Imputation accuracy and carrier frequency of deleterious recessive defects in Australian dairy cattle.

Widespread genotyping has enabled the identification of putative recessive mutations that affect fertility through early embryonic fetal loss, or compromise neonate or calf viability. The use of artificial insemination in the global dairy population can rapidly spread these harmful mutations, and testing for multiple mutations can become relatively expensive if not all tests are available on the same SNP panel. However, it is possible to provide heifer and cow predicted carrier status to farmers at no additional cost if the animals are genotyped with a standard SNP panel. Additionally, for defects where the causal mutation is unknown, but a haplotype of markers has been associated with the defect, the carrier status can be predicted based on that haplotype. The aims of this study were 3-fold: 1) to determine the accuracy of imputation of putative causal mutations for recessive deleterious conditions in Australian dairy cattle, 2) to impute carrier status for known recessive deleterious conditions in all genotyped Australian Holstein, Jersey and Red breed cows, and 3) to determine the changes in carrier frequencies across time for these recessive deleterious mutations. We used the F1 statistic, combining precision and recall, to assess the accuracy of carrier status prediction. We showed that known deleterious mutations can be accurately imputed in Australian Holstein and Jersey cattle that are not directly genotyped for the causal mutation, with F1 ranging between 0.88 and 0.99. For recessive deleterious conditions not included on the standard Australian SNP panel, carrier status could be predicted using a marker haplotype, with F1 ranging from 0.91 to 0.92. Most putative causals and haplotypes were either stable with a low carrier percentage or had a declining carrier percentage. However, several recessive mutations showed a relatively high or increasing percentage, highlighting the importance of detecting carriers to reduce the number of at risk matings. Furthermore, the high carrier percentage of the recently identified Bovine Lymphocyte Intestinal Retention Defect (BLIRD) mutation emphasizes the importance of detection of novel mutations.

Erratum to "Evaluation of updated Feed Saved breeding values developed in Australian Holstein dairy cattle" (JDS Commun. 3:114-119).

[This corrects the article DOI: 10.3168/jdsc.2021-0150.].

Evaluation of updated Feed Saved breeding values developed in Australian Holstein dairy cattle.

Although selection for increased milk production traits has led to a genetic increase in body weight (BW), the genetic gain in milk production has exceeded the gain in BW, so gross feed efficiency has improved. Nonetheless, greater gains may be possible by directly selecting for a measure of feed efficiency. Australia first introduced Feed Saved (FS) estimated breeding value (EBV) in 2015. Feed Saved combines residual feed intake (RFI) genomic EBV and maintenance requirements calculated from mature BW EBV. The FS EBV was designed to enable the selection of cows for reduced energy requirements with similar milk production. In this study, we used a reference population of 3,711 animals in a multivariate analysis including Australian heifers (AUSh), Australian cows (AUSc), and overseas cows (OVEc) to update the Australian EBV for lifetime RFI (i.e., a breeding value that incorporated RFI in growing and lactating cows) and to recalculate the FS EBV in Australian Holstein bulls (AUSb). The estimates of genomic heritabilities using univariate (only AUSc or AUSh) to trivariate (including the OVEc) analyses were similar. Genomic heritabilities for RFI were estimated as 0.18 for AUSc, 0.27 for OVEc, and 0.36 for AUSh. The genomic correlation for RFI between AUSc and AUSh was 0.47 and that between AUSc and OVEc was 0.94, but these estimates were associated with large standard errors (range: 0.18-0.28). The reliability of lifetime RFI (a component of FS) in the trivariate analysis (i.e., including OVEc) increased from 11% to 20% compared with the 2015 model and was greater, by 12%, than in a bivariate analysis in which the reference population included only AUSc and AUSh. By applying the prediction equation of the 2020 model, the average reliability of the FS EBV in 20,816 AUSb that were born between 2010 and 2020 improved from 33% to 43%. Previous selection strategies-that is, using the predecessor of the Balanced Performance Index (Australian Profit Ranking index) that did not include FS-have resulted in an unfavorable genetic trend in FS. However, this unfavorable trend has stabilized since 2015, when FS was included in the Balanced Performance Index, and is expected to move in a favorable direction with selection on Balanced Performance Index or the Health Weighted Index. Doubling the reference population, particularly by incorporating international data for feed efficiency, has improved the reliability of the FS EBV. This could lead to increased genetic gain for feed efficiency in the Australian industry.

Optimizing genomic prediction for Australian Red dairy cattle.

The reliability of genomic prediction is influenced by several factors, including the size of the reference population, which makes genomic prediction for breeds with a relatively small population size challenging, such as Australian Red dairy cattle. Including other breeds in the reference population may help to increase the size of the reference population, but the reliability of genomic prediction is also influenced by the relatedness between the reference and validation population. Our objective was to optimize the reference population for genomic prediction of Australian Red dairy cattle. A reference population comprising up to 3,248 Holstein bulls, 48,386 Holstein cows, 807 Jersey bulls, 8,734 Jersey cows, and 3,041 Australian Red cows and a validation population with between 208 and 224 Australian Red Bulls were used, with records for milk, fat, and protein yield, somatic cell count, fertility, and survival. Three different analyses were implemented: single-trait genomic best linear unbiased predictor (GBLUP), multi-trait GBLUP, and single-trait Bayes R, using 2 different medium-density SNP panels: the standard 50K chip and a custom array of variants that were expected to be enriched for causative mutations. Various reference populations were constructed containing the Australian Red cows and all Holstein and Jersey bulls and cows, all Holstein and Jersey bulls, all Holstein bulls and cows, all Holstein bulls, and a subset of the Holstein individuals varying the relatedness between Holsteins and Australian Reds and the number of Holsteins. Varying the relatedness between reference and validation populations only led to small changes in reliability. Whereas adding a limited number of closely related Holsteins increased reliabilities compared with within-breed prediction, increasing the number of Holsteins decreased the reliability. The multi-trait GBLUP, which considered the same trait in different breeds as correlated traits, yielded higher reliabilities than the single-trait GBLUP. Bayes R yielded lower reliabilities than multi-trait GBLUP and outperformed single-trait GBLUP for larger reference populations. Our results show that increasing the size of a multi-breed reference population may result in a reference population dominated by one breed and reduce the reliability to predict in other breeds.

Value of sharing cow reference population between countries on reliability of genomic prediction for milk yield traits.

Increasing the reliability of genomic prediction (GP) of economic traits in the pasture-based dairy production systems of New Zealand (NZ) and Australia (AU) is important to both countries. This study assessed if sharing cow phenotype and genotype data of NZ and AU improves the reliability of GP for NZ bulls. Data from approximately 32,000 NZ genotyped cows and their contemporaries were included in the May 2018 routine genetic evaluation of the Australian Dairy cattle in an attempt to provide consistent phenotypes for both countries. After the genetic evaluation, deregressed proofs of cows were calculated for milk yield traits. The April 2018 multiple across-country evaluation of Interbull was also used to calculate deregressed proofs for bulls on the NZ scale. Approximately 1,178 Jersey (Jer) and 6,422 Holstein (Hol) bulls had genotype and phenotype data. In addition to NZ cows, phenotype data of close to 60,000 genotyped Australian (AU) cows from the same genetic evaluation run as NZ cows were used. All AU and NZ females were genotyped using low-density SNP chips (<10K SNP) and were imputed first to 50K and then to ∼600K (referred to as high density; HD). We used up to 98,000 animals in the reference populations, both by expanding the NZ reference set (cow, bull, single breed to multi-breed set) and by adding AU cows. Reliabilities of GP were calculated for 508 Jer and 1,251 Hol bulls whose sires are not included in the reference set (RS) to ensure that real differences are not masked by close relationships. The GP was tested using 50K or high-density SNP chip using genomic BLUP in bivariate (considering country as a trait) or single trait models. The RS that gave the highest reliability for each breed were also tested using a hybrid GP method that combines expectation maximization with Bayes R. The addition of the AU cows to an NZ RS that included either NZ cows only, or cows and bulls, improved the reliability of GP for both NZ Hol and Jer validation bulls for all traits. Using single breed reference populations also increased reliability when NZ crossbred cows were added to reference populations that included only purebred NZ bulls and cows and AU cows. The full multi-breed RS (all NZ cows and bulls and AU cows) provided similar reliabilities in NZ Hol bulls, when compared with the single breed reference with crossbred NZ cows. For Jer validation bulls, the RS that included Jer cows and bulls and crossbred cows from NZ and Jer cows from AU was marginally better than the all-breed, all-country RS. In terms of reliability, the advantage of the HD SNP chip was small but captured more of the genomic variance than the 50K, particularly for Hol. The expectation maximization Bayes R GP method was slightly (up to 3 percentage points) better than genomic BLUP. We conclude that GP of milk production traits in NZ bulls improves by up to 7 percentage points in reliability by expanding the NZ reference population to include AU cows.

Predicting the effect of reference population on the accuracy of within, across, and multibreed genomic prediction.

Genomic prediction is widely used to select candidates for breeding. Size and composition of the reference population are important factors influencing prediction accuracy. In Holstein dairy cattle, large reference populations are used, but this is difficult to achieve in numerically small breeds and for traits that are not routinely recorded. The prediction accuracy is usually estimated using cross-validation, requiring the full data set. It would be useful to have a method to predict the benefit of multibreed reference populations that does not require the availability of the full data set. Our objective was to study the effect of the size and breed composition of the reference population on the accuracy of genomic prediction using genomic BLUP and Bayes R. We also examined the effect of trait heritability and validation breed on prediction accuracy. Using these empirical results, we investigated the use of a formula to predict the effect of the size and composition of the reference population on the accuracy of genomic prediction. Phenotypes were simulated in a data set containing real genotypes of imputed sequence variants for 22,752 dairy bulls and cows, including Holstein, Jersey, Red Holstein, and Australian Red cattle. Different reference populations were constructed, varying in size and composition, to study within-breed, multibreed, and across-breed prediction. Phenotypes were simulated varying in heritability, number of chromosomes, and number of quantitative trait loci. Genomic prediction was carried out using genomic BLUP and Bayes R. We used either the genomic relationship matrix (GRM) to estimate the number of independent chromosomal segments and subsequently to predict accuracy, or the accuracies obtained from single-breed reference populations to predict the accuracies of larger or multibreed reference populations. Using the GRM overestimated the accuracy; this overestimation was likely due to close relationships among some of the reference animals. Consequently, the GRM could not be used to predict the accuracy of genomic prediction reliably. However, a method using the prediction accuracies obtained by cross-validation using a small, single-breed reference population predicted the accuracy using a multibreed reference population well and slightly overestimated the accuracy for a larger reference population of the same breed, but gave a reasonably close estimate of the accuracy for a multibreed reference population. This method could be useful for making decisions regarding the size and composition of the reference population.

Genetics of complex traits: prediction of phenotype, identification of causal polymorphisms and genetic architecture.

Complex or quantitative traits are important in medicine, agriculture and evolution, yet, until recently, few of the polymorphisms that cause variation in these traits were known. Genome-wide association studies (GWAS), based on the ability to assay thousands of single nucleotide polymorphisms (SNPs), have revolutionized our understanding of the genetics of complex traits. We advocate the analysis of GWAS data by a statistical method that fits all SNP effects simultaneously, assuming that these effects are drawn from a prior distribution. We illustrate how this method can be used to predict future phenotypes, to map and identify the causal mutations, and to study the genetic architecture of complex traits. The genetic architecture of complex traits is even more complex than previously thought: in almost every trait studied there are thousands of polymorphisms that explain genetic variation. Methods of predicting future phenotypes, collectively known as genomic selection or genomic prediction, have been widely adopted in livestock and crop breeding, leading to increased rates of genetic improvement.

Exploiting biological priors and sequence variants enhances QTL discovery and genomic prediction of complex traits.

BACKGROUND: Dense SNP genotypes are often combined with complex trait phenotypes to map causal variants, study genetic architecture and provide genomic predictions for individuals with genotypes but no phenotype. A single method of analysis that jointly fits all genotypes in a Bayesian mixture model (BayesR) has been shown to competitively address all 3 purposes simultaneously. However, BayesR and other similar methods ignore prior biological knowledge and assume all genotypes are equally likely to affect the trait. While this assumption is reasonable for SNP array genotypes, it is less sensible if genotypes are whole-genome sequence variants which should include causal variants. RESULTS: We introduce a new method (BayesRC) based on BayesR that incorporates prior biological information in the analysis by defining classes of variants likely to be enriched for causal mutations. The information can be derived from a range of sources, including variant annotation, candidate gene lists and known causal variants. This information is then incorporated objectively in the analysis based on evidence of enrichment in the data. We demonstrate the increased power of BayesRC compared to BayesR using real dairy cattle genotypes with simulated phenotypes. The genotypes were imputed whole-genome sequence variants in coding regions combined with dense SNP markers. BayesRC increased the power to detect causal variants and increased the accuracy of genomic prediction. The relative improvement for genomic prediction was most apparent in validation populations that were not closely related to the reference population. We also applied BayesRC to real milk production phenotypes in dairy cattle using independent biological priors from gene expression analyses. Although current biological knowledge of which genes and variants affect milk production is still very incomplete, our results suggest that the new BayesRC method was equal to or more powerful than BayesR for detecting candidate causal variants and for genomic prediction of milk traits. CONCLUSIONS: BayesRC provides a novel and flexible approach to simultaneously improving the accuracy of QTL discovery and genomic prediction by taking advantage of prior biological knowledge. Approaches such as BayesRC will become increasing useful as biological knowledge accumulates regarding functional regions of the genome for a range of traits and species.

Toward genomic prediction from whole-genome sequence data: impact of sequencing design on genotype imputation and accuracy of predictions.

Genomic prediction from whole-genome sequence data is attractive, as the accuracy of genomic prediction is no longer bounded by extent of linkage disequilibrium between DNA markers and causal mutations affecting the trait, given the causal mutations are in the data set. A cost-effective strategy could be to sequence a small proportion of the population, and impute sequence data to the rest of the reference population. Here, we describe strategies for selecting individuals for sequencing, based on either pedigree relationships or haplotype diversity. Performance of these strategies (number of variants detected and accuracy of imputation) were evaluated in sequence data simulated through a real Belgian Blue cattle pedigree. A strategy (AHAP), which selected a subset of individuals for sequencing that maximized the number of unique haplotypes (from single-nucleotide polymorphism panel data) sequenced gave good performance across a range of variant minor allele frequencies. We then investigated the optimum number of individuals to sequence by fold coverage given a maximum total sequencing effort. At 600 total fold coverage (x 600), the optimum strategy was to sequence 75 individuals at eightfold coverage. Finally, we investigated the accuracy of genomic predictions that could be achieved. The advantage of using imputed sequence data compared with dense SNP array genotypes was highly dependent on the allele frequency spectrum of the causative mutations affecting the trait. When this followed a neutral distribution, the advantage of the imputed sequence data was small; however, when the causal mutations all had low minor allele frequencies, using the sequence data improved the accuracy of genomic prediction by up to 30%.

Power of a genome scan to detect and locate quantitative trait loci in cattle using dense single nucleotide polymorphisms.

There is increasing use of dense single nucleotide polymorphisms (SNPs) for whole-genome association studies (WGAS) in livestock to map and identify quantitative trait loci (QTL). These studies rely on linkage disequilibrium (LD) to detect an association between SNP genotypes and phenotypes. The power and precision of these WGAS are unknown, and will depend on the extent of LD in the experimental population. One complication for WGAS in livestock populations is that they typically consist of many paternal half-sib families, and in some cases full-sib families; unless this subtle population stratification is accounted for, many spurious associations may be reported. Our aim was to investigate the power, precision and false discovery rates of WGAS for QTL discovery, with a commercial SNP array, given existing patterns of LD in cattle. We also tested the efficiency of selective genotyping animals. A total of 365 cattle were genotyped for 9232 SNPs. We simulated a QTL effect as well as polygenic and environmental effects for all animals. One QTL was simulated on a randomly chosen SNP and accounted for 5%, 10% or 18% of the total variance. The power to detect a moderate-sized additive QTL (5% of the phenotypic variance) with 365 animals genotyped was 37% (p < 0.001). Most importantly, if pedigree structure was not accounted for, the number of false positives significantly increased above those expected by chance alone. Selective genotyping also resulted in a significant increase in false positives, even when pedigree structure was accounted for.

Sampling strategies for whole genome association studies in aquaculture and outcrossing plant species.

A number of farmed species are characterized by breeding populations of large full-sib families, including aquaculture species and outcrossing plant species. Whole genome association studies in such species must account for stratification arising from the full-sib family structure to avoid high rates of false discovery. Here, we demonstrate the value of selective genotyping strategies which balance the contribution of families across high and low phenotypes to greatly reduce rates of false discovery with a minimal effect on power.

A novel predictor of multilocus haplotype homozygosity: comparison with existing predictors.

The patterns of linkage disequilibrium (LD) between dense polymorphic markers are shaped by the ancestral population history. It is therefore possible to use multilocus predictors of LD to infer past population history and to infer sharing of identical alleles in quantitative trait locus (QTL) studies. We develop a multilocus predictor of LD for pairs of haplotypes, which we term haplotype homozygosity (HHn): the probability that any two haplotypes share a given number of n adjacent identical markers or 'runs of homozygosity'. Our method, based on simplified coalescence theory, accounts for recombination and mutation. We compare our HHn predictions, with HHn in simulated populations and with two published predictors of HHn. Our method performs consistently better across a range of population parameters, including populations with a severe bottleneck followed by expansion, compared to two published methods. We demonstrate that we can predict the pattern of HHn observed in dense single nucleotide polymorphisms (SNPs) genotyped in a cattle population, given appropriate historical changes in population size. Our method is practical for use with very large numbers of individuals and dense genome wide polymorphic DNA data. It has potential applications in inferring ancestral population history and QTL mapping studies.

Distributed intelligent control system for a continuous-state plant.

Continuous-state plants place specific demands on the structure and operation of multi-agent, multi-paradigm distributed intelligent controllers. An investigation of the use of distributed artificial intelligence techniques for continuous-state control is presented. The choice of agents and how they interact to control a continuous-state plant is discussed. A distinction between a priori and operational knowledge is introduced to simplify and aid the design of distributed intelligent controllers. A simulation study of a controller designed for a deep-shaft mine winder serves to demonstrate the application of distributed intelligent control to a continuous-state plant.

Measurement of respiratory mechanics in a mechanically ventilated infant lung simulator: effects of variations in the frequency response of the flow measurement system.

The frequency responses of systems used to measure flow and pressure in ventilated infants may differ, and hence affect estimates of resistance and compliance. We estimated resistance and compliance in 16 ventilated mechanical lung models using linear regression while varying the frequency response of the flow measurement system. Lung models comprised combinations of four sections of tubing and four bottles filled with steel wool. The cut-off frequencies of a filter in the flow measurement system were chosen to yield time delays of 0, +/-3, +/-6, and +/-9 ms relative to the pressure signal. When the phase lags in the measurement systems were not equal at 10 Hz, a bias in resistance approximately (relative delay) x (elastance) ensued. The bias in the resistance estimate when resistance is 5 Pa ml-1 s and compliance is 2 ml kPa-1 is approximately 28% per ms of delay mismatch. Time-shifting the flow data to eliminate the phase discrepancy reduced the resistance bias by 85%. The residual resistance bias was assumed to be due to inappropriate amplitude response. Compliance measurements were affected by less than 8% and less than 2% after time correction of the flow data. Pressure and flow signals must be synchronized to within 1 ms at 10 Hz and the amplitude responses of the measurement systems must be adequate for reliable resistance measurement.

Bandwidths of respiratory gas flow and pressure waveforms in mechanically ventilated infants.

The frequency content of airway pressure and gas flow in mechanically ventilated infants (MVIS) has not been adequately investigated. Pressure-cycled infant ventilators generate pressure pulses with short rise-times. Gas flow is approximately equal to the derivative of pressure when lung compliance is low, and hence contains high-frequency components. We defined bandwidth as that frequency fm below which 99.9% of the energy of the signal resided. Simulation of the measurement process using measurement systems with frequency response similar to sixth-order Bessel filters and a lung model comprising series resistance, inertance and compliance showed that measurement systems with frequency response flat +/- 10% to fm yield time domain errors less than 3% of the peak value. We digitized pressure and flow signals from 10-20 ventilator (Healthdyne 105) breaths in 33 stable MVIS. The transducers' (Gould P50, Hans Rudolph 8300 screen pneumotach) frequency responses had been measured between 1 Hz and 100 Hz and phase matched at 10 Hz. We calculated total respiratory resistance R and elastance E using multiple linear regression, and ensemble-average power spectral density using the FFT with a rectangular time window and padding to 2048 points. Power spectra were compensated for non-unity transducer and anti-alias filter responses up to 60 Hz. Measured data sequences that were not self-windowing due to spontaneous breathing efforts, that yielded regression R2 < 0.95 or that contained flow oscillations due to secretions in the airway were discarded. Satisfactory results were obtained from more than eight breaths in 18 infants. Mean bandwidths (+/- SD) of pressure and flow waveforms were 4.7 +/- 0.7, range 3.5-5.9 and 19.6 +/- 6.5, range 10.8-32.1 Hz, respectively. Flow bandwidths B correlated with the respiratory time constant tau (B = -77.2 tau + 26.8, R2 = 0.55, P < 0.0002), and with elastance E (B = 61.4E + 10.1, R2 = 0.74, P < 0.0001). We conclude that the bandwidth of the flow waveform increases with decreasing compliance and mechanical time constant. The frequency response of pressure and flow measurement systems should be flat +/- 10% at least up to 6 and 32 Hz respectively to obtain data with dynamic errors less than 3% in infants with low-compliance lung disease.

Effect of airway inertance on linear regression estimates of resistance and compliance in mechanically ventilated infants: a computer model study.

Respiratory inertance (I) is usually ignored when resistance (R) and compliance (C) of mechanically ventilated infants are estimated by least squares linear regression. Values of I that have been reported for these patients can cause impedances whose magnitudes approximate respiratory resistance. We show theoretically that if inertance is neglected no error is expected in resistance estimates, but a positive bias in compliance can be, proportional to the inertance, the compliance, and the sinusoidal frequency at which the measurements are made. To determine the errors in parameter estimates when the pressure waveform is non-sinusoidal, we simulated linear regression based on non-inertive and inertive models. R, C, and I of the simulated lung were varied over the range expected in an infant intensive care unit. The ventilator was simulated as a critically damped second order system with a square pulse input. The rise time (TR) of the pressure pulse was varied over the range reported in infant ICUs. Simulated measurements confirmed that resistance is correctly estimated if inertance is neglected. Maximum error in compliance estimates (13%) occurred when TR and R were low, and C and I were high. The variation in the error in estimated compliance was consistent with the theory. Coefficients of variation of the parameters, the standard errors, and R2 of the regressions tended to deteriorate with increasing compliance error, but the relationships were not single valued. These statistics may alert investigators to possible bias in compliance caused by neglected inertance, but cannot be used to correct any bias.

Measurement of the frequency response and common-mode gain of neonatal respiratory pressure and flow measurement systems. Part 1: Apparatus.

It is necessary, especially in neonatal work, for investigators to measure accurately the frequency response and common mode gain of respiratory pressure and flow transducers in air and other gas mixtures. Many of the systems designed for this task have been incompletely analysed and have unknown frequency responses themselves. We analyse aspects of systems employed previously and show that substantial amplitude and phase errors may have occurred. We describe a plethysmograph-based system which operates in any available gas mixture. A mathematical model of the acoustic microphone used as reference transducer, the microphone preamplifier, and the thermal behaviour of the plethysmograph, is developed to quantify the frequency response of the system. Maximum deviation from a perfect response is less than 1% in amplitude and 1 degree in phase for both pressure and flow measurements over the range 1-100 Hz. Measurements using a pressure transducer mounted on the tip of a catheter indicate that the error due to amplitude and phase variation in the plethysmograph is less than 0.1 dB and 0.4 degrees at 100 Hz.

Measurement of the frequency response and common-mode gain of neonatal respiratory pressure and flow measurement systems. Part 2: Results.

We show that the technique of exciting a differential pressure transducer at one port to measure its differential gain yields incorrect results in the case of asymmetrical differential pressure transducers but is acceptable in the case of symmetrical transducers. We have measured the common-mode gain of a symmetrical and an asymmetrical differential pressure transducer from 1 Hz to 100 Hz, both directly and by computation from differential gain measurements. No compensation for common-mode error is necessary when a symmetrical transducer is used in mechanically ventilated neonates. We have also measured the frequency response of neonatal Fleisch and screen pneumotachographs connected to Validyne MP45 differential pressure transducers in air, 60% oxygen and 100% oxygen, and concluded that the effect of oxygen concentration is small below 40 Hz. However, the normalised frequency response of the flow transducer differs markedly from unity at frequencies inside the flow bandwidth generated by neonatal pressure cycled ventilators and dynamic correction is therefore necessary.

Effects of temperature and composition on the viscosity of respiratory gases.

The steady-state sensitivity of resistance pneumotachographs is proportional to viscosity. Dynamic characteristics of pneumotachographs, pressure transducers, and mass spectrometers are also viscosity dependent. We derive linear equations to approximate the viscosities of O2, N2, CO2, H2O, He, N2O, and Ar for temperatures between 20 and 40 degrees C by using published viscosity data and a nonlinear extrapolation equation. We verify the accuracy of the extrapolation equation by comparison with published data. Our linear equations for pure gas viscosities yield standard errors less than 0.35 microP. We also compare a nonlinear equation for calculating the viscosities of mixtures of gases with published measured viscosities of dry air, humid air, and He-O2 and N2-CO2 mixtures. The maximum difference between published and calculated values is 1.3% for 10% CO2 in N2. All other differences are less than 0.38%. For saturated humid air at 35 degrees C, a linear concentration-weighted combination of viscosities differs from our nonlinear equation by 4.9, 2.1, and 1.7% at barometric pressures of 32, 83, and 100 kPa, respectively. By use of our method, the viscosity of normal respiratory gases can be calculated to within 1% of measured values.