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This article presents a model describing the relationship between level of disease resistance and production under constant infection pressure. The model assumes that given a certain infection pressure, there is a threshold for resistance below which animals will stop producing, and that there is also a threshold for resistance above which animals produce at production potential. In between both thresholds animals will show a decrease in production, the size of decrease depending on the severity of infection and the level of resistance. The dynamic relationship between production and resistance when level of resistance changes, such as due to infection, is modeled both stochastically and deterministically. Selection started in a population with very poor level of resistance introduced in an environment with constant infection pressure. Mass selection on observed production was applied, which resulted in a nonlinear selection response for all three traits considered. When resistance is poor, selection for observed production results in increased level of resistance. With increasing level of resistance, selection response shifts to production potential and eventually selection for observed production is equivalent to selection for production potential. The rate at which resistance is improved depends on its heritability, the difference between both thresholds, and selection intensity. The model also revealed that when a zero correlation between resistance and production potential is assumed, the phenotypic correlation between resistance and observed production level increases for low levels of resistance and subsequently asymptotes to zero, whereas the phenotypic correlation between production potential and observed production asymptotes to 1.0. For most breeding schemes investigated, the deterministic model performed well in relation to the stochastic simulation results. Experimental results reported in literature support the model predictions. Key Words: Deterministic Models, Disease Resistance, Genetics, Production, Selection, Stochastic Models

Porcine reproductive and respiratory syndrome (PRRS) is the most economically significant disease impacting pig production in North America, Europe, and Asia, causing reproductive losses such as increased rates of stillbirth and mummified piglets. The objective of this study was to explore the genetic basis of host response to the PRRS virus (PRRSV) in a commercial multiplier sow herd before and after a PRRS outbreak, using antibody response and reproductive traits. Reproductive data comprising number born alive (NBA), number alive at 24 h (NA24), number stillborn (NSB), number born mummified (NBM), proportion born dead (PBD), number born dead (NBD), number weaned (NW), and number of mortalities through weaning (MW) of 5,227 litters from 1,967 purebred Landrace sows were used along with a pedigree comprising 2,995 pigs. The PRRS outbreak date was estimated from rolling averages of farrowing traits and was used to split the data into a pre-PRRS phase and a PRRS phase. All 641 sows in the herd during the outbreak were blood sampled 46 d after the estimated outbreak date and were tested for anti-PRRSV IgG using ELISA (sample-to-positive [S/P] ratio). Genetic parameters of traits were estimated separately for the pre-PRRS and PRRS phase data sets. Sows were genotyped using the PorcineSNP60 BeadChip, and genome-wide association studies (GWAS) were performed using method Bayes B. Heritability estimates for reproductive traits ranged from 0.01 (NBM) to 0.12 (NSB) and from 0.01 (MW) to 0.12 (NBD) for the pre-PRRS and PRRS phases, respectively. S/P ratio had heritability (0.45) and strong genetic correlations with most traits, ranging from -0.72 (NBM) to 0.73 (NBA). In the pre-PRRS phase, regions associated with NSB and PBD explained 1.6% and 3% of the genetic variance, respectively. In the PRRS phase, regions associated with NBD, NSB, and S/P ratio explained 0.8%, 11%, and 50.6% of the genetic variance, respectively. For S/P ratio, 2 regions on SSC 7 (SSC7) separated by 100 Mb explained 40% of the genetic variation, including a region encompassing the major histocompatibility complex, which explained 25% of the genetic variance. These results indicate a significant genomic component associated with PRRSV antibody response and NSB in this data set. Also, the high heritability and genetic correlation estimates for S/P ratio during the PRRS phase suggest that S/P ratio could be used as an indicator of the impact of PRRS on reproductive traits.

A mathematical model was developed to investigate the impact of level of Teladorsagia circumcincta larval pasture contamination and anthelmintic treatment on genetic parameter estimates for performance and resistance to parasites in sheep. Currently great variability is seen for published correlations between performance and resistance, with estimates appearing to vary with production environment. The model accounted for host genotype and parasitism in a population of lambs, incorporating heritable between-lamb variation in host-parasite interactions, with genetic independence of input growth and immunological variables. An epidemiological module was linked to the host-parasite interaction module via food intake (FI) to create a grazing scenario. The model was run for a population of lambs growing from 2 mo of age, grazing on pasture initially contaminated with 0, 1,000, 3,000, or 5,000 larvae/kg DM, and given either no anthelmintic treatment or drenched at 30-d intervals. The mean population values for FI and empty BW (EBW) decreased with increasing levels of initial larval contamination (IL(0)), with non-drenched lambs having a greater reduction than drenched ones. For non-drenched lambs the maximum mean population values for worm burden (WB) and fecal egg count (FEC) increased and occurred earlier for increasing IL(0), with values being similar for all IL(0) at the end of the simulation. Drenching was predicted to suppress WB and FEC, and cause reduced pasture contamination. The heritability of EBW for non-drenched lambs was predicted to be initially high (0.55) and decreased over time with increasing IL(0), whereas drenched lambs remained high throughout. The heritability of WB and FEC for all lambs was initially low (∼0.05) and increased with time to ∼0.25, with increasing IL(0) leading to this value being reached at faster rates. The genetic correlation between EBW and FEC was initially ∼-0.3. As time progressed the correlation tended towards 0, before becoming negative by the end of the simulation for non-drenched lambs, with increasing IL(0) leading to increasingly negative correlations. For drenched lambs, the correlation remained close to 0. This study highlights the impact of IL(0) and anthelmintic treatment on genetic parameters for resistance. Along with factors affecting performance penalties due to parasitism and time of reporting, the results give plausible causes for variation in genetic parameter estimates previously reported.

Porcine reproductive and respiratory syndrome (PRRS), caused by the PRRS virus (PRRSV), is globally the most economically important disease in commercial pigs, and novel control strategies are sought. This paper explores the potential to use host genetics to decrease the impact of PRRS on reproductive sows. Commercial pig data (7,542 phenotypic records) from a farm undergoing an outbreak of PRRSV were analyzed to assess the impact of PRRS on reproductive traits and the inheritance of such traits. First, differing methodologies were used to partition the data into time periods when the farm was disease free and when the farm was experiencing PRRSV outbreaks. The methods were a date/threshold method based on veterinary diagnosis and a threshold/threshold method based on trends in underlying performance data, creating the DTD and TTD data sets, respectively. The threshold/threshold method was more stringent in defining periods when PRRS was likely to be having an impact on reproductive performance, resulting in a data set (TTD) that was slightly smaller (1,977 litters from 1,526 sows) than that from the date/threshold method (3,164 litters and 1,662 sows), and it showed more pronounced impacts of PRRS on performance. Impacts on performance included significant increases in mean values of mummified and stillborn piglets (0.04 to 1.13 and 0.63 to 1.02, respectively) with a significant decrease in total born alive (10.3 to 9.08). Estimated heritabilities during the healthy phase were generally less (mummified piglets = 0.03 +/- 0.01, matings per conception = 0.04 +/- 0.01) than during the PRRSV outbreak (TTD data set; mummified piglets = 0.10 +/- 0.03, matings per conception = 0.46 +/- 0.04). These results imply genetic variation for host resistance to, or tolerance of, PRRSV, particularly with the TTD data set. Genetic correlations between reproductive traits measured in the healthy phase and TTD data set varied from effectively zero for traits describing numbers of mummified or dead piglets to strongly positive for litter size traits. This indicates genetic variation in piglet losses during PRRSV outbreaks is independent of genetic variation in the same traits in healthy herds. In summary, our findings show that there is within-breed genetic variation for commercially relevant traits that could be exploited in future breeding programs against PRRSV infection. Selection for increased PRRS resistance would be desirable to the industry because effective control measures remain elusive.

The aim of this paper was to explore the effect of genetic heterogeneity in host resistance to infection on the population-level risks and outcomes of epidemics. This was done using a stochastic epidemiological model in which the model parameters were assumed to be genetically controlled traits of the host. A finite locus model was explored, with a gene controlling the transmission coefficient (i.e., host susceptibility to infection) and a gene controlling the recovery period. Both genes were simulated to have 2 alleles with underlying additive or dominance inheritance and an independent assortment of alleles. The model was parameterized for a viral pig disease (transmissible gastroenteritis), and complete homogeneous mixing among genotypes was assumed. Mean population genotype dramatically affected epidemic outcomes, and subtle effects of heterogeneity on epidemic properties were also observed. Genetic variation in the transmission coefficient led to probabilities of epidemics occurring that were slightly greater than expected, but genetic variation in the recovery rate had no such effect. Epidemics were generally less severe in genetically heterogeneous populations than expected from the constituent subpopulations. Furthermore, the genotype of the initial infected animal had a marked effect on epidemic probabilities, particularly when genetic variation was for recovery rate. The results of this model provide useful information to determine the optimum population structures and to exploit genetic variation in resistance to infection. Applications of the proposed model in genetically heterogeneous populations for identifying practical disease management strategies are also discussed.

The objectives of this study were 1) to estimate the heritability of lamb survival and growth in the Scottish Blackface breed; 2) to examine the relationship between lamb survival and live BW; and 3) to investigate the possibility of using lamb survival in a breeding program for this breed. The data used for the analyses contained information about survival and live BW at different ages on 4,459 animals. The records were collected from 1988 to 2003 in a Scottish Blackface flock. Live BW was recorded every 4 wk from birth to 24 wk. Survival was defined either by perinatal or postnatal mortality (up to weaning at 12 wk), or as cumulative survival to 1, 4, 8, and 12 wk. The pedigree file comprised 1,416 dams and 178 sires. A sire model was used to estimate genetic parameters for binary survival traits. Heritabilities of BW traits, and phenotypic and genetic correlations between BW and between survival and BW were estimated by fitting an animal model. Further, correlations of survival with live BW were estimated by using a Markov chain Monte Carlo threshold model, implemented by Gibbs sampling. The heritability estimates for cumulative lamb survival declined from birth onward (from 0.33 to 0.08), and postnatal survival had a heritability of 0.01. The direct and maternal heritabilities for BW traits ranged from 0.08 to 0.26 and from 0.06 to 0.21, respectively, whereas the maternal environmental component was between 0.04 and 0.16. The genetic correlations between BW traits at different ages were high. The genetic and phenotypic correlations between survival and BW were always positive (ranging from 0.04 to 0.54), so there was no antagonism between these traits. Therefore, it is possible to simultaneously improve both survival and live BW in a breeding program for this breed.

Genetic parameters for LM fatty acid composition were estimated in Scottish Blackface sheep, previously divergently selected for carcass lean content (LEAN and FAT lines). Furthermore, QTL were identified for the same fatty acids. Fatty acid phenotypic measurements were made on 350 male lambs, at approximately 8 mo of age, and 300 of these lambs were genotyped across candidate regions on chromosomes 1, 2, 3, 5, 14, 18, 20, and 21. Fatty acid composition measurements included in total 17 fatty acids of 3 categories: saturated, monounsaturated, and polyunsaturated. Total i.m. fat content was estimated as the sum of the fatty acids. The FAT line had a greater i.m. fat content and more oleic acid, but less linoleic acid (18:2 n-6) and docosapentaenoic acid (22:5 n-3) than did the LEAN line. Saturated fatty acids were moderately heritable, ranging from 0.19 to 0.29, and total SFA were highly heritable (0.90). Monounsaturated fatty acids were moderately to highly heritable, with cis-vaccenic acid (18:1 n-7) being the most heritable (0.67), and total MUFA were highly heritable (0.73). Polyunsaturated fatty acids were also moderately to highly heritable; arachidonic acid (20:4 n-6) and CLA were the most heritable, with values of 0.60 and 0.48, respectively. The total PUFA were moderately heritable (0.40). The QTL analyses were performed using regression interval mapping techniques. In total, 21 chromosome-wide QTL were detected in 6 out of 8 chromosomal regions. The chromosome-wide, significant QTL affected 3 SFA, 5 MUFA, and 13 PUFA. The most significant result was a QTL affecting linolenic acid (18:3 n-3) on chromosome 2. This QTL segregated in 2 of the 9 families and explained 37.6% of the phenotypic variance. Also, 10 significant QTL were identified on chromosome 21, where 8 out of 10 QTL were segregating in the same families and detected at the same position. The results of this study demonstrate that altering carcass fatness will simultaneously change i.m. fat content and oleic, linoleic, and docosapentaenoic acid content. The heritabilities of the fatty acids indicate opportunities for genetically altering most fatty acids. Moreover, this is the first report of detection of QTL directly affecting fatty acid composition in sheep.

Quantitative trait loci analyses were applied to data from Suffolk and Texel commercial sheep flocks in the United Kingdom. The populations comprised 489 Suffolk animals in three half-sib families and 903 Texel animals in nine half-sib families. Phenotypic data comprised measurements of live weight at 8 and 20 wk of age and ultrasonically measured fat and muscle depth at 20 wk. Lambs and their sires were genotyped across candidate regions on chromosomes 1, 2, 3, 4, 5, 6, 11, 18, and 20. Data were analyzed at the breed level, at the family level, and across extended families when families were genetically related. The breed-level analyses revealed a suggestive QTL on chromosome 1 in the Suffolk breed, between markers BM8246 and McM130, affecting muscle depth, although the effect was only significant in one of the three Suffolk families. A two-QTL analysis suggested that this effect may be due to two adjacent QTL acting in coupling. In total, 24 suggestive QTL were identified from individual family analyses. The most significant QTL affected fat depth and was segregating in a Texel family on chromosome 2, with an effect of 0.62 mm. The QTL was located around marker ILSTS030, 26 cM distal to myostatin. Two of the Suffolk and two of the Texel sires were related, and a three-generation analysis was applied across these two extended families. Seven suggestive QTL were identified in this analysis, including one that had not been detected in the individual family analysis. The most significant QTL, which affected muscle depth, was located on chromosome 18 near the callipyge and Carwell loci. Based on the phenotypic effect and location of the QTL, the data suggest that a locus similar to the Carwell locus may be segregating in the United Kingdom Texel population.

Economic values for a range of different maternal and carcass sheep performance traits were derived for hill sheep in the United Kingdom. A bioeconomic model that includes estimates of available energy supply and herbage intake for sheep from hill and mountain pastures, together with that from improved grassland, has provided a base from which to define the economic limitations to genetic improvement in harsh environments. The degree to which different farm systems can accommodate changes in animal performance as a result of genetic improvement was explored. Results showed that genetic improvement in harsh environments is likely to be of greater benefit to farms with fewer constraints to improvements in production, such as better quality pasture or a higher ratio of improved grassland to hill pasture. For farm types in the harshest locations, the economic value of improving litter size was only positive within defined production limits. Increasing litter size beyond these limits resulted in diminishing marginal returns because the costs of additional inputs outweighed the benefits of extra returns. Results also showed that relative improvements in maternal characteristics are at least as economically important as improvements in lamb carcass quality. The effects of variation in market prices on economic values for the major costs and returns of the sheep enterprises showed that, in general, economic values are robust. The methodology described could be adapted and applied to other extensive sheep systems worldwide.

A stochastic epidemic model is presented to study infection transmission dynamics, and hence epidemic severity and disease incidence, in a closed population. The aim was to understand the relative importance of various parameters that influence the dynamics of potential epidemics, particularly when the genetic mechanisms of resistance or tolerance to infection are considered. Simulations explored the effect of varying the transmission coefficient, latent period, recovery period, mortality rate, and the period of loss of immunity on overall epidemic outcomes. The critical parameters influencing the transmission of infection, and hence disease incidence, were the transmission coefficient, the latent period, and the recovery period; the period of loss of immunity had only trivial effects. Ideally, control strategies should decrease the transmission coefficient and/or increase the latent period and/or decrease the recovery period. By equating measured traits with disease transmission parameters, the model described in this paper can be used to identify which disease resistance genes or QTL will be truly effective in helping to develop disease-resistant livestock that suffer fewer epidemics and side-effects of infection. In particular, emphases should be placed on finding genes that decrease the transmission of infection, increase the latent period, or decrease the recovery period.

Animals will show reduced production when exposed to a constant infection pressure unless they are fully resistant, the size of the reduction depending on the degree of resistance and the severity of infection. In this article, the use of QTL for disease resistance for improving productivity under constant infection pressure is investigated using stochastic simulation. A previously published model was used with two thresholds for resistance: a threshold below which production is not possible and a threshold above which production is not affected by the infection. Between thresholds, observed production under constant infection is a multiplicative function of underlying potential production and level of resistance. Some simplifications of reality were adopted in the model, such as no genetic correlation between potential production and resistance, the absence of influence of lack of resistance on reproductive capacity, and the availability of phenotypes in both sexes. Marker-assisted selection was incorporated by assuming a proportion of the genetic variance to be explained by the QTL, which thus is defined as a continuous trait. Phenotypes were available for production, not for resistance. The infection pressure may vary across time. Results were compared to mass selection on production under constant as well as intermittent infection pressure, where the infection pressure varied between but not within years. Selection started in a population with a very poor level of resistance. Incorporation of QTL information is valuable (i.e., the increase in observed production relative to mass selection) when a large proportion of the additive genetic variance is explained by the QTL (50% genetic variance explained) and when the heritability for resistance is low (h2R = 0.1). Under constant infection pressure, incorporating QTL information does not increase selection responses in observed production when the QTL effect explains less than 25% of the genetic variance. Under intermittent selection pressure, the use of QTL information gives a slightly greater increase in observed production in early generations, relative to mass selection on observed production, but still only when the QTL effect is large or the heritability for resistance is low. The additional advantage of incorporating QTL information is that use of (preventive) medical treatment is possible, or animals may be evaluated in uninfected environments.

This paper demonstrates the use of stochastic genetic epidemiological models for quantifying the consequences of selecting animals for resistance to a microparasitic infectious disease. The model is relevant for many classes of infectious diseases where sporadic epidemics occur, and it is a powerful tool for investigating the costs, benefits, and risks associated with breeding for resistance to specific diseases. The model is parameterized for transmissible gastroenteritis, a viral disease affecting pigs, and selection for resistance to this disease on a structured pig farm is simulated. Two genetic models are used, both of which involve selection of sires. The first involves selection with the assumption of continuous genetic variation (the continuous selection model). The second involves selection with the assumption of introgression of a major recessive gene that confers resistance (the gene introgression model). In the base population, the basic reproductive ratio, R0 (i.e., the expected number of secondary cases after the introduction of a single infected animal) was 2.24, in agreement with previous studies. The probabilities of no epidemic, a minor epidemic (one that dies out without intervention), and a major epidemic were 0.55, 0.20, and 0.25, respectively. Selection for resistance, under both genetic models, resulted in a nonlinear decline in the probability of a major epidemic and a decrease in the severity of the epidemic, should it occur, until R0 was less than 1.0, at which point the probability of a major epidemic was zero. For minor epidemics, the probability and severity of the epidemic increased until R0 reached 1.0, at which point the probabilities also fell to zero. The epidemic probabilities were critically dependent on the location on the farm where infected animals were situated, and the relative risks of different groups of animals changed with selection. The main difference between the two genetic models was in the time scale; the introgression results simply depended on how quickly the resistance allele could be introgressed into the population. For the introgression model, the probability of a major epidemic declined to zero when 0.6 of the animals were homozygous for the resistance allele.

A stochastic model describing disease transmission dynamics for a microparasitic infection in a structured domestic animal population is developed and applied to hypothetical epidemics on a pig farm. Rational decision making regarding appropriate control strategies for infectious diseases in domestic livestock requires an understanding of the disease dynamics and risk profiles for different groups of animals. This is best achieved by means of stochastic epidemic models. Methodologies are presented for 1) estimating the probability of an epidemic, given the presence of an infected animal, whether this epidemic is major (requires intervention) or minor (dies out without intervention), and how the location of the infected animal on the farm influences the epidemic probabilities; 2) estimating the basic reproductive ratio, R0 (i.e., the expected number of secondary cases on the introduction of a single infected animal) and the variability of the estimate of this parameter; and 3) estimating the total proportion of animals infected during an epidemic and the total proportion infected at any point in time. The model can be used for assessing impact of altering farm structure on disease dynamics, as well as disease control strategies, including altering farm structure, vaccination, culling, and genetic selection.