No abstract

Abstract.A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period rn of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

Data from about 4000 Sahiwal cows from eight large herds in Pakistan were used to study the influence of genetic and environmental factors on some milk production traits. First-lactation mean values were 1363 kg, 1395 kg and 252 days for milk yield up to 305 days after calving, total lactation yield and lactation length, respectively. Second and third lactation yields were proportionately 0-12 and 0-18 higher, respectively, at 305 days. The effect of herdyear at calving was by far the most important source of variation for all traits. Heritabilities estimated in uni-and trivariate analyses, using restricted maximum likelihood (REML) with an expectation maximization algorithm for an animal model, ranged from 0-14 to 0-17 for first-lactation traits. The estimates were generally lower for second lactation and higher for third lactation traits. Genetic correlation between lactations for the same trait were close to unity, whilst the phenotypic were considerably lower. Repeatabilities for milk yield traits were 0-42 and for lactation length 0-31. Genetic and phenotypic correlations between first-lactation 305-day milk yield and lactation length were 0-83 and 0-71, respectively. Genetic trends for all traits were close to zero but a substantial deterioration in performance, caused by negative environmental factors, was observed. Although the heritabilities were low, the prospects for genetic improvement are good, as indicated by a rather large additive genetic variation. A multivariate animal model, including the first three lactations of 305-day milk yield, was recommended for the most accurate prediction of breeding values for milk production.

The influence of genetic and environmental factors on body weight and reproduction and their relationship to milk production traits, were studied in data of about 4700 Sahiwal cows from Pakistan. (Co)variance components were estimated using restricted maximum likelihood (REML) procedure based on the expectation maximization algorithm applying an animal model. Mean weights of females were: at birth, 21·6 kg; at 1 year, 130 kg; and at 2 years, 222 kg. Records of age at calving, cow weight post partum and calving interval were studied in the first three parities, with parities considered as different traits. For primiparous cows the average values of these traits were: 44·1 months, 319 kg and 465 days, respectively. Mean stillbirth rate was 5·3%. Heritabilities ranged for body weight traits from 0·08 to 0·21, for age at calving from 0·10 to 0·13 and for calving interval from 0·03 to 0·07. Genetic correlations of age at first calving with calving interval and 305-day milk yield were low. The genetic correlation between 305-day milk yield and calving interval was positive (unfavourable) in first parity (0·68) but negative in the third (-0·47). Cows with a high genetic value for 305-day milk yield were heavier at first calving than were low-yielding cows (rg 0·57). The genetic change in reproductive traits over the period studied was close to zero, whereas a marked deterioration was found in phenotypic performance. It is concluded that improved feeding and management, along with some selection against poor reproduction in cows, are important for improvement of reproductive performance.