Modelling spatial and temporal correlation in multi-assessment perennial crop variety selection trials using a multivariate autoregressive model
J. De Faveri
A * , A. P. Verbyla A and R. A. Culvenor B
A The University of Queensland, Queensland Alliance for Agriculture & Food Innovation (QAAFI), Brisbane, Qld 4001, Australia.
B CSIRO Agriculture & Food, Black Mountain, ACT 2601, Australia.
Abstract
Perennial crop variety selection trials are often conducted over several seasons or years. These field trials often exhibit spatial correlation between plots. When data from multiple assessment times are analysed, it is necessary to account for both spatial and temporal correlation. A current approach is to use linear mixed models with separable spatial and temporal residual covariance structures. A limitation of these separable models is that they assume the same spatial correlation structure for each assessment time, which may not hold in practice.
This study aims to provide more flexible methods for modelling the spatio-temporal correlation in multi-assessment perennial crop data, allowing for differing spatial parameters for each time, together with modelling genetic effects over time.
The paper investigates the suitability of two-directional invariant multivariate autoregressive (2DIMVAR1) models for analysis of multi-assessment perennial crop data. The analysis method is applied to persistence data from a pasture breeding trial.
The multivariate autoregressive spatio-temporal residual models are a significant improvement on separable residual models under different genetic models. The paper demonstrates how to fit the models in practice using the software ASReml-R.
A flexible modelling approach for multi-assessment perennial crop data is presented, allowing differing spatial correlation parameters for each time. The models allow investigation into genotype × time interactions, while optimally accounting for spatial and temporal correlation.
The models provide improvements on current approaches and hence will result in more accurate genetic predictions in multi-assessment perennial crop variety selection trials.
Keywords: 2DIMVAR1, BLUP, genotype by environment interaction, linear mixed models, multivariate autoregressive model, perennial crop variety selection, random regression, spatial and temporal modelling, splines.
References
Bally ISE, De Faveri J (2021) Genetic analysis of multiple fruit quality traits in mango across sites and years. Euphytica 217, 44.
| Crossref | Google Scholar |
Bjornsson H (1978) Analysis of a series of long-term grassland experiments with autocorrelated errors. Biometrics 34, 645-651.
| Crossref | Google Scholar |
Campbell M, Walia H, Morota G (2018) Utilizing random regression models for genomic prediction of a longitudinal trait derived from high-throughput phenotyping. Plant Direct 2, 1-11.
| Crossref | Google Scholar |
Costa e Silva J, Dutkowski G, Gilmour AR (2001) Analysis of early tree height in forest genetic trials is enhanced by including a spatially correlated residual. Canadian Journal of Forest Research 31, 1887-1893.
| Crossref | Google Scholar |
Culvenor RA, Norton MR, De Faveri J (2017) Persistence and productivity of phalaris (Phalaris aquatica) germplasm in dry marginal rainfall environments of south-eastern Australia. Crop & Pasture Science 68, 781-797.
| Crossref | Google Scholar |
De Faveri J (2013) Spatial and temporal modelling for perennial crop variety selection trials. PhD Thesis, The University of Adelaide, Adelaide, SA, Australia. Available at http://digital.library.adelaide.edu.au/dspace/handle/2440/83114
De Faveri J, Verbyla AP, Pitchford WS, Venkatanagappa S, Cullis BR (2015) Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials. Crop & Pasture Science 66, 947-962.
| Crossref | Google Scholar |
De Faveri J, Verbyla AP, Cullis BR, Pitchford WS, Thompson R (2017) Residual variance–covariance modelling in analysis of multivariate data from variety selection trials. Journal of Agricultural, Biological and Environmental Statistics 22, 1-22.
| Crossref | Google Scholar |
De Faveri J, Verbyla AP, Rebetzke G (2023) Random regression models for multi-environment, multi-time data from crop breeding selection trials. Crop & Pasture Science 74, 271-283.
| Crossref | Google Scholar |
De Resende MDV, Thompson R, Welham SJ (2006) Multivariate spatial statistical analysis of longitudinal data in perennial crops. Revista de Matemática e Estatística, São Paulo 24(1), 147-169 Available at https://repository.rothamsted.ac.uk/item/8q3zq.
| Google Scholar |
DeGroot BJ, Keown JF, Kachman SD, Van Vleck D (2003) Cubic splines for estimating lactation curves and genetic parameters of first lactation Holstein cows treated with bovine somatotropin. In ‘Conference on applied statistics in agriculture’. pp. 150–163. (New Prairie Press: Kansas, USA). doi:10.4148/2475-7772.1181
Diggle PJ (1988) An approach to the analysis of repeated measurements. Biometrics 44, 959-971.
| Crossref | Google Scholar |
Dutkowski GW, Silva JCe, Gilmour AR, Lopez GA (2002) Spatial analysis methods for forest genetic trials. Canadian Journal of Forest Research 32, 2201-2214.
| Crossref | Google Scholar |
Evans JC, Roberts EA (1979) Analysis of sequential observations with applications to experiments on grazing animals and perennial plants. Biometrics 35, 687-693.
| Crossref | Google Scholar |
Gabriel KR (1962) Ante-dependence analysis of an ordered set of variables. The Annals of Mathematical Statistics 33, 201-212.
| Crossref | Google Scholar |
Gilmour AR, Cullis BR, Verbyla AP (1997) Accounting for natural and extraneous variation in the analysis of field experiments. Journal of Agricultural, Biological, and Environmental Statistics 2, 269-293.
| Crossref | Google Scholar |
Haskard KA, Cullis BR, Verbyla AP (2007) Anisotropic Matérn correlation and spatial prediction using REML. Journal of Agricultural, Biological, and Environmental Statistics 12(2), 147-160.
| Crossref | Google Scholar |
Huisman AE, Veerkamp RF, van Arendonk JAM (2002) Genetic parameters for various random regression models to describe the weight data of pigs. Journal of Animal Science 80, 575-582.
| Crossref | Google Scholar |
Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38, 963-974.
| Crossref | Google Scholar |
Lodge GM, Gleeson AC (1984) A comparison of methods of estimating lucerne population for monitoring persistence. Australian Journal of Experimental Agriculture and Animal Husbandry 24, 174-177.
| Crossref | Google Scholar |
Meyer K (2005) Random regression analyses using B-splines to model growth of Australian Angus cattle. Genetics Selection Evolution 37, 473.
| Crossref | Google Scholar |
Oakey H, Verbyla A, Pitchford W, Cullis B, Kuchel H (2006) Joint modeling of additive and non-additive genetic line effects in single field trials. Theoretical and Applied Genetics 113, 809-819.
| Crossref | Google Scholar |
O’Connor KM, Hayes BJ, Hardner CM, Alam M, Henry RJ, Topp BL (2021) Genomic selection and genetic gain for nut yield in an Australian macadamia breeding population. BMC Genomics 22, 370.
| Crossref | Google Scholar |
R Core Team (2021) ‘R: a language and environment for statistical computing.’ (R Foundation for Statistical Computing: Vienna, Austria) Available at https://www.R-project.org/
Smith KF, Simpson RJ, Oram RN, Lowe KF, Kelly KB, Evans PM, Humphreys MO (1998) Seasonal variation in the herbage yield and nutritive value of perennial ryegrass (Lolium perenne L.) cultivars with high or normal herbage water-soluble carbohydrate concentrations grown in three contrasting Australian dairy environments. Australian Journal of Experimental Agriculture 38, 821-830.
| Crossref | Google Scholar |
Smith A, Cullis B, Thompson R (2001) Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics 57, 1138-1147.
| Crossref | Google Scholar |
Smith AB, Cullis BR, Thompson R (2005) The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches. The Journal of Agricultural Science 143, 449-462.
| Crossref | Google Scholar |
Smith AB, Stringer JK, Wei X, Cullis BR (2007) Varietal selection for perennial crops where data relate to multiple harvests from a series of field trials. Euphytica 157, 253-266.
| Crossref | Google Scholar |
Smith AB, Ganesalingam A, Kuchel H, Cullis BR (2015) Factor analytic mixed models for the provision of grower information from national crop variety testing programs. Theoretical and Applied Genetics 128, 55-72.
| Crossref | Google Scholar |
Stefanova KT, Smith AB, Cullis BR (2009) Enhanced diagnostics for the spatial analysis of field trials. Journal of Agricultural, Biological, and Environmental Statistics 14, 392-410.
| Crossref | Google Scholar |
Stram DO, Lee JW (1994) Variance components testing in the longitudinal mixed effects model. Biometrics 50, 1171-1177.
| Crossref | Google Scholar |
Verbyla AP (2019) A note on model selection using information criteria for general linear models estimated using REML. Australian & New Zealand Journal of Statistics 61, 39-50.
| Crossref | Google Scholar |
Verbyla KL, Verbyla AP (2009) Estimated breeding values and association mapping for persistency and total milk yield using natural cubic smoothing splines. Genetics Selection Evolution 41, 48.
| Crossref | Google Scholar |
Verbyla AP, Cullis BR, Kenward MG, Welham SJ (1999) The analysis of designed experiments and longitudinal data by using smoothing splines. Journal of the Royal Statistical Society Series C: Applied Statistics 48, 269-311.
| Crossref | Google Scholar |
Verbyla AP, De Faveri J, Deery DM, Rebetzke GJ (2021) Modelling temporal genetic and spatio-temporal residual effects for high-throughput phenotyping data. Australian & New Zealand Journal of Statistics 63, 284-308.
| Crossref | Google Scholar |
Welham SJ, Gogel BJ, Smith AB, Thompson R, Cullis BR (2010) A comparison of analysis methods for late-stage variety evaluation trials. Australian & New Zealand Journal of Statistics 52(2), 125-149.
| Crossref | Google Scholar |
White IMS, Thompson R, Brotherstone S (1999) Genetic and environmental smoothing of lactation curves with cubic splines. Journal of Dairy Science 82, 632-638.
| Crossref | Google Scholar |
