A discrete-time epidemiological model to quantify selection for disease resistance

The quantitative genetics of the prevalence of infectious diseases: hidden genetic variation due to indirect genetic effects dominates heritable variation and response to selection

Infectious diseases have profound effects on life, both in nature and agriculture. However, a quantitative genetic theory of the host population for the endemic prevalence of infectious diseases is almost entirely lacking. While several studies have demonstrated the relevance of transmission of infections for heritable variation and response to selection, current quantitative genetics ignores transmission. Thus, we lack concepts of breeding value and heritable variation for endemic prevalence, and poorly understand response of endemic prevalence to selection. Here, we integrate quantitative genetics and epidemiology, and propose a quantitative genetic theory for the basic reproduction number R0 and for the endemic prevalence of an infection. We first identify the genetic factors that determine the prevalence. Subsequently, we investigate the population-level consequences of individual genetic variation, for both R0 and the endemic prevalence. Next, we present expressions for the breeding value and heritable variation, for endemic prevalence and individual binary disease status, and show that these depend strongly on the prevalence. Results show that heritable variation for endemic prevalence is substantially greater than currently believed, and increases strongly when prevalence decreases, while heritability of disease status approaches zero. As a consequence, response of the endemic prevalence to selection for lower disease status accelerates considerably when prevalence decreases, in contrast to classical predictions. Finally, we show that most heritable variation for the endemic prevalence is hidden in indirect genetic effects, suggesting a key role for kin-group selection in the evolutionary history of current populations and for genetic improvement in animals and plants.

The economic value of R0 for selective breeding against microparasitic diseases

Background

Microparasitic diseases are caused by bacteria and viruses. Genetic improvement of resistance to microparasitic diseases in breeding programs is desirable and should aim at reducing the basic reproduction ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. Recently, we developed a method to derive the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 for macroparasitic diseases. In epidemiological models for microparasitic diseases, an animal’s disease status is treated as infected or not infected, resulting in a definition of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 that differs from that for macroparasitic diseases. Here, we extend the method for the derivation of the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 to microparasitic diseases.

Methods

When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0} \le 1$$\end{document}R0≤1, the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 is zero because the disease is very rare. When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. is higher than 1, genetic improvement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 can reduce expenditures on vaccination if vaccination induces herd immunity, or it can reduce production losses due to disease. When vaccination is used to achieve herd immunity, expenditures are proportional to the critical vaccination coverage, which decreases with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. The effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 on losses is considered separately for epidemic and endemic disease. Losses for epidemic diseases are proportional to the probability and size of major epidemics. Losses for endemic diseases are proportional to the infected fraction of the population at the endemic equilibrium.

Results

When genetic improvement reduces expenditures on vaccination, expenditures decrease with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 at an increasing rate. When genetic improvement reduces losses in epidemic or endemic diseases, losses decrease with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 at an increasing rate. Hence, in all cases, the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 increases as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 decreases towards 1.

Discussion

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 and its economic value are more informative for potential benefits of genetic improvement than heritability estimates for survival after a disease challenge. In livestock, the potential for genetic improvement is small for epidemic microparasitic diseases, where disease control measures limit possibilities for phenotyping. This is not an issue in aquaculture, where controlled challenge tests are performed in dedicated facilities. If genetic evaluations include infectivity, genetic gain in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 can be accelerated but this would require different testing designs.

Conclusions

When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0} \le 1$$\end{document}R0≤1, its economic value is zero. The economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 is highest at low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 and approaches zero at high values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0.

Genetic Parameters for Resistance to Non-specific Diseases and Production Traits Measured in Challenging and Selection Environments; Application to a Rabbit Case

Breeding for disease resistance is a challenging but increasingly necessary objective to overcome the issues with the reduced use of antibiotics and growing concern for animal welfare while limiting economic losses. However, implementing such strategies is a complex process because animals face numerous diseases, and the environments on selection farms differ from those on commercial farms. We evaluated whether selection for resistance to non-specific diseases based on a single visual record in selection (S) and challenging (Ch) environments is possible. Records from 23,773 purebred rabbits born between 2012 and 2016 were used in this study. After weaning (at 32 days of age), 17,712 rabbits were raised in the S environment and 6,061 sibs were raised in the Ch environment. Clinical signs of disease were recorded for all animals at the end of the test, at a single time point, at 70 or 80 days of age. The causes of mortality occurring before the end of the test were also recorded. Three disease traits were analyzed: signs of respiratory disease, signs of digestive disease, and a composite trait (Resist) taking into account signs of digestive, respiratory and various infectious diseases. This latter composite trait is proposed to capture the global resistance to disease. All disease traits were binary, with 0 being the absence of symptoms. Two production traits were also recorded: the number of kits born alive (4,121 litters) and the weaning weight (13,090 rabbits). Disease traits were analyzed with animal threshold models, assuming that traits are different in the two environments. Bivariate analyses were carried out using linear animal models. The heritabilities of the disease traits ranged from 0.04 ± 0.01 to 0.11 ± 0.03. The genetic correlations between disease traits in both environments were below unity (≤ 0.84), indicating genotype by environment interactions. Most of the genetic correlations between disease and production traits were not significantly different from zero, except between the weaning weight and Resist_S, with a favorable correlation of -0.34 ± 0.12. Given these genetic parameters, for the same level of exposure of rabbits to pathogens, the expected response to selection is a reduction of disease incidence of 4-6% per generation.

Impact of Genetic Selection for Increased Cattle Resistance to Bovine Tuberculosis on Disease Transmission Dynamics

Bovine tuberculosis (bTB) poses a challenge to animal health and welfare worldwide. Presence of genetic variation in host resistance to Mycobacterium bovis infection makes the trait amenable to improvement with genetic selection. Genetic evaluations for resistance to infection in dairy cattle are currently available in the United Kingdom (UK), enabling genetic selection of more resistant animals. However, the extent to which genetic selection could contribute to bTB eradication is unknown. The objective of this study was to quantify the impact of genetic selection for bTB resistance on cattle-to-cattle disease transmission dynamics and prevalence by developing a stochastic genetic epidemiological model. The model was used to implement genetic selection in a simulated cattle population. The model considered various levels of selection intensity over 20 generations assuming genetic heterogeneity in host resistance to infection. Our model attempted to represent the dairy cattle population structure and current bTB control strategies in the UK, and was informed by genetic and epidemiological parameters inferred from data collected from UK bTB infected dairy herds. The risk of a bTB breakdown was modeled as the percentage of herds where initially infected cows (index cases) generated secondary cases by infecting herd-mates. The model predicted that this risk would be reduced by half after 4, 6, 9, and 15 generations for selection intensities corresponding to genetic selection of the 10, 25, 50, and 70% most resistant sires, respectively. In herds undergoing bTB breakdowns, genetic selection reduced the severity of breakdowns over generations by reducing both the percentage of secondary cases and the duration over which new secondary cases were detected. Selection of the 10, 25, 50, and 70% most resistant sires reduced the percentage of secondary cases to <1% in 4, 5, 7, and 11 generations, respectively. Similarly, the proportion of long breakdowns (breakdowns in which secondary cases were detected for more than 365 days) was reduced by half in 2, 2, 3, and 4 generations, respectively. Collectively, results suggest that genetic selection could be a viable tool that can complement existing management and surveillance methods to control and ultimately eradicate bTB.

Relationships between genetic change and infectious disease in domestic livestock

The relations between genetic change in domestic livestock and infectious disease (including both its epidemiology and the animal's reaction to it) are examined. The overall picture is confusing because there are different, and seemingly unrelated, ways of considering the issue. An attempt is made to put these together into a more general framework. Four processes of particular interest are distinguished and discussed in more detail: (i) the way a population's genetic potential for immunocompetence can be changed by breeding, (ii) the way an animal's immunocompetence is influenced by that animal's production potential, in combination with the environmental resources that are available to it at a given time, (iii) the way the disease status of an animal (and a population of animals) is influenced by its immunocompetence, and (iv) the way the production level of an animal is influenced by activation of its immune system. Ultimately, all four processes influence the realised level of production.

This comes down to four questions that need to be addressed: (i) can we use genetic variation in immunocompetence in animal breeding? (ii) does a higher production potential (today's direction of breeding) have a negative impact on immunocompetence? (iii) does improved immunocompetence result in improved health? and (iv) how large is the negative impact of disease on production?

New advances in cloning and their potential impact on genetic variation in livestock

Cloning has advanced through the recent demonstrations that it is feasible to produce, in principle and with significant effort, an unlimited number of individuals of identical genotype from differentiated cell lines that have been frozen and thawed. These advances have been based upon understanding the importance of interactions between the stage of the cell cycle of both the oocyte and donor cell for the success of the nuclear transfer. Whilst the impact of the biological advance is immense for biomedicai applications, the significance is less clear for livestock breeding. In our view the scientific issues for breeding programmes lie in whether clones can increase genetic progress without a cost to biodiversity. Biodiversity within a species may be categorized as: (i) betvjeen-breed variation; (ix) genetic variation among parents within breeds; (iii) genetic variation among individuals within a farm; and (iv) allelic variation within an individual. In the face of a rapid global decline in breed diversity, cloning, in particular cloning of adults, may be an important route to protect biodiversity since it may allow far more genetic variation to be made available for new breed development in the future than is practicable at present. For variation among parents, the judicious use of clones may give significantly faster rates of progress without increasing the rate of loss of genetic variation and furthermore can help improve traits associated with health and welfare which are at present less tractable than, say, milk yield. Local diversity within a farm may be greatly affected if cloning is utilized to disseminate genetic progress widely and more answers are required on the importance of genetic variation within any one locality either in buffering diseases or ameliorating other management problems. Experience from clonal forestry can provide some indications but now there are models capable of answering this question directly in livestock. Allelic variation within individuals per se is not generally advantageous but at loci where it is identified to he beneficial, the use of cloning may exploit it more widely.

Genetics of animal health and disease in cattle

There have been considerable recent advancements in animal breeding and genetics relevant to disease control in cattle, which can now be utilised as part of an overall programme for improved cattle health. This review summarises the contribution of genetic makeup to differences in resistance to many diseases affecting cattle. Significant genetic variation in susceptibility to disease does exist among cattle suggesting that genetic selection for improved resistance to disease will be fruitful. Deficiencies in accurately recorded data on individual animal susceptibility to disease are, however, currently hindering the inclusion of health and disease resistance traits in national breeding goals. Developments in 'omics' technologies, such as genomic selection, may help overcome some of the limitations of traditional breeding programmes and will be especially beneficial in breeding for lowly heritable disease traits that only manifest themselves following exposure to pathogens or environmental stressors in adulthood. However, access to large databases of phenotypes on health and disease will still be necessary. This review clearly shows that genetics make a significant contribution to the overall health and resistance to disease in cattle. Therefore, breeding programmes for improved animal health and disease resistance should be seen as an integral part of any overall national disease control strategy.

A genetic epidemiological model to describe resistance to an endemic bacterial disease in livestock: application to footrot in sheep

Selection for resistance to an infectious disease not only improves resistance of animals, but also has the potential to reduce the pathogen challenge to contemporaries, especially when the population under selection is the main reservoir of pathogens. A model was developed to describe the epidemiological cycle that animals in affected populations typically go through; viz. susceptible, latently infected, diseased and infectious, recovered and reverting back to susceptible through loss of immunity, and the rates at which animals move from one state to the next, along with effects on the pathogen population. The equilibrium prevalence was estimated as a function of these rates. The likely response to selection for increased resistance was predicted using a quantitative genetic threshold model and also by using epidemiological models with and without reduced pathogen burden. Models were standardised to achieve the same genetic response to one round of selection. The model was then applied to footrot in sheep. The only epidemiological parameters with major impacts for prediction of genetic progress were the rate at which animals recover from infection and the notional reproductive rate of the pathogen. There are few published estimates for these parameters, but plausible values for the rate of recovery would result in a response to selection, in terms of changes in the observed prevalence, double that predicted by purely genetic models in the medium term (e.g. 2–5 generations).

Modeling of host genetics and resistance to infectious diseases: understanding and controlling nematode infections

This paper considers approaches to modeling the dynamics of infectious disease and the application of such models to nematode parasite infections in ruminants. Particularly, these models are developed to account for host genetics and may be used to assess the effects of using genetics to control nematode infections. Three main issues are critically examined: the infection transmission cycle from pasture to host to pasture, the expected genetic relationships between resistance and performance, and the risks of parasite evolution in response to genetic changes in the host. To obtain answers that are realistic and of practical use, the modeling approaches require a solid grounding in biology. This biology is formalized and described using mathematical techniques, with the models parameterized using experimental or field data. Transmission dynamics have been quantified by modeling and are backed by strong experimental data. Selection for resistance will be successful in reducing egg output, pasture larval contamination and hence subsequent larval challenge. Modeling frameworks have been developed to predict genetic relationships between resistance to infectious disease and performance in general, and genetic correlations predicted for nematode resistance are close to mean published values. These predicted correlations strengthen as the larval challenge increases and the dietary (protein) adequacy decreases, however modeling challenges remain. Lastly, although convincing experimental data is not yet available, arguments based on modeling suggest that the risks of parasite evolution in response to genetic changes in the host should be less than the risks arising from other control strategies, such as anthelmintics. Thus, modeling techniques predict that selective breeding for resistance should be an effective and sustainable complementary control measure.

Disease incidence and immunological traits for the selection of healthy pigs. A review

Disease is a major issue in animal production systems and society demands that the use of medicines and vaccines be reduced. This review describes the breeding approaches that could be used to improve disease resistance and focuses especially on their application to pigs. Disease reduction by genetic means has certain advantages through cumulative and permanent effects, and direct and indirect selection methods are available. Direct selection for disease incidence requires, besides a unique pig identification and disease registration system, challenge routines that are inconvenient in intensive pig production. Indirect selection for the expression of immune capacity may be an alternative but requires detailed knowledge of the different components of the immune system. There is ample opportunity for genetic improvement of the immune capacity because immune traits show substantial genetic variation between pigs. We therefore conclude that indirect selection via immune traits is very interesting, also for practical implementation, and that there is an urgent need for knowledge, within lines, about the genetic relationships between immune capacity traits and resistance to specific diseases or to disease incidence in general. Furthermore, knowledge about the relationship between immune system traits and production traits is needed as well as knowledge about the effect of selection on the epidemiology of disease at a farm/population level and on the host-pathogen interaction and coevolution.

The sustainability, feasibility and desirability of breeding livestock for disease resistance

Selective breeding for disease resistance utilises proven animal breeding methods to improve animal health, welfare and productivity. Unsurprisingly, it is receiving more and more attention from livestock breeders. However, there are a number of largely theoretical arguments that have been raised as potential problems in selection for disease resistance. These can be classified under sustainability, feasibility and desirability. This review considers each of these areas in turn. Several examples show that enhanced resistance to disease is stable under natural selection and therefore deliberate selection for disease resistance should also be stable and sustainable. The feasibility of selective breeding depends in part upon the heritability of the trait or traits used to measure disease resistance, as well as the amount of variation among animals. The heritability of traits associated with resistance to many important diseases is often high and considerable variation among animals exists. Consequently, selective breeding for enhanced disease resistance is certainly feasible. The desirability of breeding for disease resistance depends upon whether there are trade-offs with other economically important traits. By and large these remain to be defined. However, even if unfavourable associations exist, breeders can create selection indices that include traits with unfavourable associations and maximise the desired responses while attempting to minimise undesirable effects. In conclusion, so long as one or more diseases exert a significant influence on livestock production, selective breeding will be a useful tool to assist in disease control.