Abstract
In this paper we describe novel methodology for evaluating competition among strains of Rhizobium bacteria which can be found naturally occurring in or can be introduced into soil. Rhizobia can occupy nodules on the roots of legume plants allowing the plant to ‘fix’ atmospheric nitrogen. Our model defines competitive outcomes for a community (the multinomial count of nodules occupied by each strain at the end of a time period) relative to the past state of the community (the proportion of each strain present at the beginning of the time period) and incorporates this prior information in the analysis. Our approach for assessing competition provides an analogy to multivariate methods for continuous responses in competition studies and an alternative to univariate methods for discrete responses that respects the multivariate nature of the data. It can also handle zero values in the multinomial response providing an alternative to compositional data analysis methods, which traditionally have not been able to facilitate zero values. The proposed experimental design is based on the simplex design and the model is an extension of multinomial baseline category logit models that includes multiple offsets and random terms to allow for correlation among clustered responses. Supplemental materials for this article are available from the journal website.
Similar content being viewed by others
References
Agresti, A. (2002), Categorical Data Analysis (2nd ed.), New York: Wiley.
Aitchison, J. (1986), The Statistical Analysis of Compositional Data, London: Chapman and Hall. Reprinted in 2003 by The Blackburn Press.
Aitchison, J., and Bacon-Shone, J. (1984), “Log Contrast Models for Experiments With Mixtures,” Biometrika, 71, 323–330.
Aitchison, J., and Ho, C. H. (1989), “The Multivariate Poisson-log Normal Distribution,” Biometrika, 76, 643–653.
Aitchison, J., and Kay, J. W. (2003), “Possible Solutions of Some Essential Zero Problems in Compositional Data Analysis,” in Proceedings of Compositional Data Analysis Workshop—CoDaWork ’03 (Girona), Electronic publication available at http://ima.udg.es/Activitats/CoDaWork03.
Aitchison, J., and Ng, K. W. (2005), “The Role of Perturbation in Compositional Data Analysis,” Statistical Modelling, 5, 173–185.
Bacon-Shone, J. (2008), “Discrete and Continuous Compositions,” in CODAWORK 08, Girona, Spain.
Bell, T., Newman, J. A., Silverman, B. W., Turner, S. L., and Lilley, A. K. (2005), “The Contribution of Species Richness and Composition to Bacterial Services,” Nature, 436, 1157–1160.
Billheimer, D. (2001), “Compositional Receptor Modeling,” Environmetrics, 12, 451–467.
Billheimer, D., Guttorp, P., and Fagan, W. F. (2001), “Statistical Interpretation of Species Composition,” Journal of the American Statistical Association, 96, 1205–1214.
Billingsley, P. (1986), Probability and Measure, New York: Wiley.
Butler, A., and Glasbey, C. (2008), “A Latent Gaussian Model for Compositional Data With Zeros,” Journal of the Royal Statistical Society. Series C, Applied Statistics, 57, 505–520.
Connell, J. H. (1983), “On the Prevalence and Relative Importance of Interspecific Competition—Evidence From Field Experiments,” The American Naturalist, 122, 661–696.
Connolly, J., and Wayne, P. (2005), “Assessing Determinants of Community Biomass Composition in Two-Species Plant Competition Studies,” Oecologia, 142, 450–457.
Connolly, J., Wayne, P., and Bazzaz, F. A. (2001), “Interspecific Competition in Plants: How Well Do Current Methods Answer Fundamental Questions?” The American Naturalist, 157, 107–125.
Cornell, J. A. (2002), Experiments With Mixtures: Designs, Models, and the Analysis of Mixture Data (3rd ed.), Chichester: Wiley.
de Bruijn, F. J. (1992), “Use of Repetitive (Repetitive Extragenic Palindromic and Enterobacterial Repetitive Intergeneric Consensus) Sequences and the Polymerase Chain-Reaction to Fingerprint the Genomes of Rhizobium meliloti Isolates and Other Soil Bacteria,” Applied and Environmental Microbiology, 58, 2180–2187.
Duodu, S., Brophy, C., Connolly, J., and Svenning, M. M. (2009), “Competitiveness of a Native Rhizobium Leguminosarum Biovar Trifolii Strain for Nodule Occupancy is Manifested During Infection,” Plant and Soil, 318, 117–126.
Fagerli, I. L. (2006), “Distribution and Diversity of Rhizobial Soil Populations From Subarctic and Arctic Regions in Norway,” Dr. Scient Thesis, University of Tromsø, Norway. ISBN 10 82-90256-019.
Fagerli, I. L., and Svenning, M. M. (2005), “Arctic and Subarctic Soil Populations of Rhizobium leguminosarum Biovar trifolii Nodulating Three Different Clover Species: Characterisation by Diversity at Chromosomal and Symbiosis Loci,” Plant and Soil, 275, 371–381.
Firbank, L. G., and Watkinson, A. R. (1985), “On the Analysis of Competition Within Two-Species Mixtures of Plants,” Journal of Applied Ecology, 22, 503–517.
Goldberg, D. E., and Barton, A. M. (1992), “Patterns and Consequences of Interspecific Competition in Natural Communities—A Review of Field Experiments With Plants,” The American Naturalist, 139, 771–801.
Hartzel, J., Agresti, A., and Caffo, B. (2001), “Multinomial Logit Random Effects Models,” Statistical Modelling, 1, 81–102.
Hector, A., Schmid, B., Beierkuhnlein, C., Caldeira, M. C., Diemer, M., Dimitrakopoulos, P. G., Finn, J. A., Freitas, H., Giller, P. S., Good, J., Harris, R., Hogberg, P., Huss-Danell, K., Joshi, J., Jumpponen, A., Korner, C., Leadley, P. W., Loreau, M., Minns, A., Mulder, C. P. H., O’Donovan, G., Otway, S. J., Pereira, J. S., Prinz, A., Read, D. J., Scherer-Lorenzen, M., Schulze, E. D., Siamantziouras, A. S. D., Spehn, E. M., Terry, A. C., Troumbis, A. Y., Woodward, F. I., Yachi, S., and Lawton, J. H. (1999), “Plant Diversity and Productivity Experiments in European Grasslands,” Science, 286, 1123–1127.
Iwasa, Y., Nakamaru, M., and Levin, S. A. (1998), “Allelopathy of Bacteria in a Lattice Population: Competition Between Colicin-Sensitive and Colicin-Producing Strains,” Evolutionary Ecology, 12, 785–802.
Kirwan, L., Lüscher, A., Sebastià, M. T., Finn, J. A., Collins, R. P., Porqueddu, C., Helgadottir, A., Baadshaug, O. H., Brophy, C., Coran, C., Dalmannsdóttir, S., Delgado, I., Elgersma, A., Fothergill, M., Frankow-Lindberg, B. E., Golinski, P., Grieu, P., Gustavsson, A. M., Höglind, M., Huguenin-Elie, O., Iliadis, C., Jørgensen, M., Kadziuliene, Z., Karyotis, T., Lunnan, T., Malengier, M., Maltoni, S., Meyer, V., Nyfeler, D., Nykanen-Kurki, P., Parente, J., Smit, H. J., Thumm, U., and Connolly, J. (2007), “Evenness Drives Consistent Diversity Effects in Intensive Grassland Systems Across 28 European Sites,” Journal of Ecology, 95, 530–539.
Law, R., and Watkinson, A. R. (1987), “Response-Surface Analysis of Two-Species Competition—an Experiment on Phleum-arenarium and Vulpia-fasciculata,” Journal of Ecology, 75, 871–886.
Leslie, P. H. (1958), “A Stochastic Model for Studying the Properties of Certain Biological Systems by Numerical Methods,” Biometrika, 45, 16–31.
Martín-Fernández, J. A., Barceló-Vidal, C., and Pawlowsky-Glahn, V. (2003), “Dealing With Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation,” Mathematical Geology, 35, 253–278.
May, R. M. (2001), Stability and Complexity in Model Ecosystems, Princeton: Princeton University Press.
Nicol, H., and Thornton, H. G. (1941), “Competition Between Related Strains of Nodule Bacteria and Its Influence on Infection of the Legume Host,” Proceedings of the Royal Society of London. Series B, Biological Sciences, 130, 32–59.
Ramseier, D., Connolly, J., and Bazzaz, F. A. (2005), “Carbon Dioxide Regime, Species Identity and Influence of Species Initial Abundance as Determinants of Change in Stand Biomass Composition in Five-Species Communities: An Investigation Using a Simplex Design and RGRD Analysis,” Journal of Ecology, 93, 502–511.
SAS software, Version 9.1 of the SAS System for Windows. Copyright ©2002–2003 SAS Institute Inc. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc., Cary, NC, USA.
Scheffe, H. (1963), “Simplex-Centroid Design for Experiments With Mixtures,” Journal of the Royal Statistical Society. Series B, Statistical Methodology, 25, 235–263.
Schoener, T. W. (1983), “Field Experiments on Interspecific Competition,” The American Naturalist, 122, 240–285.
Suter, M., Ramseier, D., Guesewell, S., and Connolly, J. (2007), “Convergence Patterns and Multiple Species Interactions in a Designed Plant Mixture of Five Species,” Oecologia, 151, 499–511.
Thies, J. E., Benbohlool, B., and Singleton, P. W. (1992), “Environmental-Effects on Competition for Nodule Occupancy Between Introduced and Indigenous Rhizobia and Among Introduced Strains,” Canadian Journal of Microbiology, 38, 493–500.
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
Below are the links to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Brophy, C., Connolly, J., Fagerli, I.L. et al. A Baseline Category Logit Model for Assessing Competing Strains of Rhizobium Bacteria. JABES 16, 409–421 (2011). https://doi.org/10.1007/s13253-011-0058-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-011-0058-6