resistance allele, pvr2 3 , displayed a weak durability and the breakdown frequency of this allele was high when introgressed in a susceptible genetic background, but null when this allele was combined to partially resistant genetic background carrying resistance QTLs. The additive effect of these QTLs was weak, since it only delayed systemic infection and symptom expression. However, the genetic background displayed a major effect on the emergence of pvr2 3 -virulent mutants. The selection of virulent variants remained possible through sequential selection, i.e. firstly by the major resistance factor and further by the combination of the major resistance factor with the resistance QTLs, resulting in the progressive accumulation of the virulence mutations. These results suggested rules for the durable management of resistance genes and QTLs.

Materials and Methods

Pepper genotypes used in this work were Capsicum annuum inbred lines with differential resistances to PVY isolates : Yolo Wonder (allele pvr2 + ) is susceptible to all isolates, Florida VR2 (allele pvr2 2 ) is resistant to PVY pathotype (0,1,3), Perennial is carrying a polygenic resistance including the allele pvr2 3 which confers resistance to pathotype (0,1,2) and resistance QTLs conferring partial resistance to the other isolates. The pvr2 locus was mapped on the P4 chromosome, and three main QTLs with resistant alleles originating from the resistant accession Perennial were mapped on the chromosomes P1 (two QTLs) and P6, using a PVY isolate derived from the SON41 strain that overcame the pvr2 3 resistance allele (Figure 1 and [START_REF] Caranta | Polygenic resistance of pepper to potyviruses consists of a combination of isolate-specific and broad spectrum quantitative trait loci[END_REF]. These 3 QTLs displayed individual effects (R 2 ) higher than 10%. Three doubled haploid lines issued from the F1 hybrid [Perennial x Yolo Wonder] were used and selected on the basis of molecular markers at the pvr2 locus [START_REF] Rubio | Functionnal markers for selection of potyvirus resistance alleles at the pvr2-eIF4E locus in pepper using tetra-primer arms PCR[END_REF] and at markers flanking the three main resistance QTLs (Figure 1). The three selected pepper lines were: HD285 carrying the allele pvr2 3 with susceptible alleles at the 3 QTLs (susceptible genetic background) will be further named Rs, HD233 carrying the resistant allele pvr2 3 with resistant alleles at the 3 QTLs (resistant genetic background) and further named Rr, and HD223 carrying the susceptible allele pvr2 + with resistant alleles at the 3 QTLs (resistant genetic background) and further named Sr. PVY isolates and infectious clones were derived from the SON41p isolate collected in France in 1982. It belongs to pathotype (0,1,2) and is virulent towards Yolo Wonder and Florida VR2, but not towards Perennial, Rs nor Rr. Here, we define virulence as the genetic ability of a pathogen to cause a compatible interaction with a host genotype leading to disease. Five SON41p mutants were isolated from Rs and gained virulence towards the pvr2 3 allele as the result of single amino acid substitutions in the central part of the VPg [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF]). These mutants were named S101G, T115K, T115R, D119N and S120C according to the mutation in the VPg that characterized them. Infectious cDNA clones from the SON41p isolate (Genbank accession AJ439544) and from the VPg mutants were obtained by [START_REF] Moury | Mutations in Potato virus Y genome-linked protein determine virulence toward recessive resistances in Capsicum annuum and Lycopersicum hirsutum[END_REF] and [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF] Test plants with two expanded cotyledons (two to three weeks after sowing) were inoculated manually on their cotyledons. Evaluation of virus infection was performed by doubleantibody sandwich-enzyme-linked immunosorbent assay (DAS-ELISA) as described by [START_REF] Legnani | Evaluation and inheritance of the Lycopersicum hirsutum resistance against Potato virus Y[END_REF] at various time points after inoculation. Symptom severity was evaluated using a semi quantitative scale ranging each individual plant into 3 classes : 1= no visible symptom, 2=weak symptoms, 3=severe mosaic or necrotic symptoms. Symptom intensity was checked every week during 5 weeks after inoculation and the area under the symptom progress curve (AUSPC) was computed with the formula : AUSPC=Σ n i=1 [(S i +S i+1 )/2](t i+1 -t i ) where S i is the symptom intensity at the date t i (t i in days). Only the DAS-ELISA positive plants were considered for the AUSPC value calculation. For the assessment of the pathogenicity of PVY isolates and infectious clones, the same procedure was used, except that the relative concentration of the inoculum extract was previously determined by semi-quantitative DAS-ELISA as in [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF] and the extracts were adjusted to the same concentration using dilution in the extraction buffer before inoculation. For each pepper genotype-PVY isolate combination, 50 plantlets were inoculated and individually assessed for symptom and DAS-ELISA. Three to four weeks after inoculation, relative virus concentration of the test plants was determined by semi-quantitative DAS-ELISA. For serial inoculation experiments, successive sowings of Perennial and Rs were performed at 5 weeks intervals. 50 plantlets per genotype were artificially inoculated as previously described by the SON41p cDNA clone and the 5 PVY mutants (S101G, T115K, T115R, D119N and S120C). Successive passages were achieved by extracting the inoculum from systemically infected leaves pooled from 10 plants per genotype, and inoculating this extract to the 50 plantlets of the same genotype for the next passage. At each passage, the plants were individually tested by DAS-ELISA to assess the infection percentage 4 weeks after inoculation. After the 4 successive passages the virus was extracted from two pools of 20 plants per genotype and PVY mutant. These virus populations issued from successive passages in Perennial and in Rs were compared to their initial cDNA clones, for the percentage of infection and the severity of symptoms in Yolo Wonder, Rs and Perennial (50 inoculated plantlets per virus population). The viral RNA was extracted from the same virus extracts and the sequence of the VPg cistron was established as in [START_REF] Moury | Mutations in Potato virus Y genome-linked protein determine virulence toward recessive resistances in Capsicum annuum and Lycopersicum hirsutum[END_REF]. Controlled epidemics of PVY in cultivation conditions were performed in two independent insect-proof tunnels. In each tunnel, 100 plants of Rr (possessing pvr2 3 and known resistance alleles at QTLs) were planted to evaluate the ability of the virus to adapt to the polygenic resistance. Six control plants were added : 2 plants of Florida VR2 (susceptible to SON41p but not to the D119N mutant), of Rs (resistant to SON41p, but susceptible to D119N) and of Yolo Wonder (susceptible to both PVY variants). The inoculum source was introduced in each tunnel by planting two Florida VR2 plants infected by SON41p and two Rs plants infected by the PVY mutant D119N. This pvr2 3 -virulent mutant was chosen because of its prevalence (53%) over the four other mutants in experimental conditions, and it was also frequently detected in open fields [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF]. Two weeks after plantation, aphids (Myzus persicae) were deposited on the PVY-inoculated plants, in order to favour the transmission of the virus to healthy plants. Symptom observations and ELISA test of every plant were performed at 15-day intervals from June to October, during the 18 weeks covering the cultivation season. When infected plants were detected, viral RNA was extracted and the sequence of the VPg cistron was established to determine which isolate was present and if additional mutations were detected as in [START_REF] Moury | Mutations in Potato virus Y genome-linked protein determine virulence toward recessive resistances in Capsicum annuum and Lycopersicum hirsutum[END_REF].

Results

Relative breakdown frequency of monogenic versus polygenic resistance

In order to compare monogenic and polygenic resistances for their relative frequency of breakdown, young plantlets of the doubled haploid line Rs (possessing the pvr2 3 resistant allele in a susceptible genetic background) and of the Perennial cultivar (possessing the pvr2 3 resistant alleles in a partially resistant background including the resistance alleles at the 3 QTLs) and the susceptible cultivar Yolo Wonder were inoculated with the SON41p infectious clone of PVY that is avirulent towards pvr2 3 . Fifteen independent tests including 20 to 50 plants of each genotype were performed, totalizing 332 Yolo Wonder, 332 Rs and 471 Perennial plants that were checked for systemic PVY infection by DAS-ELISA (Table 1). All the Yolo Wonder plants displayed strong mosaic symptoms at 2 to 3 weeks after inoculation and were ELISA positive, whereas only 76 Rs plants were ELISA positive and displayed systemic symptoms (mosaic and necrosis) 4 to 5 weeks after inoculation. None of the 471 inoculated Perennial plants were positive in ELISA nor displayed any symptom. When virus extracts from infected Rs plants were used as inocula, all back-inoculated Rs plants were infected 10 to 14 days post inoculation, indicating a virulence gain of the virus population towards the pvr2 3 allele. Twenty nine of these virus extracts were analysed in previous studies [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF][START_REF] Ayme | Molecular dissection of the Potato virus Y VPg virulence gene reveals complex adaptations to the pvr2 resistance allelic series in pepper[END_REF] and showed that the virulence gain towards the pvr2 3 allele resulted from single amino acid substitutions that occurred at different positions in the VPg of the virus genome (namely S101C T115K, T115R, D119N and S120G) that conferred virulence towards the pvr2 3 allele.

Selection of PVY isolates for virulence towards the polygenic resistance through serial inoculations

The five cDNA clones possessing the sequence of the SON41p clone and one of the five substitutions conferring virulence towards pvr2 3 were tested for their ability to adapt to the polygenic resistance of Perennial. These PVY clones were separately submitted to repeated passages on Perennial plants and were maintained in parallel through repeated passages in Rs plantlets. The initial cDNA clones uniformly infected 100% of the Rs plants over the serial inoculations. Considering Perennial, the figure 2 shows that three of the five mutants (T115K, T115R and D119N) infected systemically 60% to 100% of Perennial plants as soon as the first passage. For these three mutants, the infectivity remained stable over the repeated passages. The other two mutants were unable to infect Perennial at the first passage, so that the S120C inoculum source had to be re-extracted from the Rs plants for the second passage.

For the same reason, the S101G inoculum for the 3 rd passage was also extracted from the Rs plants. In total, the T115K, T115R and D119N mutants were submitted to 4 effective passages in Perennial, whereas S120C and S101G were submitted to 3 and 2 effective passages in Perennial respectively. After the passages, each PVY population from Perennial and from Rs was compared to its original cDNA clone for the severity of symptoms in Yolo Wonder, Rs and Perennial hosts, for the frequency of infection of Perennial plants, and for their VPg sequence (Table 2). No differences in symptom severity were observed between the original infectious clones and their derived isolates (data not shown) with severe symptoms in Yolo Wonder plants (susceptible) as well as in Rs plants, but late and weak symptoms in Perennial. Table 2 shows that the infection rate in Perennial was also not significantly affected by the repeated passages for the mutants T115R, T115K nor D119N, but that it increased significantly (p<0.05) for the mutants S120C and S101G. Sequence data from the VPg of the isolates after repeated passages in Rs or in Perennial showed no differences with the initial PVY clone for T115K

Selection of PVY isolates for virulence towards the polygenic resistance in greenhouse production conditions

The ability of PVY SON41p and of the pvr2 3 virulent mutant D119N to break the polygenic resistance down in epidemic conditions, i.e. aphid transmission of the virus to adult plants, was assessed in plastic tunnels. Both PVY clones were introduced into the insect proof tunnels planted with the Rr pepper line possessing the allele pvr2 3 and partial resistance QTLs from Perennial. Aphid vectors (Myzus persicae) were introduced into the tunnels, in order to transmit the primary inoculum to the healthy plants (secondary infections) as happens in cultivation conditions. The epidemics progressed in the tunnels with the growth of the aphid population and the Yolo Wonder plants (fully susceptible) first displayed secondary infections with either SON41p or D119N, attesting that both isolates were transmitted to healthy plants. At 8 to 12 weeks, the SON41p isolate was also detected in most Florida VR2 plants and the D119N isolate in most of the Rs plants. Virus infection in Rr plants was detected only 12 weeks after aphid release as attested by ELISA. At the end of the trial (18 weeks), only 4 plants of Rr (two plants in each tunnel) displayed PVY infections that were associated to severe mosaic symptoms further progressing into plant necrosis. Sequence data of the VPg from the four isolates collected in these plants showed that they all possessed the D119N mutation in their VPgs and also the additional mutation T115K. This indicated that they probably derived from the D119N mutant and not from the SON41p isolate. The additional mutation T115K occurred independently in the two tunnels suggesting that it was related to the adaptation of PVY mutant D119N to the polygenic resistance of Rr.

One of these 4 isolates was used for a second year trial and selection in the same conditions. It was artificially inoculated to two Rr plantlets that were further planted together with healthy Rr plants in the insect proof tunnels. Twelve weeks after the aphid release on the inoculated plants, the aphid population spread all over the plots and secondary infections were observed in Yolo Wonder and Rs control plants but also in a few Rr plants. At the end of the experiment, respectively 75% and 87% of the Rr plants were infected as attested by ELISA test in each tunnel, showing severe systemic symptoms. Isolates were collected from 20 of these plants (10 in each tunnel) and their VPg cistron was sequenced. All the isolates, displayed the same sequence with both D119N and T115K mutations. No other mutations were detected within the VPg cistron compared to the initial SON41p infectious clone.

Pathogenicity of the PVY isolate selected in the insect-proof tunnels

One isolate from the second year experiment (isol 53) was compared to the initial infectious clone possessing the single mutation D119N and to a clone possessing the two mutations D119N and T115K for its pathogenicity towards a host range in the laboratory (Figures 3 and4). For each pepper genotype -PVY isolate/mutant combination, 100% of the 50 plantlets were infected three weeks after inoculation, except for the Perennial -D119N combination (82% infection after 4 weeks). Considering AUSPC values, symptom severity was high for all the PVY isolates in Yolo Wonder (fully PVY susceptible) as well as Rs (allele pvr2 3 in susceptible genetic background). In Sr (susceptible allele pvr2 + but resistance alleles at the QTLs), the single and double mutants issued from cDNA clones induced weak and late symptoms whereas isol 53 displayed a higher AUSPC value. In Rr and Perennial (pvr2

Discussion

Our experimental data demonstrated that the frequency of breakdown of a resistance governed by a major gene was high when introgressed in a susceptible genetic background, whereas this breakdown did not occur when the same gene was introgressed in a partially resistant genetic background. Previous analyses [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF][START_REF] Ayme | Molecular dissection of the Potato virus Y VPg virulence gene reveals complex adaptations to the pvr2 resistance allelic series in pepper[END_REF] showed that every time the Rs plants were systemically infected after SON41p inoculation, it corresponded to a resistance-breaking event due to single amino acid substitutions in the central part of the VPg cistron (29 events analysed). In these events of Rs systemic infection, back inoculations of Rs plants also showed that the PVY isolate gained virulence, and we assume that the infection of 76 Rs plants over the 332 inoculated was due to the breakdown of the resistance governed by pvr2 3 by an adapted viral variant. The Rs line differed from Perennial by the alleles at the known resistance QTLs, but also at many other loci in the genetic background. Both the QTLs detected in [START_REF] Caranta | Polygenic resistance of pepper to potyviruses consists of a combination of isolate-specific and broad spectrum quantitative trait loci[END_REF] and the remaining genetic background may be responsible for the suppression of emergence of the virulent mutants. Thus, this effect will be globally assigned to the genetic background (including known QTLs) surrounding the major gene. Such results may be extended to numerous plant resistances, since most of the polygenic resistances to diseases were shown to result from the combined effect of one major resistance QTL controlling 50% to 70% of the resistance and several minor resistance QTLs (Lefebvre andChèvre 1995, Young 1996). The higher durability of polygenic resistances is commonly hypothesized and has been observed a posteriori in a few cases [START_REF] Parlevliet | Durability of resistance against fungal, bacterial and viral pathogens; present situation[END_REF][START_REF] Lindhout | The perspectives of polygenic resistance in breeding for durable disease resistance[END_REF]. This is the first experimental evidence issued from a direct comparison in controlled conditions. How the genetic background or the resistance QTLs control the emergence of virulent variants towards the major resistance factor can be explored.

Two main hypotheses related to the higher durability of polygenic resistance can be addressed here. It may result from the requirement of multiple mutations to breakdown the multiple resistance factors, in which case it relates to the initial step of virus evolution and strictly depends on the probability of occurrence of multiple mutations. An alternative hypothesis is that, after their appearance, selection of virulent variants is more efficient or rapid in plants with monogenic resistance than polygenic resistance. This relates to the further steps of virus evolution, i.e. differential selection (competition) between virulent and avirulent variants during plant infection. Note that these two hypotheses are not mutually exclusive. Under artificial inoculation of pvr2 3 -virulent PVY clones to young plantlets, three of these clones (T115K, T115R and D119N) proved able to infect the Perennial plantlets carrying the polygenic resistance. When SON41p was inoculated to Rs plants (pvr2 3 in a susceptible background) these variants were selected at frequencies from 2,5% (for T115R) to 20% (for D119N) [START_REF] Ayme | Different Mutations In The Genome Linked Protein VPg of Potato Virus Y confer virulence on the pvr2 3 resistance in pepper[END_REF]) but they never emerged in the 471 Perennial plants inoculated in the same conditions. Taken together, these results indicate that these variants were not selected in Perennial although they were present at low frequency in the initial virus population. This strongly argues in favour of the differential selection hypothesis for increased durability of pvr2 3 due to additional genetic factors in the host genetic background.

A different pattern of evolution was observed in epidemics conditions, i.e. adult pepper plants and aphid virus transmission. In such cultivation conditions, only 2% of the polygenically resistant peppers were infected, which was lower than in artificial inoculation of young

Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009) 2). Moreover, isolates from the four infected Rr plants exhibited the T115K mutation in addition to the initial D119N mutation. This additional mutation occurred independently in the two tunnels, suggesting that the double mutation conferred an advantage for virulence towards the polygenic resistance in field conditions. Indeed, when inoculated to the pepper host range, the PVY clone with the double mutation T115K+D119N displayed higher AUSPC values and virus concentrations in Rr and Perennial plants compare to the single D119N mutant. In the second year experiment, the tunnel isolate further proved able to infect 75% to 87% of Rr plants, confirming its gain in virulence towards the polygenic resistance. Moreover, the resulting isolate (isol 53) displayed a higher virus concentration than the PVY clone with the double mutation when inoculated to Rs and Perennial and higher AUSPC values in Rs, Sr, Rr and Perennial plants. Note that Perennial displayed a higher resistance level than Rr plants (Figure 3) which indicates that resistance QTLs additional to the three ones mentioned but undetected in the analysis of [START_REF] Caranta | Polygenic resistance of pepper to potyviruses consists of a combination of isolate-specific and broad spectrum quantitative trait loci[END_REF] are present in the genetic background of Perennial. Whatever the number of QTLs, the higher virulence of isol 53 in plants possessing the major gene and/or resistance QTLs, compared to the PVY clone with the double mutation in the VPg, clearly indicates that additional mutation(s) in other genome regions of this isolate confer a higher virulence towards the major gene, the resistance QTLs from the genetic background and their combination. The direct observation of adaptation of virus populations to the resistant host revealed the progressive changes that lead to the gain of virulence, as was observed a posteriori by Le [START_REF] Guen | Bypassing of a polygenic Microcyclus ulei resistance in rubber tree, analysed by QTL detection[END_REF] who isolated Microcyclus ulei strains that bypassed enlarged sets of QTLs after large deployment of resistant rubber trees. Altogether, these results show that the gain of virulence towards the polygenic resistance in field conditions requires multiple mutations, and argue in favour of our first hypothesis : at least one additional mutation within the VPg but also additional mutation(s) in other genome parts were required for virulence towards the polygenic resistance in fields. The combination of the D119N and T115K amino acid substitutions in the VPg plus additional mutations in other genome regions is very unlikely to occur in a few host passages where virus replication is very low due to resistance. This explained why the adaptation to the polygenic resistance was not directly achieved from the SON41p initial population but required a step-by-step selection for virulence, first towards the major gene and further towards the combination of the major gene and QTLs. Despite the higher durability of the polygenic resistance compared to the monogenic one, the ability of the virus to respond to a progressive selection has to be considered when breeding resistant cultivars. Breeding for resistance in most crops often consists in introgressing major genes or major QTLs from a donor exotic germplasm into recipient elite genotypes that are susceptible to the disease. This introgression is processed through successive backcrosses by the recipient genotype and molecular marker assisted backcrosses (MAB) presently permits to accelerate the process and optimize the recovering of the recipient genetic background (Michelmore 1995, Hospital and[START_REF] Hospital | Marker-assisted introgression of quantitative trait loci[END_REF]. Considering genes like pvr2 3 , this strategy would facilitate the breakdown of the resistance through providing an evolutionnary springboard for further adaptation of the virus population to a more complex resistance, jeopardizing any further genetic progress expected from combinations with resistance QTLs. A step-by-step evolution was previously known when pyramiding major resistance genes that were individually defeated in previous cultivars, leading to multivirulent pathogen genotypes [START_REF] Pink | Strategies using genes for non-durable disease resistance[END_REF]. Resistance to PVY in pepper germplasm is very frequent with 35.6% of resistant accessions among the 884 tested [START_REF] Sage-Palloix | Structuring genetic diversity in pepper genetic resources: distribution of horticultural and resistance traits in the INRA pepper germplasm[END_REF]) and a large diversity of pvr2 alleles [START_REF] Charron | Natural variation and functionnal analyses provide evidence for coevolution between plant eIF4E and potyviral VPg[END_REF]. The pvr2 3 allele was identified in several locally cultivated populations from Asia (Perennial) and Central America (CM334), in which genotypes it was combined to other resistance genes or QTLs [START_REF] Caranta | Polygenic resistance of pepper to potyviruses consists of a combination of isolate-specific and broad spectrum quantitative trait loci[END_REF][START_REF] Dogimont | Genetic analysis of broad spectrum resistance to potyviruses in haplodiploid progenies of pepper (Capsicum annuum L.)[END_REF]. These local open-pollinated cultivars were selected and maintained by farmers who operated

Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009) Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009)

- SEVRRKHVEDDEIETQALDSH 0 S101G - G-------------------- 0 a Rs G-------------M------ 0 a Perennial G-------------M---N-- 38 b T115K - --------------K------ 100 a Rs --------------K------ 86 a Perennial --------------K------ 96 a T115R - --------------R------ 100 a Rs --------------R------ 84 a Perennial --------------R------ 100 a D119N - ------------------N-- 72

  Comment citer ce document : Palloix, A., Ayme, V.,Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript

  PVY clone, frequencies followed by different letters are significantly different at p= 0.05 (Fisher's Exact Test).

Figure 1 :Figure 3 :

 13 Figure 1 : Genetic mapping of the pvr2 locus and of the QTLs for resistance to PVY in pepper and graphical genotypes of the pepper inbred lines used in the present work. The pvr2 locus and QTLs are located according to the QTL analysis of Caranta et al. 1997 and the pepper genetic map of Lefebvre et al. 2002. The black and white colours on chromosomes P4, P1 and P6 represent respectively the Perennial and Yolo Wonder alleles. pvr2 + and pvr2 3 are respectively the susceptible and resistant alleles, s and r are used to indicate the susceptible versus resistant alleles at QTLs.

  Author manuscript occurrence, ii/ the selection pressure due to quantitative resistance factors is lower than that of major genes and does not permit the emergence of virulent mutants from the pathogen population.

Comment citer ce document : Palloix, A., Ayme, V.,

Moury, B. (2009)

. Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur /

  . Artificial inoculation tests were carried out in climatic rooms. Viruses were propagated in Nicotiana spp. to obtain high-titer inocula for tests of C. annuum. Leaf tissue from infected

		Nicotiana spp. plants developing severe symptoms of the disease was homogenised in four
		volumes of 0.03 M phosphate buffer (pH 7.0) supplemented with 2% (w/v)
		diethyldithiocarbamate, 20 mg/mL of active charcoal and 20 mg/mL of Carborundum.
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript	Comment citer ce document :
		Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to
		pathogens depends on the genetic background, experimental evidence and consequences for breeding
		strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x

  An additional mutation T115M was gained in the D119N, S120C and S101G clones after repeated passages in Rs. In these two latter clones, the additional mutation D119N was specifically gained only after repeated passages in Perennial.

	nor T115R.
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript

Comment citer ce document : Palloix, A., Ayme, V.,

Moury, B. (2009)

. Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x

  weeks after inoculation were similar in the susceptible pepper Yolo Wonder whatever the virus, but higher for the double mutant and/or the isol 53 compared to the single mutant in the other resistant genotypes. The isol 53 displayed a significantly higher concentration compared to the double mutant in Rs and particularly in Perennial.

	concentrations at 3
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript

3 and resistant alleles at the QTLs) the AUSPC values were significantly different between the single mutant (weak and late symptoms), the double mutant (intermediate AUSPC values) and isol 53 which displayed earlier and more severe symptoms. The relative virus Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x

Bai J Ona I, Leung H, Nelson RJ, Mew TW, Leach JE

  . Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x in fields for yield, quality and low symptom expression. This massal field selection in regions where potyviruses are prevalent probably led to the combination of complementary genetic factors for resistance efficiency and durability. Breeding for durable resistance in modern cultivars should promote the selection for major resistance factors together with appropriate genetic background. Further analysis of the genetic factors impeding the emergence of pvr2 3 -virulent PVY populations and their relationship with resistance QTLs will deliver criteria to select for such genetic backgrounds. citer ce document : Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x . 2000. Predicting durability of a disease resistance gene based on an assessment of the fitness loss and epidemiological consequences of avirulence gene mutation. Proceedings of the National Academy of Sciences of the United States of America 97: 13500-13505. Wijngaarden

	Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript a massal selection Comment Manuscrit d'auteur / Author manuscript Vera Cruz CM,

, P J, van den Bosch F, Jeger M J, Hoekstra RF. 2005

  . Adaptation to the cost of resistance: a model of compensation, recombination and selection in a haploid organism. Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x

	Manuscrit d'auteur / Author manuscript	Proceedings of the Royal Society B 272: 85-89. Young ND. 1996. QTL mapping and quantitative disease resistance in plants. Annual Review of Phytopathology 34: 479-501.
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript

Table 1 :

 1 Frequency of infection as attested by DAS-ELISA tests in 3 pepper genotypes: Yolo Wonder (PVY susceptible), Rs (pvr2 3 allele in a susceptible genetic background) and Perennial (pvr2 3 allele in a partially resistant genetic background), five weeks after inoculation with a pvr2 3 -avirulent PVY infectious clone (SON41p).

	Cultivar (and	Yolo Wonder	Rs (pvr2 3 ) Perennial (pvr2 3 +
	resistant genotype)	(pvr2 + )		resistant genetic
				background)
	number of inoculated	332	332	471
	plants*
	number of infected	332	76	0
	plants*
	mean % infection	100 (±0)	27,6 (±9.3)	0 (±0)
	(±SD)	-	23.3 -31.9	-
	95% confidence
	interval) €
	* Data from 15 independent tests, each including 20 to 50 plants of every genotype. The
	frequency of Rs infected plants differed from that of Perennial and Yolo Wonder plants at
	p<10 -6 (Fisher's Exact Test)

€ Confidence intervals cannot be calculated when observed standard deviations are zero Comment citer ce document : Palloix, A., Ayme, V., Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist, 183 (1), 190-199. DOI : 10.1111/j.1469-8137.2009.02827.x

Table 2 :

 2 Amino acid differences in the central part of the VPg of potato virus Y isolates and frequency of infection of Perennial plantlets after serial inoculation on distinct pepper hosts.

	Original	Host	genotype	aminoacid sequence of the	% infection
	infectious	used		central part of VPG	of Perennial*
	clone	for	serial
		inoculations
	SON41P

Acknowledgements :

We are grateful to the Comité Technique Permanent de la Sélection (CTPS, Ministry of agriculture) and to the Clause Vegetable seeds, Gautier, Rijk Zwaan, Vilmorin and Sakata seed companies for financial support and technical participation to the program. We also thank Ghislaine Nemouchi, Pascale Mistral and Vincent Simon for their excellent technical assistance, and Nathalie Boissot for critical review of the manuscript. The experiments were conducted in compliance with the current laws of France for bio-security and confinement of GMOs.


Alexis Achim
email: alexis.achim@forestry.gsi.gov.uk

Barry Gardiner

Jean-Michel Leban

PREDICTING THE BRANCHING PROPERTIES OF SITKA SPRUCE GROWN IN GREAT BRITAIN*

Keywords: branching, knots, wood quality modelling, Picea sitchensis

Predictions of the branching characteristics of Sitka spruce (Picea sitchensis (Bong.) Carr.) were made as part of the development of a timber properties simulation tool. For each annual growth unit, non-linear modelling was used to describe the average number of branches and their associated diameter, insertion angle, and probability of being alive. The parameters for the model were obtained using the branching characteristics of 60 trees collected from a range of locations across Scotland and northern England. The non-linear equations describing the branching properties gave an adequate representation of the mean of each branch property from the top to the base of the tree. Analysis of the residuals around the stem revealed that branches grew bigger on the south side but were more numerous on the north side. The predictions used a total of only six predictor variables that can be obtained from normal mensurational data and from the height growth history of the trees. Yield tables could hence be used to run two simulations of typical Sitka spruce stands managed under a thinning or no-thinning regime. As expected, the effect of thinning was to increase branch diameter, to lower the height at which branches die, and to increase the number of branches without having any effect on their insertion angle. After incorporation of clear-wood properties, the model will be used to predict the properties of sawn battens.

INTRODUCTION

The silviculture of Sitka spruce in Great Britain has undergone significant changes over the last 50 years [START_REF] Mason | Can Sitka spruce crops be improved through silviculture? HGTAC[END_REF]. From the 1920s until the 1940s, Sitka spruce was planted on relatively fertile, sheltered soils at spacings of 1.0-1.5 m. In contrast, from the 1960s to the early 1980s there was rapid afforestation with the use of cultivation and/or herbicides that allowed planting on higher, more exposed sites with initial spacings increased to 2.0-2.4 m and with greater use of systematic thinnings. Over the next 20 years the supply of softwood timber from British conifer plantations is expected to double to around 16 000 000 m 3 [START_REF] Smith | New forecast of softwood availability[END_REF] and the majority of this will be Sitka spruce (~70%) typically harvested over a rotation of 40 years. As plantations established since the 1960s come into production, the characteristics and properties of timber being harvested are changing. There are concerns about decreasing wood density, larger juvenile cores, increased area and frequency of knots, increased incidence of compression wood, and poorer stem form. Currently, the practical implications of these changes on timber utilisation cannot be easily quantified. Furthermore, there are no tools available to guide British foresters as to the effect of their silvicultural decisions on the future timber quality of stands, which is of increasing importance with the increased use of alternative silvicultural systems. It was considered that the best approach to provide predictions of these characteristics within a reasonable time frame was through computer modelling. A series of classical-style field experiments would be too expensive, take too long, and provide only information about the specific situations studied. This paper focuses on the part of a timber quality model which is designed to predict the effect of site quality and silviculture on the branching properties of Sitka spruce. As trees grow in diameter, branches become incorporated in the stem, thus creating knots which locally deviate and distort wood fibres. Knots are important factors in weakening structural timber as they lead to stress concentrations and because checking often occurs around them during drying (USDA 1999). Their negative effect on stress grading results has long been recognised in Sitka spruce [START_REF] Brazier | Growth features and structural wood performance[END_REF][START_REF] Maun | Sitka spruce for construction timber: the relationship between wood growth characteristics and machine grade yields of Sitka spruce[END_REF]. The extent of this effect depends on the proportion of the cross section of the batten which is occupied by a knot, its position in the batten (lumber), and on whether it is live (intergrown) or dead (encased) (USDA 1999). In turn, such properties are dictated by the position in the stem where the batten came from and by the history of how branch size, number, insertion angle, and condition (live or dead) evolved as the tree was growing. A decision was made to follow the modelling approach developed by [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF]. Their approach describes the branch characteristics in a tree from variables which can be obtained from a combination of stand inventory data and growth model predictions (i.e., current tree height and diameter and yearly increments). An advantage is that the model is hence independent of a knowledge of the history of silvicultural interventions, which is often unavailable. This facilitates integration with growth models such as the one presented by [START_REF] Houllier | Linking growth modeling to timber quality assessment for Norway spruce[END_REF].

This paper describes the results of this modelling effort by (1) presenting the parameters of the model as obtained using a 60-tree sample from a range of locations across Scotland and Northern England, (2) plotting the predicted values along the stem of a typical 40-year-old Sitka spruce tree, and (3) showing the effect of thinning on these predictions.

MATERIALS AND METHODS

Location of the Sample Trees

All the trees studied were of Queen Charlotte Island provenance. The details of the sample sites are given in Table 1.

Measurement Methodology

Branch characteristics were measured following the method of [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF]. The north and west sides were marked on the standing tree with spray paint. Once the sample tree was felled, the paint marks were extended along the length of the stem. Then, a 30-m measuring tape was stretched from the apex of the tree to the butt end and a series of measurements were made on all whorls in the following sequence:

• The distance from the bottom of the growth unit to the top of the tree was recorded (D top , m). • The number of branches at the whorl position and the number of branches between this and the next whorl down were counted separately. In the remainder of the text, the former will be referred to as "whorl" branches and the latter as "inter-whorl" branches. • The status (i.e., live or dead) of each branch was recorded.

• The diameter of the stem was measured at the bottom of the growth unit (immediately above the next whorl of branches) using a diameter tape.

The following additional measurements were recorded on every second whorl (see details in Fig. 1):

• Using a measuring tape, the distance (in the longitudinal axis of the tree) between the position of the top of the growth unit and the position of the base of each branch was recorded (D whorl , m). • The horizontal (Φ h , cm) and vertical diameters (Φ v , cm) of each branch were measured in axes perpendicular to the longitudinal axis of the branch. --------------------------------------------------------------------------------------------------------------

) (m) (cm) --------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------
• The angle of insertion (θ, degrees) of the branch into the stem was measured with a protractor positioned at the base of the branches. It was experimentally defined as the angle between the axis of the stem and the centre of the branch at a 5-cm distance from the stem. • The azimuth direction of the branch (α, degrees) was estimated by holding a circular protractor beside the stem and aligning it using the paint marks.

By subtracting D top values from two successive whorls, we obtained the lengths of each growth unit (U length , m).

Modelling Approach

The model uses non-linear equations to describe the changes in branch characteristics along the stem. The shapes of these equations were based mainly on those used by [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF] but adjusted on the basis of previous experiences and published information on the branching habits of Sitka spruce [START_REF] Cannell | Production of branches and foliage by young trees of Pinus contorta and Picea sitchensis: provenance differences and their simulation[END_REF][START_REF] Cochrane | Growth of a Sitka spruce plantation: Analysis and stochastic description of the development of the branching structure[END_REF].

Insertion angle

a θ ----- θ = i θ e b θ -h r [1]
where a θ , b θ , and i θ are empirically determined parameters, and FIG. 1-The branching structure of Sitka spruce and how some of the branching variables were measured. Φ v is the vertical diameter of the branch. D whorl is the distance between the base of the branch (at its geometrical centre) and the top of the growth unit (indicated by a scar on the bark). θ is the insertion angle of the branch. Adapted from [START_REF] Cochrane | Growth of a Sitka spruce plantation: Analysis and stochastic description of the development of the branching structure[END_REF].

H -D top h r = --------

[2] H where H (m) is the height of the tree.

Number of branches

N = i N U length a N e -b N D top [3]
where a N , b N , and i N are empirically determined parameters.

Branch condition

1 P live = [-----------] [4] 1 + e -(a 1 + b 1 U # )
where P live is the probability of a branch being alive, a l and b l are empirically determined parameters, and U # (dimensionless) is the growth unit number (starting with 1 at the apex of the tree (see [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF].

Branch diameter Φ = a Φ + i Φ [1 -h r ] • e -b Φ h r [5]
where Φ represents either Φ h or Φ v and a Φ , b Φ , and i Φ are empirically determined parameters. Note that Equation 5 only predicts the average (whorl or inter-whorl) branch diameter in a growth unit.

The parameters of each equation were inferred using the NLIN procedure in SAS (1990). This procedure looks for an optimal combination of parameter values through iterations. The Levenberg-Marquardt fitting algorithm was used to perform the iterations. A model for each of the 60 study trees was fitted first. The parameters so obtained were then analysed through linear regression using the REG procedure. The effects of the diameter at breast height (DBH, m), tree height (H, m), and the H:DBH (dimensionless) ratio were tested on each parameter using the following model:

y = α + β • DBH + γ • H + δ • H : DBH + ε [6]
where y represents parameters a, b, or i in Equations 1 to 5; α, β, γ, and δ are parameters; and ε is the residual error. Only the significant parameters were retained. This meant that in each equation, the parameters (a, b, and i) would be used either as constants if no significant effects were detected or as functions of DBH, H, H:DBH or any possible combination of these variables, provided their effect was statistically significant (p<0.05). Separate equations were derived for whorl and inter-whorl branches.

Link to Growth Model

The rationale behind this model is that branch characteristics can be predicted using a combination of the current stem characteristics and the height growth history of the trees. This implies that predictions of external branching characteristics can be made at any height in a tree using only six variables: U length , U # , D top , DBH, H, H:DBH. Most variables can be obtained from normal inventory data but U length has to be obtained from detailed tree measurements or by using a height growth model. The yield tables of [START_REF] Edwards | Yield models for forest management[END_REF] were used for this purpose.

The results were displayed by plotting each branch characteristic along the height of a 40-year-old Sitka spruce planted on a yield class 14 site with an initial spacing of 1.7 m. Two simulations were made: one where the stand was left unthinned and one where the stand was subjected to a series of intermediate thinnings applied every 5 years (Table 2). Note how the intermediate thinnings alter the final mean diameter at breast height of the crop. The predictions obtained from the model are intended to describe the branching properties of the average tree from each simulation.

RESULTS

Distribution Along the Stem

No effect of tree size was found on any of the parameters in Equation 1 (Table 3). Therefore, no effect of thinning could be seen on branch insertion angle in the simulation (Fig. 2). The angles of both whorl and inter-whorl branches decrease very rapidly at the top of the tree and then decrease slowly and linearly towards the base. All along the stem whorl branches are shown to grow at a more upward angle than inter-whorl branches with an almost constant difference (≈ 13 degrees).

All parameters from Equation 3 were found to vary with either DBH, H, or H:DBH (Table 4). Thinned trees had a few more whorl and inter-whorl branches (Fig. 3). The differences were of the order of 0.3 to 0.5 whorl and inter-whorl branches per growth unit. There was an almost constant number of inter-whorl branches at the top of the tree down to half tree height, and they began to decrease in number rapidly towards the base. In contrast, whorl branches were more numerous close to the base of the tree.

Because the parameters from Equation 4were found to vary as a function of DBH (Table 5) an effect of thinning could be observed in branch status (Fig. 4), for both whorl and inter-whorl branches. Thinning lowered the height at which the probability of a branch being alive went from effectively 1 to 0. This change in status always occurred higher in the tree for inter-whorl branches than for whorl branches.

The parameters from Equation 5were not influenced by tree size for inter-whorl branches but they varied with DBH and H for whorl branches (Table 6). Thinning caused both the horizontal and vertical diameters of whorl branches to increase, particularly at mid-height in the tree where the increase approached 0.5 cm (Fig. 5). The vertical diameter was slightly higher than the horizontal diameter of whorl -

------------------------------------------------------------------------------------------------------------- Main crop Yield from thinnings Cumulative production ----------------------------------------------------------------------------------------------------------------------------------- Age H Trees/ha Mean BA Vol Trees/ha Mean BA Vol Vol MAI (m) DBH (m 2 /ha) (m 3 /ha) DBH (m 2 /ha) (m 3 /ha) (m 3 /ha) (m 3 /ha) (cm) (cm) --------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------- FIG.
2-Average branch insertion angles for each growth unit in a 40-year-old Sitka spruce.

TABLE 3-Model parameters for the insertion angles of whorl and inter-whorl branches.

----------------------------------------------------------------------α β γ δ - --------------------------------------------------------------------- -----------------------------------------------------------------------TABLE 4-Model parameters for the number of branches in each whorl or inter-whorl. ---------------------------------------------------------------------- --------------------------------------------------------------------- -----------------------------------------------------------------------branches, whereas the two were indistinguishable in inter-whorl branches. The diameters of inter-whorl branches increased slowly and linearly from the top to the base of the simulated trees. Whorl branches increased in diameter from the top of the tree and then started decreasing before mid-height was reached.

- α β γ δ -
TABLE 5-Model parameters for the probability of a whorl and inter-whorl branch being alive. ---------------------------------------------------------------------- ---------------------------------------------------------------------- --------------------------------------------------------------------- 3 to 6, the values between brackets represent the asymptotic standard deviations of the parameter estimates. α, β, γ, δ are the parameters used in Equation 6.

----------------------------------------------------------------------- α β γ δ ----------------------------------------------------------------------- Inter-
- α β γ δ -

0022) -----------------------------------------------------------------------* In Tables

Model Residuals

When analysed by azimuth direction, the model residuals showed that, on average, branch diameter was under-predicted on the south side of the trees but overpredicted on the north side (Fig. 6). For the purpose of this analysis the residuals were not investigated directly but as a proportion of the predicted diameter. This is because it made sense to assume that the extent of an effect of azimuth direction would be related to the size of the branch. We found this proportional difference to be higher for inter-whorl branches than for whorl branches.

As a result of this investigation, we suggest that a cosine function could take the observed effect into account. Equation 5would thus be transformed into:

Φ = (a θ + i Φ [1 -h r ]•e -b Φ h r ) • (1 + p cos(α + d)) [7]
where α is expressed in radians and p and d are the experimentally determined parameters (Table 7).

On the other hand, more branches were measured overall on the north side of trees (plotted in four 90-degree sectors in Fig. 7). No function was used to describe the directional effect but eventual predictions could be weighted for each 90-degree sector according to the numbers presented in Fig. 7.

Plotting the residuals against growth unit number showed that the chosen functions gave an adequate representation of the mean of each branch property from the top to the base of the tree (Fig. 8). The only notable exceptions were for the insertion angle and number of inter-whorl branches: insertion angle was over-predicted at the very top of the tree but it was slightly under-predicted for the rest of the upper half of the tree; the model under-predicted the number of branches at the top of the tree and, conversely, over-predicted in the middle. 7. The values of the a Φ , b Φ , and i Φ parameters can be found in Table 6. -----------------------------------------------------------------------Horizontal Vertical ---------------------------------------------------------------Inter-whorl Whorl Inter-whorl Whorl -----------------------------------------------------------------------p -0.062 -0.021 -0.059 -0.019 d -0.23 -0.62 -0.14 -0.57 ----------------------------------------------------------------------

DISCUSSION

Variations in Properties

The model description of how branching properties vary along a Sitka spruce stem corresponds well to our knowledge of the branching habits of this species. [START_REF] Cannell | Production of branches and foliage by young trees of Pinus contorta and Picea sitchensis: provenance differences and their simulation[END_REF] had already illustrated the strong tendency of Sitka spruce to produce numerous whorl and inter-whorl branches, often more than 10 in a year. He observed that it produced around three times as many first-order branches as lodgepole pine (Pinus contorta Dougl.). In this respect Sitka spruce is, unsurprisingly, more similar to Norway spruce (Picea abies Karst.). [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF] predicted slightly higher numbers of (whorl and inter-whorl) branches in a 38-yearold Norway spruce, but similar numbers of whorl branches.

In that study, as in the current one, the number of whorl branches was fairly constant along the stem although the number of inter-whorl branches clearly decreased towards the base. This implies that only self-pruning of inter-whorl branches had started taking place at this stage in the tree development. Even for the oldest of our sample stands it was not considered necessary to model the height of the first branch as the trees had, in effect, no lower clear bole. The practical implication of this behaviour is that, under current silvicultural systems, characterised by rotation lengths rarely exceeding 45-50 years, clear wood can only be obtained through pruning. This may explain the long history of interest in the subject in Britain (for a complete discussion see [START_REF] Henman | Pruning conifers for the production of quality timber[END_REF]. As predicted in our simulation, [START_REF] Cochrane | Growth of a Sitka spruce plantation: Analysis and stochastic description of the development of the branching structure[END_REF] observed inter-whorl branch angles to be bigger than those of whorl branches in young Sitka spruce trees, although the difference we predicted was smaller. This seems related mainly to the fact that they observed most inter-whorl branches to point downwards. The parameters from Equation 1show that our model predicts that insertion angles remain smaller than 90° along any stem, meaning that on average the branches point upwards. The downward increase in angle corresponds well to what was predicted by [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF] for Norway spruce, although their model predicted a bigger difference between the top and the base of the tree. [START_REF] Lemieux | Characterization and modeling of knots in black spruce (Picea mariana) logs[END_REF] reported that lower branches in black spruce (Picea mariana [Mill.] B.S.P.) first point upwards and gradually change to point downwards If the difference in branch insertion angles between the top and the base of a tree is taken as an indirect measure of knot straightness, the results suggest that Sitka spruce has generally straighter knots than these other two species of spruce. The average diameters of whorl and inter-whorl branches modelled in this study are very similar to those modelled by [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF]. The shape of the topto-base profile is also in accordance with them and with the ones described by [START_REF] Makinen | Evaluation of models for branch characteristics of Scots pine in Finland[END_REF] for Scots pine (Pinus sylvestris L.) and [START_REF] Maguire | Models for describing basal diameter and vertical distribution of primary branches in young Douglas-fir[END_REF] for Douglas fir (Pseudotsuga menziesii [Mirb.] Franco). This profile implies that the largest whorl branches are located in the middle section of the trees and smaller ones are found near the base. However, as pointed out by [START_REF] Vestol | Prediction of knot diameter in Picea abies (L.) Karst[END_REF], the effect of the latter on the properties of battens might be just as detrimental since they are more likely to be dead. In fact, branch condition should be at least partly responsible for the smaller branch diameters observed near the base. [START_REF] Lemieux | Characterization and modeling of knots in black spruce (Picea mariana) logs[END_REF] observed a reduction in knot diameter as a result of branch death inside black spruce butt logs. Interestingly, inter-whorl branches did not show the same peak at mid-height but a slow, steady increase from top to base. A possible explanation comes from the fact that the bigger whorl branches will shade the inter-whorl branches, hence slowing their diameter growth. The process is possibly more severe close to mid-height, where whorl branches are bigger, than at the base of the tree. It is reasonable to assume that the same process explains why inter-whorl branches are likely to die earlier.

Our observation that branches are non-uniformly distributed around the stem tends to support the hypothesis that some environmental factors bias the distribution of knots around the stem [START_REF] Lemieux | Shape and distribution of knots in a sample of Picea abies logs[END_REF]). In the Northern Hemisphere crowns have been observed to be generally weighted asymmetrically towards the south [START_REF] Rouvinen | Structure and asymmetry of tree crowns in relation to local competition in a natural mature Scots pine forest[END_REF][START_REF] Skatter | The cause of the prevalent directions of spiral patterns in conifers[END_REF]. However, there seem to be inconsistencies in how this is reflected in the distribution of diameters and numbers of branches around the stem. Results from other studies do not corroborate our observation that knot diameter peaks in the south to south-west direction but that more branches grow in the northern quadrant. Conversely, [START_REF] Lemieux | Characterization and modeling of knots in black spruce (Picea mariana) logs[END_REF] found that black spruce trees in Canada had more knots in the southern direction but those in the northern side were on average bigger. [START_REF] Lemieux | Shape and distribution of knots in a sample of Picea abies logs[END_REF] reported knot volume to be higher in the southern and south-eastern portions of Norway spruce logs from Finland due to the presence of larger and more numerous knots. The fact that no general trend can be identified suggests that the position of the sun at higher latitudes is unlikely to be the main driver for the observed biases. The reality of what drives the production of branches and their subsequent growth is more complex, with factors such as ground slope, exposure direction, and the presence of a forest edge likely to have an important role [START_REF] Grace | Modelling branch development for forest management[END_REF]. [START_REF] Maguire | Models for describing basal diameter and vertical distribution of primary branches in young Douglas-fir[END_REF] highlighted the need to understand branch distribution around the stem. The type of function that we used to model this effect could arguably be used to model the frequency distribution of knots around the stem in the study of [START_REF] Lemieux | Shape and distribution of knots in a sample of Picea abies logs[END_REF] but would not be adequate to explain their measured distribution of diameters. The more elaborate concepts used in phyllotaxy -the study of the arrangement of leaves on the axis of a plant -could help further the understanding of the arrangement of branches around the stem [START_REF] Pont | Use of phyllotaxis to predict arrangement and size of branches in Pinus radiata[END_REF].

Modelling Approach and Link to Yield Model

It is acknowledged that silvicultural interventions can have a major impact on branch characteristics but we assume they can be taken into account indirectly through their effect on stem morphology (a combination of diameter at breast height and height) at a given age. Our simulation of two thinning regimes can be regarded as a preliminary examination of this assumption. It is encouraging to see that the results were in accordance with what was expected. Increased branch (or knot) size is a widely acknowledged effect of thinning (e.g., [START_REF] Brazier | Growth features and structural wood performance[END_REF][START_REF] Maguire | Predicting the effects of silvicultural regime on branch size and crown wood core in Douglas-fir[END_REF][START_REF] Makinen | Growth, suppression, death, and self-pruning of branches of Scots pine in southern and central Finland[END_REF]. Likewise, a lowering of the live crown is expected after thinning. The fact that our predicted increase was small seems to be in accordance with the observations of [START_REF] Makinen | Growth, suppression, death, and self-pruning of branches of Scots pine in southern and central Finland[END_REF]. Although it is known to be mainly related to the height growth of the parent shoot [START_REF] Cannell | Production of branches and foliage by young trees of Pinus contorta and Picea sitchensis: provenance differences and their simulation[END_REF][START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF]), an increase in branch initiation would also be expected as a result of improved light conditions in thinned stands [START_REF] Maguire | Models for describing basal diameter and vertical distribution of primary branches in young Douglas-fir[END_REF]. Because our predictions were very similar for the thinned and unthinned simulations at the top of the tree, it is also plausible that the increased numbers resulted from a difference in self-pruning. How this process is influenced by thinning is, however, poorly understood [START_REF] Makinen | Growth, suppression, death, and self-pruning of branches of Scots pine in southern and central Finland[END_REF]. In contrast to the other properties, the insertion angles of the branches were not affected by thinning, as was also observed by [START_REF] Deleuze | Modelling crown shape of Picea abies: spacing effects[END_REF] in Norway spruce.

Despite the model seeming to be successful in predicting the effect of a sequence of thinnings, a few minor modelling artefacts were observed. For example, the higher branch diameter at the base of thinned trees than in unthinned trees seems illogical. This is because the branches at the base of thinned and unthinned trees were all below the predicted height of the first live whorl at the time of first thinning and would therefore have all stopped growing. This artefact occurred as a result of the branch condition model and the branch diameter model being derived independently. To account for this, we intend to insert logical constraints between the equations when they are included in our timber properties simulator for Sitka spruce.

In conclusion, it can be said that Sitka spruce branch characteristics show substantial within-stem variability. The main practical implication of this variability is that it offers potential for improved grade yield of timber sawn from such trees [START_REF] Samson | Method for assessing the effect of knots in the conversion of logs into structural lumber[END_REF][START_REF] Lemieux | Shape and distribution of knots in a sample of Picea abies logs[END_REF]. It is therefore desirable that this model be developed to describe the impact of knots on the properties of the sawn timber. The necessary steps to make this possible are:

(1) Estimate internal knot characteristics. Because predictions can be made at any time in the development of a tree, this can be achieved by considering that the branching characteristics of year t become the internal characteristics of year t+1. Such predictions would have to be tested against real measurements of knots.

(2) Make the model stochastic, i.e., capable of describing the variability at different levels. The within-whorl variation needs to be described if virtual battens are to be modelled. This can only be achieved by also quantifying the variability within trees, between trees, and between stands [START_REF] Colin | Branchiness of Norway spruce in north-eastern France: predicting the main crown characteristics from usual tree measurements[END_REF]. Adding a random tree effect to the models might be helpful for this purpose [START_REF] Garber | Vertical trends in maximum branch diameter in two mixed-species spacing trials in the central Oregon Cascades[END_REF].

(3) Amalgamate the branching model with a model describing the properties of the clear wood. Such a model is currently under development at Forest Research [START_REF] Macdonald | Towards a timber quality model for British grown Sitka spruce[END_REF].

(4) Integrate with a batten performance model. Such algorithms have already been developed by [START_REF] Maun | Sitka spruce for construction timber: the relationship between wood growth characteristics and machine grade yields of Sitka spruce[END_REF].

  FIG. 3-Average branch numbers in each growth unit; (a) No thinning, (b) Intermediate thinning, no delay.

FIG. 5 -

 5 FIG. 5-Average branch diameters in each growth unit; (a) No thinning, (b) Intermediate thinning, no delay.

FIG. 6 -

 6 FIG. 6-Average ratios of residual over predicted values for branch diameters in 45degree sectors; (a) inter-whorl horizontal diameter, (b) inter-whorl vertical diameter, (c) whorl horizontal diameter, (d) whorl vertical diameter. Φ represents branch diameter.

  FIG. 7-Total number of branches measured in the experiment by sector.

FIG. 8 -

 8 FIG. 8-Mean residuals and their standard deviations for the first 40 growth units; (a) inter-whorl insertion angles, (b) whorl insertion angles, (c) inter-whorl branch numbers, (d) whorl branch numbers, (e) inter-whorl probabilities of being alive, (f) whorl probabilities of being alive, (g) inter-whorl horizontal branch diameter, (h) whorl horizontal branch diameter, (i) inter-whorl vertical branch diameter, (j)

TABLE 1 -

 1 Sample sites showing stand characteristics. Yield Class estimated from[START_REF] Edwards | Yield models for forest management[END_REF].

TABLE 2 -

 2 Stand characteristics for the two simulations (extracted from[START_REF] Edwards | Yield models for forest management[END_REF]. BA

	is the volume,
	is the basal area, Vol

TABLE 6 -

 6 Model parameters for the vertical and horizontal diameters of whorl and interwhorl branches.

TABLE 7 -

 7 Parameters for Equation

ACKNOWLEDGMENTS

The authors would like to thank Elspeth Macdonald, Jason Hubert, Franka Brüchert, and Francis Colin who initiated and encouraged this work. We wish to express particular thanks to Shaun Mochan, Keijo Heikkila, Joanna Forbes, Dave Clark, and the numerous Technical Support Unit staff who helped with the measurements in the field. Thanks also to David Vinué Visús for ensuring the quality of the database and to Monica De Ioanni for drawing Fig. 1. We are grateful for funding from the Scottish Forestry Trust (John Eadie Fellowship) which enabled the third author to instigate this work.