“Microevolutionary system identification and climate response predictions by use of BLUP prediction error method”
Authors: Rolf Ergon,Affiliation: University of South-Eastern Norway
Reference: 2023, Vol 44, No 3, pp. 83-110.
Keywords: Reaction norm evolution, Dynamical BLUP model, System identification, Prediction error method
Abstract: 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 and mean phenotypic output data, as well as individual phenotypic and fitness data, for consecutive generations. A reaction norm model of the evolutionary system is then used to find predictions and the parameters in this model, together with environmental reference values and initial state variables, are finally tuned. 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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DOI: 10.4173/mic.2023.3.1References:
[1] Arnold, P.A., Kruuk, L.E., and Nicotra, A.B. (2019). How to analyse plant phenotypic plasticity in response to a changing climate, New Phytologist. 222(3):1235--1241. doi:10.1111/nph.15656
[2] Boutin, S. and Lane, J.E. (2014). Climate change and mammals: evolutionary versus plastic responses, Evolutionary applications. 7(1):29--41. doi:10.1111/eva.12121
[3] Bowers, E.K., Grindstaff, J.L., Soukup, S.S., Drilling, N.E., Eckerle, K.P., Sakaluk, S.K., and Thompson, C.F. (2016). Spring temperatures influence selection on breeding date and the potential for phenological mismatch in a migratory bird, Ecology. 97(10):2880--2891. doi:10.1002/ecy.1516
[4] Cantet, R., Angarita-Barajas, B., Forneris, N., and Munilla, S. (2022). Causal inference for the covariance between breeding values under identity disequilibrium, Genetics, Selection, Evolution: GSE. 54(1):64--64. doi:10.1186/s12711-022-00750-6
[5] Ergon, R. (2018). The environmental zero-point problem in evolutionary reaction norm modeling, Ecology and Evolution. 8(8):4031--4041. doi:10.1002/ece3.3929
[6] Ergon, R. (2019). Quantitative genetics state-space modeling of phenotypic plasticity and evolution, Modeling, Identification and Control. 40:51--69. doi:10.4173/mic.2019.1.5
[7] Ergon, R. (2022). The important choice of reference environment in microevolutionary climate response predictions, Ecology and evolution, 2022. 12(4). doi:10.1002/ece3.8836
[8] Ergon, R. (2022). Microevolutionary system identification and climate response predictions, Modeling, Identification and Control, 2022. 43(3):91--99. doi:10.4173/mic.2022.3.1
[9] Ergon, R. (2022). A BLUP derivation of the multivariate breeder’s equation, with an elucidation of errors in blup variance estimates, and a prediction method for inbred populations, Modeling, Identification and Control, 2022. 43(4):131--140. doi:10.4173/mic.2022.4.2
[10] Ergon, R. (2023). Dynamical BLUP modeling of reaction norm evolution, accommodating changing environments, overlapping generations, and multivariate data, Ecology and Evolution. 13(7):e10194. doi:10.1002/ece3.10194
[11] Ergon, T. and Ergon, R. (2017). When three traits make a line: Evolution of phenotypic plasticity and genetic assimilation through linear reaction norms in stochastic environments, Journal of Evolutionary Biology. 30(3):486--500. doi:10.1111/jeb.13003
[12] Goudet, J., Kay, T., and Weir, B.S. (2018). How to estimate kinship, Molecular ecology. 27(20):4121--4135. doi:10.1111/mec.14833
[13] Hadfield, J.D., Wilson, A.J., Garant, D., Sheldon, B.C., and Kruuk, L.E. (2010). The misuse of BLUP in ecology and evolution, The American Naturalist. 175(1):116--125. doi:10.1086/648604
[14] Henderson, C.R. (1950). Estimation of genetic parameters, Ann. Math. Stat.. 21:309--310.
[15] klimaservicesenter, N. (2023). 2023, https://seklima.met.no/observations/.
[16] Kruuk, L.E. (2004). Estimating genetic parameters in natural populations using the ‘animal model’, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences. 359(1446):873--890. doi:10.1098/rstb.2003.1437
[17] Lande, R. (1979). Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry, Evolution. pages 402--416. doi:10.2307/2407630
[18] Lande, R. (2009). Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation, Journal of evolutionary biology. 22(7):1435--1446. doi:10.1111/j.1420-9101.2009.01754.x
[19] Liu, W. (2013). Introduction to hybrid vehicle system modeling and control, Appendix A: System Identification, State and Parameter Estimation Techniques, John Wiley & Sons. doi:10.1002/9781119278924.app1
[20] Ljung, L. (1999). System Identification: Theory for the User, 2nd Edition, Prentice-Hall, Upper Saddle River, NJ.
[21] Ljung, L. (2010). Perspectives on system identification, Annual Reviews in Control. 34(1):1--12. doi:10.1016/j.arcontrol.2009.12.001
[22] Ljung, L., Hjalmarsson, H., and Ohlsson, H. (2011). Four encounters with system identification, European Journal of Control. 17(5-6):449--471. doi:10.3166/ejc.17.449-471
[23] Lynch, M. and Walsh, B. (1998). Genetics and analysis of quantitative traits, sinauer associates. Inc., Sunderland, MA. 980.
[24] Mathew, B., Leon, J., and Sillanpaa, M.J. (2018). Impact of residual covariance structures on genomic prediction ability in multi-environment trials, Plos one. 13(7):e0201181. doi:10.1371/journal.pone.0201181
[25] Merila, J. and Hendry, A.P. (2014). Climate change, adaptation, and phenotypic plasticity: the problem and the evidence, Evolutionary applications. 7(1):1--14. doi:10.1111/eva.12137
[26] Nussey, D.H., Wilson, A.J., and Brommer, J.E. (2007). The evolutionary ecology of individual phenotypic plasticity in wild populations, Journal of Evolutionary Biology. 20(3):831--844. doi:10.1111/j.1420-9101.2007.01300.x
[27] Price, G.R. etal. (1970). Selection and covariance, Nature. 227:520--521.
[28] Robertson, A. (1966). A mathematical model of the culling process in dairy cattle, Animal Science. 8(1):95--108.
[29] Robinson, G.K. (1991). That BLUP is a good thing: the estimation of random effects, Statistical science. pages 15--32.
[30] Scheiner, S.M., Barfield, M., and Holt, R.D. (2020). The genetics of phenotypic plasticity, XVII. response to climate change. Evolutionary Applications. 13(2):388--399. doi:10.1111/eva.12876
[31] Stoica, P. and Soederstroem, T. (1989). System identification, Prentice-Hall International.
[32] Thomson, C.E., Winney, I.S., Salles, O.C., and Pujol, B. (2018). A guide to using a multiple-matrix animal model to disentangle genetic and nongenetic causes of phenotypic variance, PLoS One. 13(10):e0197720. doi:10.1371/journal.pone.0197720
[33] Walsh, B. and Lynch, M. (2018). Evolution and selection of quantitative traits, Oxford University Press.
BibTeX:
@article{MIC-2023-3-1,
title={{Microevolutionary system identification and climate response predictions by use of BLUP prediction error method}},
author={Ergon, Rolf},
journal={Modeling, Identification and Control},
volume={44},
number={3},
pages={83--110},
year={2023},
doi={10.4173/mic.2023.3.1},
publisher={Norwegian Society of Automatic Control}
};