Functional traits, growth models, cross validation

The final paper from my PhD has been published!

Our intent for this paper was to encourage thorough testing of multiple growth model forms and an increased emphasis on assessing model fit relative to a model’s purpose. Our paper is open access and accompanied by open access code (thanks Jian Yen) to do everything we wrote about!

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Our newest open access paper

During my PhD I was interested in seeing if we could use plant functional trait data to predict plant growth through time across multiple species. 

Some battles involved with this quest were determining which growth models to use, which predictor variables to use and how to evaluate all of this relative to our objectives. 

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Figure one: different growth models fitted to the same species data. 

It was actually relatively easy to find a growth model that described any one plant species’ growth pretty well. However, I didn’t want to find the best growth model for each individual species – I wanted to find one growth model to describe all my species’ growth. I also actually didn’t really want to just describe my plant species’ growth – I really wanted to predict the growth of new species. 

To do this, I had to work out which models could describe the growth of one species adequately, describe the growth of all species adequately, predict the growth of one species adequately and predict the growth of all species adequately both inside and outside of my dataset.

I also had to figure out what I meant by ‘adequately’. 

In this paper, we outline the methods we used to model and evaluate predictive trait-based models of growth for multiple plant species. 

We use three data sets on plant height over time and two validation methods—in-sample model fit and leave-one-species-out cross validation—to evaluate nonlinear growth model predictive performance based on functional traits. 

In-sample measures of model fit differed substantially from out-of-sample model predictive performance; the best fitting models were rarely the best predictive models. Careful selection of predictor variables reduced the bias in parameter estimates and there was no single best model across our three data sets. Testing and comparing multiple model forms is important. 

Again, our intent is to encourage thorough testing of multiple growth model forms and an increased emphasis on assessing model fit relative to a model’s purpose. 

We hope to contribute to the practice of growth modeling by developing methods and code for the evaluation of predictive capacity of non-linear growth models. 

 This paper is accompanied by an R package, growmodr, to fit and validate nonlinear growth models (available at < ). An example of fitting and validating a growth curve model is in Appendix 1.

Thanks to Jian Yen and Pete Vesk for accompanying me on this paper’s journey .. it was mostly fun!

Here are some of the plants we were working with:


Some plants of the mallee

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A field ecologist’s adventures in the virtual world: using simulations to design data collection for complex models

The third paper from my PhD is soon to be published! It is very satisfying to see this particular chapter in (early view) print! 

At an early stage of my PhD, Peter Vesk and I spent a few confusing hours attempting to conduct a ‘power analysis’ for our multi-species trait-based non-linear hierarchical growth model, but to no avail. Turns out, it just isn’t quite that easy. This led to some pretty extreme note taking during my many months of fieldwork in Murray Sunset National Park – where I made sure to collect information relating to the process behind collecting height-growth of multiple species in this semi-arid landscape. 

Using this information and powered by an extreme determination from this field ecologist to ‘model well’, Cindy Hauser and I spent many solid hours together over about two years crafting a simulation of monstrous proportions. We attempted to simulate my entire fieldwork process, subset this simulated data under various constraining scenarios, analysis all our scenario-driven datasets and evaluate how particular decisions made in the field would effect the precision, accuracy and bias of our modelled growth parameters. 

The journey was long and contained many dimensions, so it is lovely to see this project in finally in print! 


A colourful schematic of part of our simulation


Field data collection can be expensive, time consuming and difficult; insightful research requires statistical analyses supported by sufficient data. Pilot studies and power analysis provide guidance on sampling design but can be challenging to perform, as ecologists increasingly collect multiple types of data over different scales. Despite a growing simulation literature, it remains unclear how to appropriately design data collection for many complex projects.  Approaches that seek to achieve realism in decision-making contexts, such as management strategy evaluation and virtual ecologist simulations, can help. 

For a relatively complex analysis, we develop and demonstrate a flexible simulation approach that informs what data are needed and how long those data will take to collect, under realistic fieldwork constraints. We simulated data collection and analysis under different constraint scenarios that varied in deterministic (field trip length, travel and measurement times) and stochastic (species detection and occupancy rates, and inclement weather) features. In our case study, we fit plant height data to a multi-species, three-parameter nonlinear growth model. We tested how the simulated datasets, based on the varying constraint scenarios, affected the model fit (parameter bias, uncertainty and capture rate). Species prevalence in the field exerted a stronger influence on the datasets and downstream model performance than deterministic aspects such as travel times. When species detection and occupancy were not considered, the field time needed to collect an adequate dataset was underestimated by 40%. 

Simulations can assist in refining fieldwork design, estimating field costs and incorporating uncertainties into project planning. We argue that combining data collection, analysis and decision-making processes in a flexible virtual setting can help address many of the decisions that field ecologists face when designing field-based research.  

The paper is available here.
Please get in touch if you have any questions / comments! 

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Doctor of Philosophy

It is a pleasure to write that I am now, nearly, degreed.

My PhD was recently accepted into the Library at The University of Melbourne. I thought I would mark the occasion with short summary of the beast.


Some Mallee biodiversity

Overall summary:

Plant height and growth are fundamental to the understanding of species’ ecological strategies, to the description and prediction of ecosystem dynamics and to vegetation management. I explored how plant functional traits can be used to predict woody plant growth for many species.  I demonstrated internal and out-of-sample prediction of species growth trajectories from traits, I dissected methods to evaluate the predictive capacity of growth models and I outlined a virtual ecologist approach to designing robust field studies for complex analysis.


Ominous skies and more mallee biodiversity

Chapter summaries:

Chapter one incorporates plant functional traits into multi-species hierarchical non-linear models of plant growth. This approach increases our understanding of trait-growth relationships but also aids our ability to draw predictive inferences from them.  I built and parameterized models with a case-study of time since fire in semi-arid mallee woodland. I demonstrated inference by predicting species height-growth trajectories from traits to species with few data, to species with no growth data, only trait information, and for hypothetical species with defined trait combinations.

Chapter two contributed to the growth modeling literature by focusing on evaluating the predictive capacity of non-linear growth models using cross-validation.  I demonstrated why cross-validation is important compared to naïve performance metrics and demonstrated the value of using multiple metrics to capture different aspects of model performance.

Gaining greater predictive capacity in trait-based ecology may also require stronger quantitative tests of model transferability, which is a severe test of how general a model actually is.  In chapter three I tested the out-of-sample predictive ability or transferability of my trait-growth models by using traits to predict the growth trajectories between species in three different ecosystems.

The worth of predictions and inference from data analysis is intimately linked to the statistical and ecological assumptions of fitted models and fundamentally to the data underlying the analysis. My final chapter demonstrated a virtual ecologist approach to aid in the design of studies that use complex analysis techniques.  I used a simulation based on realistic fieldwork constraints such as species detection and occupancy rates, as well as travel times and unpredictable field conditions. This assists planning how much data is needed and how long that data will take to collect for hierarchical multi-species nonlinear models.


In the unlikely event someone would like to read my thesis, get in touch and I will send you the open access link.


Red roads and more mallee biodiversity



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VicBioCon 2018


After a successful inaugural Victorian Biodiversity Conference earlier this year, a group of motivated students and early career researchers from a wide range of Victorian Universities (RMIT, La Trobe, Monash, Federation, Charles Sturt, Melbourne, Deakin) have begun planning our next conference to be held 6th-7th of February 2018 at La Trobe University, Melbourne


Some colourful examples of Victorian Biodiversity

This event aims to be a low cost and accessible conference to promote networking between graduate and postdoctoral researchers, as well as practitioners in government and NGOs working on research related to Victorian biodiversity.

The conference will provide an important and rare opportunity for young researchers to hear from government, industry and non-governmental organisations, as well as foster inter-University interactions through a series of plenaries, invited talks, workshops and networking opportunities.


Some more Biodiversity for you … all plant themed, of course. 

Abstract submission closes on the 15th of November, submit yours here: abstract submission!

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Growth races in The Mallee

The second paper from my PhD has been accepted for publication:

Thomas, FM and Vesk, PA (2017) Growth races in The Mallee: height growth in woody plants examined with a trait-based model.  Austral Ecology, early view.

In this paper Peter Vesk and I explore growth trajectories of woody plants in the Victorian Mallee, a semi-arid region of south-eastern Australia.


An early time-since-fire site in Murray Sunset National Park

We examine the influence of plant functional traits on growth trajectories. We test trait-growth relationships by examining the influence of specific leaf area, woody density, seed size and leaf nitrogen content on three aspects of plant growth; maximum relative growth rate, age at maximum growth and asymptotic height.

Woody plant species in the semi-arid mallee exhibit fast growth trajectories. Small seeded species were likely to be the fastest to reach maximum height, while large-seeded species with high leaf nitrogen were likely the slowest. Tall species had low stem densities and tended to have low specific leaf area.


Some colour from Murray Sunset. Westringia rigida (Lamiaceae); Beyeria opaca (Euphorbiaceae); Acacia brachybotrya (Mimosaceae); Phebalium squamulosum (Rutaceae); Eremophila glabra (Scrophulariaceae) and Halgania cyanea (Boraginaceae).

We modeled plant growth using a hierarchical multi-species model that formally incorporates plant functional traits as species-level predictors of growth, which provides a method for predicting species height growth strategies as a function of their traits.

We further extended this approach by using the modeled relationships from our trait-growth model to predict: growth trajectories of species with limited data; real species with only trait data and; hypothetical species based only on trait coordination. We hope this highlights the potential to use trait information for ecological inference and to generate predictions that could be used for management.

Please email if you would like more information.


Some fine mallee forms.


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Are trait-growth models transferable? Predicting multi-species growth trajectories between ecosystems using plant functional traits

I have a new paper out! Read it here:

Plant functional traits are increasingly used to generalize across species, however few examples exist of predictions from trait-based models being evaluated in new species or new places.  In this paper Peter Vesk and I ask, can we use functional traits to predict growth of unknown species in different areas?

We used three independently collected datasets (thank you Daniel Falster and Annette Muir for contributing their data), each containing data on heights of individuals from non-resprouting plant species over a chronosquence of time-since-fire sites from three ecosystems in south-eastern Australia. We examined the influence of specific leaf area, woody density, seed size and leaf nitrogen content on three aspects of plant growth; maximum relative growth rate, age at maximum growth and asymptotic height.


Growth curves for species occurring in three different ecosystems

We then tested our capacity to perform out-of-sample prediction of growth trajectories between ecosystems using species functional traits.  We believe there is evidence to suggest that growth trajectories themselves may be fundamentally different between ecosystems and that trait-height-growth relationships may change over environmental gradients.

Please get in touch if you are interested in this work!


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The Victorian Biodiversity Managers’ Network

I recently attended a Forum on Planning and Monitoring for Biodiversity Management held by the Indigenous Flora and Fauna Association’s Victorian Biodiversity Managers’ Network, in conjunction with Rob Scott from Naturelinks, hosted at The Arthur Rylah Institute.

The Indigenous Flora and Fauna Association (IFFA) is a volunteer based organization created in 1986 whose aim is “to promote the appreciation, study, conservation and management of indigenous flora and fauna through research and discussion, networking and advocacy, and information exchange”. Check out their website here:

The Victorian Biodiversity Managers’ Network is in creation! IFFA recognised the need for a network to promote biodiversity management and to bring together people who manage land for biodiversity in Victoria to facilitate knowledge exchange.

IFFA recently hosted a workshop with a people from a wide range of organisations to brainstorm the scope of a biodiversity managers’ network. From this workshop it was decided the scope and direction of the Victorian Biodiversity Managers’ Network would be to:

  • developing best-practice industry standards and industry promotion
  • information and knowledge sharing using a website and workshops
  • building capacity of biodiversity managers through short courses and industry accreditation

The Forum on Planning and Monitoring for Biodiversity Management was held as one of the first official events of the Victorian Biodiversity Managers’ Network.   One of the benefits of this event and of the Network, was that it brought together many people from different organisations; local councils, consultants, non-government and government organisations, landcare groups and friends networks.

The focus of the day was Planning and Monitoring and this was focused around an introduction to the Open Standards for the Practice of Conservation – a systematic method for managing conservation projects:

Dr Kate Fitzherbert from Bush Heritage spoke first and discussed their use of the Open Standards for the Practice of Conservation and outlined how this logical and transparent process helps to understand projects in their environmental, political and social context and helps to figure out which are the right factors to monitor.

Doug Evans from Nillumbik Landcare Network spoke about their use of the open standards to outline the collective environmental assets of the Landcare network and figure out cost effective and practical methods to manage them.

Phil Pegler from Parks Victoria spoke about the conservation action planning and the continual evolution of approaches to respond to issues of community and stakeholder engagement, organisation culture, defining goals and measuring success and prioritizing resources.

Emma Mann and Scott Nutt from Banyule City Council presentation showed us their use of GIS technology for data collection, which provides a faster, more precise and easier to access method for collecting and storing environmental data.

Dr Chris Jones from The Arthur Rylah Institute spoke about monitoring methods for environmental management and gave us an overview of commonly used methods to address different monitoring challenges. He outlined some important questions when thinking about monitoring such as why are you monitoring? What are you trying to monitor? How will you use this data?


Chris Jones speaking to a full room about monitoring techniques

Lincoln Kern from Practical Ecology discussed and provided some examples of planning and monitoring in the commercial ecological management market, and also introduced the National Standards for the practice of ecological restoration in Australia developed by the Society for Ecological Restoration Australasia

The second part of the Forum was a workshop where Stuart Cowell from Conservation Management took us through a case study using some of the tools and processes of the Open Standards. We learnt about ‘results chains’ and their use in testing possible strategies, identifying conservation actions and prioritising monitoring for conservation management projects.

The final part of the day was a panel discussion about improving planning and monitoring practices in Victoria and an exploration of how The Biodiversity Managers’ Network can support this.


Workshop participants learning about Open Standard Result Chains

It was a great day and an exciting start to a new network of passionate people who want to manage Victoria’s vegetation using best practices.  The Bushland Managers’ Network will soon have a website; and The Wild Melbourne crew were at the forum recording all the talks, so these will become available shortly. In the meantime if you would like anymore information about The Biodiversity Managers’ Network email: 



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