Correcting for spatial heterogeneity in plant breeding experiments with P-splines

An important aim of the analysis of agricultural field experiments is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper explores the use of two-dimensional smooth surfaces to model random spatial variation. We propose the use of anisotropic tensor product P-splines to explicitly model large-scale (global trend) and small-scale (local trend) spatial dependence. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. Each component in the model is shown to have an effective dimension. They are closely related to variance estimation, and helpful for characterising the importance of model components. An important result of this paper is the formal proof of the relation between several definitions of heritability and the effective dimension associated with the genetic component. The practical value of our approach is illustrated by simulations and analyses of large-scale plant breeding experiments. An \texttt{R}-package, \texttt{SpATS}, is provide

Flexible modelling of spatial variation in agricultural field trials with the R package INLA

The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ( AR1⊗AR1 ) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the AR1⊗AR1 and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA

Statistical interaction modeling of bovine herd behaviors

While there has been interest in modeling the group behavior of herds or flocks, much of this work has focused on simulating their collective spatial motion patterns which have not accounted for individuality in the herd and instead assume a homogenized role for all members or sub-groups of the herd. Animal behavior experts have noted that domestic animals exhibit behaviors that are indicative of social hierarchy: leader/follower type behaviors are present as well as dominance and subordination, aggression and rank order, and specific social affiliations may also exist. Both wild and domestic cattle are social species, and group behaviors are likely to be influenced by the expression of specific social interactions. In this paper, Global Positioning System coordinate fixes gathered from a herd of beef cows tracked in open fields over several days at a time are utilized to learn a model that focuses on the interactions within the herd as well as its overall movement. Using these data in this way explores the validity of existing group behavior models against actual herding behaviors. Domain knowledge, location geography and human observations, are utilized to explain the causes of these deviations from this idealized behavior

Landscape genetics reveal broad and fine‐scale population structure due to landscape features and climate history in the northern leopard frog (Rana pipiens) in North Dakota

Prehistoric climate and landscape features play large roles structuring wildlife populations. The amphibians of the northern Great Plains of North America present an opportunity to investigate how these factors affect colonization, migration, and current population genetic structure. This study used 11 microsatellite loci to genotype 1,230 northern leopard frogs (Rana pipiens) from 41 wetlands (30 samples/wetland) across North Dakota. Genetic structure of the sampled frogs was evaluated using Bayesian and multivariate clustering methods. All analyses produced concordant results, identifying a major east–west split between two R. pipiens population clusters separated by the Missouri River. Substructuring within the two major identified population clusters was also found. Spatial principal component analysis (sPCA) and variance partitioning analysis identified distance, river basins, and the Missouri River as the most important landscape factors differentiating R. pipiens populations across the state. Bayesian reconstruction of coalescence times suggested the major east– west split occurred ~13–18 kya during a period of glacial retreat in the northern Great Plains and substructuring largely occurred ~5–11 kya during a period of extreme drought cycles. A range‐wide species distribution model (SDM) for R. pipiens was developed and applied to prehistoric climate conditions during the Last Glacial Maximum (21 kya) and the mid‐Holocene (6 kya) from the CCSM4 climate model to identify potential refugia. The SDM indicated potential refugia existed in South Dakota or further south in Nebraska. The ancestral populations of R. pipiens in North Dakota may have inhabited these refugia, but more sampling outside the state is needed to reconstruct the route of colonization. Using microsatellite genotype data, this study determined that colonization from glacial refugia, drought dynamics in the northern Great Plains, and major rivers acting as barriers to gene flow were the defining forces shaping the regional population structure of R. pipiens in North Dakota

Spatial Models for Field Trials

An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product Penalized splines (P-splines). A special ANOVA-type reformulation leads to five smooth additive spatial components, which form the basis of a mixed model with five unknown variance components. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. We show the relation between several definitions of heritability and the effective dimension or the effective degrees of freedom associated to the genetic component. The approach is illustrated with large-scale field trial experiments. An R-package is provided

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

Adjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.MTM2014-55966-P Grains Research and Development Corporation (GRDC) of Australia National Institute of Agricultural Technology (INTA) of Argentina, Res. DN 1126/13 Integrated Breeding Progra