doi:10.1017/S1751731109990280
Evaluation of crude annual parturition rate estimates
in a small-holder African ruminant farming system
M. Lesnoff
a-and R. Lancelot
Centre de Coope´ration Internationale en Recherche Agronomique pour le De´veloppement (CIRAD), Campus International de Baillarguet, 34398 Montpellier Cedex 5, France
(Received 25 September 2008; Accepted 14 May 2009; First published online 3 June 2009)
Many parameters have been proposed for evaluating livestock reproduction performances in tropical farming systems. In tropical free-ranged and small-holder systems, where reproduction cycles cannot be individually observed without expensive field surveys, one of these parameters is the average number of parturitions (h) expected by reproductive female, if the female spends the whole year in the herd. A frequent approach for estimatinghis to use the ratiohc5m/T, so-called ‘crude annual
parturition rate’, wheremis the observed number of parturitions andTis the total time of presence of the reproductive females in the herd during the year. The bias encountered whenhis estimated byhcwas evaluated in this paper. Six methods
of estimation were used, whereTwas the exact observed time of presence (hc1) or approximated by monthly, quarterly,
half-yearly and half-yearly averages or final size of the reproductive herd size (hc2tohc6). Data came from long-term follow-up of cattle
and small-ruminant herds (with data recorded at animal level) in extensive agro-pastoral systems in Senegal. In general,hwas correctly estimated byhc1. Neverthelesshc1was sensitive to competing risks (e.g. deaths, sales and slaughtering of
reproductive females) and was seriously biased when intensive withdrawals of females occurred before or during the parturition peak. Reliability of crude rates progressively decreased fromhc2tohc6, corresponding to the degradation of information used
for approximatingT. This decrease was much lower for cattle (for which all methods had acceptable reliability) than for small ruminants. Among the compared methods, the lower reliability was observed forhc6that we do not recommend for small
ruminants. Methodshc5and hc6are currently used in rapid cross-sectional retrospective surveys based on the recall of the
farmers on the demographic events which occurred in the herd over the last past 12 months. The study has showed that such surveys and estimateshc5andhc6 can generate seriously biased results. More globally, annual parturition rates can be highly
variable depending on the 12-month periods considered. Annual parturition rates estimated on short-term data, even with precise herd follow-up surveys, must be considered cautiously.
Keywords: parturition rate, bias, tropical ruminant livestock, small-holder farming systems, Senegal
Implications
In African small-holder free-ranged farming systems, reproduction is a key component for improving livestock productivity. Reliable estimates of parturition rates are needed to orientate decision makers and research. Naı¨ve, crude rates can be misleading. Annual parturition rates can be highly variable depending on the 12-month periods considered. Rates estimated on short-term data, even with gold standard field survey methods, must be considered cautiously.
Introduction
Many parameters have been proposed for evaluating reproduction performances of ruminants in tropical farming systems. In intensive farming conditions or experimental stations, reproduction is controlled and continuous obser-vations of the reproductive status of females (e.g. anoes-trus, oesanoes-trus, service and gestation periods) are available. This enables to calculate detailed parameters such as the percentage of mated or inseminated females that become pregnant or the average number of services per conception (Mukasa-Mugerwa, 1989). In free and extensively ranged systems (even in Northern countries, e.g. Marzin and Lie´nard (1984)), reproduction is generally uncontrolled. Males and females are reared together and births occur throughout the
aPresent address: Institut d’Economie Rurale, Programme Bovins, BP 258,
Bamako, Mali.
year, although seasonal peaks are generally observed. Mating and reproductive cycles cannot be individually monitored without cumbersome protocols and cruder reproduction parameters must be used.
One of these parameters is the number of parturitions, say
h, encountered in average by a reproductive female, if this female spends the whole year in the herd. In such a parameter, for simplification, females are classified as reproductive when they are older than a given age (which can depend on farming systems). A frequent estimate ofhis the ratio hc5m/T,
so-called ‘crude annual parturition rate’ (e.g. ILCA, 1990; Lhoste
et al., 1993), wheremis the observed number of parturitions during the year in the herd andTthe corresponding total time of presence of the reproductive females. This estimate is simple to calculate but suffers from several difficulties. It is only valid if instantaneous hazard rates (i.e. probabilities of occurrence in a very short period of time) of parturition and of its competing events (such as mortality or other exits from the herd) are constant with time. In that situation, m follows a Poisson distribution and hc is the maximum likelihood
esti-mator ofh(Kalbfleisch and Prentice, 1980; Laird and Olivier, 1981; Agresti, 1990). In other cases,hcis biased and
repre-sents an apparent parturition rate. For instance, when par-turitions and females’ sales or slaughtering are seasonal, hc
can vary without biological meaning, depending on whether the main parturition season is sooner or later than sales or slaughtering periods (this point is discussed later). An addi-tional source of bias in hccomes from the calculation of T.
AccurateTestimates can only be obtained from longitudinal herd follow-up with data recorded at animal level (for exam-ples of protocols, see Poiveyet al. (1981), Fauge`re and Fauge`re (1986), Fauge`reet al. (1991), de Leeuwet al. (1995), van Klink
et al. (1996) and Metz and Asfaw (1999)). In other protocols, such as herd follow-up surveys without animals identification (Berthet-Bondet and Bonnemaire, 1986; Landais and Sissokho, 1986; Huttner et al., 2001; Madaniet al., 2002; Bebeet al., 2003) or cross-sectional retrospective surveys based on farm-ers’ recall (SEDES, 1975; CIRAD-IEMVT, 1989; ILCA, 1990; Planchenault, 1991; Lhosteet al., 1993; Lesnoffet al., 2008),
Tneeds to be approximated. A common approach is to replace
Tby estimates of the average reproductive herd size (following the same principle as in the life table method in human demography (Chiang, 1984)). Accuracy of this approximation depends on the frequency (e.g. monthly, quarterly or yearly) of data used to estimate the average herd-size.
The objective of the article is to evaluate the bias of the crude annual parturition rateshc, without or with approximations ofT,
when estimating h. Empirical bias of hc was calculated by
comparison to a gold-standard, calculated on term long-itudinal herds’ follow-up data on cattle and small ruminants.
Material and methods
Data sets
Data used for bias calculation were collected during two past research programs (PPR:Pathologie et productivite´ des petits ruminants and ABT:Alimentation du be´tail tropical) jointly implemented by ISRA (Senegalese Institute of Agricultural Researches) and CIRAD (French Agricultural Research Centre for International Development). Herds were selected in traditional villages sampled from northern to southern Senegal. Two sites, N’Diagne and Kolda, were considered in the article (Table 1), representing different rainfall patterns. N’Diagne is located in northern Senegal (16.10W; 15.38N) and is classified in the Sahelian eco-climatic type with an average annual rainfall of 300 mm. Kolda is located in Upper-Casamance in southern Senegal (14.94W; 12.88N) and is classified in the Sudano-Guinean eco-climatic type with an average annual rainfall of 1.110 mm.
In each site, herds have been monitored by field enu-merators using the same protocol (Fauge`re and Fauge`re, 1986; Fauge`re et al., 1991). At the first farm visit, all the animals present in the herds have been recorded and identified with ear-tags. Herds have been subsequently visited every 15 days. At each visit, exact dates of all par-turitions, exits (natural deaths, slaughtering, sales, gifts, loans and withdrawals) and entries (purchases, gifts and loans) occurred since last visit have been recorded. Data have been stored in a relational database especially designed for herd follow-ups (with animal identification) in tropical extensive farming systems (Juane`s and Lancelot, 1999). Recorded information have already been analyzed in other contexts (Fauge`re et al., 1990a and 1990b; Cle´ment
et al., 1997; Lesnoff, 1999; Lancelotet al., 2000; Ickowicz and Mbaye, 2001; Ezanno et al., 2003).
Five data sets have been used in the article (Table 1): cattle (one), goats (two) and sheep (two). Study periods were 1994–97 for cattle (Kolda) and 1985–95 for small ruminants (N’Diagne and Kolda).
Table 1Data sets used to estimate the relative bias in annual parturition rates
Site Species Monitoring perioda Number of herdsb Number of femalesb
N’Diagne Goats 1985–95 49 972
Sheep 1985–95 144 2557
Kolda Goats 1985–95 92 993
Sheep 1985–95 102 1004
Cattle 1994–97 12 509
aPeriod considered in the article. b
Annual parturition rate
Gold standard estimate. When estimating h over a
12-month period, one approach to eliminate bias due to vari-able competing risks (Prentice and Kalbfleisch, 1978) is to calculate hazard rates over successive short sub-periods of times (e.g. day, week, fortnight or month) and then to sum the sub-period rates over the whole period. Calculating rates for each sub-period independently and then summing sub-period rates enables to represent more accurately the expected average number of parturition by reproductive female spending whole year in the herd. This approach is close to the one used in the non-parametric Kaplan–Meier survival model when instantaneous hazard death rates are calculated at each time of death or censoring and then summed to get the cumulative hazard rate (Collett, 2003). Time was decomposed into monthly intervals. Finer decom-position can improve the estimate. Nevertheless, improvement was negligible on our data sets (results not detailed here). Shorter sub-periods also had the drawback to generate larger databases, especially for long-term follow-up (e.g. a weekly decomposition of the demographic data of sheep in N’Diagne generated a database of size higher than 80 Mo).
For a given 12-month period, the annual parturition rate estimate used as reference was defined as the sum of the monthly rates:
href ¼X
12 j¼1
hc; j;
where j is the index of the month in the 12-month period,
hc,j5mj/Tj, Tj is the time of presence of the reproductive
females (defined as females older than a given exact age) in the herd in monthj,mjis the number of parturitions in monthj.
Crude estimate and approximations. For the 12-month
period, the crude estimate (without approximation) of the annual parturition rate was calculated byhc15m/T, where
Tis the time of presence of the reproductive females in the herd in the period ðT ¼P12j¼1TjÞ and m the number of
parturitions ðm ¼P12j¼1mjÞ.
Five approximations of the crude estimate (hc2 to hc6)
were calculated by m/Tapprox, where Tapprox represents
estimates of average reproductive herd size. Denotingtthe time (in month) within the 12-month period (t50 and
t512 correspond to beginning and end of the year, respectively) and nt the number of reproductive females
present at timetin the herd,Tapproxwas calculated by:
– Tapprox; 25P12t50nt=13 (monthly average),
– Tapprox; 35Pt50;3;6;9;12nt=5 (quarterly average),
– Tapprox; 45Pt50;6;12nt=3 (half-yearly average),
– Tapprox; 55Pt50;12nt=2 (yearly average),
– Tapprox; 65n12 (end of the 12-month period).
Bias calculation
To take into account for seasonal patterns, successive 12-month periods have been built (within study periods) by
shifting the annual observation period of one month each time: 36 successive 12-month periods have been built for the period 1994–97 and 120 for the period 1985–95. For each 12-month period, bias has been evaluated as follows. We calculated the reference rate href and then the crude
ratehc1and its approximations (hc2tohc6). The relative bias
(in percentage) was calculated as 100 3 (1 2 (hci/href)) for
i51 to 6. A positive relative bias means an overestimation of href. Distributions (location and variability) of href and
of the bias ofhc1tohc6were summarized with descriptive
statistics and graphical analyses.
Results
Time series of href for each site and species in the study
periods are provided in Figure 1. Cattle href in Kolda
ranged from 0.33 to 0.54/year with an average of 0.43/year (Table 2). For small ruminants,hrefwas in average lower in
N’Diagne than in Kolda (Table 2), but with higher dispersion (for instance, for goats, averagehrefwere 0.84 and 1.25/year
in N’Diagne and Kolda, respectively, while corresponding ranges were 0.66 and 0.33/year).
Average bias ofhc1tohc6was low for all sites and species
(Table 2); depending on the site and the estimation method, average bias varied from 20.5% to 0.7% for cattle, from 22.7% to 1.8% for goats and from 23.0% to 0.5% for sheep. Bias dispersion was sensitive to the site, the species and the estimation method. This dispersion was lower for cattle than for small ruminants (Figures 2 and 3): in absolute value, minimum and maximum biases for cattle were 1.9% (hc2) and
6.9% (hc5), while biases higher than 10% were frequent for
small ruminants, particularly withhc6. Highest bias dispersion
has been observed in N’Diagne for sheep. In absolute values, maximum biases were 19.6%, 19.2%, 17.2%, 18.2%, 24.6% and 64.5% with hc1tohc6, respectively.
For small ruminants, bias dispersion has increased from hc1 to hc6 (Figure 3). For instance, in N’Diagne, bias
standard deviation (s.d.) increased from 2.3 (hc1) to 8.8 (hc6)
for goats and from 3.5 to 13.8 for sheep. This pattern was less obvious for cattle: bias s.d. has increased from 1.6 (hc1)
to 2.8 (hc5) (Figure 2).
Time series of biases over the study periods has shown complex patterns depending on the estimation method and the period, mixing seasonal and irregular fluctuations. Series of sheep in N’Diagne are presented in Figure 4 as an example. Besides fluctuations, Figure 4 has confirmed the increasing amplitude of the bias dispersion fromhc1to
hc6. It has also showed that even the less variable estimate
hc1can be affected by large drops.
Discussion
An important feature observed in the study was the high variability of the successive 12-month parturition rates href
(the same result was noted by Marzin and Lie´nard (1984) in a French extensive farming system). For instance, for sheep in
N’Diagne, href has dropped from 1.15 to 0.87/year only by
shifting the 12-month period three months later. This varia-bility was mostly due to the marked seasonality of parturitions in the observed systems (particularly in N’Diagne) and to the location of the parturition peaks which can shift of one or two months according to the year. For instance, in N’Diagne, highest observed values of href corresponded to 12-month
periods including a parturition peak and, by chance, a part of the start of the following peak. Such phenomena make it difficult to get a representative estimate of the annual par-turition rate when data are only recorded over one or two
years. Longer data are needed to eliminate the effect of the successive 12-month rates variability.
In general, href has been correctly estimated by hc1. In
absolute value, bias was lower than 11% in all sites and species, except for sheep in N’Diagne (19.6%, corresponding to the negative drop observed in Figure 4). Rate hc1 is
simpler to calculate and to analyze with inferential statistical methods (href needs within-year decomposition and
involves more parameters). Nevertheless, one drawback of
hc1 is its potential sensitivity to competing risks, such as
mortality and other exits from the herd (sales, slaughtering,
Table 2Average annual parturition rates (minimum and maximum in brackets) hrefand hc1to hc6(see text for detail) for each site and species over
the study period 1994–97 for cattle and 1985–95 for small ruminants
Annual parturition rate
Site Species href hc1 hc2 hc3 hc4 hc5 hc6
N’Diagne Goats 0.84 0.82 0.82 0.82 0.82 0.82 0.84 (0.57, 1.23) (0.55, 1.19) (0.55, 1.20) (0.54, 1.19) (0.55, 1.19) (0.55, 1.23) (0.55, 1.27) Sheep 0.91 0.88 0.89 0.88 0.89 0.88 0.89 (0.71, 1.15) (0.68, 1.11) (0.68, 1.11) (0.69, 1.12) (0.68, 1.13) (0.67, 1.19) (0.68, 1.56) Kolda Cattle 0.43 0.43 0.43 0.43 0.43 0.43 0.42 (0.33, 0.54) (0.34, 0.54) (0.34, 0.54) (0.34, 0.54) (0.33, 0.54) (0.33, 0.56) (0.31, 0.58) Goats 1.25 1.24 1.24 1.24 1.24 1.25 1.28 (1.09, 1.42) (1.08, 1.41) (1.08, 1.41) (1.08, 1.42) (1.03, 1.47) (0.95, 1.53) (0.90, 1.59) Sheep 1.25 1.21 1.21 1.21 1.21 1.22 1.23 (1.07, 1.41) (1.01, 1.38) (1.02, 1.38) (1.02, 1.38) (0.96, 1.40) (0.88, 1.48) (0.84, 1.54)
Figure 1 Time series of the reference annual parturition rateshreffor goats, sheep and cattle in N’Diagne and Kolda sites. The x-axis represents the rank (in the monitoring period) of the first month of each 12-month period used for the calculation of the annual rates.
gifts and loans) of reproductive females. For instance, in farming systems with marked seasonal parturitions, large withdrawals of females before parturition peak will artificially
decrease the number m of parturitions observed in herds, and subsequently hc1. An example of this effect was the
drop that has been observed for sheep in N’Diagne (Figure 4). It was due to massive exits of ewes within a short period of time (Lesnoff, 1999). In such situations,hc1represents an
apparent annual parturition rate, without biological mean-ing, rather than the average parturition rate of a reproductive female spending all the year in the herd. The same drawback applies to approximate crude rates (Figure 4). Therefore, when using crude rates hc, we recommend to also calculate
href(if data have been collected in a herd follow-up survey),
and to check that discrepancies between these estimates remain at an acceptable level, and that no events such as in Figure 4 has occurred.
In this study, reliability of the crude rate has progressively decreased from hc2 to hc6, corresponding to the
degrada-tion of informadegrada-tion used for approximatingT. This decrease was much lower for cattle (for which all methods had an acceptable reliability) than for small ruminants, in relation with a higher precocity of goats and sheep and a faster turnover of these animals in herds. Among compared esti-mates, the lower reliability has been observed for hc6: bias
reached 26.0% for goats and 64.5% for sheep. Therefore, we do not recommend using this estimate, especially for small ruminants. Reliability of hc2and hc3 was acceptable,
with the same reservation as for hc1 regarding the
sensi-tivity to competing risks.
Estimation method Relative bias (%) −20 0 20 40 60 Goats N’Diagne Sheep N’Diagne hc1 Goats Kolda hc1 −20 0 20 40 60 Sheep Kolda hc6 hc5 hc4 hc3 hc2 hc2 hc3 hc4 hc5 hc6
Figure 3 Box-and-whisker plots of the relative bias (%) of the estimated annual parturition rateshc1tohc6compared to the reference valuehreffor small ruminants in N’Diagne and Kolda sites (see Figure 2 for details on box-and-whisker plots).
Estimation method Relative bias (%) −10 −5 0 5 10 hc1 hc2 hc3 hc4 hc5 hc6
Figure 2 Box-and-whisker plots of the relative bias (%) of the estimated annual parturition rateshc1tohc6compared to the reference valuehreffor cattle in Kolda site. For a box, the closed point located in the box represents the median and the two ‘hinges’ are the first and third quartile. The ‘whiskers’ extend out from the box to the most extreme data, which is <1.5 3 IQR away from the box (IQR: inter-quartile range). Eventual outliers are represented by open circles.
Rates hc5 and hc6 can be used in rapid cross-sectional
1-year retrospective surveys based on interview of farmers and their recall of the demographic events that occurred in the herd over the last past 12 months (ILCA, 1990; Lesnoff
et al., 2008). These surveys are quicker and less expensive than herd follow-up – especially in large areas or in nomadic systems – and can be implemented after unpre-dictable crises (such as droughts or disease outbreaks) to estimate their impacts. Nevertheless, the study has shown that hc5 and hc6 only provide very approximate results.
Calculation bias may also be worsened by farmers’ recall errors during retrospective interviews. Results of retro-spective surveys andhc5 andhc6estimates should be
con-sidered with caution. When possible, other surveys methods and estimates should be preferred.
Finally, the observed variability between the estimates and between the successive 12-month periods have shown that comparisons of parturition rates, for instance, during a literature review or when analyzing field data for testing impacts of innovations, should use estimates calculated with the same method and on the same 12-month periods. In the first case, however, the frequent lack of methodolo-gical details reported in the articles on small-holder tropical livestock farming systems remains a constraint.
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