A D Costard

Z G Vitezica

‡ C R Moreno

J.-M Elsen

A dynamic deterministic model to optimize a multiple-trait selection scheme 1

Keywords: genetic algorithm, global optimization, marker-assisted selection, selection scheme

A mathematical approach was developed to model and optimize simultaneous selection on 2 traits, a quantitative trait with underlying polygenic variation and a monogenic trait (e.g., resistance to a disease). A deterministic model allows global optimization of the selection scheme to maximize the frequency of the desired genotype for the monogenic trait, while minimizing the loss of genetic progress on the polygenic trait. An additive QTL or gene was considered. Breeding programs with overlapping generations, different se-lection strategies for males and females, and assortative mating were modeled. A genetic algorithm was used to solve this optimization problem. This modeling approach may easily be adapted to a variety of underlying genetic models and selection schemes. This model was applied to an example where selection on the Prp gene for scrapie resistance was introduced as an additional selection criterion in an already existing dairy sheep selection scheme.

INTRODUCTION

Gene or QTL information could improve selection efficiency and allow the implementation of markerassisted selection. Marker-assisted selection has been proposed to improve classical selection schemes for complex traits with low heritability or that are difficult or expensive to measure [START_REF] Lande | Efficiency of marker assisted selection in the improvement of quantitative traits[END_REF][START_REF] Meuwissen | Potential improvements in rate of genetic gain from marker-assisted selection in dairy cattle breeding schemes[END_REF][START_REF] Dekkers | Optimizing selection for quantitative traits with information on an identified locus in outbred populations[END_REF]. Strategies to use QTL or gene information in marker-assisted selection are mainly based on indices combining the EBV for QTL and the EBV for the residual polygenic effect. Marker-assisted selection increases the QTL frequency in the short-term, but can result in less response in the long-term [START_REF] Lande | Efficiency of marker assisted selection in the improvement of quantitative traits[END_REF]. Several studies [START_REF] Gibson | Short term gain at the expense of long term response with selection of identified loci[END_REF]Larzul et al., 1997b;[START_REF] Pong-Wong | Response to mass selection when an identified major gene is segregating[END_REF] have explored the interactions between selection methods and time horizon. [START_REF] Dekkers | Optimizing selection for quantitative traits with information on an identified locus in outbred populations[END_REF] optimized selection on an identified QTL in a simple selection scheme (phenotypic selection, random mating) using an optimal control approach [START_REF] Lewis | Optimal Control[END_REF]. The method was extended by [START_REF] Chakraborty | A method to optimize selection on multiple identified quantitative trait loci[END_REF]. The benefit of optimal selection on a single identified QTL and the differences between optimal and standard QTL selection were evaluated by [START_REF] Dekkers | Potential gain from optimizing multigeneration selection on an identified quantitative trait locus[END_REF]. [START_REF] Manfredi | A dynamic deterministic model to evaluate breeding strategies under mixed inheritance[END_REF] optimized selection and mating on a QTL for a sex-limited trait using sequential quadratic programming. In these studies, selection was for a single quantitative trait affected by 1 identified QTL of meaningful size as well as polygenes. The objective of this study is to optimize simultaneous selection on 2 traits, a monogenic trait controlled by an identified QTL or gene and a second independent polygenic trait that is unaffected by the major locus with a genetic algorithm [START_REF] Holland | Genetic algorithms and the optimal allocation of trials[END_REF][START_REF] Goldberg | Genetics algorithms in search, optimization and machine learning[END_REF][START_REF] Mongeau | Exploitation de la structure en optimisation globale[END_REF]. A deterministic and dynamic model is presented for breeding programs including overlapping generations, different selection strategies for males and females, and nonrandom mating.

MATERIALS AND METHODS

Animal Care and Use Committee approval was not obtained for this study because no animals were used.

Genetic Model

A population of infinite size with overlapping generations and different classes of animals defined by sex s (s = 1 for males and s = 2 for females), age a, and EBV categories c (elite, not elite) was considered. Animals of identical sex and age may be classified in different subsets according to their EBV mean and their use as reproducers (e.g., the number of progeny per year). The QTL or gene has 2 alleles (B and b). Genotypes BB, Bb/bB, and bb are denoted as g1, g2, and g3, respectively. The polygenic effects are assumed to follow the infinitesimal genetic model with variance σ 2 . The identified QTL or gene is unlinked with genes that influence the quantitative trait. For generation t, each class of animals has a QTL or gene effect with a genotype frequency of ƒ sactg , and a polygenic effect denoted by the within class average EBV μ sactg . Selection can involve the EBV of the quantitative trait, the identified QTL or gene, or both of them. Random mating and assortative mating according to genotype or to EBV categories can be used. The deterministic and dynamic model includes different equations that correspond to a general scheme presented in Figure 1. The phenomena underlying the evolution of the population are aging, selection, and matings. The equations describing the scheme are as follows:

Without selection, after year t = 1, the genotype frequency and the average EBV for an animal of sex s, category c, and genotype g do not change between t and t-1.

f f sactg sa c t g sactg sa c t g = = - - - - ( ) ( ) ( ) (
) .

1 1

1 1 m m
Selection. Different selection steps after year t = 1 can be considered for males and females (Figure 1). For the last selection step, males and females are distributed in 2 categories, elite and not elite. The selection rate W sac can vary at each step for males and females. The expression for W sac is

W w f sac s actg s a c t g g = å ( ) ( ) , - - 1 1
where w sactg is the proportion of individuals with sex s, age a, and category c at generation t with genotype g that are selected to become breeding animals. At each step, candidates for selection can be evaluated through their phenotype, genotype, or both. Assuming that EBV are normally distributed, w sactg is equal to where f is the normal cumulative distribution function for variance σ 2 , and β 1g and β 2g are lower and upper thresholds for genotype g (β 1g may be -∞ and β 2g may be +∞) defining the interval selected.

w sactg g s a c t g g s a c t g = - - - - - - - f b m fb m ( ) ( ) , ( ) ( ) ( ) ( ) 2 1 1 1 1 1
When individuals are selected according to EBV and genotype information, the selection thresholds may vary according to the genotype (Figure 2a), and the state variables ƒ sactg and μ sactg are given by

f w W f sactg sactg sac s a c t g = - - ( ) ( ) ; 1 1 [1] m m j b m jb m sactg sa c t g g sa c t g g sa = + - - - - - - - - ( ) ( ) ( ) ( ) ( ) [ ( ) ( 1 1 1 1 1 2 1 c c t g sactg w ( ) )] , -1 rs [2]
where j( ) x is the normal density function, ρ is the accuracy or the correlation between true and polygenic EBV, and σ the genetic SD. Phenotypic selection is a special case of these equations, where β 1 and β 2 are the same for all genotypes (i.e., β 11 = β 12 = β 13 = β 1 and β 21 = β 22 = β 23 = β 2 ; Figure 2b).

In the case of selection for a monogenic trait, the genotypes are ranked because some genotypes are better than others from a biological point of view (e.g., favorable or unfavorable genotypes for a disease). Let g [k] be the kth ranked genotype. These constraints must be verified:

f W f W s a c t g k sac k r s a c t g k sac k ( ) ( ) [ ] ( ) ( ) [ ] - - = - - - = < ³ å 1 1 1 1 1 1
and 1 1 r å because there cannot be more individuals in those classes than in the whole population. The selection proportions are

w i f k r sactg k [ ] ; = £ 1 1 - w i f k r sactg k [ ] = > 0 ; and w W f f sactg r sac sa c t gk k r s a c t g r [ ] ( ) ( ) [ ] ( ) ( ) [ ] = - - - = - - - å 1 1 1 1 1 1 ot therwise.
Selection within the rth genotype was random. The genotype frequency ƒ sactg and the EBV mean μ sactg of the population in generation t are obtained from Eq.

[1] and [2].

Mating. Mating between different classes (selected, elite, and not elite) of females and males can be considered (Figure 1). The probability for a progeny to be of genotype g, given that its parents carry the genotypes h (sire) and k (dam), is τ ghk . The probability that a parent of sex s has genotype g is F s(t-1)g and is defined as

F f s t g s ac sac t g a c ( ) ( ) , , - - = å 1 1 d
where δ sac is the proportion of individuals of age a and class c among the parents with sex s. This quantity depends on demographic constraints (e.g., reproductive age) and breeder decisions (e.g., relative use of progeny tested males). From the parameters τ ghk and F s(t-1)g , different matings (random or assortative) can be considered.

For random mating, none of the characteristics of the parents (e.g., EBV or genotype) are considered in matings. The genotype frequency and the EBV mean for the newborn animals of age 1 and category 1 are where s = 1 for sire, s = 2 for dam, a 1 and a 2 , and c 1 and c 2 are the age and category for the sire and dam.

f F F s tg g hk h k h t k t 11 1 1 2 1 = å - - t , ( ) ( ) ; m t d d s tg s tg ghk a c a c t h h t a c a c f f F f 11 11 1 1 1 1 1 2 2 1 2 1 1 1 1 2 2 2 2 = - - ( ) ( ) (t t k k t a c a c h k a c t h a c t k F - - - - å å å + 1 2 1 1 1 2 1 2 2 1 1 1 1 2 2 ) ( ) , , , ( ) ( ) ( ) , m m
For genotypic assortative mating, the mating may be organized according to the genotypes of the parents. The optimization of these matings may be achieved by choosing a value for α hkt , which is the proportion of newborn animals in generation t from a sire with genotype h and a dam with genotype k. This proportion is constrained by

a hkt k h t F å = - 1 1 ( ) ; a hkt h k t F å = - 2 1 ( ) .
In this situation, the genotype frequency and the EBV mean are given by

f s tg g hk h k hkt 11 = å t a , ; m t a d d s tg s tg ghk hkt a c a c t h h t a c a f f F f 11 11 1 1 1 1 1 2 2 1 2 1 1 1 1 2 2 = - - ( ) ( ) 2 2 2 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 c t k k t a c a c h k a c t h a c t F ( ) ( ) , , , ( ) ( ( - - -
- å å å + m m ) ) ).
k Finally, other assortative matings can be considered. Most often the structure of the parent population includes different groups involved in mating such as males on progeny testing, elite males or females, selected non elite males or females. For instance, males in progeny testing may be mated exclusively to nonelite females. To include assortative matings in the model, reproducers are classified according to mating groups m. F msc(t-1)g is the probability that a parent of group m, and sex s has genotype g. It is defined as

F f msg t msac sac t g a c ( ) ( ) , , - - = å 1 1 d
where δ msac is the proportion of animals of age a, class c, and sex s within the mth group. When mating groups are considered, the equations of genotype frequency and EBV mean are modified accordingly. For instance in genotypic random mating:

f F F s tg g hk m h t m k t m m h k 11 1 1 2 1 1 2 2 1 = - - å å å t ( ) ( ) , ; m t d d s tg s tg ghk m a c a c t h m h t m a c f f F f 11 11 1 1 1 1 1 2 1 2 1 1 1 11 1 2 2 2 = - - ( ) ( ) 2 2 1 2 1 1 1 2 2 2 2 2 1 1 2 1 1 1 a c t k m h t a c a c m m h k a c t h F ( ) ( ) , , , ( ) ( -
- - å å å å å + m m m 2 1 2 2 a c t k ( ) ).
-

Optimization

The deterministic model described above allows global optimization of the selection scheme to maximize the frequency of the desired genotype for a monogenic trait, while minimizing the loss of genetic progress on a polygenic trait. These objectives may be achieved by taking into account the whole population (male and female) or a part of the population (female or male) for a given age. The decrease in genetic progress for the polygenic trait may be considered as a penalty term, which may be defined as a strict or as a progressive penalty. Under a strict penalty, the objective function is put to 0 when the genetic progress is below a threshold. Under a progressive penalty, this term is proportional to the decrease in genetic progress.

The frequencies of the favorable genotype and the average EBV in the population may be considered during all periods of selection (e.g., in the use of discounting) or only in the last year of selection.

The decision variables w sactg and α hkt , describing the evolution of the population, have to be optimized. In our approach, we did not calculate the derivatives of the objective function, differing from the approaches used by [START_REF] Dekkers | Optimizing selection for quantitative traits with information on an identified locus in outbred populations[END_REF] and [START_REF] Manfredi | A dynamic deterministic model to evaluate breeding strategies under mixed inheritance[END_REF]. A genetic algorithm (GA) was used to find the optimum solutions [START_REF] Goldberg | Genetics algorithms in search, optimization and machine learning[END_REF]. A GA is an optimization technique based on an evolution of a population of artificial individuals. Each individual is a point in the research space and is characterized by its "chromosome" C k , which determines the individual fitness h(C k ); k = 1,..., n; n is a population size. The evolution process consists of successive generations. At each generation, individuals with high fitness are selected; the "chromosomes" of selected individuals are recombined and subjected to small mutations. A GA implemented as in [START_REF] Carroll | The genetic algorithm (ga) driver[END_REF] was used in our study.

APPLICATION

This model was applied to an example, where selection for scrapie resistance, which is controlled by a single gene (the PrP gene), was introduced as an additional selection criterion in an already existing dairy sheep selection scheme. It is expected that genetic progress in the polygenic trait (e.g., milk production) will be reduced under this selection objective.

Scrapie is a spongiform encephalopathy in sheep similar to bovine spongiform encephalopathy in bovine and Creutzfeldt-Jakob disease in humans. In sheep, genetic variability of the resistance to scrapie has been demonstrated and is mainly determined by the PrP polymorphisms [START_REF] Elsen | A scrapie epidemic in a closed flock of Romanov[END_REF][START_REF] Fabre | Regulation of ovulation rate in mammals: Contribution of sheep genetic models[END_REF]. Thus, selection on the PrP locus was proposed to improve scrapie resistance in sheep populations. Equations corresponding to this example are given in the Appendix.

The population (Figure 3) was composed of animals, males and females, aged from 0 to 6 yr. Females were selected on their own performance (with a selection rate W 221 ) after their first lactation between 2 and 3 yr of age (Figure 3). The selected females were distributed in 2 categories, elite (W 232 ) and nonelite (1 -W 231 ). Among the young males born from matings between elite reproducers, a fraction W 111 was mated to nonelite females and their EBV for the polygenic trait were estimated after a progeny test. A fraction W 131 of these males was selected 2 yr later. Among the selected males, a proportion W 142 was mated to the elite females to produce young male candidates for selection in the next generation. The replacement of females resulted from mating between nonelite females and elite, nonelite males or males in progeny testing; and between elite females and elite males. Two alleles (favorable vs. unfavorable) were considered for the Prp gene; thus, 3 genotypes exist (g = 1 favorable genotype, g = 2 intermediary genotype, and g = 3 unfavorable genotype). The PrP genotypes were known for females and males. Only males were selected on their PrP genotype and on their EBV value before and after progeny testing. The proportion δ of males in progeny test among reproductive males was equal to 0.2. The proportion λ a of females with age a (4, 5, and 6 yr) among reproductive females was 0.4, 0.3, and 0.3, respectively. This selection scheme was applied during 15 yr (t = 15) with the following parameter values: W 221 = 0.8; W 232 = 0.1; W 111 = 0.225; W 131 = 0.2; W 142 = 0.3; σ = 36. The accuracy for females (ρ f ) was 0.73. The accuracy for males before and after progeny test was 0.56 (ρ m1 ) and 0.77 (ρ m2 ), respectively. The accuracy for elite males (ρ m3 ) was 0.89. The GA parameters were as follows: population size = 100; number of generations = 1,000; creep mutation probability = 0.02; crossover probability = 0.5; jump mutation probability = 0.01.

The aim was to maximize scrapie resistance, minimizing the loss of genetic progress in milk production. The objective function chosen was the frequency of homozygous favorable females (s = 2, g = 1) with a penalty on the genetic progress, constraining it not to be less than a percentage π of the progress obtained without scrapie selection (ΔG T ). The objective function can be written as follows: gives more importance to younger females. All of the females were considered in the objective function because all of them will participate in the renewal. The second term is proportional to the difference in genetic progress obtained in this selection scheme and without selection on scrapie resistance. First, the model was used with different initial frequencies of the favorable genotype without any constraint on genetic progress (π = 100%). Three initial frequencies of the favorable genotype were considered (0.03, 0.3, and 0.69). Then, situations with different constraints on genetic progress were considered while fixing the initial frequencies. Finally, simplifications of the strategy were explored to make the optimized selection procedures more practicable for farms.

Effect of Different Initial Frequencies Without Constraint on Genetic Progress

Whatever the initial frequency, the unfavorable genotype disappeared after 15 yr of selection (Table 1). The loss of genetic progress was more important (18.1%) with a low initial frequency of the favorable genotype than with a high initial frequency (2.0%). This loss is much greater in the first few years, and impacts in the first few years are very important if counting discounted returns. The optimal selection proportions and mating rules evolve during the 15 yr process. The favorable genotype frequency increased, keeping a high selection proportion of the homozygous-resistant males before and after their progeny test. When the initial frequency of the favorable genotype (0.03 or 0.3) was low, the selection proportions of males carrying this genotype were high (0.9 and 0.7) during the first years to rapidly fix this genotype in the sires. These selection proportions decreased progressively when all sires became resistant. When the initial frequency of the favorable genotype (0.69) was high, the selection proportions for the favorable genotype were less, in particular before progeny testing (0.32 instead of 0.9 and 0.7). Moreover, the selection proportions after the progeny test were constant from the beginning, whereas they were constant only after yr 9 and 4 for the case of low frequencies (0.03 and 0.3). Whatever the initial frequencies of the favorable genotype, none of the susceptible males were selected, eliminating all of them from the beginning. A fully favorable population of sires was reached more rapidly with a high initial frequency of the favorable genotype (yr 3) than with a low frequency (yr 8).

The reduction of the unfavorable genotype frequencies in the dam population occurred very slowly because (i) dams were selected just once, (ii) the selection threshold was the same across genotype classes, and (iii) the selection pressure was low. With a high initial frequency of the favorable genotype, the objective was reached and the dam population was fully resistant. However, with a low frequency, only sires were resistant at the end of yr 15, with the unfavorable genotype still segregating in the dam population.

Effects of Different Constraints on the Loss of Genetic Progress

In contrast to the situation described above in which no constraint was put on genetic progress, a 10% maximum loss of genetic progress at the end of the process was allowed (π = 90%) for the situation with the decreased initial frequency (0.03). The case with the ini-tial low frequency of the favorable genotype was studied because the loss of genetic progress with this frequency was the most important (18.1%). In this situation, the optimal selection proportions of males with a favorable genotype were less and fluctuated between high and low values (Figure 4). These fluctuations can be explained by the fact that the genetic progress must be kept over a threshold. Each year, the selection intensity varies to compensate for the loss in genetic progress. Contrary to the previous case, the selection proportions of favorable and heterozygous genotypes were high and similar (0.7). The selection proportions for homozygous unfavorable sires were null. After the elimination of unfavorable genotype carriers, the selection proportions of the favorable genotype (20 to 30%) were greater than for the heterozygous genotype (5 to 20%). The heterozygous genotype was conserved for a longer time than without any constraint on the genetic progress. The objective of achieving a fully resistant population of sires was reached less rapidly with 10% of maximum loss of genetic progress (yr 11) than without any constraint on genetic progress (yr 8). In the dam population, proportions of favorable homozygous and heterozygous genotypes were similar. Dams with an unfavorable genotype were almost entirely eliminated, being kept at less than 5%. Thus, the optimal strategy of selection depends on the constraints put on genetic progress. If the priority is to reach a population fully resistant to the disease, the loss of genetic progress may not be essential; the selection on genotype information is drastic at the beginning of the process and the animals are quickly fully resistant. If a more important penalty is put on the loss of genetic progress, the selection changes, with cycles of high and low selection proportions for the favorable genotype. Eventually, the unfavorable genotype disappears and the population is divided between favorable homozygous and heterozygous genotypes.

In the previous case (Figure 4a), the selection proportions decreased gradually as the population became progressively resistant. With a constraint on genetic progress, the fluctuation of selection proportions was larger (Figure 4b). The selection proportions of the favorable genotype were high during the first years, inducing an increase in resistance during this period; they were less than with previous cases to maintain acceptable genetic progress. This optimal strategy would not be practicable for breeders because of the annual varia- tions of the selection proportions. However, a detailed analysis of selection proportions and assortative mating during the 15 selection years suggests some simplifications.

Simplifications of the Optimal Strategy

Two cases were analyzed: (1) a low initial frequency of the favorable genotype and a maximum 10% loss of genetic progress accepted after 15 selection years and (2) a low initial frequency of the favorable genotype without any constraint on the loss of genetic progress. The results are given in Table 2. The first case shows the evolution of the objective function without any penalty on loss of genetic progress. The second case shows the evolution of the objective function with a maximum loss of 10% in the genetic progress.

In the optimal strategy, the selection proportions of the males before progeny testing (W 111 , Figure 3) varied between years and thus needed to be optimized. On the contrary, some selection proportions were constant after a few years of selection, suggesting some simplifications.

1. Within genotype selection proportions of males after progeny testing: The stabilization of these Optimizing multiple-trait selection selection proportions is late, after the 11th selection year. However, the fixation of these selection proportions was tested. The values of the objective function were less than in the optimal strategy. Thus, these selection proportions have to be optimized. 2. Within genotype selection proportions for elite males: The results of the previous optimization suggest a suboptimal strategy where these selection proportions are constant. The objective function value obtained with this simplification was similar to the optimal one (Table 2). Consequently, it appears that it is not critical for within genotype selection proportions for elite males to be optimized every year.

Another question was to check if assortative mating based on the genotypes was necessary or not. The slight difference in the objective function value between the fully optimized scheme and the simplified one shows that mating optimization was not necessary.

Globally, 2 simplifications were thus possible: fixed selection proportions for elite males and random mating. The case combining simplifications gave a value of the objective function similar to the optimal one. Moreover, the penalty weight of the loss on genetic progress was identical with or without simplifications. Implementing other simplifications could give a reduced value of the objective function than the one obtained in the fully optimized scheme, but these were not considered here.

In our example, we proposed that the objective was to maximize the genotypic frequency of the favorable female genotypes with a penalty on genetic progress. Avoiding loss of genetic progress increases the time needed to reach fixation of the favorable genotype. For example, sires are all resistant at the end of yr 8 or after yr 11 without any constraint or with a maximum loss of 10% of genetic progress, respectively. Other objective functions are possible and must be adapted to the aim of the breeder. For example, the frequency of males may be considered instead of the frequencies of females. Males have a more important impact on the selection scheme. In this example, the objective was to keep the homozygous genotype; however, in the case of breeds with a risk of extinction, it could be preferable to keep heterozygote genotypes. Another option could be to consider the whole process, rather than only the final state of the population, possibly using a discounting factor if sooner is better.

DISCUSSION

In this paper, a method was developed to optimize selection on an identified QTL or gene and a quantitative trait over multiple generations. The breeding program modeled assumed assortative mating and overlapping generations. This modeling may easily be adapted to a variety of situations concerning the underlying genetic model and the selection scheme. In this study, 2 alleles were considered, but the methodology can consider a multi-allelic case. However, the number of alleles (and genotypes) should be limited. The number of optimized parameters increases in an exponential manner with the number of alleles considered. For instance, when 3 genotypes (2 alleles) are considered, 10 parameters have to be optimized, and if 10 genotypes (4 alleles) are considered, the optimization problem would involve 108 parameters. Only the case with an additive QTL or gene was considered here, but dominance could be included. The method can also be extended to multiple QTL or genes with any type of linkage between them (epistasis).

Different methodologies to solve multiple-generation selection problems in animal breeding are possible. In this study, a GA was used to solve the optimization problem. Genetic algorithms are more flexible when additional constraints have to be added than optimal control theory, the method used by [START_REF] Dekkers | Optimizing selection for quantitative traits with information on an identified locus in outbred populations[END_REF], because to optimize selection the derivative of the selection criterion has to be calculated with optimal control theory. Use of a GA bypasses this difficulty.

Additive variance was assumed to be constant over generations, and genotyping errors and relationship errors were assumed to be nonexistent. The reduction of the additive variance by selection could be considered in the model.

The strategy developed here consisted of selecting animals that were resistant to a particular disease to decrease the number of infected animals. The aim was to reduce the incidence of the disease, while keeping the genetic progress on the traditional production traits. In this model, inbreeding was not considered. A possibility for taking this into account would be to add the notion of family for males. Males of one family participate for the renewal of the males for their family and males of different families participate for the renewal of the females. This possibility would allow a certain genetic variability to be maintained. Domestic animal diseases might represent a risk to human health. Thus, identification of genes involved in disease resistance is an important genetic research subject. The scrapie case is an example where a national selection program for scrapie resistance was implemented as a precautionary measure. This dynamic and deterministic model was applied here in the scrapie case; however, it can be extended to other genes and selection schemes. For example, genes affecting important performance traits such as adiposity or meat quality in pigs (Le [START_REF] Roy | Evidence for a new major gene influencing meat quality in pigs[END_REF]Larzul et al., 1997a;[START_REF] Hamilton | The effect of the Halothane and Rendement Napole genes on carcass and meat quality characteristics of pigs[END_REF] or prolificacy in sheep [START_REF] Davis | Major genes affecting ovulation rate in sheep[END_REF][START_REF] Fabre | Regulation of ovulation rate in mammals: Contribution of sheep genetic models[END_REF] could use this model. Moreover, this deterministic model could evolve to a stochastic model for a limited number of breeding animals in a small population. Our model would need to be simplified for use in stochastic simulation because stochastic simulations with a large number of choice variables can be impractical. (  ) .

APPENDIX: EQUATIONS OF THE EXAMPLE

Two-year males after progeny testing: ).

Figure 1 .

 1 Figure 1. Selection scheme description with individual classes (rectangles), selection steps (•), and selection proportion W sac (sex s = 1, 2; age a = 1,...,a s ; category c = 1,2).

Figure 2 .

 2 Figure 2. Selection threshold for genotype g1 (…), g2 (---), and g3 (-•-) under combined genotypic and phenotypic selection (a) and phenotypic selection (b).

.

  The 1st term is the mean of homozygous favorable females of the elite (c = 1) and non elite (c = 2) group weighted by the coefficient 1 a (a is the age), which

Figure 3 .

 3 Figure 3. Population description with 7 categories (rectangles), 7 mating paths (thick lines), selection steps (dotted lines), and 5 selection proportions W sac (sex s=1, 2; age a=1, ..., a s ; category c=1,2).

Figure 4 .

 4 Figure 4. Selection rate evolution for the favorable genotype (g = 1) without (a) and with (b) constraint in loss of genetic progress before progeny test (-), after progeny test ( …. ), and for elite males (--).

Table 1 .

 1 Final genotype frequencies for young females, objective function, and loss of genetic progress for 3 initial frequencies (genotype 1, favorable genotype; genotype 2, intermediary genotype; genotype 3, unfavorable genotype) without any constraint on loss of genetic progress

		Initial frequency		Final frequency for young females
								Loss of genetic
	Genotype 1	Genotype 2	Genotype 3	Genotype 1	Genotype 2	Genotype 3	Objective function	progress, %
	0.03	0.28	0.69	0.77	0.23	0.00	0.68	18.10
	0.30	0.50	0.20	0.91	0.09	0.00	0.88	6.40
	0.699	0.28	0.03	0.97	0.03	0.00	0.96	2.00

Table 2 .

 2 Value of the objective function with some simplifications in 2 cases without constraint on loss of genetic progress (L-0) and with 10% of loss of genetic progress (L-10)

	Item

This work was supported by the European Union project QLRT-2000-01733 "Scrapiefreesheep" and by the EU Network of Excellence, Neuroprion

.2 Corresponding author: Anne.Devalle@toulouse.inra.fr Received January23, 2008. Accepted November 18, 2008.

at INRA Institut National de la Recherche Agronomique on July 31, 2013 www.journalofanimalscience.org Downloaded from

Costard et al.

2 1 Costard et al.


X Xande

C Re ´gnier

H Archime `de

B Bocage

J Noblet

D Renaudeau

Nutritional values of sugarcane products in local Caribbean growing pigs

Keywords: Creole pig, sugarcane products, digestibility, energy value Implications

A total of 24 castrated male Creole were used for digestibility studies on three sugarcane (SC) products: final molasses, SC juice and ground SC. Digestibility of macronutrients were determined in three consecutive experimental trials between 35 and 60 kg BW. The first trial measured the effect of a constant rate of incorporation of those SC products in a control diet (23% on a dry matter (DM) basis) on digestibility of energy and nutrients. The second and the third trials were designed to determine the effects of increasing rates of inclusion of SC juice and ground SC in the control diet on the digestibility of nutrients and energy. The DM content of molasses, SC juice and ground SC were 74.3%, 19.3% and 25.8%, respectively. Free sugar contents were 73.8%, 81.6% and 51.5% of DM for molasses, SC juice and ground SC, respectively. In contrast with molasses and SC juice, NDF content of ground SC was very high (40.3% DM). Energy digestibility coefficients (DC) were 99.0% and 83.6% for SC juice and molasses, respectively. For ground SC, amounts and composition of intakes differed from feed allowance as a consequence of chewing-then-spitting out most of the fibrous contents of ground SC. Expressed as a percentage of energy intake and energy allowance, DC of energy for ground SC were 68.6% and 31.9%, respectively. On an intake basis, digestible energy (DE) and metabolisable energy (ME) values were higher for SC juice (17.3 and 17.2 MJ/kg DM, respectively) than for molasses (13.1 and 12.6 MJ/kg DM, respectively) or ground SC (12.3 and 11.8 MJ/kg DM, respectively). On an allowance basis, the corresponding values for ground SC were only 5.7 and 5.6 MJ/kg DM, respectively. The gradual inclusion rate of SC juice in the diet up to 66% resulted in a linear increase of the DC of the diet organic matter and energy (P , 0.001) by 0.10% per 1% in SC juice DM. On the other hand, the partial substitution of the control diet by ground SC up to 74% resulted in a linear (P , 0.05) reduction of digestibility of nutrients and energy. Each 1% increase of ground SC incorporation rate resulted in a 0.13% and 0.61% linear decrease of DC of the energy, expressed as a percentage of energy intake or energy allowance, respectively. In conclusion, our study provides updated energy values of SC products usable as energy sources for feeding pigs.

Introduction

Cereal grains which are the basis of livestock production in the more-developed countries face a competing demand to -E-mail: David.Renaudeau@antilles.inra.fr feed the increasing human population [START_REF] Preston | Research, extension and training for sustainable farming systems in the tropics[END_REF]. This scenario will give opportunities to alternative feeds that can replace cereals in livestock diets. Sugarcane (SC) is a perennial tropical crop with a high-energy yield per unit area (80 tons dry matter (DM)/ha; [START_REF] Preston | The greenhouse effect and its implications for world agriculture[END_REF]. In several tropical countries (Cuba, Dominican Republic, Costa Rica, Guadeloupe, Vietnam), many studies and development of feeding strategies for pig production have been based on the use of this local resource and/or its byproducts. Most studies were focused on the growth performance obtained when pigs were fed SC-based diets, especially as juice or molasses but also as ground cane stalks [START_REF] Preston | Sugar cane products as energy sources for pigs[END_REF][START_REF] Gonza `lez | Growth performance of pigs feed sugarcane juice (Saccharum officinarum) and mulberry leaf meal (Morus alba)[END_REF]Xande ét al., 2009). The determination of digestible and metabolisable energy (ME) values of these SC products is a first step to their evaluation as feedstuffs for pig feeding. However, there is little information on nutritional values of SC products available that can allow practical feed formulation of mixed diets. Regarding those products, digestive utilisation of SC molasses in pigs is the most described in the literature (Ly and Preston, 1969; Christon and Le Dividich, 1978; Bayley et al., 1983). In contrast, little is published about the digestive utilisation of nutrients and energy of SC juice and ground SC stalks.

In SC production area, small scale farmers traditionally use whole or chopped SC as a feeding source for pigs (Bravo et al., 1996). The Caribbean native pigs, that is, Creole (CR) pigs are well-known for their rusticity and according to their low nutrient requirements [START_REF] Renaudeau | Influence of energy intake on protein and lipid deposition in Creole and Large White growing pigs in a humid tropical climate[END_REF], they are likely to have comparative advantages over 'exotic' high-performance genotypes, when the feeding system is based on unconventional feedstuffs such as SC products and by-products.

The objectives of our study were: (1) to measure the in vivo total tract digestibility of dietary energy or nutrients of SC final molasses, SC juice and ground SC stalks in growing CR pigs, (2) to measure in vivo the effect of increased inclusion rates of SC juice or ground SC stalks in the diet, on total tract digestibility values in growing CR pigs.

Material and methods

Care and use of animal were performed according to the certificate of authorisation to experiments on living animals, number A-971-18-01 (issued by the French ministry of agriculture to the head of the experiment unit).

Experimental design and animal management Nutritional values of SC products (final molasses, juice and ground cane stalks) were studied on a total of 24 castrated CR pigs at the experimental facilities of the Institut National de la Recherche Agronomique in Guadeloupe (latitude 168N, longitude 618W). The experiment was conducted in two replication of 12 pigs each. Within each replication, three blocks of four littermates were chosen where each littermate was randomly assigned to one dietary treatment. All in all, 6 replicates per dietary treatments were obtained. At about 30 kg BW, pigs were moved to individual digestibility cages in an open front experimental room. Climatic parameters were not controlled and followed those of the outdoor conditions. Nutritional values of SC products (final molasses, SC juice and ground SC) were studied in three consecutive experimental trials. The first trial was designed to measure the effect of a constant rate (23% on a DM basis) of incorporation of SC products (SC molasses, SC juice and ground SC) in a control soybean meal-corn diet (19.8% DM of CP and 16.6 MJ DE/kg DM; DE, digestible energy) on feed digestibility. The second and the third trials were designed to determine the effects of increasing rates of inclusion of SC juice and ground SC on digestibility of nutrients and energy. Within each trial, pigs were adapted to the diet for 10 days before total collection of faeces and urine for 8 days. During the adaptation and the collection periods, the amount of feed offered daily was 35 g DM/kg per BW. The basal diet was a commercially available piggrower feed in pellet form (Table 1). The molasses were also produced commercially (Gardel SA, Moule, Guadeloupe, French West Indies). Twice a week, 1 ton of fresh SC was delivered to our experimental facilities, cleaned and Mean chemical composition measured on a total of 18, 6, 24 and 24 samples for the soybean meal-corn control diet, SC molasses, SC juice and ground SC, respectively. milled for juice production or ground in small size particles (less than 1 cm). The SC juice and the ground SC were stored at 48C to prevent any fermentation reactions. The average chemical composition of the SC products is presented in Table 1. For each experimental trial, one littermate was fed with the control diet and the other three littermates were fed with an experimental diet in which a constant (trial 1) or a gradual amount (trials 2 and 3) of the control diet was replaced by a SC product. The experimental diets were prepared by mixing molasses, SC juice or ground SC with the basal diet (8, 8 and 13 g DM/day per kg BW; trial 1), various amounts of SC juice with basal diet (8, 16 and 24 g DM/day per kg BW; trial 2), and various amounts of ground SC with basal diet (13, 26 and 39 g DM/day per kg BW; trial 3) just before feeding. For ground SC, the following protocol was applied for the distribution of the diet: first, the control diet was distributed and once it was completely consumed, the ground SC was distributed. According to [START_REF] Xande | Influence of sugarcane diets and a high fibre commercial diet on growth and carcass performance in local Caribbean pigs[END_REF], with a ground SC diet pigs show a specific 'sucking-spitting' feeding behaviour and the DM extraction rate, that is, DM intake/DM offered, of ground SC averaged 62%; this ratio was taken into account in order to allow a constant DM intake of SC products (i.e. 8 g DM/day per kg BW; trial 1) or a similar variation of DM intake from ground SC in trial 3 than from SC juice in trial 2 (8, 16 and 24 g DM/day per kg BW). Between each experimental trial, each littermate was randomly assigned to one dietary treatment. All animals had free access to water from one individual low-pressure nipple drinker.

Measurements

All the pigs were weighed at the beginning and at the end of the adaptation period, and at the end of the collection period. Every morning, any feed refusal and spillage were collected. Samples of allowed feed and refusals were dried at 1038C for 24 h to measure the DM content. One sample of the control diet was also taken daily and pooled at the end of the sampling period for DM determination and further chemical analyses. Samples of molasses, SC juice and ground SC were daily and individually collected, stored at 2208C and pooled at the end of the collection period. One representative sample of SC products was dried at 658C for 96 h for further chemical analyses. During the 8-day collection period, faeces and urine were daily and individually collected and stored at 48C. Urine was collected into a flask containing sulphuric acid (0.1 Nitrogen (N); 10% v/v) in order to avoid ammonia losses during collection and storage. Faeces and urine were separately weighed, homogenised and sub-sampled at the end of the collection period for analysis (digestibility sample). One faeces sample was heat dried (48 h at 1038C) for DM determination and the second was freeze-dried for further chemical analyses.

Chemical analyses

The diet samples were analysed for DM, ash, organic matter (OM), crude protein (CP, N 3 6.25), ether extract (EE) and starch, according to the AOAC methods (AOAC, 1990), for free sugars according to [START_REF] Mth | Adaptation de la me ´thode a `l'orcinol sulfurique au dosage automatique des glucides neutres totaux: conditions d'application aux extraits d'origine ve ´ge ´tale[END_REF] and for gross energy (GE) content using an adiabatic bomb calorimeter (IKA, C5000, Staufen, Germany). Dry faecal samples were analysed for DM, ash, EE and CP and fresh samples of urine for N. Cell wall components (NDF, ADF and ADL) in diet samples were determined according to the Van Soest and Wine method (1967).

Calculations and statistical analyses From the results of the digestibility trial, apparent digestibility coefficients (DC) of DM, OM, CP, ash, EE, free sugars and energy were calculated for each pig. In the case of ground SC, it was expressed relative to allowance or intake quantities. DE content was estimated as the difference between measured GE and estimated energy loss in faeces (Noblet, personal communication).1 ME content of diets was calculated as the difference between DE and energy loss in urine estimated from N loss (g/day) according to the equation of Le [START_REF] Goff | Comparative total tract digestibility of dietary energy and nutrients in growing pigs and adult sows[END_REF].2 N retained was obtained as the difference between N intake and N losses in faeces and urine.

In a first approach, we statistically controlled that measurements performed in trials 2 and 3 were not affected by the dietary treatment offered in trials 1 and 2, respectively. For that purpose, we used the MIXED procedure of SAS (1997) with an unstructured variance co-variance matrix. According to Wald Z test (SAS Institute, 1997), the covariance estimates were not significantly different from zero. We concluded there was no correlation between two successive measurements carried out on the same animal, suggesting that the adaptation period allowed suppressing the remnant effects. Then, in a second approach, we analysed the results obtained for each trial independantly using an ANOVA (Proc GLM, SAS Institute, 1997) including the effects of diet, replicate, block within replicate and the interaction between diet and replicate. Comparison of means was performed according to the PDIFF option using Tukey test for contrasts (SAS Institute, 1997). In trial 1, the digestive utilisation of SC products was calculated according to the difference method (Noblet and Shi, 1994). Assuming that energy and nutrient digestibility of the control diet was constant in the experimental diets, we calculated DC of energy and dietary chemical fractions of SC products from the rate of incorporation in feed and the DC of control and mixed (control 1 SC products) diets. For trials 2 and 3, linear or quadratic regressions between DC measured on complete diet and rate of incorporation of SC juice or ground SC were calculated. According to that chemical composition of allowed and intake feed for dietary treatments including ground SC, DC of ground SC were calculated on a intake basis (method 1) and allowance basis (method 2).

Results

General aspects and chemical composition of the dietary ingredients

One pig fed diet 4 (control 1 ground SC) was removed during the first replicate of trial 1 after 5 days of sampling period because of leg problems, which had consequences on its daily consumption. For trial 2, this pig was replaced by a littermate pig with a similar initial BW. The results obtained with another pig fed diet 2 (control 1 molasses) during the second replicate of trial 1 were removed from the ANOVA because of 2 days of diarrhoea observed after the 5th day of sampling period. This pig was successfully treated and then used in the following two trials. For both replicates, sampling period in trial 3 lasted only 7 days instead of 8 days for practical reasons (day off in the first replicate), and weather reasons (tropical hurricane in the second replicate).

As shown in Table 1, ground SC refusal composition was obviously different from allowed ground SC composition, with a chewed aspect (trial 1 and 3). With ground SC, pigs showed a peculiar feeding behaviour: they chew the cane stalks to extract the juice and then spit out most of the fibrous residue. In connection with a ratio intake/allowance for ground SC DM of 50.8%, the composition of DM intake from ground SC was different from the DM composition of ground SC offered; NDF and ADF contents decreased from 40.3% to 21.2% and from 26.6% to 14.2%, respectively, while free sugar contents increased from 51.5% to 78.0%. In addition, the amount of ground SC refusals linearly increased when ground SC allowance increased from 0% to 74% of total feed offered (trial 3; Table 6). Then, expressed as a percentage of ground SC allowance, DM extraction rate from ground SC (DM intake/DM allowed) was maintained constant and averaged 36%. In SC products, measured GE was numerically lower in SC molasses than in SC juice and ground SC allowed and intake (15.7 v. 17.7 MJ/kg DM, respectively).

Effect of SC products on total tract digestibility of energy and nutrients (trial 1) According to the experimental design, there was no statistical difference for average BW and total DM intake (P . 0.05) between diets (33.6 kg BW and 33.1 g DM/day per kg BW, respectively) during the first trial (Table 2). In this trial, the faeces DM was not affected by the inclusion of SC products in the control diet (P . 0.05). The incorporation of molasses did not significantly affect the total tract digestibility of DM, OM and energy when compared with the control diet. However, DC of CP was lower (82.7% v. 86.4%; P , 0.01) and DC of EE and sugars were higher than in the control diet (88.3% v. 82.1%, P , 0.05; and 97.6% v. 96.1%, P , 0.001, respectively). In comparison with the control treatment, the inclusion of SC juice in the diet increased DC of DM, OM, free sugars and energy (P , 0.001). For the experimental diet in which a fraction of the control diet was replaced by ground SC, DC of nutrients and energy were calculated on nutrients or energy intake basis; when compared to the control diet, the DC of DM, OM and energy were significantly reduced (83.6% v. 87.5%, 85.3% v. 89.6% and 84.6% v. 88.7%, respectively; P , 0.05). The ME/DE ratio was not affected (P . 0.05) by inclusion of molasses or ground SC in the control diet; it averaged 96.0%. This ratio was significantly higher (P , 0.01) with SC juice treatment (i.e. 96.5%). According to their low N content, daily N intake in diets with SC products was lower than with the control diet (28.0 v. 38.7 g/day; P , 0.01). Whatever the dietary treatment, , 50% of N intake was retained.

Estimated DC of nutrients and energy of SC products using the difference method are presented in Table 3. The DC of OM and energy of molasses averaged 84.4% and 83.6%, respectively. The corresponding values for SC juice were equal to 99.3% and 99.0%, respectively. The DC calculated for ground SC offered or consumed differed significantly with lower values for ground SC offered. On average, DE values of the control diet, molasses, SC juice and ground SC intake and offered were 16.55, 13.11, 17.34, and 12.31 and 5.72 MJ/kg DM, respectively.

Effect of gradual increase of SC juice on total tract digestibility of energy and nutrients (trial 2) The effects of a gradual increase in the rate of incorporation of SC juice (trial 2) on total tract digestibility of nutrients and energy are presented in Table 4. There was no statistical difference in average BW (P . 0.05) between diets. SC juice incorporation in diet increased from 0 to 66 g/100 DM between diets 1 and 4, respectively. The response of SC juice incorporation rate on DC was linear and the quadratic effect was not significant (P . 0.05). Despite an important numerical increase (33.6% to 42.1% between diets 1 and 4), faeces DM was not affected by the level of SC juice. The gradual decrease of N retained from diet 1 to 4 was related to the dilution of the N source from control diet with the progressive inclusion of SC juice. Except for CP and EE, the gradual inclusion rate of SC juice from diet 1 to diet 4 increased the DC of all components (P , 0.001). The DC of energy increased from 88.9% to 95.4%. In contrast, the DC of EE significantly decreased (P , 0.01) from 88.9% to 80.5% between diets 1 and 4. The ME/DE ratio increased from 95.9% to 97.6%, respectively, between diets 1 and 4.

According to the regression analysis of the DC of the nutrients or energy with the rate of SC juice inclusion, each 1% increase of SC juice inclusion rate resulted in a linear increase of 0.10% of the DC of OM and energy (Table 5). In contrast, the digestibility of CP was not affected by SC juice levels in diet. From these relationships, DC of nutrient and energy of SC juice can be calculated; they averaged 99.8%, 85.4% and 99.1% for OM, CP and energy, respectively. These values are similar to the values obtained in trial 1, (i.e. 99.0% for energy). Each 1% increase of SC juice inclusion rate resulted in a linear increase of 0.007 and 0.011 MJ/kg DM of DE and ME, respectively; average DE and ME values of SC juice obtained by regressions were then 17.32 and 17.08 MJ/kg DM, respectively.

Xande ´, Re ´gnier, Archime `de, Bocage, Noblet and Renaudeau Effect of gradual increase of ground SC on total tract digestibility of energy and nutrients (trial 3) The effects of a gradual increasing rate of incorporation of ground SC (trial 3) on nutrient intake and extraction rate are presented in Table 6. Average BW was not significantly affected (P . 0.05) by ground SC incorporation level. The total DM intake was significantly reduced between diets 1 and 4 in connection with the increase of ground SC refusals. Expressed in g/100 g ground SC intake, the nutrient extraction rate was not influenced by the increase of No control diet was refused whatever the dietary treatment.

5 Digestibility coefficients of nutrients 5 digested nutrients or energy expressed as a percentage of nutrient or energy intake. Values calculated according to the difference method: digestibility coefficients (DC) of energy and organic matter and CP of SC products were calculated from the rate of incorporation in feed and the DC of control and mixed (control 1 SC products) diets and expressed as a percentage of nutrient or energy offered.

2

Values calculated according to the difference method and expressed as a percentage of nutrient or energy intake.

3 DC of free sugars was found 100% whatever the SC product considered.

Nutritional values of sugarcane products in pigs ground SC incorporation rate. As a consequence, the amount of daily nutrient or energy intake from ground SC linearly increased with the rate of ground SC incorporation.

As the chemical composition of ground SC refusals differed from that of ground SC allowance with an increase of fibre content and a decrease of soluble free sugars, the DC was calculated on ground SC allowance basis or on actual ground SC intake. The increase of ground SC inclusion in the diet from 0% to 74% resulted in a linear decrease (P , 0.05) of faecal DM from 33.8% to 17.4% and in a linear reduction (P , 0.05) of DM, OM and energy digestibility coefficients (Table 7). In contrast, with a progressive inclusion of ground SC, the free sugars DC increased when expressed on an intake basis (96.4% v. 98.7%; P , 0.001).

The regression analysis of the nutrients DC with incorporation rate of ground SC in the diet is presented in Table 8. Whatever the expression of the DC, a linear decrease of the DC was shown for OM, CP and energy. Each 1% increase of ground SC incorporation rate resulted in a 0.12% and 0.13% linear decrease of the DC of OM and energy, respectively, when expressed as a percentage of energy intake (method 1). The average DC of energy, DE and ME values were lower when method 2 was used instead of method 1 (28.2% v. 77.6%,4.90 v. 13.58 MJ/kg DM and 4.74 v. 13.15 MJ/kg DM, respectively).

Discussion

Nutritional and energy values of SC juice

The chemical composition of SC juice determined in this study is similar to the values published in Brazilian tables [START_REF] Rostagno | Brazilian tables for poultry and swine: composition of feedstuffs and nutritional requirements, 2th edition[END_REF]. Total soluble sugars represented the main part of the identified OM (i.e. 83%). In these sugars, sucrose is the predominant carbohydrate (about 90%) and fructose and glucose represent less than 10% [START_REF] Meade | Cane sugar handbook; a manual for cane sugar manufacturers and their chemists, 10th edition[END_REF]. The non-sugar OM in SC juice (i.e. 17.0%) is represented by chlorophyll, tannins, wax and fibre [START_REF] Meade | Cane sugar handbook; a manual for cane sugar manufacturers and their chemists, 10th edition[END_REF]. In our experiment, these non-sugars OM content in SC juice was about 16.8 g/100 g DM.

Our results show that OM and energy digestibility of SC juice is close to 100% according to its high content of water soluble sugars, which are known to be entirely digestible (Noblet et al., 2003). Logically, total tract digestibility of energy of the diet is linearly enhanced as more as the inclusion rate of SC juice in the diet is increased. This result also suggests that SC juice does not interact with the control corn-soybean meal diet. However, our DE and ME values for SC juice (17.3 and 17.1 MJ/kg DM) are higher than those calculated in the Brazilian tables (15.9 and 15.2 MJ/kg DM; [START_REF] Rostagno | Brazilian tables for poultry and swine: composition of feedstuffs and nutritional requirements, 2th edition[END_REF] despite a GE value similar to ours (17.1 v. 17.5 MJ/kg DM). In fact, in Brazilian tables, DE and ME values were not measured but estimated from the chemical composition of SC juice. From that, it can be suggested that equations used to estimate energy values of SC juice in those tables underestimate the actual values. Our results also show a higher DC of OM for the SC juice than in the Brazilian tables (99.5% v. 93.4%;[START_REF] Rostagno | Brazilian tables for poultry and swine: composition of feedstuffs and nutritional requirements, 2th edition[END_REF].

Nutritional and energy values of final SC molasses

The chemical composition of molasses is closely dependant on the technological process applied for the extraction of raw sugar. [START_REF] Bayley | Utilisation of sugarcane final molasses by the pig: energy metabolism[END_REF] showed that the range for ash and soluble sugars contents in Cuban commercial conditions was from 5.7 to 16.3 g/100 DM and from 46 to 76 g/100 DM, respectively. In our study, the SC molasses contained 15.1 g/100 g DM of ash and 71.0 g/100 g DM of soluble sugars (sucrose, fructose and glucose). During the crystallisation processes, non-sugars OM were concentrated in molasses and represented more than 13% of the total OM. The DC of OM and energy are lower in molasses than in SC juice (215%). This result can be related to the high ash content that increases endogenous energy losses (Noblet and Shi, 1994) and the low digestibility of the nonsugars OM in molasses. Comparing the digestive utilisation of SC molasses with a mixture of soluble sugars representative of sugars composition of molasses, [START_REF] Bayley | Utilisation of sugarcane final molasses by the pig: energy metabolism[END_REF] showed a reduced DC of energy with SC molasses.

In fact, [START_REF] Figueroa | Ileal and total digestibility studies in pigs fed molasses type A or starch diets supplemented with torula yeast or soybean meal[END_REF] showed that the non-identified OM in SC molasses is poorly digested, which considerably reduces the dietary DE density of this material. In this study, the DC for N was higher than the value reported in the INRA tables (68.1% v. 40.0%; [START_REF] Sauvant | Tables de composition et de valeur nutritive des matie `res premie `res destine ´es aux animaux d'e ´levage[END_REF].

However, these values should be used with caution according to the low accuracy of the N digestibility due to both low N content in molasses and possible effects of molasses products (minerals) on digestion and transit [START_REF] Brooks | Effect of sex, fat, fibre, molasses and thyroprotein on digestibility of nutrients and performance of growing swine[END_REF][START_REF] Christon | Utilisation de la me ´lasse de canne a `sucre dans l'alimentation du porc: essai d'interpre ´tation des acquisitions re ´centes[END_REF]. The mechanism by which protein digestibility was depressed by molasses is not fully understood. [START_REF] Christon | Utilisation de la me ´lasse de canne a `sucre dans l'alimentation du porc: essai d'interpre ´tation des acquisitions re ´centes[END_REF] reported that the depressive effect of molasses on N retention in rat is mainly related to an excretion of endogenous N in faeces. They concluded that this high endogenous N losses could be explained an abrasive effect of ash and minerals like potassium (K).

The energy DC (83.6%) is similar to the value reported in the French tables (85%; [START_REF] Sauvant | Tables de composition et de valeur nutritive des matie `res premie `res destine ´es aux animaux d'e ´levage[END_REF]. The DE values of molasses (13.1 MJ/kg DM) are in accordance with Bayley et al. (1983) study (13.6 MJ/kg DM) and with French (Sauvant et al., 2002; 12.7 MJ/kg DM) and Brazilian [START_REF] Rostagno | Brazilian tables for poultry and swine: composition of feedstuffs and nutritional requirements, 2th edition[END_REF] 13.5 MJ/kg DM) feeding tables.

Nutritional and energy values of ground SC stalks The DM of faeces was reduced when inclusion of ground SC increased. Similarly, [START_REF] Henry | Effets nutritionnels de l'incorporation de cellulose purifie ´e dans le re ´gime du porc en croissance-finition. 1-Influence sur l'utilisation digestive des nutriments[END_REF] reported lower faeces DM when increasing levels of pure cellulose were included in growing pig's diet. According to these latter authors, the increase of faecal DM is directly related to the high water holding capacity of fibre.

To our knowledge, no study has been published on the digestive utilisation of energy and nutrients of SC ground stalks in growing pigs. Our results show that DC and energy values of ground SC vary with the method used for their calculations (intake v. allowance basis). In fact, only one part of ground SC allowed was effectively consumed because the pigs chew the cane stalks to extract juice and spit out most of the fibrous residue [START_REF] Mederos | Growth performance of pigs fed hand-chopped sugarcane stalks[END_REF]. This peculiar feeding behaviour could be considered as an adaptation to increase the energy extraction rate in ground SC. In fact, with this feeding behaviour, pigs avoid very bulky intakes and subsequent low energy intakes. As a result, the chemical composition of the actual ground SC intake widely differed from that of ground SC allowed: it contained a lower fibre and higher free sugar contents. From that, two expressions of nutrients and energy DC were needed to characterise the nutritional value of ground SC (intake v. allowance basis). In our work, the chemical composition of ground SC intake was maintained constant at a level of about 60% whatever its incorporation rate. This suggests that the feeding behaviour remains comparable whatever the level of proposed ground SC. In contrast, Bravo et al. (1996) showed that sugar extraction rate decreased from 85.4% to 68.8% when ground SC allow-ance increased from 17 to 51 g DM/day per kg BW. In this latter study, SC particle size averaged 3 cm. According to Mederos et al. (2004), the juice extraction rate was more efficient in 3 cm sized ground SC particles than in milled SC. Thus, it can be assumed that the small size of ground SC particles used in the present experiment could have limited the ability of the pigs to extract juice from ground SC. From a practical point of view, this result suggests that grinding conditions and/or particle size could influence the sugar extraction rate and then the energy value of ground SC. However, other criteria such as the SC variety (hard v. smooth stalk), the pigs BW and/or breed could also affect the sugar extraction rate. According to [START_REF] Bravo | Preliminary studies on the use of chopped sugarcane stalks as the basal diet for fattening pigs[END_REF], the efficiency of sugar extraction by the pigs appeared to be higher than when the juice was extracted mechanically with a 3 roll-mill (Vencedora Magtron, Joac ¸aba, SC 89600-000, Brazil). All in all, in a small scale farming system context, we have to take into account this point for the global efficiency of the production system.

From our observations, the coefficient of variation for the extraction rate of nutrients and energy from ground SC within each dietary treatment was high (. 30%) suggesting important between-animal variability. In addition, energy digestibility was negatively correlated with NDF extraction rate (r 5 20.42; P 5 0.08) suggesting that a large between-pig variability exists in the ability to suck and spit ground SC and in the ability to ingest dietary fibre from the ground SC. In consequence, the digestive utilisation of nutrients and energy from ground SC was closely dependant on the inter-individual feeding behaviour variations.

In comparison with the other SC products, the energy DC of ground SC was lower mainly because of its high dietary fibre content. The reduced digestibility of high fibre diets is explained by low digestibility of the fibre fraction and possible negative interactions with the other nutrients (Le [START_REF] Goff | Influence of dietary fibre on digestive utilisation and rate of passage in growing pigs, finishing pigs and adult sows[END_REF]. From the latter authors, each extra 1% increase in NDF content decreases by one percentage point the DC of energy in growing pigs. From that, it can be suggested that the reduced energy DC related to the inclusion of ground SC in the experimental diet could be related to its high consecutive fibre content. In addition, the negative effect of dietary fibre on energy DC was emphasised by the high ADF content of ground SC.

In our experimental conditions, the actual DM and energy intake from ground SC represented less than 40% and 35% of DM and energy allowance, respectively. First, it can be suggested that time dedicated for the sugar extraction chewing would limit the ability of the pigs to increase their feeding level [START_REF] Xande | Influence of sugarcane diets and a high fibre commercial diet on growth and carcass performance in local Caribbean pigs[END_REF]. Second, in connection to their high water holding capacity, dietary fibre increases gut fill and satiety. From that, it can be also suggested that the low DM and energy intake from ground SC was related to the high dietary fibre content. According to the net energy (NE) system, the metabolic utilisation of high fibre diets is accompanied by an increase of heat expenditure and a decrease of retained energy (Noblet et al., 1994). From that, it can be expected that the NE/ME ratio would be Nutritional values of sugarcane products in pigs much lower for ground SC than for juice in connection with a high-energy expenditure connected to chewing activity. Then, the low growth performance obtained in our previous study with pigs fed ground SC (i.e. 200 g/day; [START_REF] Xande | Influence of sugarcane diets and a high fibre commercial diet on growth and carcass performance in local Caribbean pigs[END_REF] is mainly related to the fact that a small part of energy allowed in ground SC (about 25%) was available for growth purposes.

3

  Levels of significance: *P , 0.05, **P , 0.01, ***P , 0.001. Within a line, least square means with different superscripts differed (P , 0.05) according to the dietary treatment. 4 Digestibility coefficient values expressed as percentage of nutrient or energy intake. 5 Digestibility coefficient values expressed as percentage of nutrient or energy offered.

Table 1

 1 Chemical composition of the control diet and the SC products 1

	Item	Control	SC molasses	SC juice	Ground SC allowed	Ground SC intake 2
	DM (%)	88.4	74.3	19.3	25.8	43.7
	Chemical composition (% DM)
	Ash	5.9	15.1	1.6	1.5	1.0
	CP	19.8	4.7	1.4	1.2	0.5
	Crude fat	4.0	-	-	-
	NDF	11.2	-	-	40.3	21.2
	ADF	3.6	-	-	26.6	14.2
	ADL	-	-	-	4.4	0.0
	Starch	51.8	-	-	-	-
	Free sugars	8.4	73.8	81.6	51.5	78.0
	Gross energy (MJ/kg DM)	18.7	15.7	17.5	17.9	17.6

SC 5 sugarcane; DM 5 dry matter.

1

Table 2

 2 Effect of feeding diets containing SC products on digestibility of nutrients, ME and N retention in CR pigs (trial 1; least square means) 1 Item Control Control 1 SC molasses Control 1 SC juice Control 1 ground SC r.s.d.

	Statistical analyses 2

SC 5 sugarcane; r.s.d. 5 residual standard deviation; ME 5 metabolisable energy; CR 5 Creole; DM 5 dry matter; DE 5 digestible energy; D 5 diet; R 5 replicate; B 5 block within replicate; D 3 R 5 diet 3 replicate; NS 5 not significant. 1 Diets were prepared by mixing molasses, SC juice or ground SC with the control diet. 2 Levels of significance: *P , 0.05, **P , 0.01, ***P , 0.001. Within a line, least square means with different superscripts differed (P , 0.05) according to the dietary treatment. 3 Expressed as percentage of total DM allowed.

4

Table 3

 3 Estimated apparent digestibility coefficients of SC products according to the difference method

	Item	Control	SC molasses 1	SC juice 1	Ground SC offered 1	Ground SC intake 2
	Digestibility coefficient (%) 3
	Organic matter	89.6	84.4	99.3	30.4	68.6
	CP	86.4	68.1	82.9	70.3	73.7
	Energy	88.7	83.6	99.0	31.9	68.6
	DE (MJ/kg DM)	16.55	13.11	17.34	5.72	12.31
	ME (MJ/kg DM)	15.87	12.56	17.22	5.56	11.82
	SC 5 sugarcane; DE 5 digestible energy; ME 5 metabolisable energy.

1

Table 4

 4 Effect of feeding diets including various levels of SC juice on digestibility of nutrients, ME and N retention in CR pigs (trial 2; least square means) 1

	SC juice inclusion (%) 2

SC 5 sugarcane; r.s.d. 5 residual standard deviation; ME 5 metabolisable energy; CR 5 Creole; r.s.d. 5 residual standard deviation; DM 5 dry matter; DE 5 digestible energy; D 5 diet; R 5 replicate; B 5 block within replicate; D 3 R 5 diet 3 replicate; NS 5 not significant. 1 Diets were prepared by mixing molasses, SC juice or ground SC with the control diet. 2 Diet 1 was 35 g DM/day per kg BW of control diet and diets 2, 3 and 4 were a mix of 8, 16 and 24 g DM/day per kg BW of SC juice with control diet, respectively. 3 Levels of significance: *P , 0.05, **P , 0.01, ***P , 0.001. Within a line, least square means with different superscripts differed (P , 0.05) according to the dietary treatment.

Table 5

 5 Relationship between incorporation rates of SC juice in the diet and digestibility coefficients of energy and nutrients (trial 2)

	Parameters 1

Table 6

 6 Effect of feeding diets including various levels of ground SC on intake and extraction rate of nutrients in CR pigs (trial 3; least square means) 1 Diet 1 was 35 g DM/day per kg BW of control diet and diets 2, 3 and 4 were a mix of 13, 26 and 39 g DM/day per kg BW of ground SC with control diet, respectively.

	Ground SC inclusion (%) 2

SC 5 sugarcane; CR 5 Creole; r.s.d. 5 residual standard deviation; DM 5 dry matter. 1 Diets were prepared by mixing molasses, SC juice or ground SC with the control diet.

2

Table 7

 7 Effect of feeding diets including various levels of ground SC on digestibility of nutrients, ME and N retention in CR pigs (trial 3; least square means) 1 SC 5 sugarcane; r.s.d. 5 residual standard deviation; ME 5 metabolisable energy; CR 5 Creole; DM 5 dry matter; DE 5 digestible energy; D 5 diet; R 5 replicate; D 3 R 5 diet 3 replicate.Diets were prepared by mixing molasses, SC juice or ground SC with the control diet.Diet 1 was 35 g DM/day per kg BW of control diet and diets 2, 3 and 4 were a mix of 13, 26 and 39 g DM/day per kg BW of ground SC with control diet, respectively.

	Ground SC inclusion (%) 2

1 2

Table 8

 8 Relationship between incorporation rates of allowed ground SC in the diet and digestibility coefficients of energy and nutrients 5 sugarcane; Y 5 digestibility coefficient values of nutrients or energy expressed as a percentage of nutrient or energy intake; a 5 digestibility coefficient of control diet; b 5 the linear variation of digestibility coefficient with the increase of ground SC incorporation rate; DM 5 dry matter; DE 5 digestible energy; ME 5 metabolisable energy.

	Parameters

SC 1 Parameters estimated from the following model: Y 5a 1 b 3 (ground SC incorporation rate), with Y, a and b. Incorporation rate 5 ground SC intake/total intake (g DM/g DM). 2 Parameters estimated from the following model: Y 5a 1 b 3 (ground SC incorporation rate), with Y, a and b. Incorporation rate 5 ground SC allowance/total allowance (g DM/g DM).

Average values calculated from results obtained during trials 1 and

according to the difference between measured values of ground SC allowed and refusals.Xande ´, Re ´gnier, Archime `de, Bocage, Noblet and Renaudeau

Energy loss in faeces (MJ/kg DM) 5 18.73

1.92

A 1 2.23 3 EE 1

4.07 3 N, with A, EE and N for ash, ether extract and nitrogen contents in faeces (g/kg DM), R 2 5 0.93, r.s.d. 5 0.35. 2 Energy loss in (kJ/day) 5 345 1 31.1 3 N loss in urine (g/day), R 2 5 0.94, r.s.d. 5 110. This equation was calculated from a 641 sets of data.

Nutritional and energy values calculated using the regression analysis with the following model: Y 5a 1 b 3 (SC juice incorporation rate), with Y, a and b. Incorporation rate 5 SC juice intake/total intake (g DM/g DM).

Calculated from the regression equation for a 100% incorporation rate of SC juice in the diet.Xande ´, Re ´gnier, Archime `de, Bocage, Noblet and Renaudeau

Levels of significance: *P , 0.05, **P , 0.01, ***P , 0.001. Within a line, least square means with different superscripts differed (P , 0.05) according to the dietary treatment.

Calculated from the regression equation for a 100% incorporation rate of ground SC in the diet.

Acknowledgements

This work was supported by the Guadeloupe Region and the European funds (FSE FEOGA). The authors gratefully acknowledge C. Anais, K. Benony, M. Bructer, E. M. Giorgi, K. A. Racon and F. Silou for their technical assistance, Y. Jaguelin, M. Baucal, S. Calif, T. Etienne and G. Saminadin for the laboratory analysis.