Physiological response curve analysis using nonlinear mixed models

Abstract

Nonlinear response curves are often used to model the physiological responses of plants. These models are preferable to polynomials because the coefficients fit to the curves have biological meaning. The response curves are often generated by repeated measurements on one subject, over a range of values for the environmental variable of interest. However, the typical analysis of differences in coefficients between experimental groups does not include a repeated measures approach. This may lead to inappropriate estimation of error terms. Here, we show how to combine mixed model analysis, available in SAS, that allows for repeated observations on the same experimental unit, with nonlinear response curves. We illustrate the use of this nonlinear mixed model with a study in which two plant species were grown under contrasting light environments. We recorded light levels and net photosynthetic response on anywhere from 8 to 10 points per plant and fit a Mitscherlich model in which each plant has its own coefficients. The coefficients for the photosynthetic light-response curve for each plant were assumed to follow a multivariate normal distribution in which the mean was determined by the treatment. The approach yielded biologically relevant coefficients and unbiased standard error estimates for multiple treatment comparisons.

Non-linear mixed-effects modeling for photosynthetic response of Rosa hybrida L. under elevated CO₂in greenhouses - Short communication

“…CO 2 enrichment reduced R D in the two rose cultivars. Th e parameter estimates regarding α were similar to those reported by Peek et al (2002). It was shown that the quantum effi ciency is an intrinsic characteristic, and its upper ceiling in C 3 plants is set fi rmly by physiochemical limitations (Skillman 2008).…”

Unsteady flow affects swimming energetics in a labriform fish (Cymatogaster aggregata)

“…We specified the relationship between speed and Ṁ O 2 as a second-degree polynomial and individual fish as a random effect. Mixed models are useful as they control for temporal autocorrelation among data points in physiological response curves (Peek et al, 2002;Bolker et al, 2009;Nakagawa et al, 2013). This same model was used to test for differences between estimated (Ṁ O2E ) and observed Ṁ O2 values in the two unsteady flow treatments.…”

Produção de forragem de capins do gênero Panicum e modelagem de respostas produtivas e morfofisiológicas em função de variáveis climáticas.

“…As limitações computacionais existentes até poucos anos atrás faziam com que modelos com significado biológico e análises estatísticas precisas fossem conflitantes, levando à preferência por modelos lineares e/ou polinomiais (que geram bons resultados estatísticos) em relação àqueles não-lineares, com maior significado biológico (Cacho, 1993). Entretanto, os avanços computacionais na área estatística já permitem o uso de modelos não-lineares na modelagem de fenômenos biológicos e, além disso, o correto emprego de análises de medidas repetidas no tempo (Peek et al, 2002), .…”