Derivation of the economic value of R0 for macroparasitic diseases and application to sea lice in salmon

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.

Economic optimization of full-sib test group size and genotyping effort in a breeding program for Atlantic salmon

BACKGROUND

Breeding companies may want to maximize the rate of genetic gain from their breeding program within a limited budget. In salmon breeding programs, full-sibs of selection candidates are subjected to performance tests for traits that cannot be recorded on selection candidates. While marginal gains in the aggregate genotype from phenotyping and genotyping more full-sibs per candidate decrease, costs increase linearly, which suggests that there is an optimum in the allocation of the budget among these activities. Here, we studied how allocation of the fixed budget to numbers of phenotyped and genotyped test individuals in performance tests can be optimized.

METHODS

Gain in the aggregate genotype was a function of the numbers of full-sibs of selection candidates that were (1) phenotyped in a challenge test for sea lice resistance (2) phenotyped in a slaughter test (3) genotyped in the challenge test, and (4) genotyped in the slaughter test. Each of these activities was subject to budget constraints. Using a grid search, we optimized allocation of the budget among activities to maximize gain in the aggregate genotype. We performed sensitivity analyses on the maximum gain in the aggregate genotype and on the relative allocation of the budget among activities at the optimum.

RESULTS

Maximum gain in the aggregate genotype was €386/ton per generation. The response surface for gain in the aggregate genotype was rather flat around the optimum, but it curved strongly near the extremes. Maximum gain was sensitive to the size of the budget and the relative emphasis on breeding goal traits, but less sensitive to the accuracy of genomic prediction and costs of phenotyping and genotyping. The relative allocation of budget among activities at the optimum was sensitive to costs of phenotyping and genotyping and the relative emphasis on breeding goal traits, but was less sensitive to the accuracy of genomic prediction and the size of the budget.

CONCLUSIONS

There is an optimum allocation of budget to the numbers of full-sibs of selection candidates that are phenotyped and genotyped in performance tests that maximizes gain in the aggregate genotype. Although potential gains from optimizing group sizes and genotyping effort may be small, they come at no extra cost.

Enhancing genetic disease control by selecting for lower host infectivity and susceptibility

Infectious diseases have a huge impact on animal health, production and welfare, and human health. Understanding the role of host genetics in disease spread is important for developing disease control strategies that efficiently reduce infection incidence and risk of epidemics. While heritable variation in disease susceptibility has been targeted in livestock breeding, emerging evidence suggests that there is additional genetic variation in host infectivity, but the potential benefits of including infectivity into selection schemes are currently unknown. A Susceptible-Infected-Recovered epidemiological model incorporating polygenic genetic variation in both susceptibility and infectivity was combined with quantitative genetics selection theory to assess the non-linear impact of genetic selection on field measures of epidemic risk and severity. Response to 20 generations of selection was calculated in large simulated populations, exploring schemes differing in accuracy and intensity. Assuming moderate genetic variation in both traits, 50% selection on susceptibility required seven generations to reduce the basic reproductive number R₀ from 7.64 to the critical threshold of <1, below which epidemics die out. Adding infectivity in the selection objective accelerated the decline towards R₀ < 1, to 3 generations. Our results show that although genetic selection on susceptibility reduces disease risk and prevalence, the additional gain from selection on infectivity accelerates disease eradication and reduces more efficiently the risk of new outbreaks, while it alleviates delays generated by unfavourable correlations. In conclusion, host infectivity was found to be an important trait to target in future genetic studies and breeding schemes, to help reducing the occurrence and impact of epidemics.