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Nutrients and environment influence arbuscular mycorrhizal colonization both independently and interactively in Schizachyrium scoparium

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Abstract

Background and aims

Arbuscular mycorrhizal fungi (AMF) are important for plant nutrient and water acquisition. Much is known about how nutrient addition and environment affect AMF, but little is known about nutrient by environment interactions. We measured AMF colonization with nutrient additions and along an environmental gradient to assess these interactions.

Methods

We measured AMF colonization in roots of little bluestem (Schizachyrium scoparium (Michx) Nash) with nutrient addition and across an environmental gradient. We assessed how AMF colonization changed across different fertilization treatments, and used ridge regression to determine nutrient, environment, and nutrient by environment interaction variables that predicted AMF colonization.

Results

The addition of nitrogen decreased AMF colonization, while mean annual temperature (MAT) and soil pH both positively predicted the percentage of AMF colonization in Schizachyrium scoparium. Additionally, we found an interaction term between MAT and phosphorus treatments that significantly affected percent AMF colonization.

Conclusions

Our results show the importance of understanding environmental conditions on AMF as well as nutrient by environment interactions when assessing how AMF respond to nutrient addition. Here we present a full-factorial nutrient addition study along an environmental gradient to assess how AMF root colonization is influenced by abiotic factors in addition to nutrients.

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Abbreviations

AAI:

Annual aridity index

AMF:

Arbuscular mycorrhizal fungi

MAT:

Mean annual temperature

N:

Nitrogen

P:

Phosphorus

K+μ :

Potassium with micronutrients treatment

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Acknowledgements

We would like to sincerely thank Lori Biederman for constructive review of the manuscript as well as various aspects of data collection. We would also like to thank the editor and two anonymous reviewers for their beneficial critique of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Iceland, Saemundargata 2, 101, Reykjavik, Iceland

    Paul N. Frater

  2. Department of Ecology, Evolution, and Behavior, University of Minnesota, 1987 Upper Buford Circle, Falcon Heights, MN, 55108, USA

    Elizabeth T. Borer, Eric Seabloom & Lauren Sullivan

  3. USDA Agricultural Research Service, 808 East Blackland Road, Temple, TX, 76502, USA

    Philip A. Fay

  4. USDA Agricultural Research Service, University of Nebraska-Lincoln, 251 Filley Hall, Lincoln, NE, 68583, USA

    Virginia Jin

  5. Department of Mathematics, Utah Valley University, 800 West University Parkway, Orem, UT, 84058, USA

    Brian Knaeble

  6. School of Natural Resources, University of Nebraska-Lincoln, 1400 R Street, Lincoln, NE, 68588, USA

    David A. Wedin

  7. Department of Physiological Diversity, Helmholtz Center for Environmental Research – UFZ, Permoserstr. 15, 04318, Leipzig, Germany

    W. Stanley Harpole

  8. German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103, Leipzig, Germany

    W. Stanley Harpole

  9. Institute of Biology, Martin Luther University Halle-Wittenberg, Am Kirchtor 1, 06108, Halle (Saale), Germany

    W. Stanley Harpole

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  1. Paul N. Frater
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Correspondence to Paul N. Frater.

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Responsible Editor: Tatsuhiro Ezawa

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Appendix - Description of Ridge Regression

Appendix - Description of Ridge Regression

We used ridge regression as opposed to a traditional multiple linear regression as a high degree of multicollinearity existed among our continous explanatory variables. Ridge Regression (RR) guards against fitting a model with extremely large fitted coefficients, which may occur inadvertently when using OLS in the presence of multicollinearity. While ordinary least-squares (OLS) regression fits a model Y = Xβ + ϵ by selecting β so as to minimize ‖Y ‐ Xβ‖2, RR minimizes ‖Y ‐ Xβ‖2 + ‖kβ‖2, where k is the shrinkage parameter. The shrinkage parameter imposes a penalty on regression coefficients that are large. When k is zero RR is the same as OLS. As k increases the penalty for large coefficients increases.

The RR estimate can be obtained with the formula (XTX + kI)−1XTY, and it has an interpretation as a Bayes estimate (Seber & Lee 2012, p. 321). The RR estimate is biased, but there exists k a such that the mean square error of the RR estimate is less than the mean square error of the OLS estimate (Hoerl & Kennard 1970). We set the shrinkage parameter as the minimizer of prediction error with leave-one out cross validation (Golub et al. 1979).

To find the optimal shrinkage parameter we performed our initial RR using lm.ridge() in the R package MASS with k as a vector of 50,000 integers spaced evenly from 0 to 500. Package MASS provides a function select () that chooses the optimal k based on leave-one-out cross validation.

Using leave-one-out cross validation we obtained an optimal shrinkage parameter (k) of 310.5. We then used this k to fit a linear model using linearRidge() in R package ridge since the summary from this output contains t-statistics and p-values determined by the methods in Cule et al. (2011). We performed another RR using the most parsimonious model determined by boot.stepAIC() in package bootStepAIC (Rizopoulos 2009). The optimal k from this secondary RR was 25. The results from this output can be seen in Table 6.

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Frater, P.N., Borer, E.T., Fay, P.A. et al. Nutrients and environment influence arbuscular mycorrhizal colonization both independently and interactively in Schizachyrium scoparium. Plant Soil 425, 493–506 (2018). https://doi.org/10.1007/s11104-018-3597-6

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