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Milk from cattle, camels, and, to a lesser extent sheep and goats is one of the most important products of pastoral production in semiarid northern Kenya. Goats are kept primarily for subsistence meat production and for market sales or exchange of live animals. Although its contribution to overall consumption in pastoral households is limited, milk from goats is generally highly valued (McCabe, 1987). Goats confer an advantage in terms of food security since their drought mortality rates are lower compared to cattle, and their postdrought herd recovery rate is much faster than for cattle and camels. Due to their short gestation period, goats usually are the first animals to produce milk after a dry year or a drought period. They may as well play a critical role in balancing yearround supply with milk for subsistence due to their ability to lactate during dry seasons, when, for instance, cattle produce little or no milk at all (Schwartz & Schwartz, 1985; Grandin et al., 1991). The influence exerted by maternal milk yield on survival and growth of goat kids would seem to be of equal importance. Previous analyses in this series (Chapters 3 and 4) have shown that the total amount of milk available to kids until weaning is a critical risk factor affecting kid survival and has a strong impact on their growth performance. Hence, milk production can be assumed to make a significant contribution to overall biological productivity of goat herds and, ultimately, to the benefits derived from pastoral goatkeeping.
Traditional pastoral grazing systems have always had to cope with the effects of environmental seasonality on the achievement of their goals. This is clearly reflected by their management methods which involve flexible slaughter dates and stocking rates, herd mobility, as well as species mix. However, patterns of pastoral land use have changed considerably throughout semiarid areas of Kenya due to the simultaneous pressure applied by several different factors on these systems, including human demographic factors and the commercialisation of pastoral production (Fratkin, 1992; Sikina et al., 1993; Schwartz et al., 1995; Roth, 1996). One of the central problems confronting pastoral producers in Northern Kenya today is the reduction in the mobility of their households and herds. The strategy of mobility is probably one of the most adapted means of overcoming the seasonal variation in pasture resources (Niamir, 1990). Alternatives to herd mobility as an efficient strategy to reduce the impact of seasonal nutritional deficits on livestock production are few. One possibility is to manipulate the total seasonal nutrient requirements of the herd, instead of attempting to improve the supply side of the nutrient balance. This could for instance be accomplished by limiting reproduction to a short time period in a year, so as to synchronize reproductive stages of high nutrient requirements with pasture forage production. The present chapter investigates the effect of such a controlled seasonal breeding strategy on milk production in a herd of Small East African (SEA) goats.
The analysis is based on fitting polynomial growth curve models to both daily and cumulative milk yield data obtained from an experiment conducted under simulated pastoral herd management in Isiolo District, Northern Kenya. Part of these data have been analysed previously using a different methodology and to address different objectives. Using the incomplete gamma function (Wood, 1967), the study of Wahome et al. (1994) focused on characterising the general shape of the lactation curve and the main factors that influence milk production levels in SEA goats under pastoral management. Although it is the most widely used functional form for modelling lactation curves for domestic livestock, the incomplete gamma function has a number of well known limitations, including overprediction of daily milk yield at the beginning of lactation, underestimation of peak daily milk yields, and failure to account for autocorrelated error terms (Pérochon et al., 1996; Scott et al., 1996). That the incomplete gamma function does not account for the correlation between repeated measurements on the same animal is likely to invalidate the analysis of functional parameters and inferences concerning the effect of treatment and/or classification factors on the shape of the lactation curve. Moreover, the incomplete gamma function is a rather inflexible method for describing the evolution of daily milk yields over time. It is generally incapable of dealing with major alterations in milk yield induced by such events and effects as fluctuations in nutrient supply and season of kidding. However, under semiarid rangeland conditions, milk production is more a [page 92↓]function of season or nutrient availability than stage of lactation (Nicholson, 1984). Hence, both individual animal and seasonal variation cause estimates to have large standard errors. Multiple peaks can be expected to arise in lactation curves in response to changing nutritional conditions, but are normally considered to be aberrant and are often omitted from consideration when fitting the incomplete gamma function to lactation data (e.g., Pérochon et al., 1996). In contrast, fitting polynomial growth curves to longitudinal lactation data using the general linear mixed model framework (Laird & Ware, 1982) is a particularly flexible method for simultaneously accommodating variability due to the environment, individual animal differences, and dependent error terms.
Experimental data
Data were from an experiment in which milk production was recorded in several seasonal breeding groups of SEA goats maintained at the Ngare Ndare Research Station of the University of Nairobi in Isiolo District, northern Kenya. Details of the experiment with regard to herd management and data recording were described before in Chapters 2 and 3. In short, breeding groups of 18 does each, with a balanced age and weight structure, were established. The experiment was initiated at the end of January 1984, when a buck was introduced into the first breeding group for two months. The buck was transferred afterwards to consecutive groups for the same duration, so as to achieve yearround mating, kidding, and weaning. Mating in the last breeding group (number 18) started at the end of March in 1987. Kids were weaned at an age of 16 weeks. Prior to analysis, data from the individual breeding groups were grouped into six different mating seasons. Three complete production cycles years were obtained for five of these six consecutive two month mating seasons. The sixth season had only two complete cycles, because data from the last breeding group (number 18) had to be discarded due to incomplete records. The experimental treatment thus consisted of six mating seasons, the first one, labelled as mating season 1, ranged from February to March, and the last one, labelled as mating season 6, ranged from December to January. Mating seasons 4 and 5 (August to October, and October to December, respectively) had to be assumed to have taken place over a period of three months due to a delay of one month which occurred in setting up the first breeding group of mating season 4 in 1984.
Time in the experiment was divided into periods of two weeks, each period starting and ending on a Monday. Routine measurements of weight (kg) of all animals and milk production of dams were carried out at the beginning of each twoweek period. Adult animals were weighed using a weighing crate and measurements were made to the nearest 0.5 kg. Handmilking was done on two consecutive days of each fortnightly period with the kid close by, except for does whose kids died, which were milked daily. On the first day, the right half of the udder was milked in the evening and the following morning. The left half of the udder was similarly milked on the second day. Kids were not allowed to suckle during the night preceding the morning milking. The total volume of milk collected on the two consecutive days was taken as the average daily yield of the doe for the current period.
Pasture condition was judged during every recording period using a subjective phenological pasture condition score using score values from 1 to 4 according to greenness and abundance of the herblayer (range condition score [I]). Scores of 1 to 2 generally occurred during the dry seasons, and 3 and 4 during and immediately after the rainy seasons. The contribution of bushes, trees, and of high quality litter such as leaves, flowers and fruits to diet of goats was taken into account by upgrading the herblayer condition score to a maximum value of 5 (range condition score [II]).
Traits studied
Lactation curves (average daily milk yield (g)) and cumulative milk yield (kg) curves were estimated from the series of biweekly milk yield measurements obtained from the experiment, ranging from the postpartum recording date to the 28th week of lactation. The average daily milk yield of each doe for each two week period was assumed to be equivalent to the total volume of milk collected at the recording date. Total milk yield for each period was then calculated as the sum of the product of the measured daily milk yield and the length of the time interval (14 days). Observations pertaining to does which entered a new reproductive cycle or were found to be pregnant before the end of the current lactation were discarded from the data set.
Statistical analysis
The general linear mixed model framework, as implemented in the SAS procedure MIXED (SAS Release 6.12, 1996), was used fit polynomial growth curve models to daily and cumulative milk yield data. The aim [page 93↓]was to characterize the evolution of daily and total yield curves over time for subjects in the six different mating season groups, and to investigate the effects of other covariates on the shape of these curves. In this respect, approximating the actual functional form of response curves through a natural polynomial in time was found to be particularly useful, since this method allows the estimating of separate polynomial growth curves for each treatment and/or classification factor level, which then could be used to compare performances at different time points (Rowell & Walters, 1976; Cullis & McGilchrist, 1990; Jones, 1993; Diggle et al., 1994; Cnaan et al., 1996).
The general form of the linear mixed models used to model milk production over time is as follows. According to Laird and Ware (1982), a general linear mixed model for longitudinal data with a sequence of p measurements on subject i can be specified as
where y _{i} = a p _{i}x1 vector of the response variable for subject i X _{i} = a known p _{i}xq design matrix β = an unknown qx1 vector of fixed effects coefficients Z _{i} = a known p _{i}xr design matrix γ_{i} = _{}an unknown rx1 vector of random subject coefficients, assumed to be independently distributed across subjects with distribution γ_{i }~Ν(0, σ²B), where B is the between subjects covariance matrix ε_{i} = _{}a p _{i}x1 vector of within subjects errors assumed to be distributed as ε_{i}~Ν(0, σ²W _{i}), where W _{i }is the within subjects covariance matrix 
The columns of the model matrices X _{i} and Z _{i} consist of indicator variables corresponding to the levels of the fixed and random subject effects, respectively. Note that the fixedeffect part of model (1) can incorporate polynomial time trends, treatment and/or classification factor effects and their interactions with polynomial terms, as well as timechanging covariates such as range condition scores (Cnaan et al., 1996). In its most general form, the specification of the random effects through the design matrix Z _{i} can be entirely independent of that of the fixed effects design matrix X _{i}, but often is assumed to be a subset of X _{i}. In longitudinal studies, these between subject components of variance are used to model the random deviations of the intercept and possibly higher degree polynomial powers of the time of observation for subject i from the subject's group mean intercept and higher degree polynomial time trends (Jones, 1993; Cnaan et al., 1996).
The linear mixed model formulation is very general since different subjects can have different numbers of observations as well as different numbers of observation times. Therefore, subjects with incomplete data do not need to be discarded from the analysis. Equation (1) can further be expanded to incorporate additional random effects by defining a p _{i}xv design matrix, U _{i}, of random effects and a corresponding unknown vx1 vector, τ _{i}, of random effects coefficients:
The random effects, τ _{i}, are assumed to be identically and independently distributed as τ_{i}~N(0, σ²I), where I denotes the pxp identity matrix. In the present study, the effect of production cycle (three levels) and its interaction with the mating season treatment were considered as such random effects and included in all preliminary models fitted to the data. Model construction and data analysis encompassed the same steps as those described previously in Chapter 4. Using plots of individual and group mean profiles as a starting point to obtain a visual picture of possible models for the data, various models that included random subject effects, serial correlation, and both random subject effects and serial correlation were computed. In addition, one model with and one without random subject effects were fitted to the data using an unstructured covariance matrix. Akaike’s Information Criterion (AIC) was used a decision criterion for final model selection. The serial correlation structure employed was a heterogeneous firstorder autoregressive structure (ARH[1] in the SAS PROC MIXED terminology).
Table 5.1 summarizes the predictor variables included in preliminary analyses. Selection of suitable final models was based upon fitting successive nestedmodel versions, and omitting variables from the linear
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predictor when the likelihood ratio (LR) statistic indicated that the model including an additional parameter did not fit significantly better than the simpler model. Fixedeffects terms and interactions among fixedeffects were excluded from the model when the probability of obtaining a greater χ²value than the observed LR test statistic from a χ² distribution with r degrees of freedom was greater than 0.15, r denoting the additional parameters that have to be estimated in the larger of the two models. The same procedure was applied to test for the significance of random effects, except that the pvalue for the LR statistic was obtained by taking half of the probability of a greater χ² from a χ² distribution with one degree of freedom, given that only a onesided test is needed in this case and only one additional parameter is estimated upon including a random effect into the model. Orthogonal polynomials were used instead of natural polynomials to model time trends in order to avoid problems caused by multicollinearity between polynomial powers of the time of observation (Steel and Torrie, 1980; Draper & Smith, 1981).
In order to avoid bias in estimated fixed effect coefficients due to multicollinearity in the linear predictor, the effects of postpartum live weight, litter size, and range condition scores [I] & [II] on response patterns were studied separately from those of mating season and parity. The assumptions of normality and homogeneity of variances across the cells of the betweengroups design were tested using the KolmogorovSmirnov One Sample Test and the Bartlettchisquare test, respectively. Graphical inspection was used to assess the correlation of mean response values with the variability (standard deviations and variances) across the cells of the design. In cases where the data did not fulfil one of the foregoing assumptions, the BoxCox procedure as described by Neter et al. (1996) was applied to identify an appropriate transformation of the continuous response variable from the family of power transformations. When making multiple comparisons of factor level means, the experimentwise error rate was controlled at the prespecified level of α=0.05 by using both the Bonferroni and Tukey multiple comparison procedures. The procedure giving the narrower confidence limits was then chosen to report significance probabilities of differences in factor level means (Neter et al., 1996). Tests of hypotheses concerning specific linear combinations of parameter estimates were obtained by specifying appropriate estimate and contrast statements in the SAS procedure MIXED.
Lactation curves
Summary information on the models fitted to daily milk yield data appear in Table 5.2. Mean response values were found to be highly correlated with the variability across cells of the design at each followup time point, so a square root transformation of milk yield data was used to stabilize variances. Lagged range condition score [I] was not significant in any of the models fitted to the data. In both final models the general level of estimated response profiles varied quite substantially between individual dams, that is, some were intrinsically high yielders, others low yielders. The importance of this stochastic variation is indicated by the numerical magnitude of the highly significant dam variance component (p <0.001 in both models) in Table 5.2, whose realized value represents a random intercept, i.e. the amount by which all measurements on the same experimental unit are raised or lowered relative to the population average.
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Two additional results to note are that average yield levels in each mating season treatment group differed considerably between replications of the experiment (σ^{2} _{PC} _{x} _{MS}=4.7, p <0.01), whereas the expected variation between production cycles only, irrespective of mating season, was much smaller, though still statistically significant (σ^{2} _{PC}=1.0, p <0.05).
From the response profiles depicted in Figure 5.1 it is apparent that milk yields in the first two weeks of lactation where negatively affected (<400g·day^{—} ^{1}) when kidding took place between June and September (mating season groups 1 and 2), whereas maximum initial yields of about 450 to 550 g·day^{—} ^{1} were achieved at the onset and during the long rainy season (groups 5 and 6). The characteristic peak in milk yield curves usually observable after 4 to 6 weeks of lactation appeared only when does had access to adequate forage supply. This was the case for goats in group 3 during the short rains with a peak yield of 428g·day^{—} ^{1}, and for [page 96↓]those in groups 5 and 6 during the long rains, which produced maximum yields of 532 and 580g·day^{—} ^{1}, respectively. Milk yields in groups 1 and 2 were significantly lower (p <0.05) than those achieved in groups 5 and 6 in lactation weeks four to eight.
Figure 5.1. Estimated lactation curves (least squares means) by mating season (MS).  

The most rapid decline in milk production rates early in lactation were observed at the onset of the long dry season in mating season groups 1 and 6. By 12 weeks, yields in group 1 were significantly lower than in all other group (p <0.05), but recovered slightly from a low level of 105g·day at weaning to a local maximum value of 115g·day^{—} ^{1} around 24 weeks in response to improving feeding conditions during the short rains. In contrast, lactating does in group 6 rapidly dried off during the course of the long dry season and yields dropped below 100g·day^{—} ^{1} shortly after weaning. Although lowest in the first two weeks of lactation, yields in group 2 never fell much below 300g·day^{—} ^{1} until weaning, and started to decline gradually thereafter. The goats in this group produced their maximum milk yield at 14 weeks during the short rains. In group 3, milk production rates decreased slowly until weaning and plateaued at about 270g·day^{—} ^{1} up to 24 weeks. The pronounced responses to changing environmental conditions observable in the lactation curves of the first three treatment groups were absent in that for group 4. Here, milk yields declined almost linearly from parturition until the end of followup. Does kidded at the onset of the long rains in group 5 also showed continuously declining milk production rates following the peak in the sixth week of lactation.
Polynomial contrasts revealed a significant quadratic trend (p <0.05) in average daily milk yields with increasing parity stage from parturition until 20 weeks of lactation. Thereafter, no systematic trend across parity levels could be detected. In the first two weeks of lactation, milk production rates ranged from 390g·day^{—} ^{1 }in the first lactation to 455g·day^{—} ^{1} in the fourth or later lactations. Peak milk production was attained between the second and fourth lactation week and declined gradually thereafter until the end of the followup period. The highest level of production was observed in the third parity, although it did not differ significantly from that achieved in the second parity and was barely discernible from the latter after three months of lactation. Until 10 weeks, the lowest yields were produced by first lactating does, but thereafter these showed a greater persistence and produced increasingly more milk per day than does in their fourth or later lactation. Over the entire observation period, all pairwise comparisons of milk yields across parity levels failed to reach significance.
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Figure 5.2. Estimated lactation curves (least squares means) by a) litter size, b) postpartum live weight (kg), and c) lagged range condition score [II] in each time interval.  

Litter size markedly affected milk production levels (Figure 5.2a). Yields in does nursing twins were significantly lower than in those nursing a single kid until the 24th lactation week (p <0.01). The latter produced 98g·day^{—} ^{1} or 32 percent more milk in the first two weeks of lactation. This difference in yields reduced to 14g·day^{—} ^{1} or 16 percent until the end of followup at 28 weeks. A clear differential effect on milk production rates was also exerted by postpartum live weight state of does (Figure 5.2b). As expected, milk yield level was a linear function of postpartum live weight (p <0.001) at each measurement time. During the first two weeks of lactation, the lightest does produced approximately 41 percent less milk than the heaviest ones (p <0.001). This difference decreased only slightly up to weaning (39 percent) and 28 weeks of lactation (36 percent), and remained significant until 24 weeks. Up to 12 weeks, significant differences (p <0.05) in daily milk yields could only be detected between the lightest goats and those weighing more than 30 kg postpartum. Does heavier than 35 kg after parturition continued to produce significantly more milk until 18 weeks of lactation than those weighing less than 30 kg. At later stages up to 24 weeks of lactation, the only significant difference observed was that between the lightest and heaviest animals.
Differential effects of lagged range condition scores [II] in each followup time interval on milk production rates were substantial, as may be seen from the response profiles depicted in Figure 5.2c. Not surprisingly, milk yields in each time interval were found to be an increasing function of range condition. This trend was fairly consistent over the entire observation period, although crisscrossing of lactation curves of scores 4 and 5 occurred around weaning time. The difference in average yields during the first two weeks of lactation between scores 1 and 4 and 5 amounted to 143 and 126 g·day^{—} ^{1} (+51 and +45 percent), respectively. By the end of the observation period, this discrepancy had decreased in absolute terms to respectively 89 and 105 g·day^{—} ^{1}. Both differences, as well as that between score 1 and 3 were significant throughout the observation period (p <0.01). Milk yields under intermediate forage conditions of 2 and 3 were also significantly lower at all observations times than under scores of 4 and 5 (p <0.01).
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Cumulative milk yields
Cumulative milk yield data were transformed to the square root scale prior to model fitting in order to correct for correlated means and variances across cells of the design at each measurement time. In contrast to the analysis of daily milk yields, in all preliminary models fitted, patterns of cumulative milk yield over time did not differ significantly between parity stages. This was in accordance with the findings of the analysis of daily milk yields reported above that revealed no significant differences across parity stages at individual observation time points, despite the fact that some discrepancies in the shape of the corresponding lactation curves had been detected. Cumulative milk yields were finally assessed in terms of mating season, litter size, and postpartum live weight of does (Table 5.3). The latter two effects were, again, analysed separately since they were confounded with the mating season treatment effect.
As may be seen from the statistical results presented in Table 5.3, a very large betweenanimal variation in total milk yields was present in both models fitted. Due to the interaction of the random doe effect with the linear slope, individual response profiles did not only differ in their general level, but also in shape. The intercepts of mating season group response profiles were also not constant across production cycles, as indicated by the relatively large production cyclexmating season variance component. In comparison, the [page 99↓]variation in the general level of response profiles due to the production cycle random effect itself was much smaller, though still significant at the five percent level.
Figure 5.3. Estimated cumulative milk yield curves (least squares means) by mating season (MS).  

Total milk produced by mating season after 4 weeks of lactation ranged from 8.3 kg in group 2 to 16.2 kg in group 6 (Figure 5.3 and Table 5.4). The highest yield until weaning time, however, was achieved in group 5 with 48.2 kg, followed by group 6 with 46.4 kg. Intermediate levels of production of slightly more than 40 kg were predicted for groups 3 and 4. Nutritional constraints experienced during the long dry season clearly had a detrimental effect on response patterns in the first two mating season groups, although after weaning this trend was attenuated to some extent in group 2 by a rise in milk yields during the short rainy season. Cumulative yields at 28 weeks of lactation were lowest in group 1 with an average of only 36.6 kg milk per doe, approximately 42 percent less than in group 3 which displayed the best lactation performance. Average production levels in groups 4 and 5 were only slightly lower than in the latter. Although not statistically significant, total milk production until 28 weeks of lactation was markedly lower in groups 2 and 6, amounting to 52 and 53.2 kg milk, respectively. Throughout the observation period, significant differences could only be detected between mating season groups 1 and 3 to 5 from 8 weeks onwards, and between groups 1 and 6 from 8 to 24 weeks of lactation.
Total milk production in does nurturing twins was significantly lower at all stages than in does nurturing a single kid (Table 5.4). By 4 weeks,the former had produced about 22 percent less milk than the latter. The relative difference in total yields diminished slightly during later stages and amounted to 19 percent at 28 weeks of lactation. Total milk yields across postpartum live weight classes (Table 5.4) followed the expected course, with a significant linear trend at all stages with increasing live weight of does after birth (p <0.01). The mean total yield predicted for the lightest group was only 70, 65, and 67 percent of that predicted for the heaviest group at 4, 16, and 28 weeks of lactation, respectively.
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Using data from the same experiment, Wahome et al. (1994) have previously presented estimates of curves for daily milk production over a period of 31 weeks following kidding, according to vegetation condition around parturition time, year, dam parity, and litter size. As mentioned above, the analytical strategy adopted by these authors was to fit an incomplete gamma function to the testday yield records of each animal on study using a nonlinear estimation procedure, and to subject the resultant estimates of functional parameters to an analysis of variance. Estimated least squares means of the functional parameters were subsequently employed in constructing lactation curves for each level of the predictor variables. Principally, this approach must be based upon a sample of equidistant and complete series of milk yield records taken at a common set of observation times up to a specified endoflactationdate in order to be technically feasible and to produce valid parameter estimates (Diggle et al., 1994). It follows that incomplete or truncated series, as well as series with missing records at individual testdays must either be deleted or, alternatively, a missing value imputation technique (which introduces substantial amounts of error) has to be applied to these data (see, for example, the study of ZoaMboé et al. (1996, 1997)). Similar considerations would need to be made when addressing the problem of irregularly spaced recording intervals, but this was not the case for the present data. Wahome et al. (1994), however, did not state how they dealt with missing and/or incomplete lactation data. In contrast, with the general linear mixed models employed in this study it is easy to handle missing values in the dependent variable since the subjects are allowed to have unequal numbers of repeated observations or to be measured at different occasions. To obtain valid and efficient estimates requires only [page 101↓]that the missingness itself not be related to the outcome (see Cnaan et al. (1997) for further details). Thus, difference in analytical approach alone could be expected to result in discrepancies between model predictions obtained in this work and those reported by Wahome et al. (1994). Moreover, the present analysis focused on the investigation of the effect of mating season on lactation performance, and used only 231 lactations observed during this particular experiment entered the statistical analysis, while Wahome et al. (1994) state that in their analysis records of 257 does were used to fit lactation curves (note that the latter figure differs from that given in the abstract of the same paper, i.e., 267 lactations). Obviously, they must have used records pertaining to animals maintained at the Ngare Ndare research station, but which did not participate in the restricted breeding experiment. In the following discussion, we highlight any major discrepancies between both sets of results whenever they occur.
Average daily milk production in this flock of SEA goats was within the range reported by Devendra and Burns (1983) for smallsized indigenous African breeds such as Maradi and West African Dwarf goats. Daily yields were also comparable to those obtained by Ruvuna et al. (1995) for SEA and Galla goats under more favourable environmental conditions in Western Kenya, and those reported by Blackburn and Field (1990) for the same breeds under arid conditions in Northern Kenya. For SEA goats, Ruvuna et al. (1995) give estimates of average initial and peak morning yields of 345 and 347 g·day^{—} ^{1}, respectively, while the lactation curves presented by Blackburn and Field suggest average initial and peak yields during the wet season of about 400 and 550 g·day^{—} ^{1} , and thus were similar to those estimated from the present data. Additionally, after adjusting for the effect of mating season or range condition, the shape of estimated lactation curves were similar to those reported from other studies, where an initial rise in yields up to the second to sixth week of lactation was followed by a steady decline in yields until the end of lactation (Ehoche and Buvanendran, 1983; Raats et al., 1982). However, the rapid fall in yields after weaning noted in several other studies (e.g., MorandFehr and Sauvant, 1980; Zygoyiannis and Katsaounis, 1986) and which was attributed to the removal of the suckling stimulus could not be detected.
Although comparative lactational performance is difficult to assess based on absolute figures, it is nevertheless clear that the average cumulative milk production until 12 weeks of lactation of 31.7 kg (95 percent confidence limits : [28.9; 34.7]) estimated in this experiment is low compared to the performance reported for other, larger sized African breeds such as, for example, Boer goats. Based on the average daily yields reported by Raats et al. (1983), Boer goats can be expected to produce between 123 and 207 kg over a lactation period of 12 weeks, depending on parity number and litter size. To some extent, this superiority in milk production is not surprising, since milk yield usually tends to be positively correlated with almost all body dimensions, including liveweight and udder volume (Devendra and Burns, 1983; Gall, 1980). Apart from differences due to adult size, however, the comparatively low milk yields in SEA goats are certainly also related to both the genetic potential of this breed as well as to the poor nutritional environment to which animals are exposed. For instance, the substantial effect of forage quality and quantity on offer on milk yield was demonstrated by the large deviation in average daily milk yield curves between range condition score levels. Also, the statistical analysis revealed a remarkable variation in the scale (intercept) as well as in the linear slope of cumulative milk production curves among does, even after adjustment was made for the random effect of production cycle and its interaction with mating season. This indicates considerable scope for selection on milk production within local herds of SEA goats. For selection purposes, total yield until 4 weeks of lactation appears to be a fairly good indicator of cumulative lactation performance. The growth curve model fitted to cumulative milk yields, adjusted for the effect of mating season, gave an estimated correlation between adjacent observations on the same animal of ρ=0.98, so that the correlation between total yields measured at the end of week 4 and 28 amounts to ρ^{6}=0.90.
Effect of litter size
Litter size had a substantial influence on lactation curve differences for both daily and cumulative yield traits. Does suckling twins produced on average about 32 and 16 percent less milk per day during the first and last two weeks of followup, respectively, than those suckling a single kid. Although it is well established that litter size can be an important source of variation affecting milk production in goats, the results reported in the literature would have suggested a relationship in the opposite direction. Almost all workers found that milk yields improved with litter size, and often this trend was attributed to the associated increase in suckling stimulus (e.g., Ehoche and Buvanendran, 1983; Mavrogenis et al., 1984; Raats et al., 1982; Skinner, 1972; Zygoyiannis and Katsaounis, 1986). Landau et al. (1996) point out that the number of fetuses also has a beneficial effect on mammary development in goats, which apparently is mediated through the activity of placental lactogen. On the other hand, both of these stimulating effects could be more than offset when animals are maintained under nutritional conditions promoting negative energy balances during late pregnancy. This interpretation seems to be supported by Sauvant et al. (1991), who argue that reduced milk production in twin nursing goats most likely results from illmanagement of body reserves, and not from [page 102↓]deficient mammary development. Although reproducing animals are able to maintain high levels of milk production even under conditions of restricted feed supply by mobilizing body reserves, there are obviously limits to this socalled buffereffect (Santucci et al., 1991). Upon examining body weight development patterns during pregnancy and early lactation, the present data revealed that at least in the first and fourth or greater parity does, relative body weight increases until parturition were lower, and mobilization of body reserves during the early stages of lactation appeared to be much more pronounced in animals carrying twins than in those carrying singles. However, this pattern was reversed for second and third kidding does, so that the increased physiological stress associated with carrying twin fetuses to term can only provide partial explanation for the observed negative trend in milk yields with increasing litter size.
Effect of dam parity
Although the effect of dam parity on milk yield in goats is well established, the present analysis failed to reveal clearcut differences in terms of scale and shape of lactation curves with increasing number of kiddings. Only slight evidence for the effect of parity on the linear slope of curves for daily production was obtained (p <0.15), while the curves for cumulative yield up to 28 weeks following freshening were not affected at all by this factor. As indicated by Devendra and Burns (1983), effects of parity as well as age on daily production may be difficult to detect due to the influence of various environmental and managemental factors. However, up to 20 weeks of lactation, initial and peak yields followed a quadratic trend with increasing parity. Maximum initial and peak daily yields were achieved by third parity dams. Overall, this trend in milk yield compares favourably with the results reported by other workers. For instance, Alpines, Saanens and Toggenburgs displayed increasing milk yields up to the third to fourth lactation (Kennedy et al., 1981); similar patterns were also described by Gipson and Grossman (1990) in their review on lactation curves in dairy goats. The main reason for the initial rise in milk production with advancing parity is that milk yield is proportional to the mammary alveolar surface area, which can be assumed to increase between successive lactations (Gall, 1980; Raats et al., 1982). Parity number also affected the persistency in milk yields. If persistency is defined as the average rate of decline in estimated daily milk production following peak yield (attained at 24 weeks of lactation for all parities) until the end of lactation (28 weeks), then first lactation does tended to be more persistent than multiparous does. The corresponding figures ranged from 0.71 to 0.84 percent per day during the first and fourth or greater parity, respectively. Although the term is not consistently defined in the literature, several other workers, including Sachdeva et al. (1974) and Gipson and Grossman (1990), confirm that persistency is a declining function of parity number. In their study of dairy cow lactation curves, Stanton et al. (1992) propose that the higher persistency of first lactating animals could, in part, be attributed to the maturation process that these younger animals are undergoing. The concomitant increase in milk potential over time tends to counteract the normal decline in milk yields with advancing stage of lactation. With respect to the present data, the estimated relative increase in body weight of 15.2 percent over the reproductive cycle for first lactating does, as opposed to 8.4, 1.1, and 3.4 percent in second, third, and fourth and higher parity goats, could be regarded as evidence in support of the latter interpretation.
The average yield curves estimated by Wahome et al. (1994) differed from the present results, in that their analysis revealed a highly significant difference in scale among parityspecific lactation curves, while curve shapes did not differ among parity classes. Consequently, the tendency of first parity does to exhibit a somewhat higher persistency than multiparous does as detected in the present study was not reported by Wahome et al. (1984). Also, both initial and peak daily milk yield levels were lower than that estimated in this work, with estimates of initial and peak yields ranging between approximately 230 and 395 g·day^{—} ^{1}, and between approximately 245 and 420 g·day^{—} ^{1}, respectively. Some of these differences may be due to the presence of multicollinearity in the ANOVA model used by Wahome et al. (1994) to derive estimates of lactation curve parameters for each level of the predictor variables considered. For instance, their model simultaneously took into account the effects of parity, litter size, and doe body weight, which tend to be correlated with each other. Model interpretation is complicated in the presence of strong linear relationships amongst the explanatory variables because the true effect may be masked by redundant predictor variables. In general, collinearity causes individual parameter estimates to be biased and less precise than would otherwise be the case if correlated predictor variables were deleted from the model (Everitt and Dunn, 1991; Jobson, 1991). Additionally, as indicated by Kowalski and Guire (1974), nonlinear functions such as the one fitted to individual sequences of observations by Wahome et al (1994) do not have the convenient property shared by the class of polynomial functions employed in this study, which is that the “mean curve” fitted to the mean response values at every observational time point is equivalent to that obtained by fitting individual records to a set of such polynomials and averaging the functional coefficients. Since this is generally not true for nonlinear functions, individual curves are subject to distortion through group averaging, which may oversmooth the fitted curves and mask the inherent betweensubjects variability (Kowalski and Guire, 1974; Van Der Linden et al., 1970). Indeed, the present analysis revealed that interanimal heterogeneity in milk production [page 103↓]potential was a major source of variation in observed milk yield profiles. Lastly, the significance levels of individual model factors reported by Wahome et al. (1984), on which they based their model selection, are likely to be invalid because the fundamental assumptions concerning the statistical independence of observations and the homogeneity of variances over time are not fulfilled. Data collected in a longitudinal study do not meet these requirements by nature (Doren et al., 1988; Cnaan et al., 1997; Kenward, 1985, 1987; Van Der Linden et al., 1970). As pointed out by Van Der Linden et al. (1970), it is precisely the dependence between adjacent observations which enables us to construct mathematical equations describing yield or growth patterns over time. The most important consequence of the lack of independence is that, due to the inflation of fixed effects test statistics, testing of the hypothesis of prime interest in a longitudinal setting, i.e., that the mean response among treatment or classification groups is the same at each measurement time is ruled out (Diggle, 1988; Doren et al., 1988; Pérochon et al., 1996).
Effect of postpartum body weight of dam
In agreement with the findings of most workers, milk yield increased considerably with postpartum body weight of dam. As already mentioned above, this is to be expected from the well documented positive correlation between milk yield and almost all body dimensions. However, the effect of body weight is likely to be confounded with other sources of variation, particularly with age and parity number. Because of the presence of multicollinearity, milk yield estimates based on models attempting to adjust for all three factors cause interpretational difficulties. On the other hand, assessing, for instance, the effect of dam postpartum body weight within parity classes may be prevented by highly unbalanced and small observation numbers. Obviously, the number of animals in the highest and lowest body weight classes will tend to be underepresented, respectively, in first lactating and multiparous dam categories. This was the case with the present data and, therefore, it was not possible to investigate whether the effect of postpartum dam body weight on milk yield was independent of that of parity. Nevertheless, the comparatively large differences in milk yield across body weight levels, in conjunction with the marginal effect of parity on milk yields could be regarded as evidence in support of this hypothesis. In their study on Red Sokoto goats, Ehoche and Buvanendran (1983) arrived at similar conclusions. These authors found that doe liveweight was the most important factor influencing milk yield, even after adjustment was made for dam age. Similarly, in his review on the effect of body conformation on production in dairy goats, Gall (1980) concludes that differences in body weight account for about 20 to 30 percent of the variation in milk yield of goats. Consistent with the present results, he also states that this relationship is most pronounced when based on weight measurements taken shortly after kidding. With respect to the inevitable correlation between dam age, dam body weight, and thus milk yield, Lampeter (1970) argues that the primary influence on milk production appears to be that of weight, and not of age acting independently of weight.
The main explanation for the increase in milk yield with postpartum body weight then rests upon the assumption that, as noted above, this trait is closely related to udder volume and mammarian tissue mass (Gall, 1980). Additionally, it may also reflect an increased capacity to buffer against the rise in metabolic requirements in relation to the lactation process. The present data revealed that when pregnancy coincided with the long dry season, the accumulation of body reserves during this reproductive stage may be insufficient to sustain the high initial milk yield levels commonly observed in goats.
Effects of mating season
The seasonal variation in forage quality and quantity was clearly reflected in the milk yield profiles according to mating season group. Similarly to McDowell et al. (in Iloeje et al. 1980), who showed that the feed component alone could account for about 30% of all variation in lactation performance, it can be assumed that with no variation in feed quality and quantity the effect of mating season would be negligible. Does kidding in the period from October to April (mating seasons 3, 4, and 5) generally had access to a higher level of nutrition and were able to sustain a higher level of milk production than does kidding in the long dry season (mating seasons 1 and 2). Does which kidded at the end of the long rains (group 6) had the advantage of a high primary productivity throughout gestation and produced the largest peak yields (580 g·day^{—} ^{1} attained at about 4 weeks of lactation). Scale and shape of lacation curves differed markedly between mating season groups, and the typical lactation curve shape with an initial rise to a distinct peak and a subsequent decline until the end of lactation usually observed in well nourished animals could only be seen for lactations that were initiated during or at the end of the rainy season (mating seasons 5 and 6). Similarly to the observations made by Nicholson (1984) in a pastoral herd of Boran cows in Southern Ethiopia, improvements in nutritional conditions caused a rapid rise in milk production at virtually any stage of lactation. Perhaps the most striking feature emerging from the estimated response profiles is that marked peaks in milk yield occurred as late as 22 (group 3) and 24 (group 1) weeks of lactation. In one case (group 1), maximum milk yield was reached only after 14 weeks of lactation, at which time the natural decline of [page 104↓]production was counterbalanced by increased forage availability at the onset of the short rains. Generally, multiple peaks in milk production are likely to be observed whenever a rainy season occurs after about the first half of the lactation period. This is in accordance with the study of Blackburn and Field (1990) noted above, who found multiple peaks in lactation curves of does which kidded during the long dry season.
Methodological issues
From the foregoing, several consequences for evaluating lactation performance in goat herds exposed to seasonally fluctuating nutrient supplies emerge. Firstly, it will generally be difficult (if not entirely impossible) to identify the principal lactation phases (ascending phase, peak, and descending phase) which commonly characterize lactation curves and on which comparative assessments of lactation performance are usually based. Moreover, when average daily milk yield curves have multiple peaks, it is not clear how such concepts as persistency or even lactation length could be meaningfully defined. Secondly, from a statistical point of view, the conclusion cannot be avoided that when the major influence on milk production is the season in which lactation is initiated, there will be little point in trying to fit smooth and wellbehaved nonlinear algebraic curves such as the incomplete gamma, inverse polynomial, or general exponential to lactation data. This tends to be further exacerbated by the fact that, in semiarid regions, environmental conditions may exhibit considerable interyear variability, so that seasonal patterns of nutrient availability cannot be expected to be fully reproducible. While under controlled environmental conditions, the form of the responseovertime curve may be suggested by theoretical considerations, this is clearly not the case in such a setting. In the absence of a mathematical form for yield curves over time that is prescribed by some theory, it appears justifiable to concentrate efforts on finding an empirical function that provides an adequate summary of the available data (Kenward, 1985; Lindsey, 1993). For several reasons, the polynomial functions used in this study are particularly useful in this respect. Firstly, they can approximate any yield pattern if a sufficiently complex model (in terms of degree of polynomial in time) is selected and enough observations over time are available to fit the specified function (Burchinal et al., 1994). Secondly, as demonstrated in this study, fitting polynomial functions in time to longitudinal data using the general linear mixed model (GLMM) approach has the advantage of yielding both individualspecific and population average trajectories, and that hypotheses regarding the relationship between response patterns and predictors of interest can be tested (Cnaan et al., 1997; Verbeke, 1997). GLMM‘s make full use of the information on the variability of the experimental unit that is contained in the data, and accommodate the correlatedness of repeated measurements in computing test statistics for the comparison of profiles (Kenward, 1987; Ware, 1985; Zeger and Liang, 1992). If the variancecovariance structure is defined correctly and the variance components estimated with sufficient precision, an immediate result of the linear mixed model approach is that the fixedeffects parameters are estimated with greater precision than if the covariance structure had been ignored (Littell et al., 1996; Rawlings and Spruill, 1994).
It should be emphasized that taking into account major environmental influences (such as the effects of mating season and range condition considered in this study) in the fitted model is not only of interest in its own right, but essentially constitutes a prerequisite for making valid inferences with regard to the impact of other predictor variables on response trajectories. In contrast to polynomial functions, nonlinear functions are not well suited for modelling the mean structure, since they are less flexible and will tend to smoothout environmental perturbations. In the context of fitting nonlinear models to growth data, in which similar problems with respect to estimation and interpretation arise, Fitzhugh (1976) states that any equationbound method already imposes artificial mathematical constraints on the biological variation inherent in response curves. And they are certainly even less capable of capturing variations in response caused by erratic fluctuations in environmental conditions. This becomes evident when one compares the response profiles by mating season group obtained in this study with the vegetation score specific lactation curves reported by Wahome et al. (1994). The authors classified individual milk yield sequences according to average vegetation condition over the first 6 weeks of lactation and estimated lactation curves for each of five average vegetation condition score levels. In spite of the fallacy associated with using the arithmetic mean as a measure of central tendency for ordinal data, this approach to classifying individual lactation sequences according to environmental condition can be assumed to capture similar effects on lactation performance as the mating season treatment effect considered in the present work. The principal difference between both predictors is that the levels of the mating season variable refer to fixed points in time and as such tend to represent a smaller range of environmental states. Note, however, that the response profiles for the browseadjusted lagged, range condition scores (RC II) estimated in this study cannot be compared to those of Wahome et al. (1994): RC (II) was entered as a sequence or timechanging effect (Lindsey, 1993) into the fitted model, and thus the response profiles for the five condition score levels give an impression of the relative effect of the vegetation state on milk production at each time point during lactation. Nevertheless, changes in the production environment throughout lactation should affect the shape of lactation curves in a similar way in both cases, with improvements in nutrient availability causing a rise in milk production and [page 105↓]nutritional stress during the dry season leading to a rapid decline in average daily yields. None of such patterns, including multiple peaks, were apparent in the lactation curves presented by Wahome et al. (1994). Obviously, these features were averaged out in the process of fitting the incomplete gamma function to individual lactation sequences.
Evaluating milk production in pastoral goat herds exposed to strong seasonal changes in forage supply is perhaps best carried out in terms of cumulative milk yields, instead of average daily yields. The present analysis has shown that cumulative production until a specified timepoint can be used as a criterion for assessing the relative performance of treatment or classification groups. Turning to the question of evolution of cumulative milk production over time, this analysis has shown that, with respect to the effect of mating season, the level of peak daily yields attained during lactation are not decisive in determining overall lactational performance. For instance, while the largest peak yields were achieved by goats which kidded toward the end of the long rainy season (mating season 6), total milk production in this group surpassed that achieved in all others only until about 12 weeks of lactation. Thereafter, cumulative milk yields in group 6 levelled off rapidly due to nutritional constraints experienced during the long dry season.
With regard to the total amount of milk produced until 28 weeks of lactation, the current production system could benefit from the introduction of a restricted breeding management allowing does to be bred in the period from June to November (mating seasons 3, 4, and 5). A slightly different recommendation emerges with respect to total milk production until weaning. In this case, maximum milk production can be expected to be achieved by does mated between October and January (mating seasons 5 and 6). In contrast, joining does just prior to or during the long rainy season (mating seasons 1 and 2) is likely to lead to very poor milk production (less than 34 kg per doe until weaning). The present experiment has revealed that such low levels of milk output are insufficient to promote adequate liveweight development of kids until weaning (Chapter 4). Similarly, the failure to provide sufficient milk to the kids during this stage has also been found to significantly increase the incidence of early kid deaths (Chapter 3).
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