Dynamical <scp>BLUP</scp> modeling of reaction norm evolution, accommodating changing environments, overlapping generations, and multivariate data

Ergon, Rolf

doi:10.1002/ece3.10194

Cited by 1 publication

(6 citation statements)

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“…Next, we must find how fitness affects the mean reaction norm trait predictions for the offspring of any given parent generation. As shown in Ergon (2023), and as verified by Theorem 2 below, the incremental changes in mean trait values can be found from the predicted random effects by use of Robertson's secondary theorem of natural selection (Ch. 6, Walsh and Lynch, 2018;Robertson, 1966)…”

Section: Dynamical Blup Prediction Modelmentioning

confidence: 78%

“…In the formulation of the linear mixed model, we assumed a MISO system, with linear reaction norms as functions of environmental cues u 1,t , u 2,t , etc., but there is nothing in the theory that prevents us from use of non-linear reaction norms that are also functions of u 1,t u 2,t , u 2 1,t , u 2 2,t , etc., as discussed in Ergon (2018). A more general model for a MIMO system is developed in Ergon (2023).…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Although the theory is limited to MISO systems, an extension of the GRAD algorithm to multiple-input multiple-output (MIMO) systems is demonstrated in Ergon (2022b). Such extensions are possible also for the BLUP algorithm (Ergon, 2023). The applicability of PEM in an evolutionary context is, however, not limited to the algorithms discussed, it should in principle work for any type of parametrized prediction model that includes mean reaction norm traits, or other latent variables.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The GRAD prediction model is based on the multivariate breeder's equation (Lande, 1979), which means that it implicitly assumes that the additive genetic relationship matrix is a unity matrix (Ergon, 2023). Applied on the reaction norm traits in Equation ( 2a), the multivariate breeder's equation for the incremental changes in mean traits from generation to generation becomes…”

Section: The Grad Prediction Modelmentioning

confidence: 99%

“…Hadfield et al (2010) criticized this approach on the ground that BLUP underestimates the variances of the random effects in the linear mixed model. However, as shown in Ergon (2022c), this underestimation is precisely what is needed, in order to obtain the correct incremental changes for prediction of phenotypic traits of non-plastic organisms, and as shown in Ergon (2023), this is the case also for reaction norm traits of plastic organisms.…”

Section: Introductionmentioning

confidence: 99%

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Microevolutionary system identification and climate response predictions by use of BLUP prediction error method

Ergon

2023

MIC

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Animals and other organisms in wild populations may adjust to climate change by means of plasticity and evolution, and it is an important task to find the contributions from each of these effects. Attempts to solve this disentanglement problem by use of best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) methods, as borrowed from the field of domestic breeding, have been criticized because of errors in the variances of the predicted random effects. A primary purpose of this article is to show how the problem can be solved by use of BLUP in a prediction error method (PEM), borrowed from the well-established engineering system identification discipline.The PEM approach is first to collect environmental input data u t and mean phenotypic output data y t , as well as individual phenotypic and fitness data, for consecutive generations from t = 1 to T . A reaction norm model of the evolutionary system is then used to find predictions y t , and the parameters in this model, together with environmental reference values and initial state variables, are finally tuned such that T t=1 y t − y t 2 is minimized.The main contribution is the use a dynamical BLUP model in a BLUP/PEM method for parameter estimation and mean reaction norm trait predictions. The model is dynamical in the sense that the incidence matrix in an underlying linear mixed model, as well as the corresponding residual covariance matrix, are functions of time. For comparisons, a selection gradient prediction model as presented in Ergon (2022a,b) is also used in a GRAD/PEM method. The advantages of the BLUP/PEM method are that it can utilize genetic relationship information, and that it produces better estimates of environmental reference values. The treatment is limited to multiple-input single-output (MISO) systems. Generations are assumed to be non-overlapping.Simulation examples show that BLUP/PEM may find good estimates of environmental reference values and initial state variables, as well as good mean reaction norm trait predictions. Details for use of additional fixed effects, as well as appropriate methods for model validation remain to be worked out.

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Section: Dynamical Blup Prediction Modelmentioning

confidence: 78%

Section: Summary and Discussionmentioning

confidence: 99%