Population analysis of a purebred Hereford and a multibreed synthetic beef cattle herd

Analyse demographique d'un troupeau de race pure Hereford et d'un troupeau synthetique multiracial de bovins a viande. Les enregistrements des carrieres des femelles nees de 1966 a 1975 sont utilises pour estimer et comparer les parametres demographiques d'un troupeau de race pure Hereford (HE) et d'un troupeau synthetique multiracial (SY1) de bovins a viande, soumis tous 2 a une politique de reforme rigoureuse dans laquelle toute genisse ou toute vache ne produisant pas un veau sevre par an etait eliminee. La taille moyenne instantanee de la population etait de 118 vaches et 39 genisses dans le troupeau HE, de 155 vaches et 56 genisses dans le troupeau SY1. Le troupeau SY1 etait un ensemble composite d'origine multiraciale comprenant 33% de Charolais, 33% d'Angus et 20% de Galloway, le reste provenant d'autres races bovines a viande. Les 2 troupeaux etaient conduits de maniere identique. Neuf parametres issus de l'analyse des carrieres des femelles sont etudies : la probabilite, a la naissance, de survivre jusqu'a un âge donne ; le quotient de survie Px (probabilite, a un âge donne, de survivre jusqu'a la classe d'âge suivante) ; l'esperance de vie a un âge donne (nombre moyen d'annees restant a vivre a une femelle atteignant l'âge x) ; le quotient de fecondite (probabilite pour une femelle, a un âge donne, de produire une fille) ; la contribution relative d'une femelle d'un âge donne a la procreation des generations futures ; le taux net de reproduction Ro (nombre moyen de filles de remplacement produites par une femelle) ; le taux instantane d'accroissement de la population (r) et l'intervalle de generation (T). On observe des differences entre les 2 troupeaux sur les parametres demographiques specifiques de l'âge, le troupeau SY1 presentant des valeurs plus elevees que le troupeau HE. Le troupeau SY1 presente des valeurs moyennes plus elevees que le troupeau HE pour le taux net de reproduction Ro (1,57 ± 0,11 contre 1,21±0,15 ; p < 0,07) et pour le taux instantane d'accroissement r (0,09 ± 0,01 contre 0, 03 ± 0,02 ; p < 0,04), ce qui indique un taux d'accroissement de la population plus eleve dans le troupeau SY1. L'intervalle de generation T est plus eleve (p < 0,01) dans le troupeau SY1 que dans le troupeau HE (5,09 ± 0,11 contre 4,25 ± 0,19 annees). Ces resultats montrent qu'une meme conduite et qu'une meme politique de reforme peuvent se traduire par des parametres demographiques differents, phenomene resultant sans doute dans cette etude d'un effet d'heterosis sur la survie des veaux dans le troupeau synthetique d'origine multiraciale SY1. Sur la duree, la politique rigoureuse de reforme entraine une reduction des parametres Ro, r et T jusqu'a un point ou la taille du troupeau HE ne peut plus etre maintenue (Ro < 1 en 1972 et dans les cohortes ulterieures).

The goal of faster genetic improvement in operations producing seed stock dictates that the generation interval should be shortened, and hence intense selection and/or stringent culling practices are usually employed. Arthur et al (1992) reported the reasons for disposal of cows from a purebred Hereford and 2 multibreed synthetic beef cattle herds managed at the same location and under a stringent culling policy. The longevity and lifetime productivity of the cows were reported by Arthur et al (1993). There is very little information available for beef cattle on the effect, over time, of such a stringent culling policy on population parameters and on the sustainability of herd numbers. The objective of this study was to construct age-specific and overall life tables to characterize and compare a purebred Hereford and a multibreed synthetic beef cattle herd under a stringent culling system.

Herd management and breeding plan
The data used for the study were from the University of Alberta ranch at Kinsella, located 150 km south-east of Edmonton, Alberta, Canada. Two main breeding populations were established in 1960, namely the purebred Hereford (HE) and the Beef Synthetic. The history of the ranch and the formation of the breeding populations have been reported in detail by Berg (1980). The Beef Synthetic population was renamed Beef Synthetic #1 (SY1) in 1982, after another synthetic group composed of beef breeds was developed. To satisfy the criteria of relatively stable herd numbers, consistent management, detailed identification and production records required for such analyses, records on females born at the Kinsella ranch from 1966 through to 1975 and followed till disposal were used. The average herd size and standard deviation of the cow herd was 155 ! 6.7 for SY1 and 118 ! 3.4 for HE. The corresponding values for the heifers were 56 ! 3.0 for SY1 and 39 ±3.5 for HE. All the females had left the herd at the time of data analyses.
The Beef Synthetic #1 (SY1) population is a multibreed composite group with mainly Charolais, Angus and Galloway breeding. The average breed composition of the SY1 females is presented in table I. The management and breeding plan of the herds were described in detail by Berg et al (1990). In summary, the 2 herds were treated as similarly as possible. The breeding herds were on the range year round and dependent on natural grazing, except for 3-4 months is winter when supplementary feed was provided. The level of supplementary feed depended on the pasture conditions and severity of the winter. Selection of sires was within each herd and was based on pre-and postweaning gain. On a few occasions, Hereford bulls from outside the HE herd were used for breeding. Sires were selected for breeding as yearlings and about 25% of these bulls were again used in the following year. All sound heifers were exposed to bulls as yearlings to calve as 2 year olds. Cows and heifers were exposed to bulls for 60 d in the breeding season which was July/August each year. Breeding occurred in single-sire groups of about 25 cows.
To prevent reproductive failure resulting from poor serving capacity of a particular bull, mating groups were monitored during the first half of the breeding season. Any bull found to have poor serving capacity was replaced with a proven older bull for the rest of the breeding season. Calving was mainly in April and May and 2 year olds were calved separately, closely supervised and remained separated until breeding commenced. Calves remained with their dams until weaning in early October each year. Heifers and cows failing to wean a calf each year were culled.
Heifers and cows were also culled for unsoundness and defects such as bad udders, leg and feet problems, etc. The frequencies of the various reasons for disposal for the herds have been reported by Arthur et al (1992). The lifetime productivity of these cows has also been reported by Arthur et al (1993).

Demographic analyses
Life table statistics were computed for the 2 herds in this study. The cohort method of life table construction was used. This method follows an actual cohort (birth year group) from birth to the end of the last member's life (Caughley, 1966(Caughley, , 1967Mertz, 1970). Data on 10 full cohorts (1966 through 1975; all animals had left the herd) were used in the construction of the life tables for each herd. The model utilized females only and involved annual seasonal breeding and overlapping generations. The time reference was immediately postpartum, with birth considered age 0 and time interval being 1 year. Leaving the herd for any reason was equated with mortality. The biological flow chart of the model is illustrated in figure 1.
Six age-specific life table statistics and 3 overall life table statistics were computed (Caughley, 1966(Caughley, , 1967Mertz, 1970;Pianka and Parker, 1975). The agespecific life table statistics computed were as follows: survivorship (probability at birth of an animal surviving to a particular age, Lx); survival rate (probability at a particular age of surviving to the next age, Px); mortality rate (probability at a particular age of dying before the next age, Qx = 1 &mdash; Px); expected herd life (additional number of years an animal of a particular age is expected to remain in the herd, Ex); birth rate (probability of a cow of a particular age producing a live female calf, Mx); and reproductive value (relative contribution of an animal of a particular age to future generations, Vx). The overall life table statistics computed were net reproductive rate (expected number of daughters produced by each animal, Ro), instantaneous rate of population increase (a measure of herd number increase or decrease, r) and generation interval in years. The computational formulae for these life table statistics have been summarised by Schons et al (1985). In many studies populations are characterized by constructing a life table pooled across cohorts (Krehbiel et al, 1962;Greer et al, 1980;Melton, 1983). Another method to cancel out any differences between cohort and distortions due to small numbers of animals at older ages is to average each life table statistic over all cohorts and at each age, if age-specific (Schons et al, 1985 (Lee and Desu, 1972) was computed, using the Survival procedure in SPSS (1990), to compare the age-specific survivorship of the two herds. The D statistic is based on a score that compares the Lx values or another statistic between herds and tests the null hypothesis that the herds are samples from the same survival distribution. Differences between the 2 herds in the overall life table statistics (Ro, T and r) were tested using a t-test.
Within each herd, simple linear regression analysis was done for each of the overall life table statistics to examine the nature of the slope (Steel and Torrie, 1980).

RESULTS AND DISCUSSION
Comparison of the survivorship (Lx) values of the 2 herds using the Lee-Desu D statistic showed significant difference between the herds (D = 3.98; p < 0.05) leading to the rejection of the null hypothesis that the survival distributions of the 2 herds are the same. The survival patterns (L!) for HE and SY1 were similar up to age 2 years, after which there was a faster rate of the decline in HE compared to SY1 (fig 2). A detailed discussion on the L! curves and the reasons for disposal of the females of the 2 herds have been reported previously (Arthur et al, 1992(Arthur et al, , 1993. The probabilities at a particular age of surviving to the next age (Px) are presented in table II. There was a high probability for survival from birth to age 1 year and from age 1 to age 2 years (greater than 0.9). This was due to the facts that firstly there were very few deaths prior to age 2 years and, secondly, all available females entered the breeding herd as replacements. From age 2 years, causes other than death, viz culling for reproductive failure, calving problems, calf survival and udder problems, become additional sources of mortality, resulting in relatively lower Px values after age 1 year. In general, SY1 had higher survival probabilities than HE after age 1 year. The age-specific mortality rate (Qx) is a mirror image (1 -Px) of the age-specific survival rate (Px) and the results are opposite those of the Px statistic discussed. SY1 had higher values for expected herd life (Ex) at all ages compared to HE (fig 3), indicating that at any particular age SY1 females were expected to live longer than HE females. The age-specific birth rate (probability of a cow of a particular age producing a live female calf, Mx) is a very important statistic in beef cattle production, because it influences the number of replacement heifers available, population growth and generation interval. Mx is dependent on the sex ratio of progeny. At older ages there were fewer cows present in the herd, hence the likelihood that the sex ratio of progeny of cows at these ages was not 1:1 was high. This deviation from the expected 1:1 sex ratio contributed to the relatively high or low Mx values obtained at older ages (table II). Mean Mx across all ages was 0.46 and 0.48 for HE and SY1, respectively. Reproductive value (Vx) is also defined as the ratio of the expected size of a herd (at some future time) founded by a cow or group of cows of a particular age to the expected size of a herd founded simultaneously by a heifer calf or group of heifer calves aged 0 (MacArthur and Wilson, 1967). The Vx values for both herds peaked at age 2 years and gradually dropped off with SY1 having higher values than HE at all ages (table II). The rise in the V! values up to age 2 years was due to the lack of reproduction until 2 years of age (Mx values are zero for ages 0 and 1 year).
The overall life table statistics for the 2 herds are presented in table III.
The means for net reproductive rate (Ro) were greater than unity and those for instantaneous rate of population increase (r) were greater than zero for both herds.
These results, which represent the average for the entire study period, indicate that cows in both herds were more than replacing themselves and that herd numbers were increasing. The means for these statistics were higher in SY1 than is HE. For natural populations r can be used as a measure of a population's capacity for sustained change in numbers; the higher the r the more fit the population.
Alternatively, the environment in which a population has its highest r is the optimal environment for that population (Mertz, 1970). Because of human influence on livestock management for production efficiency, the application of r as a measure of a population's capacity for sustained change in numbers is limited. Herd differences in generation interval (T) also followed a pattern similar to Ro and r with SY1 having higher means than HE.
Examination of the trend in the overall life table statistics indicated that the means of these statistics had been decreasing with time. For Ro both herds had a negative regression coefficient although the coefficient for SY1 was smaller than that for HE (fig 4). For HE the predicted Ro values were less than unity for the 1972 and later cohorts, indicating that those cohorts were not replacing themselves. The pattern for r was similar to Ro and hence the results are not presented. For T, the regressions for SY1 (T = 5.73 -O.11Y) and for HE (T = 4.84 -0.108Y) were significant and both herds had negative regression coefficients. Y in the equations represents year cohorts, with the 1966 cohorts having a value of 1. The declining trend in the overall life table statistics was probably the result of the stringent culling policy. The contribution of inbreeding to this decline, if any, would be minimal since efforts were made to prevent inbreeding in both herds, through the selection of breeding bulls, as well as through the occasional use of Hereford bulls from outside the HE herd. The breed composition of the multibreed SY1 herd stabilized around 1970 (table I). The trends in the overall life table statistics were also evaluated using only the 1970 to 1975 cohorts for both herds, to reflect the period of stable breed composition of SY1. For these cohorts the regressions for SY1 Population analysis of a commercial herd of Angus cattle in Wyoming was reported by Schons et al (1985) using similar biological model and computational formulae. The Lx curves of herds in this study (Kinsella herds) and that of the Wyoming herd (Schons et al, 1985) are presented in figure 2. The most noticeable difference between the Lx curves of the Kinsella herds and that of the Wyoming herd occurred at ages 1 and 2 years, where the Lx values for the Kinsella herd were almost double those of the Wyoming herd. This is attributable to differences in replacement heifer policy at the 2 locations. In the Kinsella herds all sound heifers were included in the breeding herd and exposed to bulls as yearlings, hence an Lx of over 0.9 at 1 year of age. In the Wyoming herd, not all heifers entered the breeding herds. Replacement heifers were selected based on weaning weight, yearling weight, dams record, and in some years on information on their sires. Hence just over 50% of the heifers (Lx of 0.52) were used as replacements. Another difference between the Kinsella and Wyoming herds is in the slope of the Lx curves after age 2 years, although the curves were all smooth with no major disruptions. The slopes of the Kinsella herds are sharper than that of the Wyoming herd. This is likely due to differences in the culling policies at the 2 locations. Culling was very stringent in the Kinsella herds; any cow failing to wean a calf each year was culled. Cows were also culled for caesarian sections, bad udders, and leg and feet problems (Arthur et al, 1992). In the Wyoming herd cows were culled for some of the reasons as in the Kinsella herds, but culling was not as stringent. The Lx curve reported by Krehbiel et al (1962Krehbiel et al ( ), using data (1939Krehbiel et al ( -1961 from the Virginia Beef Cattle Improvement Association (VBCIA), was similar to that of the Wyoming herd except for its slightly steeper slope. Px values for the Kinsella herds were higher than that of the Wyoming herd at age 1 year, similar at age 2 years generally lower at subsequent ages, due to the same reasons discussed for differences in Lx values between the 2 locations.
Ex curves from the Wyoming (Schons et al, 1985) and VBCIA (Krehbiel et al, 1962) herds peaked at age 1 year, whereas those of the Kinsella herds were highest at age 0 but peaked again at ages 4 and 5 years (fig 3). Although the Ex values reported by Greer et al (1980) for a herd of mostly Hereford cattle in Montana did not include ages 0 and 1 years, the values for ages 2 to 10 years provided did not show any peak beyond the highest value at age 2 years. The difference in the direction of the Ex curves between ages 0 and 1 years for the Kinsella herds (decreasing) compared with those of the other studies (increasing) is probably due to differences in replacement heifer policy. All heifers were used as replacements in the Kinsella herds versus the selection of a proportion of heifers which was used as replacement in the other studies. In the Kinsella herds females were expected to wean a calf each year. Culling for reproductive failure and calf survival problems accounted for 63% of all mortalities (Arthur et al, 1992). There was therefore an indirect reproduction related automatic selection with age. This automatic selection could be responsible for the rise in the Ex curves after first calving (age 2.years) and reaching a peak at ages 4 and 5 years, which is unique to the Kinsella herds. Mx values for the Kinsella herds (overall average of 0.46 for HE and 0.48 for SY1) were generally higher than those of the Wyoming herd (overall average of 0.42). Mx is a function of sex ratio, fecundity and foetal mortality. In the Kinsella herds any females which failed to calve in any year was culled, hence there is an indirect automatic selection for females with high reproductive efficiency. This could account for the higher Mx value in the Kinsella herds compared to the Wyoming herd, where culling for reproductive failure was not as stringent. Vx values in the Wyoming herd are higher than those of the Kinsella herds, probably due to differences in culling policy and replacement heifer management as discussed for Lx. Means of overall Ro and r values for the SY1 herd were higher than, whereas those of the HE herd were similar to, those of the Wyoming herd. Generation intervals (T) for the Kinsella herds were lower than that of the Wyoming herd. The value of T for most beef cattle herds is between 4.5 and 6 years (Neumann and Snapp, 1969) hence the Kinsella herds are at the lower end of the range, due to the stringent culling policy.
In addition to the reproduction-related automatic selection with age, the stringent culling policy had the effect of reducing T. In situations where genetic progress is being made for any trait, this reduction in T may be beneficial, as a lower T increases the rate of genetic gain. In these herds, direct selection of bulls for pre-and postweaning gain was occurring, which resulted in positive genetic gain (Sharma et al, 1985). The rate of this genetic progress was thus enhanced by the reduction in T for the females. It is however recommended that in using such a stringent culling policy careful monitoring should be exercised to ensure that cows are able to replace themselves (Ro § 1) so that herd numbers de not decrease (r > 0).

CONCLUSION
The results of this study and those of other studies in beef cattle indicate that life table statistics can differ among herds where management and culling policies differ. However, this study also shows that the same management and culling policy may result in different life table statistics. This is probably due to the influence of heterosis for calf survival in the multibreed composite SY1 herd. The stringent culling policy had the effect of reducing the net reproductive rate, instantaneous rate of population increase and generation interval in both herds over time. However, in the SY1 herd the trend stabilized in 1970 and the ability to maintain herd numbers was retained, while in the HE herd the trend continued to the point where herd size could not be maintained (Ro < 1 for 1972 and later cohorts, fig 4). If the decline in these overall life table statistics needs to be stopped, it is suggested that strategies that aim at reducing mortality rates in 2 and 3 years olds should be considered.