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Pain experienced by lame cattle is often masked by their instinctive stoicism, leading to delayed detection and treatment of lameness. This paper investigates the usefulness of posture scoring during locomotion and the evaluation of daily activity levels as indicators of pain and discomfort resulting from lameness in dairy cattle. In this study, 345 lactating cattle were observed over a seven-month winter housing period. The posture of each cow was scored twice weekly using a subjective five-point numerical rating scale. Daily activity levels were measured objectively using pedometers. The effect of lameness on behaviour was addressed. Increased posture scores were associated with the presence of foot lesions (P < 0.001) and with reduced daily activity levels (P < 0.001). In comparison to sound cows, lame cows showed lower daily activity levels (P < 0.001). These results improve understanding of pain-related behaviours in cattle, and such an approach may assist future development of welfare assessment systems.

Measurements of conformation and pelvic characteristics of pedigree Belgian Blue cows were compared in cattle from 11 herds. In seven herds comprising 56 cows caesarean sections were routinely used to deliver pedigree calves and in four herds comprising 52 cows they were given the opportunity to calve naturally per vaginum. Cows in the seven herds were approximately 10 months younger than those in the other herds. External pelvic measurements were linear distances between the tuber coxae, between the tuber coxarum and the tuber ischium, between the tuber ischii, the vertical distance between the underside of the tail and the tuber ischii, and heights of the tuber coxae and tuber ischii from the floor. Internal pelvic measurements were the vertical distance between the ventral body of the sacrum and the pubic symphysis and the horizontal distance between the wings of the ileum at the widest point of the pelvic inlet, both made with a Rice pelvimeter. Condition scores were assessed for all cows. There were correlations (P < 0·001) between internal pelvic height and width, external measurements, and age. For cattle that calved unassisted, pelvic height (P < 0·05) and area (P < 0·05) were significantly larger than those delivered by elective caesarean section. From internal pelvic measurements of 74 cows, those which always delivered live calves had a larger pelvic area (P < 0·01) than cows that delivered a dead foetus following any parturition.

Individuals in communities in which different strains of pathogen are circulating can acquire resistance by accumulating immunity to each strain. After considering susceptibility, models of infection and immunity are defined for vector-borne diseases such as malaria and trypanosomiasis. For these models the prevalence of infection, the number of infections per individual, and the mean duration of infection, increase rapidly in young individuals, but decrease in older individuals as immunity is acquired to the various strains of pathogen; the mean interval between successive infections lengthens with age. The bivariate Poisson distribution is shown to be a close approximation to some stochastic processes. The models explain observed cross-sectional patterns of age prevalence, and longitudinal patterns in which individuals typically continue to become infected as they age, albeit with decreasing frequency. In these models the time spent infected depends on parasite diversity, as well as the inoculation and recovery rates. It is shown that control measures can cause an increase in the number of infections and the prevalence of infection in older individuals, and in the average prevalence in the community, even when strain-specific immunity is life-long.

A survey was made of 37 dairy farms in Wirral, mid-Cheshire, mid-Somerset and Dyfed, Wales, to assess the incidence and prevalence of lameness in the cows between May 1989 and September 1991. The incidence was obtained from records made whenever a cow was examined for lameness or received preventive foot-trimming. The mean annual incidence was 54.6 new cases per 100 cows with a range from 10.7 to 170.1 and the mean values during summer and winter were 22.9 and 31.7, respectively. The prevalence of lameness was measured by regular visits at which locomotion was scored on a scale of 1 to 5, and the prevalence of lameness was calculated for each visit as the proportion of cows with scores of 3 or more. The mean annual prevalence over the whole period was 20.6 per cent with a range from 2.0 to 53.9 per cent for the 37 farms. The mean prevalences during summer and winter were 18.6 and 25.0 per cent, respectively. The prevalence measured at a single visit in midsummer or midwinter was significantly correlated with the mean prevalence over the whole corresponding period and may be useful as an assessment of the extent of lameness in a herd and the efficacy of control measures. There was evidence that training farmers to recognise early cases of lameness and request veterinary treatment resulted in a marked reduction in the duration of cases of lameness.

A qualitative scoring method was devised to describe foot shape in dairy cattle, which relied solely on visual observations. Four independent trained observers used the method to assess the foot shape of 248 cows located on three farms on two different occasions, and the percentages of agreement and near-agreement for intra-observer and interobserver variation on scores for foot shape were calculated. Score assessment methods were suitable for describing features with a broad variation within one score value; reducing the number of observers did not improve best agreement between separate observations by more than 80 per cent.

Measurements describing pelvic conformation of pedigree Belgian Blue cows were obtained from a sample of nine herds in Flanders, Belgium, comprising 111 adult breeding cows, and from 11 herds in the United Kingdom comprising 108 similar cows. All herds in the Belgian sample (111 cows) managed parturition by elective caesarian section as did seven herds (56 cows) in the UK sample; the remainder of UK herds (52 cows) allowed cows the opportunity to calve naturally per vagina before resorting to caesarian section. The data described the external and internal measurements, and pelvic area characteristic of this breed, irrespective of the different selection pressures applied over a number of years to this breed through variation in farm management and market forces present in either country. From these data, generalized linear models were constructed to predict pelvic area; they correctly identified cows with either small or large pelvic areas. There were no significant differences in pelvic conformation between cattle bred either in Belgium or the UK, although those cows bred in herds where natural calving was allowed to take place had significantly larger internal pelvic height (p < 0.05) and area (p < 0.05) than other Belgian Blue cows. The correlation coefficients between internal pelvic height and width and external pelvic measurements were significant (p < 0.001). These results might facilitate the selection of breeding cows with larger pelvic area so that a higher proportion of cows can calve naturally than currently occurs. However, selection for other traits such as relatively low birth weight combined with higher weaning weight should be carried out at the same time.

Radiographs of 152 cats under four years of age were examined for evidence of physeal closure. Radiographic closure was compared between entire male, castrated male, and female (neutered and entire] cats. Physeal closure in castrated males was delayed when compared to that of entire males.

Information from 37 dairy farms, in four regions of England and Wales provided data on 8991 lesions and the preventive trimming of 4837 cows' feet., American Association of Bovine Practitioners Proceedings of the Annual Conference, 1996

A survey of cubicles and indoor and outdoor walking surfaces on 37 farms served by four veterinary practices in Somerset, Cheshire, Wirral and west Wales was carried out in 1989 to 1991. A study of the space requirements of Friesian/Holstein cows at pasture showed that they required approximately 240 cm x 120 cm lying space and a further 60 cm lunging space for rising. By these standards, 87 per cent of the cubicles were too short and 50 per cent were too wide or too narrow. Over 1500 observations on cows lying down, rising and standing indicated that only 12 per cent of the cubicles permitted real freedom of movement; 91 per cent of top partition rails were judged to be too low and 70 per cent of bottom rails too low or too high. In addition, the kerb was very high in 76 per cent of the cubicles. As a result, 10 per cent of cows appeared moderately or severely restricted when lying down, 33 per cent when rising and 55 per cent when standing. Over 2000 cubicle beds were also studied; 75 per cent had a concrete base and of those, 63 per cent were judged to have too little bedding and 11 per cent next to none. Higher incidences and prevalences of lameness were associated with limited borrowing space (P

Fertility data from 16 dairy herds vaccinated against hardjo infection were used to assess pregnancy rates in cattle vaccinated around the day of mating. There was no improvement in pregnancy rates 30-60 d after vaccination. Pregnancy rates in the period 5 d before and 10 d after vaccination were statistically lower than those found in 30-60 d around vaccination.

Data are presented on the number of fibers and the proportion of different fiber types within fascicles of whole vastus lateralis muscles from 5 male children, 5 to 15 years of age, and compared with results from 25 male adults, middle aged and old individuals. The results verify a difference in the proportion of fibers with different properties within a fascicle. The proportion of type 2 (fast twitch) fibers on the border of fascicles is larger than the proportion internally: the children have (P less than 0.01) greater difference than the adults and the middle aged, whereas the old have (P less than 0.001) less difference than the other age groups. The mean number of fibers per fascicle increases (P less than 0.05) from childhood to adult age, and thereafter reduces (P less than 0.01). The results imply that fascicles continuously rearrange during the normal growth and development and the normal aging process. It is argued that the causes of the difference in fiber type proportions within fascicles are local factors in the muscle, secondary to the overall age related functional demands put on the fiber population.

Normal and abnormal cells are positioned at the vertices of a regular two-dimensional lattice. Abnormal cells divide k times as fast as normal cells. Whenever a cell divides, the daughter is the same type as the parent and replaces an adjacent cell. The Kolmogorov forwards and backwards equations are derived, and then used to obtain bounds for the distribution function of the time when all the abnormal cells are forced from the plane. These bounds are used to comment on the non-asymptotic variance of the number of abnormal cells at a given time and on a method of estimating k.

Records of 3085 patients registered with breast cancer at the Mersey Regional Cancer Registry have been analysed to evaluate the relative importance of possible prognostic factors. In a subgroup of 1759 patients, clinical stage and histological grade are shown to be strongly related to survival after treatment. In addition histological grade is related to the distribution of times to death after treatment. The results of this and 3 other studies have implications for the design and analysis of clinical trials in the primary treatment of breast cancer. Images Fig. 1 Fig. 2 Fig. 3

SUMMARY Williams & Bjerknes (1972) suggested a model for the growth of abnormal cells in a plane. Abnormal cells are assumed to divide k times faster than normal cells. In this paper an unbiased minimum variance estimator of k is obtained and the estimates obtained from simulated growths are compared with the actual values. A method of estimating k from the ' crinkliness' of a growth, as suggested by Mollison (1972), is also considered. 1. THE MODEL In the human body ceLls are all the time dividing and reproducing. In some circumstances it is reasonable to assume that: (i) cells are of two types, normal and abnormal; (ii) if a cell in the basal layer of the epithelium divides, then the daughter cell is of the same type as the mother cell, and both of them remain in the epithelium displacing a neighbouring cell; (iii) cells can divide in the basal layer and nowhere else. Using these assumptions as a basis, Williams & Bjerknes (1972) constructed a stochastic model which they hoped represented cancer growths; of course, they fully understood the tentative nature of the study. In this paper we consider the same model. The basal layer is assumed to be a two-dimensional plane, in which cells are located at every vertex of a regular lattice. At the start there is one abnormal cell, and all the other cells are normal. A daughter cell is equally likely to displace any one of its nearest neighbours. The cellular division times are assumed to be exponentially distributed with the abnormal cells dividing k times faster than the normal cells; k can be considered to be the carcinogenic advantage. Williams & Bjerknes (1972), Mollison (1972), and Downham & Morgan (1973 a, b) investigate such properties as the times taken for the growth to reach a given size, the number of cells in the growth at a given time, and the probability that the growth regresses to zero, i.e. the probability that the abnormal cells are forced from the basal layer by the normal cells. Richardson (1973) obtains some general results for a similar model. In this paper inferential arguments are used to obtain minimum variance estimators of k. For this model it is necessary to consider only the cell divisions around the periphery of the growth of abnormal cells, since any other division does not alter the number of abnormal cells in the basal layer; that is, we need study only divisions for those cells which have at least

For the simple two-dimensional random walk on the vertices of a rectangular lattice, the asymptotic forms of several properties are well known, but their forms can be insufficiently accurate to describe the transient process. Inequalities with the correct asymptotic form are derived for six such properties. The rates of approach to the asymptotic form are derived. The accuracy of the bounds and some practical implications of the results are discussed.

SUMMARY The asymptotic distribution of the order of an autoregression selected by a generalization of Akaike's FPE criterion is given. Some of the properties of the distribution are investigated. The use of this criterion is illustrated by a simulation study.

This paper collates the results of five surveys which were made to determine the average catch of anglers not making a return at game fisheries. This pilot study shows that the average catch per licence/permit () may be estimated from the average and the proportion of unprompted returns, (mu) and (pu) respectively, by the empirical equation , for trout and sea trout, Salmo trutta L. Salmon, Salmo salar L., catcrl’rates may be best estimated from . Typical values for United Kingdom waters are tabulated for recent seasons. Rod catches of stillwater and migratory fish closely follow the Negative Binomial distribution. Their means and variances are shown to be related empirically by Taylor's power law: for daily records of stillwater trout and migratory fish, and for annual records of salmon, and of sea trout. A method of estimating the expected frequency distribution of catches at any water is shown. The distribution is truncated where the nil catches are not recorded and is censored where the bag is limited; here a microcomputer was programmed to compute the estimates of the mean and variance of the catches and to print the full distribution.

Debrisoquine and sparteine tests were carried out in 215 random white British subjects. There is a high degree of correlation between the urinary 'metabolic ratios' of the two drugs. New mathematical techniques have been developed (1) to define phenotypes and (2) to identify the genotypes within the dominant phenotype. The members of 15 families were tested with both debrisoquine and sparteine. The results indicate that persons who are 'poor metabolisers' of sparteine are also 'poor metabolisers' of debrisoquine and are autosomal Mendelian recessives.

We have described above the outline of a general recursive method for deriving the likelihood of a model. In order to implement this procedure automatically we need to develop two sets of algorithms, (i) for taking a pedigree in a simple numerical representation, and specifying the order in which we peel individuals off, a non-trivial problem for large pedigrees, and (ii) for carrying out the necessary algebraic manipulations so that L is ultimately obtained, as a function of the parameters which need to be estimated in the model. These have been developed: (i) for zero-loop pedigrees, (ii) for an autosomal locus with three genotypes and arbitrary penetrances, and programmed, and are in the process of generalization to more complex cases.

The imago of the peppered moth exists in two sharply distinguished forms, speckled and black. Clarke and Sheppard (1966) have shown that the frequency of the black moth decreases from 99% in Liverpool to 10% in North Wales. If these frequencies are in equilibrium, albeit dynamic equilibrium, then such a gradient is called a cline. Haldane (1948) briefly describes several clines, and then defines a model that may represent the life-cycle of certain species. The assumptions defining his model are as follows.

A register of adult patients from Salford, England (population 150,000) who came into any form of special psychiatric care was maintained from 1959 to 1963. — Those seeking psychiatric care for the first time in their lives were classed as inceptions (1,945 cases). — Inception rates were calculated for the population at risk. The effects of sex, age, marital state and social class were considered for all cases and for those in specific diagnostic categories. — Considering all categories of mental illness, women had higher rates than men, but only up to the 60's. Both sexes showed an early peak in the 30's then a decline, followed by a rise beginning in the 60's and climbing steeply at older ages. The married had lower rates of inceptions than did the single, widowed or divorced. Persons in the unskilled manual labourer class had higher rates than other occupational categories. — Schizophrenia, as expected, had higher rates among the young, among men, among the single, and among the unskilled. — Depressive psychosis was nearly twice as common in women as in men. Although the married had the lowest rates of depressive psychosis among marital categories, the differences were not as marked as for schizophrenia, nor were the differences in rates for the social classes remarkable. Nothing to suggest the existence of involutional melancholia was found in the inception rates. Attention is drawn to the bimodal age curve for depressive psychosis, and its possible implications for the definition of the syndrome and its causes. — Psychoneurosis was the largest diagnostic category up to 40 years in both sexes, and then declined in numbers. Women, and especially single women, had higher rates than men. No social class variation in psychoneurosis was discovered. — Epidemiological features of psychopathy, addictive disorders, senile psychosis, organic disorders and epilepsy are also presented. — Comparisons are made with Lundby, Sweden and New Haven, Connecticut. The Salford rates fall between these two. — The age distributions of inceptions of schizophrenia and psychoneurosis are compared with that of Huntington's chorea. The resemblance is great, and these data therefore provoke serious consideration of the existence of genetic susceptibility to schizophrenia and psychoneurosis, although there are good reasons for seeking multiple causes including social causes.

The Poisson distribution is often suitable for analysing non-infectious disorders with low prevalence rates. The numbers of babies born with hypospadias in the Liverpool Congenital Malformations Registry during 1960 to 1982 do not fit a Poisson distribution with constant prevalence rates, but a change-point Poisson process does fit. A significance test is described and its power is considered in two simulation studies. A small discrepancy is noted that does not diminish appreciably when Bartlett's correction is applied.

Moran (1958) constructed a model to study the effect of mutation on the gene-frequency of a population of haploid individuals. The model, and others developed from it, have been studied by many authors: in particular, a mathematical solution is given by Karlin and McGregor (1962), and Cannings (1974) considers a class of models of which Moran's model is a member. In this note we develop an algorithm for studying the model numerically. From our studies a disquieting feature becomes apparent that is likely to affect various other models. We finish the paper with some tentative proposals. There is a fixed number N of gametes each of which is of type a or A. The number of a gametes at time t, X, say, represents the state of the process. If X, = j immediately before the death of an individual, then the new gamete is of type a with probability

INVESTIGATIONS have been made using the model for the growth of all abnormal cells suggested by Williams and Bjerknes1. They showed that the mathematics of the problem remained largely the same for different cell lattices, and so, for reasons of programming simplicity, consideration is limitted to growths on square lattices.

Summary Dreaming under anaesthesia was investigated in a prospective study of 120 day case paediatric patients, aged 5–17 years, who underwent a variety of surgical procedures. Patients were anaesthetised using the ‘Liverpool technique’ of paediatric anaesthesia (nitrous oxide-oxygen-relaxant). No patient reported awareness, but 23 of 120 patients (19%) reported dreams. Analysis of the data revealed that the choice of muscle relaxant, (nondepolarising or depolarising) had a statistically significant effect on the incidence of dreaming (p < 0.05). It is suggested that the technique of intermittent intravenous suxamethonium may result in increased muscle spindle discharge and cause cerebral arousal and an increased incidence of dreaming.

One hundred and fourteen transcutaneous oxygen traces were obtained from 46 adults using a mass spectrometer. Such traces usually rise to a plateau about which they fluctuate. To estimate the plateau level, here called the asymptote, two models are described--a time-series model and a growth model. If yt is the trace measurement at time t, for the time-series model. yt + 1 = m + alpha (yt-m) + epsilon t, and for the growth model dyt/dt = beta (m-yt), where parameters alpha and beta represent the rate of approach to the asymptote m. Least squares estimates of these parameters were determined for every trace. For every trace, the estimated asymptotes are similar for both models but the other parameters show less agreement. Considering the traces for each person in pairs, each trace pair is allocated to one of four groups according as the traces were recorded on the same or different sites and on the same or different days. The correlation coefficient (r) between the estimated asymptotes is greatest for traces recorded on the same site and day (r greater than 0.94, P less than 0.001) and least for traces from different sites and days (r greater than 0.71, P less than 0.001). The time series estimates of the asymptote are more credible than the growth model.

The proportions of different fiber types (type 1 and type 2) on the borders of fascicles are shown to differ from the proportions internally. This finding is based on the analysis of a total of 245 fascicles from whole cross-sections of the vastus lateralis muscle from 13 men, aged from 26-80 years. Generally, the difference is more marked in the young than in the old. It is argued that the causes of this difference are likely to be local factors in the muscle.

The percentages of Type I muscle fibres were measured systematically in ATPase-stained, transverse cryostat sections of whole tibialis cranialis muscles from 8 young, adult beagles. The distance of the section from the origin of the muscle does not significantly affect the mean percentage. There are no identifiable differences in mean percentages between right and left muscles. Differences in mean percentages between individuals are significant when sexes are combined (P less than 0.01) and within sexes (males: P less than 0.01; females: P less than 0.05). Within sections, the percentage tends to be lowest at the superficial (craniolateral) border and to vary less from site to site deeper within the muscle. Fibre cross sectional areas were measured systematically in the same sections of the right muscle from 3 males and 3 females. Mean areas for each section were greater for Type II than for Type I fibres. Mean areas for each fibre-type varied moderately and non-systematically between the sample sites within sections. A needle biopsy taken from deep within this muscle should provide a more consistent and reliable estimate of fibre-type proportion in the whole muscle than a superficial specimen. Proportions are not affected by the distance of the sample site from the muscle origin, and left or right muscles are suitable for sequential samples.

The Poisson distribution is often suitable for analysing non-infectious disorders with low prevalence rates. The numbers of babies born with hypospadias in the Liverpool Congenital Malformations Registry during 1960 to 1982 do not fit a Poisson distribution with constant prevalence rates, but a change-point Poisson process does fit. A significance test is described and its power is considered in two simulation studies. A small discrepancy is noted that does not diminish appreciably when Bartlett's correction is applied.

Individuals in communities in which different strains of pathogen are circulating can acquire resistance by accumulating immunity to each strain. After considering susceptibility, models of infection and immunity are defined for vector-borne diseases such as malaria and trypanosomiasis. For these models the prevalence of infection, the number of infections per individual, and the mean duration of infection, increase rapidly in young individuals, but decrease in older individuals as immunity is acquired to the various strains of pathogen; the mean interval between successive infections lengthens with age. The bivariate Poisson distribution is shown to be a close approximation to some stochastic processes. The models explain observed cross-sectional patterns of age prevalence, and longitudinal patterns in which individuals typically continue to become infected as they age, albeit with decreasing frequency. In these models the time spent infected depends on parasite diversity, as well as the inoculation and recovery rates. It is shown that control measures can cause an increase in the number of infections and the prevalence of infection in older individuals, and in the average prevalence in the community, even when strain-specific immunity is life-long.

Gestational age was assessed in 200 Sudanese newborns using the method of external superficial characteristics. Breast size, skin texture and ear firmness were found to be the best. Skin colour was not found to be of value.