Characterization of the Egg Production Curve in Poultry Using a Multiphasic Approach1 W. J. KOOPS_

Transcription

1 Characterization of the Egg Production Curve in Poultry Using a Multiphasic Approach1 W. J. KOOPS_ Department of Animal Breeding, Agricultural University, P.O. Box 338, 6700 AH Wageningen, The Netherlands M. GROSSMAN Department of Animal Sciences, University of Illinois, Urbana, Illinois INTRODUCTION Egg production in poultry shows considerable individual variation over the laying period. Number of eggs produced per unit of time is the basis for important egg production traits. Egg production curves describe the relation between number of eggs and time of the laying period. Linear or nonlinear regression models have been shown to be useful to characterize the mean egg productioncurve. These models include: Wood (Wood, 1967), compartmental (McMillan et al., 1970 a,b), modified Wood (McNaUy, 1971), Adams-BeU (Adams and Bell, 1980), and modified compartmental (Yang et al., 1989). Information on egg production curves based on the mean of group observations do not necessarily provide appropriate information for use on individual hens, unless the curves have been synchronized. The compartmental model has been used to describe mean egg production for groups of hens that have been synchronized for age at first egg (Gavora et a/., 1971; Cason and Britton, 1988; Yang et al., 1988). To better understand the biology of egg production, and for the purpose of genetic evaluation for breeding programs, it is necessary to study the egg production of individual XThisresearch is supported in part by the Illinois Agricultural Experiment Station Hatch Project , Estimation of Genetic Parameters. Presented at the 40th Annual National Breeders Roundtable, 2-3 May 1991, St. Louis, MO. 2Supported in part by the Department Endowment, University of Illinois. lo of Animal Sciences and the George A. Miller

2 hens. The compartmental model and the Wood model have been applied to egg production of individual hens (Gavora et al., 1982). The R2 value obtained from fitting the models to individual egg production varied from 0 to.97. Means of parameter estimates obtained from fitting individual egg production curves were not equal to parameter estimates obtained from fitting the mean of these curves. This is because models used to fit the data were nonlinear and because the curves were not synchronized. McNally (1971) noted that the egg production curve for a group of hens had the same general form as the lactation curve. He described the mean egg production curve, therefore, with a modified Wood (1967) model. Traditional models to describe lactation curves in dairy cattle (e.g., Wood, 1967) assume lactation to be a single phase process. A new approach to describe lactation curves was developed by Grossman and Koops (1988). The approach was based on a multiphasic lactation process, which considers milk yield over the course of a lactation to result from accumulation from more than one phase of lactation. Egg production is based on cyclic processes, with a period of 24 to 27 h or more, depending on age (Bahr and Palmer, 1989). These cyclic processes result in clutches of one or more eggs laid on consecutive days, and each clutch is followed by one or more pause days (Nalbandov, 1976). The length of a clutch varies little within a hen, and is assumed to be highly heritable (Nalbandov and Opel, 1974). Despite the highly repeatable nature of a clutch, the egg production curve shows an increase in the number of eggs and then a decrease with increasing age (Bahr and Palmer, 1989). The existence of clutches and pauses support the hypothesis for a multiphasic pattern of the egg production curve. Variation in length of clutch and in length of pause, due to the effect of aging, can result in differences between phases. The objective of this study is to characterize the egg production curve in poultry by a multiphasic model that includes parameters that are biologically interpretable. Data were used at three levels of observation, starting with data on actual time of lay during the day and progressing to daily and weekly data. 11

3 CHARACTERIZATION OF EGG PRODUCTION CURVE Parameters for Egg Production Curve Egg production in the hen is characterized by the number of eggs in a clutch and the pause between clutches, where oviposition failed to occur (Fraps, 1954). Number of eggs in a clutch is determined by the ovulatory cycle, which results in circadian rhythms of oviposition. Deviation of the period of about 24 h (circadian rhythm) from the period of exactly 24 h (daily rhythm) is referred to as "lag" (Fraps, 1954). Pause is defined as the period of time from the last egg of a clutch to the first egg of the next clutch, and consists of one circadian rhythm plus an additional period of time that will be referred to as "delay". It is expected that lag is determined by genetics (Nalbandov and Opel, 1974), whereas delay is determined by environment, especially by the light:dark ratio. The functional relationship between egg production and time is usually characterized by linear or nonlinear regression of cumulative number of eggs (dependent variable) on time of oviposition (independent variable). This relationship is understood best if time of oviposition is recorded in units smaller than days, preferably in hours or even minutes. Then the linear model to describe this relationship can include parameters for lag and delay, assuming constant values over time. For a hen with a daily rhythm of oviposition, the linear model to describe egg production is Yt = 1 + (1/24)t [1] where Yt is cumulative number of eggs at time t (in hours), from time of first egg, and 1/24 is the slope, indicating one egg each 24 hours. For a hen with a circadian rhythm of oviposition for the first clutch, Equation [1] can be modified by including a parameter to account for lag: Yt = 1 + [1/(24 + ),)]t [2] 12

4 where 1/(24 + ),) is the slope, indicating one egg each (24 + ),) hour period, and,xis the lag in hours. If ), is negative, then the circadian rhythm is less than 24 hours and the hen is able to produce one egg in each 24-hour period and more than one egg in some 24-hour periods. If ), is zero, then the circadian rhythm is equal to the daily rhythm and the hen is able to produce strictly one egg in each 24-hour period, ff ), is positive, then the circadian rhythm is more than 24 hours and the hen is not able to produce one egg in each 24-hour period. As a result of the positive lag in rhythm of oviposition, the hen eventually will fail to produce an egg in some 24-hour period. Failure of the hen to produce that egg ends the clutch and results in a pause. For a hen with a circadian rhythm of oviposition for more than one clutch, Equation [2] can be modified by including sequence number of the clutch and a parameter to account for delay: Yt = 1 + [1/(24 + ),)][t- 6(c-1)] [3] where ), is average lag in hours, 6 > 0 is average delay in hours, and c is the sequence number of the clutch (c = 1, 2,...). Equation [3], therefore, is suitable to characterize egg production by parameters that represent lag and delay. In practice, observations on oviposition are not taken hourly but daily, when only the presence of an egg is recorded. Now the relation between cumulative number of eggs and day of oviposition for each hen over clutches is Yt' = 1 + [1/(24 +.).)1124t'- 6(c- 1)1 [41 where t' is observed day of oviposition, from day of first egg, for cumulative egg number Y. With daily observations about oviposition, however, the usual information available is time in days and number of eggs, but not number of the clutch. Number of the clutch, however, can be derived from the available information. The number of pauses is equal to the number of the clutch minus 1: (c - 1). The number of pauses is also equal to the number 13

5 of nonproductive days, which is the difference between number of days and number of eggs minus 1: [t' - (Yt'- 1)] Substituting [t' - (Yt' " 1)] for (c- 1) in Equation [4] yields: Yt' = 1 + [1/(24 + )`)][24t'- 6{t'-(Yt'-1)}] [51 and solving Equation [5] for Yt' results in the relation between cumulative number and day of oviposition: of eggs Ye = 1 + [1/{1 + )`/(24-6)}]t' [6] where [1/{1 + ),/(24-6)}] is the average slope over clutches. Equation [6], however, is not suitable to characterize egg production because the parameters that represent lag and delay are confounded and cannot be estimated separately. Individual variation in the slope is expected to be the result of individual differences in lag and not in delay. This is because lag is expected to be determined genetically, whereas delay is expected to be determined environmentally, probably by the light:dark ratio. Therefore, Equation [6] can be rewritten to express lag as a function of delay, day of oviposition, and cumulative number of eggs: 5, = (24-6)[t'/(V e - 1)- 11 [71 where 5,is a point estimate of the average lag over t' days of oviposition- For individuals in a common environment, it is possible to assume a constant value for 6, and then estimate the lag parameter. For individuals not in a common environment, however, it is reasonable to expect that the delay will not be very different because the light:dark ratios are not very different. 14

6 Estimation of Parameters for Egg Production Curve If Equations [1] through [3] are used as regression models, number of eggs is assumed to be the random variable, having an error distribution, and time of oviposition is assumed to be the fixed variable, measured without error. In practice, however, number of eggs is the fixed variable, because it is based on the observed presence of an egg, and time in hours is the random variable, because it is based on frequency of collection. The appropriate analysis for egg production models, therefore, is to express time of oviposition as a function of number of eggs. Solving Equation [3] for t results in: tv = (24 + ),)(Y - 1) + 6(c- I) [8] where h' is observed time of oviposition in hours, from time of first egg, for cumulative egg number Y. This model was applied to egg production data, where time of oviposition was recorded more or less hourly, to estimate parameters for lag and delay. Data were from an experiment on ovarian function, during August and September, 1990, at the University of Illinois Department of Animal Sciences, in which time of oviposition was observed sometime during each hour from about 7 a.m. to 4 p.m., Monday through Friday, and recorded to the nearest 10 or 15 minutes. For an egg laid from 4 p.m. to 7 a.m., and on weekends, only the presence was observed and recorded. Chickens were exposed to a light:dark ratio of 15:9 hours, with hours of light between 5 a.m. and 8 p.m. Three hens were sampled: one with one clutch, one with two clutches, and one with four clutches over a 16-day period (Table 1). Equation [8] was fitted to data, with time in hours, for each of the three hens using linear regression analysis (Figure 1); estimates for lag and delay, their standard errors, and residual standard deviations are in Table 2. For each hen, residual standard deviation was low, less than 1 h. Equation [8] fitted better to data of hen 4a than to data of others because there was no pause. Lag (3,) ranged from -.08 h to 2.10 h, where higher values for lag indicate longer periods of circadian rhythm and, consequently, smaller clutches. A zero or negative value for lag indicates periods of circadian rhythm equal to or less than 24 15

7 h, which enables the hen to produce large clutches without pause. Delay (6) was about 16 h. For each hen in Table 1, average lag was also estimated using Equation [7] over the entire time period in days, assuming a delay of 16 h. These estimates for lag may be different from those in Table 2 because of the error associated with observing time in days as a multiple of 24 hours. Average lag for hen 4a was 0 h; for hen 9c, it was.53 h; and for hen 27d, it was 1.6 h. For hen 4a, oviposition of egg 15 was observed at 335 h, whereas oviposition was "observed" at 336 h when time was based on days (24 x 14 = 336). For hen 9c, however, oviposition of egg 15 was observed at h, whereas oviposition was "observed" at 360 h when time was based on days (24 x 15 = 360). As a result, the difference between estimates of lag for hen 4a (-.08 vs 0) was smaller than for hen 9c (1.14 vs.53). EFFECT OF AGING ON EGG PRODUCTION CURVE Characterization of the egg production curve assumed constant values for lag and delay over time so that Equations [1] through [7] can be applied only over a period of time when lag is expected to be constant. It has been observed in practice, however, that there are at least two effects that may influence these values over time. One is the effect of sexual maturation and the other is the effect of senescence. Sexual maturation is the process by which the hen reaches sexual maturity, resulting in the ability to reproduce. Age at which the hen lays her first egg is often used as a measure of age at sexual maturity. Age when the hen is able to rep.roduce (age at sexual maturity), however, is not the same as the age when the hen is able to produce (age at first egg) (Morris, 1966). It can be expected, therefore, that age at first egg is earlier than age at sexual maturity. Until sexual maturity is achieved, there is an increase in length of the clutch and a decrease in lag. The effect of senescence in the hen can be seen about 6 to 10 weeks after the hen starts to lay, when there is a decrease in the length of the clutch with age (Van Tierthoven, 1983), which means that there is an increase in the lag with increasing time. 16

8 To account for effects on lag of sexual maturation to describe these effects mathematically as a function of time: and of senescence, it is possible ), = fro(t) + fdt) [9] where fro(t)is a function that describes the effect of sexual maturation and f_(t) is a function that describes the effect of senescence. If degree of sexual maturity follows an increasing sigmoid pattern over a relatively short period of time, then the decreasing effect on lag from first egg to Sexual maturity can be described by a negative exponential function: f_(t) = ae "_t' [10] where e is the base of the natural logarithm, a is the intercept (when t' = 0), and _ is the rate of decay. If degree of senescence also follows an increasing sigmoid pattern, but over a relatively long period of time, then the increasing effect on lag, within one cycle of production, can be approximated by a linear function: fs(t) = 7t'+ P [11] where p is the intercept and 3' is the slope. Substituting Equations [10] and [11] into Equation [9], the function to describe the effects of sexual maturity and senescence on lag is: = ae "l_t' + "it' + p, [12] This continuous function describes a pattern for lag that decreases exponentially to a minimum and then increases linearly. 17

9 Estimation of parameters for effect of aging To examine the effect of aging on lag, ), of Equation [7] can be computed for short periods of time and plotted against age. Then Equation [12] can be used to estimate parameters that relate the effects of sexual maturation and of senescence to lag. Weekly egg production were obtained on 400 hens from a commercial strain, recorded over a period of 37 wks. Each hen was hatched on 12 April 1988 and caged individually in the same house. Chickens were exposed to a light:dark ratio of 15:9 hours. Records were excluded if the hen laid her first egg after week 5 or if she did not lay more than 14 eggs during each of nine consecutive 4-week periods, starting after the week she laid her first egg and ending on week 36. Remaining hens were divided into four groups, according to week of first egg. For each group, the average number of eggs per week was computed, and Equation [7] was used to obtain _,for each week, assuming a value for S of 16 h based on estimates for delay in Table 2. Equation [12] was fitted to _,using a nonlinear regression procedure; estimates of parameters, their standard errors, and residual standard deviations are in Table 3. Based on estimates for/_ and their standard errors, that parameter was eliminated from the model, and Equation [12] was rewritten as: ), = ae 4t' + 7t' [12a] Parameters for Equation [12a] were estimated using the same procedure, and results are in Table 4. Elimination of _ from J the model changed residual standard deviations only slightly and generally reduced the standard error of estimates, especially for 3'. Observed predicted values from Equation [12a] are in Figures 2a to 2d, by group. lag and Linear functions of the parameters in Table 4 are easier to interpret in order to characterize the course of lag over a complete cycle. Two such characteristics are the minimum value for lag ()'m), which is reached at time t',,. To derive these values, the derivative of _ in Equation [12a] was taken with respect to t', set to zero, and solved for t'm and )'m: 18

10 t'm= _rn = ae'_t'm + "/t'm Another characteristic is duration of sexual maturation (3//_), which is defined as the time from week of first egg at which 95% sexual maturity is reached. A fourth characteristic is the effect of senescence (' ), which can be interpreted as "persistency" of egg production. Characteristics were computed (Table 5) based on estimated parameters (Table 4). Minimum lag, time at minimum, and duration decreased with increasing week of first egg, whereas persistency was similar for each group (Figures 3a to 3d). Minimum lag for hens with early week of first egg was higher than for hens with later week. Time at minimum lag for hens with early week of first egg is later than for hens with later week. Duration of sexual maturation for hens with early week of first egg was longer than for hens with later week. Persistency was similar for the four groups, with an average increase in lag of about one hour in 125 days. EGG PRODUCTION FUNCTION The previous development to characterize the egg production curve in poultry can be used to construct a new function to model egg production. Taking the derivative of Equation [6] with respect to t', and replacing Xby _ from Equation [12a], yields a function to describe egg production: Yt' = D/{1 + (ae "lw + 3't')/(24-6)} [13] where Yt,is predicted number of eggs at t' days after first egg, over a period of D days. For daily data, D -" 1. For weekly data, number of eggs is accumulated over seven days, so D = 7. To illustrate the function, Equation [13] was applied to weekly data used in the previous section, with estimates of parameters from Table 4 and assuming 6 = 16. Results 19

11 for each of the four groups indicate that the egg production curve (Figures 3a to 3d) follows the inverse of the lag curve over time (Figures 2a to 2d). DISCUSSION Egg production in poultry is characterized by a multiphasic model, where each phase is determined by the number of eggs in a clutch and the pause between clutches. Number of eggs in a clutch is determined by circadian rhythm, which consists of daily rhythm and lag. Pause consists of a circadian rhythm and an additional period called delay. It is expected that lag is determined genetically, whereas delay is determined by environment, especially by the light:dark ratio. A multiphasic model was developed to estimate average lag and delay, over a relatively short period of time. The effect of age on lag was investigated in terms of sexual maturation and of senescence, assuming a constant delay. Data were used at three levels of observation, starting with data on actual time of lay during the day and progressing to daily and weekly data. Using hourly data with Equation [8] to estimate lag for individual hens gave consistent results that were easy to interpret. Using daily data with Equation [7], however, introduced a systematic error because of the less precise method of observation. The effect of aging on lag was described by a model including effects of sexual maturation and of senescence (Equation [12a]). This model was applied to average weekly estimates of lag on four groups by week of first egg, over a period of about 36 weeks after week of first egg. Minimum lag, time at minimum, and duration decreased with increasing week of first egg, whereas.persistency was similar for each group. The previous development to characterize the egg production curve in poultry led to a new function based on multiphasic characteristics of egg production. To illustrate the function, Equation [13] was applied to weekly data. Results for each of the four groups indicate that the egg production curve follows the inverse of the lag curve over time. This function permits parameters to be expressed as biologically interpretable characteristics, such as minimum lag, time at minimum, duration of sexual maturation, and persistency. 2o

12 Further application of this function, as well as the relation of delay to the dark:light regimen, needs to be investigated. ACKNOWLEDGMENTS We thank Dr. Janice Bahr, University of Illinois Department of Animal Sciences, and DEKALB Poultry Research, Inc., for providing egg production data. REFERENCES Adams, C. J., and D. D. Bell, Predicting poultry egg production. Poultry Sci. 59: Bahr, J. M., and S. S. Palmer, The influence of aging on ovarian function. CRC Critical Reviews in Poultry Biol. 2(2): Cason, J. A., and W. M. Britton, Comparison of compartmental models of egg production. Poultry Sci. 67: and Adams-BeU Fraps, R. M., Egg production and fertility in poultry. Pages in: Progress in the Physiology of Farm Animals, Vol. 2, J. Hammond, ed. Butterworth, London. Gavora, J. S., L. E. Liljedahl, I. McMillan, and K. Ahlen, Comparison of three mathematical models of egg production. Brit. Poultry Sci. 23: Gavora, J. S., R. J. Parker, and I. McMillan, Mathematical model of egg production. Poultry Sci. 50: Grossman, M., and W. J. Koops, Multiphasic analysis of lactation curves in dairy cattle. J. Dairy Sci. 71: McNally, D. H., Mathematical model for poultry egg production. Biometrics 27: McMillan, I., M. Fitz-Earle, and D. S. Robson, 1970a. Quantitative genetics of fertility I. Lifetime egg production of Drosophila meianogaster - theoretical. Genetics 65:

13 McMillan, I., M. Fitz-Earle, L. Butler, and D. S. Robson, 1970b. Quantitative genetics of fertility II. Lifetime egg production of Drosophila melanogaster - experimental. Genetics 65: Morris, T. R., The effect of light on sexual maturity in the female domestic fowl. Ph.D. Dissertation, University of Reading, UK. Nalbandov, A. V., Pages in: Reproductive Physiology of Mammals and Birds. Third edition. Freeman and Co., NY. Nalbandov, A. V., and H. Opel, Egg laying. Pages in: Animal Agriculture, H. H. Cole (ed.). Freeman and Co., NY. Van Tienhoven, A., Page 210 in: Reproductive Physiology of Vertebrates. Second edition. CorneU Univ. Press, Ithaca, NY. Wood, P. D. P., Algebraic model of the lactation curve in cattle. Nature 216: (London) Yang, N-, C. Wu, and I. McMillan, A new mathematical model of poultry egg production. Poultry Sci. 68:

14 TABLE 1. Observed cumulative number of eggs 09, time of oviposition in hours or days from time of first egg, and number of clutch (c) for three hens Hen 4a Hen 9c Hen 27d Cure. no. Time Time No. of Time Time No. of Time Time No. of of eggs in h in d clutch in h in d clutch in h in d clutch (Y) (c) (c) (c) pi P P P P P P P P P 15 1 P :Refers to the presence of an egg, but missing data on time. 23

15 TABLE 2. Estimatefl for lag (_) and delay (6), their standard errors, and residual standard deviations Hen no. No. of Parameter Residual clutches _ se 6 se stand, dev. 4a c d See Equation [8] in text; ), and 6 in hours. 2No estimate for delay because there was no pause. TABLE 3. Estimatefl for parameters, their standard errors, and residual standard deviations Week of No. of Parameter Residual first egg 2 hens _ se fl se "f se /_ se stand, dev See Equation [12] in text; _ and/_ in hours, fl in days"1, and "r in hours/day. 2Data were weekly observations beginning in the week after week of first egg. 24

16 TABLE 4. Estimates "tfor parameters, their standard errors, and residual standard deviations Week of No. of Parameter Residual first egg: hens a se /_ se _' se stand, dev /See Equation [12a] in text; _, in hours,/_ in days':, and _' in hours/day. 2Data were weekly observations beginning in the week after week of first egg. TABLE 5. Estimates t for characteristics of the function to describe lag. Week of No. of Characteristic first egg: hens Minimum Time at Duration Persistency lag minimum :Minimum lag in hours; time at minimum and duration in days, and persistency in hours/day. 2Data were weekly observations beginning in the week after week of first egg. 25

17 FIGURE 1. Linear regression of time of oviposition on cumulative number of eggs for hens 4a (o), 9c (o), and 27d (A). 480 Time (h) _/_._'w 96 _" Cumulative eggs (n) 26

18 FIGURE 2. Observed (,) and predicted (_) values for lag by group. Figure2a. Group2 Figure2b. Group3 (First egg in week 2) (First egg in week 3) 3 Lag (h) 3 Lag (h) 2 2 "" 0 ' " ' ' Time (d) Time (d) Figure 2c. Group 4 Figure 2d. Group 5 (First egg in week 4) (First egg in week 5) 3 Lag (h) 3 La_ (h) 0 ' " ' ' ' ' " ; Time (d) Time (d) 27

19 FIGURE 3. Observed (., A,,, or -) and predicted (_) values for number of eggs per week by group. Figure3a. Group2 Figure3b. Group 3 8 _umber of eggs per week 8 Number of eggs per week I Days after first egg Days after first egg Figure 3c. Group 4 Figure 3d. Group 5 8 _'umber of eggs per week I 8 Number of eggs per week _ [ 73 a a 2 I J Days after fi_t egg Days after first egg 28

20 Question: B. McKay Is lag (A) increasing in a linear function and delay in some other manner through the entire egg production cycle? Response: W. Koops We assume that lag first decreases according to the degree of sexual maturity and then increases linearly according to the degree of senescence. Delay, however, is assumed to be constant over the entire egg production cycle. Question: G. Herbert Does the lag parameter represent a potential selection trait for increasing egg production from part record data on individual birds? Response: W. Koops The lag parameter is a trait of the individual and, it is a potential trait for selection to increase egg production. The point about part record selection requires further study. Question: M. Boichard Do you think that the 6 parameter (delay) may be influenced by senescence also? Response: W. Koops We assume that delay is caused by the light:dark ratio, and if that ratio does not change over time we do not expect the delay to change. We do not expect a relation between delay and senescence. 29