Theoretical developments of modelling techniques and novel visualisations for studying the biodiversity and ecosystem function relationship; and their application for calculating the economic value of biodiversity.

Abstract

The biodiversity and ecosystem function (BEF) relationship studies how species diversity within an ecosystem affects the outputs (called ecosystem functions) the system produces. In recent decades, there has been great interest in modelling this BEF relationship using the number and the relative proportions of the species within the ecosystem. This thesis makes advancements in statistical modelling and visualisation techniques that can lead to improved insights into the BEF relationship and develop a modelling framework to link biodiversity and the economic value derived from specific ecosystem functions. While these methodological advancements to the modelling and visualisation techniques have primary applications in BEF research, they also have broader relevance and can be used across several different disciplines such as chemistry, geology, demographic studies, etc. where compositional data is encountered. The species in an ecosystem can contribute to its functioning through their inherent characteristics along with any positive or negative interactions with other species in the ecosystem. The Diversity-Interactions (DI) modelling framework captures this complexity and provides a multi-faceted description of the BEF relationship by modelling any ecosystem function measured at the species community level using species identity and interaction effects as predictors. The species interactions in a DI model can take different forms (e.g., a unique interaction term for each pair of species, or a single interaction term for any pair of species) and may include a non-linear parameter (𝜃�) as an exponent to the species interactions to capture non- linear BEF relationships. The structure of the interaction terms describes the underlying biological processes in the ecosystem while the value of 𝜃� can determine the shape of the BEF relationship. In this thesis, I perform a simulation study to assess the robustness of 𝜃� across the various interaction structures and suggest an optimal model selection procedure for DI models when 𝜃� differs from 1. I also develop software tools in R to provide a unified interface for performing post-fit analyses from a DI model, thereby streamlining the process of model fitÝng and usage, while enhancing the utility of DI modelling framework. I also develop PieGlyph and DImodelsVis, two R packages that provide novel visualisation tools for deriving insights from BEF data and interpreting DI models, respectively. PieGlyph offers users the functionality to superimpose any 2d plot such as a scatterplot, bar chart, ternary diagrams, etc. with interactive pie-chart glyphs (pie-glyphs) that convey additional information about the relative proportions of species within any community. The DImodelsVis package provides visualisation tools to aid with the diagnostics, selection, and interpretation of models fit within the DI framework. However, both packages are general-purpose visualisation software and can be used in any scientific discipline, provided the data has compositional variables which are used as predictors in a regression model with a continuous or categorical response. Employing the DI modelling framework as a foundation, I finally develop a methodological framework for performing an economic assessment of plant species diversity in an ecosystem. The results of applying this framework to data from a six-species grassland crop rotation experiment linking the economic value derived from various species communities (defined as potential profits from selling biomass yield as forage) to multiple dimensions of diversity under single and multiple response setÝngs is presented. The results indicate that species mixtures containing as little as three species are significantly more profitable than single species grass communities (called monocultures) receiving double nitrogen fertilisation. This indicates that using species diversity as a nature-based solution against high nitrogen fertilisation is an economically viable option. Furthermore, the mixtures also exhibited a higher average performance across multiple ecosystem functions compared to monocultures and no trade-offs were found between economic performance and average performance across all functions, supporting the notion that sustainable agricultural approaches can also be economically profitable.