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A Baseline Category Logit Model for Assessing Competing Strains of Rhizobium Bacteria

TL;DR: In this article, the authors describe a methodology for evaluating competition among strains of rhizobium bacteria which can be found naturally occurring in or can be introduced into soil and propose an extension of multinomial baseline category logit models that includes multiple offsets and random terms to allow for correlation among clustered responses.
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.

Summary (2 min read)

1. INTRODUCTION

  • Competition occurs among species when a required resource is limited and the species ‘compete’ to each obtain the resource.
  • Offsets have previously been used with models for discrete responses (logistic regression in Agresti 2002) but multiple offsets have not been used with multinomial models or for the purpose of assessing competition among species.
  • The experimental response in their motivating example is the number of nodules acquired by each strain of rhizobia in each community and this is a multinomial vector.
  • The novel features are the marrying of simplex designs with multinomial responses in a discrete modeling framework that defines competitive outcomes for a community of species relative to a previous state of the community and incorporates this prior information in the analysis.

2. METHODS

  • The authors propose a multinomial baseline category logit model (Agresti 2002) to measure the competition between J species that will allow the assessment of competitive relationships among species and consequences for community structure.
  • This model is analogous to the specification of the RGRD model in Connolly and Wayne (2005, Equation (4)).
  • The authors extend this model to include a community specific random effect to allow for variation from community-to-community (Hartzel, Agresti, and Caffo 2001).
  • To interpret the model the final proportions of success counts for each species can be predicted for a range of initial communities and these predictions used to determine the outcome of competition.
  • Π̂ij /pij compares the predicted proportion of success counts relative to initial proportion present for an individual species, also known as Compositional change measure (1).

3.1. EXPERIMENTAL DESIGN

  • When a Rhizobium strain has occupied a nodule on the root of a legume, it normally has the ability to ‘fix’ nitrogen (N) from the atmosphere and supply the host plant with N and provide additional N in the legume environment.
  • Competition was investigated among M. loti strains Ml8,Ml19 and Ml16; named A, B and C, respectively, from here on.
  • Nodule occupancy of the rhizobial strains was determined by ERIC-PCR fingerprinting (de Bruijn 1992).
  • Several of the responses for individual species were zero.

3.2. MODEL FITTING

  • The authors fitted a series of multinomial baseline category logit random effects models to the multinomial data.
  • The authors maximized the log of the likelihood function given in (2.5) using the NLMIXED procedure in SAS software .
  • The authors predicted from the fitted model for a range of initial compositions using Equation (2.6).
  • Approximate standard errors were generated for these tests using the Delta method (Billingsley 1986).

3.3. RESULTS

  • The final model, after extensive model selection using AIC , included the initial proportions of each strain and density in the linear predictor.
  • Two interaction terms piApiB and piBpiC were also included and these interactions were found to be of similar strength and so were constrained to be equal.
  • While the inclusion of the random effects to account for variation from community-to-community was not significant , this component was included in the models to respect the structure in the experimental design.
  • Based on these two compositional change measures, strain C was the most competitive strain, particularly at high density, while there was no out-right winner between strains A and B. Ta bl e 2.

4. DISCUSSION

  • In this paper the authors present an experimental design and modeling framework for assessing multinomial responses from multiple species competition studies.
  • It also provides a multivariate alternative to the univariate methods used for discrete responses based on Lotka–Volterra models (Leslie 1958; May 2001) that allows for correlation among responses within a community.
  • Strain C occupied a large number of the nodules even when it was least represented in the inoculum particularly at high inoculum density, which in general is an indication of a highly competitive strain (Thies, Benbohlool, and Singleton 1992).
  • The authors have shown that using an appropriate simplex design allows the fitting of model (2.7) through which they can assess the relative competitiveness of species, whether species interfere with or interact with each other, and the outcome of these interspecific relationships on community composition.
  • The authors model is also closely related to the Lotka–Volterra differential equations for competing species.

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Supplementary materials for this article are available at 10.1007/s13253-011-0058-6.
A Baseline Category Logit Model for Assessing
Competing Strains of Rhizobium Bacteria
C. BROPHY,J.CONNOLLY,I.L.FAGERLI,S.DUODU,and
M. M. S
VENNING
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 in-
troduced 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 mul-
tivariate 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 facil-
itate 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.
Key Words: Competition with discrete response; Compositional data analysis; Dis-
crete multivariate analysis; Random effects; Simplex design; Zero values.
1. INTRODUCTION
Competition occurs among species when a required resource is limited and the species
‘compete’ to each obtain the resource. Competition has been widely studied experimen-
tally across many organisms (Nicol and Thornton 1941; Connell 1983; Schoener 1983;
C. Brophy (
) is a Lecturer in Statistics, Department of Mathematics & Statistics, National University of Ire-
land Maynooth, Maynooth, Co. Kildare, Ireland (E-mail: caroline.brophy@nuim.ie). J. Connolly is Associate
Professor in Statistics, UCD School of Mathematical Sciences, Environmental & Ecological Modelling Group,
University College Dublin, Belfield, Dublin 4, Ireland. I. L. Fagerli was a Research Student and M. M. Svenning
is Professor and Head, Department of Arctic and Marine Biology, University of Tromsø, 9037 Tromsø, Norway.
S. Duodu is a Researcher, National Veterinary Institute, P.O. Box 750, Sentrum, 0106 Oslo, Norway.
© 2011 International Biometric Society
Journal of Agricultural, Biological, and Environmental Statistics, Volume 16, Number 3, Pages 409–421
DOI: 10.1007/s13253-011-0058-6
409

410 C. BROPHY ET AL.
Firbank and Watkinson 1985; Goldberg and Barton 1992; Iwasa, Nakamaru, and Levin
1998). The analytical approaches for assessing effects range from multivariate models for
continuous responses (Connolly and Wayne 2005) to univariate approaches for discrete re-
sponses (May 2001) to compositional methods (Aitchison 1986; Aitchison and Ng 2005).
Here we develop a modeling approach for discrete multinomial response data that extends
the current competition literature in three ways: (1) it is analogous to a competition model
derived for continuous responses by Connolly and Wayne (2005) that defines competitive
outcomes relative to the past state of the community and incorporates this prior information
in the analysis, (2) it allows for the multivariate nature of the response data, (3) it will han-
dle zero response values. Our model is a baseline category logit model extended to include
random effects (Hartzel, Agresti, and Caffo 2001) to allow for correlated responses and
multiple offset terms to allow for initial starting values of species. Offsets have previously
been used with models for discrete responses (logistic regression in Agresti 2002)butmul-
tiple offsets have not been used with multinomial models or for the purpose of assessing
competition among species.
The models developed in this paper are motivated by a study of competition among
strains of rhizobia bacteria, which are found naturally occurring in soil or can be introduced
deliberately into soil. Rhizobia can occupy nodules on the root of legume plant species
resulting in atmospheric nitrogen fixation and thereby supply the host plant with N and
provide additional N in the legume environment. This natural source of N can be beneficial
to the productivity of grassland systems and can reduce the cost of running the system. It
is possible that some strains of rhizobia are superior at occupying nodules and at fixing N.
Does the proportion of strains of rhizobia present in the soil at a given point in time affect
the proportion of nodules that the strain will occupy at a later time? To answer this question
we applied three strains of rhizobia to the roots of a legume species in a range of initial
proportions and after a period of time counted the number of nodules each strain occupied.
There were a limited number of available sites for nodulation and the strains competed to
occupy them. For each community (root section) we have a vector of initial proportions
and a final multinomial response vector. We modeled the change from initial proportion
applied to final proportion of nodules occupied for each strain.
In a community, a good competitor is one that gains proportionately more over time
than other species (Connolly, Wayne, and Bazzaz 2001). Connolly and Wayne (2005) and
Ramseier, Connolly, and Bazzaz (2005) developed a multivariate modeling approach to
assessing the effects of the species identity, environment and species initial relative abun-
dance on the outcome of competition. The continuous and multivariate response measured
was the relative growth rate of each species in a community over a period of time. The
variable(s) modeled were the differences in relative growth rates between pairs of species
in a community, giving the name RGRD (relative growth rate difference) to the models.
The RGRD model does not currently facilitate discrete responses.
When the response for each species in a community is a discrete whole number each
experimental community provides a multinomial response vector. There is a long his-
tory of modeling approaches to community dynamics for such discrete responses (May
2001) and these can been related to a discrete version of the Lotka–Volterra model

MODELING MULTINOMIAL DATA 411
(Leslie 1958). However, these approaches rarely deal with the multivariate nature of these
types of data. Other approaches have been to use compositional data analysis methods
for changing compositions (Aitchison 1986; Aitchison and Ng 2005), but these meth-
ods break down when species with zero compositions occur in the response. Some ap-
proaches to facilitate zero methods have been developed (e.g. Aitchison and Kay 2003;
Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn 2003; Butler and Glasbey 2008)
but these rely on assumptions about the type of zero or are suited only to analysis for
specific hypotheses e.g. to compare compositions of different groups.
In a simplex design (Scheffe 1963; Cornell 2002), the initial relative abundances of
competing species are manipulated so that not all experimental communities have all
species equally present to begin with. This design has been used in a range of multi-
species competition studies (e.g. Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007;
Suter et al. 2007) as it allows a broad coverage of the design space and facilitates the
simultaneous assessment of species identity, the effect of species on each other and, if
required, environmental effects (Connolly, Wayne, and Bazzaz 2001). Ideally, in compe-
tition studies, the simplex design would comprise a wide range of compositions in the
simplex space at a number of overall densities (Ramseier, Connolly, and Bazzaz 2005;
Kirwan et al. 2007).
In this paper we propose an experimental and analytical framework for assessing com-
petition among species where the outcome is discrete. The experimental response in our
motivating example is the number of nodules acquired by each strain of rhizobia in each
community and this is a multinomial vector. We describe a multinomial modeling frame-
work for discrete responses from this multi-strain competition experiment and the experi-
mental design needed to estimate model parameters, and we detail how to predict and test
predictions from the models. The novel features are the marrying of simplex designs with
multinomial responses in a discrete modeling framework that defines competitive outcomes
for a community of species relative to a previous state of the community and incorporates
this prior information in the analysis.
2. METHODS
We propose a multinomial baseline category logit model (Agresti 2002) to measure
the competition between J species (categories) that will allow the assessment of compet-
itive relationships among species and consequences for community structure. The cate-
gorical response vector is (y
i1
,...,y
iJ
) for i =1,...,c (the number of communities) and
j = 1,...,J (the number of species) and represents the number of ‘success counts’ for
each species at time t with
J
j=1
y
ij
= n
i
being the total number of success counts for
community i. A multinomial baseline category logit model is a series of J 1 models
relating the jth to the J th species where the J th species is called the baseline category.
The ordering of the j = 1toJ species and the use of a particular species as the ‘base-
line’ is arbitrary and independent of interpretation. We can model the vector of parameters
i1
,...,π
iJ
), the proportion of success counts for each species in the ith community at

412 C. BROPHY ET AL.
time t, with
J
j=1
π
ij
=1, as
log
π
ij
π
iJ
=x
i
β
j
for j =1,...,J 1 (2.1)
where x
i
denotes the vector of K explanatory variables for the ith community, β
j
is the
parameter vector of coefficients for the j th model and could include abiotic effects such
as an environmental treatment. If β
j
= 0, then
π
ij
π
iJ
= 1 and we conclude that species j
and J have the same proportion of success counts at time t. While model (2.1) can assess
proportion of success counts by species relative to the baseline species at a given point in
time (t), it can not address questions of competitive relations or consequences for commu-
nity dynamics without incorporating information on the proportions of each species in the
community at time 0 (or some other reference time) (Connolly, Wayne, and Bazzaz 2001).
If the proportion of each species initially present in the ith community at time 0 is given
by the vector (p
i1
,...,p
iJ
), then we propose the model:
log
π
ij
/p
ij
π
iJ
/p
iJ
=x
i
β
j
for j =1,...,J 1 (2.2)
which can be rewritten as
log
π
ij
π
iJ
=x
i
β
j
+log
p
ij
p
iJ
for j =1,...,J 1 (2.3)
where log(
p
ij
p
iJ
) is an offset term, i.e. a regression term with known coefficient equal to 1.
If β
j
=0, it indicates no change in relative abundance from time 0 to time t between the
two competing species j and J and implies that the two species are equally competitive.
This model is analogous to the specification of the RGRD model in Connolly and Wayne
(2005, Equation (4)).
We extend this model to include a community specific random effect to allow for varia-
tion from community-to-community (Hartzel, Agresti, and Caffo 2001). The model com-
paring the j th to the J th species is
log
π
ij
π
iJ
=x
i
β
j
+log
p
ij
p
iJ
+z
i
u
ij
for j =1,...,J 1 (2.4)
where z
i
denotes the design vector for the random effect for the ith community and u
ij
is
assumed multivariate normal with an unstructured covariance matrix () to keep indepen-
dence of the choice of baseline category (Hartzel, Agresti, and Caffo 2001).
We can fit model (2.4) using maximum likelihood. Denoting the linear predictor, lp
ij
=
x
i
β
j
+log(
p
ij
p
iJ
) +z
i
u
ij
, the likelihood function for the ith response vector is, integrating
out the random effects and omitting a fixed constant:
i
−∞
···
−∞
J 1
j
exp(lp
ij
)
1 +
J 1
j=1
exp(lp
ij
)
y
ij
1
1 +
J 1
j=1
exp(lp
ij
)
y
iJ
×f(u
ij
;) du
ij
. (2.5)

MODELING MULTINOMIAL DATA 413
We predict (denoted by the ˆsymbol, which is also used to denote the maximum likelihood
estimate of model parameters) the proportion of success counts for the j th species from
the model at the median value of the random effect using the equations:
ˆπ
ij
=
exp
x
i
ˆ
β
j
+log
p
ij
p
iJ

1 +
J 1
j=1
exp
x
i
ˆ
β
j
+log
p
ij
p
iJ

for j =1,...,J 1,
ˆπ
iJ
=1
J 1
j=1
ˆπ
ij
for J.
(2.6)
While this model may be applied to a wide range of count data it is particularly relevant
to data from experiments based on a simplex design (Scheffe 1963; Cornell 2002) in which
the initial p
ij
values and overall initial density of species are deliberately manipulated. The
relative abundance of each species at time 0, (p
ij
,...,p
iJ
), may be important determinants
of species relative competitiveness and hence of the final composition
ij
,...,π
iJ
) of the
ith community. At its simplest, the x matrix in model (2.4) would include the relative
abundances p
ij
,...,p
iJ
giving:
log
π
ij
π
iJ
=
J
k=1
β
jk
p
ik
+β
jD
D
i
+log
p
ij
p
iJ
+u
ij
for j =1,...,J 1 (2.7)
where p
ik
is the initial proportion of the kth species for k =1,...,J, D
i
is the total density
of the ith community and u
ij
is a random effect with variance σ
2
j
and may be correlated
with the other J 2 random effects. Interactions among the p
ik
s and between the p
ik
’s
and other independent variables, such as a treatment factor or community density (D) may
also be included in the model specification.
For model (2.7), if β
jk
=0 for all k = 1,...,J and β
jD
=0, then the relative propor-
tions of the j th and J th species are the same at times 0 and t, and species j and J are
equally competitive i.e. (
π
ij
π
iJ
) =(
p
ij
p
iJ
). When these parameters are not zero and interaction
effects are present, the number of competition coefficients may mean it is difficult to see
their combined impact on community relative composition. To interpret the model the fi-
nal proportions of success counts for each species can be predicted for a range of initial
communities and these predictions used to determine the outcome of competition. Predic-
tions can be displayed graphically using ternary diagrams (where there are three competing
species), and we distinguish between two numerical comparisons. Compositional change
measure (1): ˆπ
ij
/p
ij
compares the predicted proportion of success counts relative to ini-
tial proportion present for an individual species. This measure determines how a species
performs relative to its own expectation (p
ij
) but even a species that performs better than
expected may not be the most competitive species. Compositional change measure (2):
ˆπ
ij
/p
ij
ˆπ
ij
/p
ij
for j =j
, compares two species and determines which is the more competitive of
the two.

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  • ...They have been used in understanding the BEF relationship in a number of plant and invertebrate assemblages (Sheehan et al. 2006; Kirwan et al. 2007; Connolly et al. 2009, 2011; Frankow-Lindberg et al. 2009; Nyfeler et al. 2009; O’Hea, Kirwan & Finn 2010; Brophy et al. 2011)....

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TL;DR: In this article , the authors used an univariate multiple logit regression model to determine the synergistic expression of transgenes and endogenous AMGs in the head kidney post-bacterial infection.

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TL;DR: The inoculation of legumes with effective rhizobia or bradyrhizobia represents an inexpensive alternative to the use of chemical nitrogen fertilizers, whose prices have risen due to the high cost of energy involved in their production.
Abstract: The inoculation of legumes with effective rhizobia or bradyrhizobia represents an inexpensive alternative to the use of chemical nitrogen fertilizers, whose prices have risen due to the high cost of energy involved in their production. These fertilizers are also pollution hazards. The process of symbiotic biological nitrogen fixation requires that the host crop be adequately nodulated by the specific root-nodule bacteria effective in nitrogen fixation. Not all the strains of Rhizobium or Bradyrhizobium that can produce nodules on a given host are able to use N2 rapidly and efficiently. Nonetheless, selection of an effective (i.e. N2-fixing) strain is a prerequisite for any crop to be inoculated. A second important characteristic is the competitiveness of the strain. Unfortunately, effectiveness and competitiveness are generally mutually exclusive and are not dependent upon each other. Little information exists on the effects of systemic fungicides on symbiotic nitrogen fixation or nodulation. It has been reported that the systemic fungicide benomyl increased the relative abundance of nodules formed by the inoculated strain, the number of added rhizobia on the root, the total N content, and the percentage N of soybean plants grown in four soils when the seeds were inoculated with a benomyl-resistant strain of Bradyrhizobium japonicum. It was also found that oxamyl (a basipetally translocated fungicide) applied to the seeds, foliage, or both increased the yield, N content, percentage N, and weight of nodules, pods, and grains along with the number of nodules formed by the inoculated strain when soybean seeds were inoculated with oxamyl-resistant Rhizobium japonicum.

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Cites background from "A Baseline Category Logit Model for..."

  • ...Recently Brophy et al. (2011) described a novel methodology for evaluating competition among strains of Rhizobium bacteria which can be found naturally occurring in or can be introduced into soil....

    [...]

References
More filters
Journal ArticleDOI
TL;DR: Elevated CO2 significantly changed community composition towards the previously more poorly performing species Silene, Legousia and Papaver, and these new methods proved a powerful system for identifying the biotic and abiotic factors determining change in biomass composition in multispecies communities.
Abstract: Summary 1 The effect of elevated CO2 on species’ performance was investigated in communities composed of five annual weeds that are characteristic of early old field succession in central Europe: Centaurea cyanus L., Matricaria chamomilla L., Silene noctiflora L., Papaver rhoeas L. and Legousia speculum-veneris (L.) Chaix. 2 The experiment was based on a simplex design, repeated at two overall levels of initial stand density, to give a wide range of five-species communities across which the initial composition and species abundance varied systematically. 3 A multivariate method, based on analysing the differences in relative growth rates (RGRD) between pairs of species, was extended for use with more than two species, in order to assess the relative importance of various determinants of change in stand biomass composition. 4 On average, Centaurea (54.6% of final yield) gave the highest yield, followed by Matricaria (22.9%), Silene (16.9%), Legousia (3.1%) and Papaver (2.7%). 5 The major determinants of change in community structure were species identity and CO2 level. Elevated CO2 significantly changed community composition towards the previously more poorly performing species Silene, Legousia and Papaver. 6 Despite strong effects of intra- and interspecific competition on individual species performance, species’ initial abundance had relatively little impact on the change in community composition. Most cases where such effects were significant involved Silene: performance of Papaver was poorer in communities with higher initial presence of Silene and higher initial abundances of Centaurea and Matricaria always facilitated performance of Silene. 7 These new methods proved a powerful system for identifying the biotic and abiotic factors determining change in biomass composition in multispecies communities.

37 citations


"A Baseline Category Logit Model for..." refers background or methods in this paper

  • ...Connolly and Wayne (2005) and Ramseier, Connolly, and Bazzaz (2005) developed a multivariate modeling approach to assessing the effects of the species identity, environment and species initial relative abundance on the outcome of competition....

    [...]

  • ...This design has been used in a range of multispecies competition studies (e.g. Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007; Suter et al. 2007) as it allows a broad coverage of the design space and facilitates the simultaneous assessment of species identity, the effect of species on each…...

    [...]

  • ...…the framework as it allows the estimation of the parameters in model (2.7) which can identify how competitors react to changing initial presence of other species in addition to its own changing initial presence and to environmental change (Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007)....

    [...]

  • ...Ideally, in competition studies, the simplex design would comprise a wide range of compositions in the simplex space at a number of overall densities (Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007)....

    [...]

  • ...The βjk coefficients in model (2.7) can not be estimated in a design containing only communities with each species equally present (Ramseier, Connolly, and Bazzaz 2005)....

    [...]

Journal ArticleDOI
TL;DR: In standard multivariate statistical analysis, common hypotheses of interest concern changes in mean vectors and subvectors as mentioned in this paper, and it is now well established that compositional data analysis is a special case of multivariate analysis.
Abstract: In standard multivariate statistical analysis, common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositi...

34 citations


"A Baseline Category Logit Model for..." refers methods in this paper

  • ...Our analysis can be considered to be a compositional data analysis problem (Aitchison 1986) as it is essentially an extension of the ‘paired comparison lattice’ example presented in Aitchison and Ng (2005)....

    [...]

  • ...The method can handle zero values within the multinomial responses, a problem which has plagued other approaches such as compositional data analysis methods previously considered for this type of problem (Aitchison and Bacon-Shone 1984; Aitchison 1986; Billheimer 2001; Billheimer, Guttorp, and Fagan 2001; Aitchison and Kay 2003; Aitchison and Ng 2005)....

    [...]

  • ...…responses, a problem which has plagued other approaches such as compositional data analysis methods previously considered for this type of problem (Aitchison and Bacon-Shone 1984; Aitchison 1986; Billheimer 2001; Billheimer, Guttorp, and Fagan 2001; Aitchison and Kay 2003; Aitchison and Ng 2005)....

    [...]

  • ...Other approaches have been to use compositional data analysis methods for changing compositions (Aitchison 1986; Aitchison and Ng 2005), but these methods break down when species with zero compositions occur in the response....

    [...]

  • ...The analytical approaches for assessing effects range from multivariate models for continuous responses (Connolly and Wayne 2005) to univariate approaches for discrete responses (May 2001) to compositional methods (Aitchison 1986; Aitchison and Ng 2005)....

    [...]

Journal ArticleDOI
TL;DR: A method is proposed for assessing the relative importance of species identity, neighbour species influence and environment as determinants of change in community biomass composition in two-species short-term competition experiments based on modelling the differences in relative growth rates of species.
Abstract: A method is proposed for assessing the relative importance of species identity, neighbour species influence and environment as determinants of change in community biomass composition in two-species short-term competition experiments. The method is based on modelling the differences in relative growth rates (RGR) of species (hence called the RGRD method). Using a multiple regression approach it quantifies the effects of initial species' abundance, species identity and environment on RGRD and hence on change in community biomass composition. The RGRD approach is relatively simple to use and deals readily with statistical difficulties associated with correlated responses between species from the same stand. It can be easily adapted to analyse sequential harvest data. An example based on data from two-species mixtures of the annual species Stellaria media and Poa annua is used to illustrate the method. The main determinant of change in community biomass composition was species identity, reflected in the difference in growth rates between the species. Change in community composition was not, in general, significantly affected by the influence of neighbours or fertiliser level. The unimportance of the influence of neighbours in affecting the composition of these communities contrasts with the strong role of intra- and interspecific competition in determining the size of individuals of both species (Connolly et al. in Oecologia 82:513-526, 1990).

32 citations


"A Baseline Category Logit Model for..." refers background or methods in this paper

  • ...It provides an analogue to RGRD methods for assessing continuous response competition (Connolly and Wayne 2005; Ramseier, Connolly, and Bazzaz 2005)....

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  • ...The analytical approaches for assessing effects range from multivariate models for continuous responses (Connolly and Wayne 2005) to univariate approaches for discrete responses (May 2001) to compositional methods (Aitchison 1986; Aitchison and Ng 2005)....

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  • ...…data that extends the current competition literature in three ways: (1) it is analogous to a competition model derived for continuous responses by Connolly and Wayne (2005) that defines competitive outcomes relative to the past state of the community and incorporates this prior information in…...

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  • ...Connolly and Wayne (2005) and Ramseier, Connolly, and Bazzaz (2005) developed a multivariate modeling approach to assessing the effects of the species identity, environment and species initial relative abundance on the outcome of competition....

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Journal ArticleDOI
TL;DR: The negative feedback suggests that there is niche partitioning between the species, which permits their coexistence in Swiss fens, and the overall convergence of communities.
Abstract: It is known that convergence and divergence can occur in complex plant communities, but the relative importance of biotic and abiotic factors driving these processes is less clear. We addressed this issue in an experiment using a range of mixed stands of five species that are common in Swiss fens (Carex elata, C. flava, Lycopus europaeus, Lysimachia vulgaris and Mentha aquatica) and two levels of water and nutrients. One hundred and seventy-six experimental mixtures were maintained in large pots (75 l) for two consecutive growing seasons in an experimental garden. The stands varied systematically in the initial relative abundance of each of the five species and in overall initial stand abundance. The changes in biomass over 2 years were modelled as linear functions of treatments and the initial biomass of each species. The dynamics of the system were mainly driven by differences in the identity of species and by a negative feedback mechanism but also by different abiotic conditions. In all mixtures, C. elata became more dominant over time, which caused an overall convergence of community composition. In addition, the rate of change of each species’ biomass was negatively related to its own initial abundance. Thus, a negative feedback further contributed to the convergence of communities. Species responded differently to water level and nutrient supply, causing community dynamics to differ among treatments. However, the different abiotic conditions only slightly modified the overall convergence pattern. Competitive interactions between more than two species were weaker than the negative feedback but still significantly influenced the species’ final relative abundance. The negative feedback suggests that there is niche partitioning between the species, which permits their coexistence.

27 citations


"A Baseline Category Logit Model for..." refers methods in this paper

  • ...This design has been used in a range of multispecies competition studies (e.g. Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007; Suter et al. 2007) as it allows a broad coverage of the design space and facilitates the simultaneous assessment of species identity, the effect of species on each…...

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  • ...This design has been used in a range of multispecies competition studies (e.g. Ramseier, Connolly, and Bazzaz 2005; Kirwan et al. 2007; Suter et al. 2007) as it allows a broad coverage of the design space and facilitates the simultaneous assessment of species identity, the effect of species on each other and, if required, environmental effects (Connolly, Wayne, and Bazzaz 2001)....

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Journal ArticleDOI
TL;DR: Results show that Rlt 20-15 expresses its nodulation competitiveness during infection, either at infection thread initiation or during successive growth in the infection threads.
Abstract: The stages in the nodulation process that determined the competitiveness of R leguminosarum bv trifolii (Rlt) strain 20–15, which proved to be highly competitive for nodulation in Iceland fields tests over several years, is analysed White clover (Trifolium repens L) roots were inoculated with inoculum mixtures containing three strains (Rlt 20-15, Rlt 8-9 and Rlt 32-28) in different proportions and cell densities Competitiveness in root colonization, formation of infection threads and nodule development was assessed for Rlt 20-15 and its weakest competitor, Rlt 32-28 ERIC-polymerase chain reaction (PCR) DNA fingerprinting was used to identify inoculated strains recovered from root surfaces and individual nodules GFP or DsRed tagged strains were used to determine identity in root hairs and nodules Both strains colonized the root equally at all inoculum ratios tested But, Rlt 20-15 initiated significantly more infection threads and formed more nodules than Rlt 32-28 These results show that Rlt 20-15 expresses its nodulation competitiveness during infection, either at infection thread initiation or during successive growth in the infection threads The data presented support earlier observations that this strain competed well in the field in spite of its inferior ability to survive in the soil

19 citations


Additional excerpts

  • ...This method has also successfully described competition effects in a similar experiment (Duodu et al. 2009)....

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Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "A baseline category logit model for assessing competing strains of rhizobium bacteria" ?

In this paper the authors describe novel methodology for evaluating competition among strains of Rhizobium bacteria which can be found naturally occurring in or can be introduced into soil. Their 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. Supplemental materials for this article are available from the journal website.