Model‐based approaches to unconstrained ordination

Hui, Francis K. C.; Taskinen, Sara; Pledger, Shirley; Foster, Scott D.; Warton, David I.

doi:10.1111/2041-210x.12236

Cited by 213 publications

(300 citation statements)

References 59 publications

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“…We have demonstrated how a JSDM can be applied to field data to measure impact and identify the species driving compositional change in a plant community. We emphasize that interpreting negative residual covariation as due to species interactions relies on having measured and correctly modelled the major environmental variables, fertility and rainfall in our case, that control species abundances (Hui, Taskinen, Pledger, Foster, & Warton, ). Our approach of crossing a natural fertility gradient with manipulation of biomass removal no doubt helped to disentangle competitive from environmental effects in this system, as it meant differences between the biomass treatments at each site were not confounded with environmental variation.…”

Section: Discussionmentioning

confidence: 99%

Measuring competitive impact: Joint‐species modelling of invaded plant communities

et al. 2019

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Non‐native species can dominate plant communities by competitively displacing native species, or because environmental change creates conditions favourable to non‐native species but unfavourable to native species. We need to disentangle these mechanisms so that management can target competitively dominant species and reduce their impacts. Joint‐species distribution models (JSDMs) can potentially quantify competitive impacts by simultaneously modelling how species respond to environmental variation and to changes in community composition. We describe a JSDM to model variation in plant cover and show how this can be applied to compositional data to detect dominant competitors that cause other species to decline in abundance. We applied the model to an experiment in an invaded grassy‐woodland community in Australia where we manipulated biomass removal (through slashing and fencing to prevent grazing by kangaroos) along a fertility gradient. Non‐native species dominated plant cover at high fertility sites in the absence of biomass removal. Results from the JSDM identified three of the 72 non‐native plant species (Bromus diandrus, Acetosella vulgaris and especially Avena fatua) as having a strong competitive impact on the community, driving changes in composition and reducing the cover of both native and non‐native species, particularly in the absence of grazing. The dominant non‐native grasses Bromus diandrus and Avena fatua were among the tallest species in the community and had the greatest impact on shorter‐statured species, most likely through competition for light under conditions of high fertility and low grazing. Synthesis. We demonstrate a method to measure competitive impact using a joint‐species distribution model, which allowed us to identify the species driving compositional change through competitive displacement, and where on the landscape competitive impacts were greatest. This information is central to managing plant invasions: by targeting dominant non‐native species with large competitive impacts, management can reduce impacts where they are greatest. We provide details of the modelling procedure and reproducible code to encourage further application.

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Section: Discussionmentioning

confidence: 99%

Measuring competitive impact: Joint‐species modelling of invaded plant communities

et al. 2019

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“…Our model can be regarded as an extension of the LVM proposed for model‐based unconstrained ordination in Hui et al. () and can be written in the following hierarchical form:

\begin{matrix} Responses: & false[y_{i j} {bold-italicu}_{i}, {bold-italicx}_{i} false] \sim Neg‐Bin false(y_{ij}; μ_{ij}, ϕ_{j} false) \\ log false(μ_{ij} false) = {normalη}_{normalij} = x_{i}^{'} {boldβ}_{j} + u_{i}^{'} {boldλ}_{j} \\ Latent Variables: false[{bold-italicu}_{i} false] \sim N false(bold0, I false) \\ Priors: false[β_{j} false] \sim N false(bold0, c_{0} I false), false[λ_{j} false] \sim N false(bold0, c_{0} I false), false[ϕ_{j} false] \sim Unif false(0, c_{1} false), \end{matrix}

where ‘∼’ denotes ‘is distributed as’,

N (\cdot, \cdot)

denotes a multivariate normal distribution with mean and covariance matrix given by the first and second arguments respectively,

Unif (0, c_{1})

denotes a uniform distribution with minimum zero and maximum

c_{1}

, and I denotes an identity matrix. To elaborate,

y_{ij}

denotes the observed count for species j at site i and is assumed to come from a negative binomial (Neg‐Bin) distribution with mean

...

…”

Section: Methodsmentioning

confidence: 99%

“…To this end, we modelled pairwise co‐occurrence using an extension of the latent variable model (LVM, Skrondal & Rabe‐Hesketh ) approach for model‐based unconstrained ordination recently proposed by (Walker & Jackson ) and (Hui et al. ). LVMs offer an explicit, model‐based approach to partitioning out the different drivers of species co‐occurrence patterns.…”

Section: Introductionmentioning

confidence: 99%

Fine‐scale hydrological niche differentiation through the lens of multi‐species co‐occurrence models

Letten

Keith

Tozer³

et al. 2015

Journal of Ecology

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Summary1. Theory suggests spatial heterogeneity can facilitate species co-occurrence at fine scales, but environmental data are rarely collected at sufficiently high resolution to test this empirically. Whilst there is emerging evidence that subtle variation in soil hydrology represents a fundamental fine-scale niche axis within plant communities, this is largely derived from studies of soil hydrology in isolation from other environmental factors. 2. We assessed the comparative importance of fine-scale hydrological niche differentiation for species co-occurrence using a high-resolution study of soil hydrology and other edaphic variables, coupled with a long-term (24 years) data set of herbaceous plant plots in a heathland community in south-east Australia.3. For the analysis, we employed novel latent variable models (LVMs), which offer an explicit, model-based approach to partitioning out the different drivers of species co-occurrence patterns. Whilst the regression component of an LVM models the species-specific environmental responses, the latent variable component can be used to identify residual patterns of co-occurrence, which may be attributable to unmeasured factors and/or biotic interactions. 4. Relative to a host of plant resources, non-resource factors and 'unmeasured' latent variables, soil hydrology emerged as the best predictor of negative co-occurrences within the community, with the dominant species exhibiting strongly differentiated responses across a comparatively narrow moisture gradient. Nevertheless, strong species-specific responses to environmental variability only emerged at scales greater than those at which plants may be expected to compete for resources, throwing doubt on the direct role of spatial heterogeneity as a mechanism for local-scale coexistence. 5. Synthesis. This study confirms the vital role of hydrological niches for the maintenance of within-community plant diversity, but also highlights the need for more rigorous analysis of scale dependencies to better understand the underlying coexistence mechanisms at play. In addition, it illustrates the inferential gains made possible with model-based approaches to the analysis of species co-occurrence. R code illustrating model fitting and inference is provided as a supplement.

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“…The VGAM package for the R language provides facilities for model-based indirect gradient analysis (Yee 2010;Yee and Hadi 2014). This work was a major breakthrough in model-based indirect gradient analysis, due Plant Ecol to its rigourous foundations in maximum likelihood theory and its degree of numerical robustness and stability; it led the way for more recent progress including sparse estimation of nonlinear model parameter vectors (Walker and Jackson 2011), clustering of sites and species (Pledger and Arnold 2014), and a general review and comparison of maximum likelihood approaches to indirect gradient analysis (Hui et al 2014). Although this literature is promising, there remains much to explore.…”

Section: Introductionmentioning

confidence: 99%

Indirect gradient analysis by Markov-chain Monte Carlo

Walker

2015

Plant Ecol

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Classical gradient analysis continues to be used to explore and test theories and models in community ecology. Yet the foundations of classical gradient analysis were developed at a time when computational power was limited, relative to current computational power. I argue that this history has left a lasting legacy on the field. Consequently, many gradient analyses do not to take advantage of current computer technology. Here I show how to use computationally intensive Markov-chain Monte Carlo methods to improve gradient analyses of presenceabsence community data. The methods that I use were developed by quantitative social scientists in the early 1990s, and therefore tested and efficient software already exists for practical data analysis. As an example, I analyze the classic dune meadow vegetation data. A main advantage of the Bayesian approach to indirect gradient analysis is that, unlike essentially all classical indirect methods, it is able to make empirically testable probabilistic predictions of observed species occurrence patterns. The Bayesian approach also poses challenges for statistical ecology. In particular, the development of Markov-chain Monte Carlo methods for a wider class of Bayesian indirect gradient analysis models would permit more flexible approaches to generating probabilistic predictions.

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Model‐based approaches to unconstrained ordination

Cited by 213 publications

References 59 publications

Measuring competitive impact: Joint‐species modelling of invaded plant communities

Measuring competitive impact: Joint‐species modelling of invaded plant communities

Fine‐scale hydrological niche differentiation through the lens of multi‐species co‐occurrence models

Indirect gradient analysis by Markov-chain Monte Carlo

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