The geometric-biodiversity coupling of surface habitats

We can understand the relationship between habitat and biodiversity coupling using three simple metrics of structural complexity. These scale-independent components describe a plane of geometric possibilities upon which to formally examine ecological patterns in the context of habitat structure.
The geometric-biodiversity coupling of surface habitats

The relationship between habitat structural complexity and biodiversity is foundational to understanding community ecology and informing conservation strategies.   However, elucidating the contribution of surface structure to support life has proved to be difficult in practice.

Coral reef surfaces provide habitat for the corals that build the reef and innumerable other species.  Photo: Damaris Torres-Pulliza

This work started with an online advertisement for a PhD position. The scope was to produce a uniquely detailed picture of the biomechanical and ecological impact of, and recovery from, Tropical Cyclone Ita that affected the coral reefs at Lizard Island, in the Great Barrier Reef - with Joshua S. Madin, Maria A. Dornelas and Oscar Pizarro as Principal Investigators.  My role focused on detecting change in habitat structural complexity across the storm disturbance using Structure from Motion (SfM) surface reconstructions.

The spiral method1 facilitates navigation control underwater to ensure complete photographic coverage and attain proper 3D surface rendering.  Photo: Damaris Torres-Pulliza

As autogenic ecosystem engineers, stony corals build the very structures they prefer to live amongst—that is, they construct their very own niches.  In this context, we wanted to know whether more complex coral reef habitats led to higher biodiversity of the corals themselves, as is often assumed. However,  I soon realised that, while biological diversity can be readily quantified2, there was widespread disagreement about how to quantify habitat structure3. I was stuck, because, a prerequisite to detangling the link between reef structure and coral diversity was to identify the metric or set of metrics able to reliably describe the surface.

3D surface reconstruction, (2014).  Animation: Damaris Torres-Pulliza

In aquatic environments, there is a traditional emphasis on using the rugosity index as a proxy to habitat structure.  That is in part because it is easy to estimate rugosity in the field by using a tape and a chain draped to the substrate4.  Structure from Motion1 is a newer method that allows capturing the reef structure digitally over large continuous areas and without damaging the substrate.  The technique produces realistic 3D surface reconstructions that, when back at the office, allows deriving practically any surface metric available, including rugosity5However, having too many choices of metrics is, in itself, a problem.   The outcome of a few months of exploratory work and critical thinking was hundreds of R plots showing matches and mismatches among structural metrics with no clear explanation.  Overwhelmed, I grabbed a pencil and notebook as a way to compile some core findings through sketching.

Research guided brainstorming and sketching: Damaris Torres-Pulliza

Later that year, the project's team gathered at the University of St Andrews for a workshop where we discussed several figures showing that rugosity and fractal dimension were mediated by topographic height range. Was this the geometric constraint we were looking for? Indeed, we were able to prove that three simple variables - rugosity, height range and fractal dimension - precisely captured the geometry of hundreds of reef patches from diverse environments (r2>98%).  The geometric theory was elaborated mathematically.  Then, by using a dataset containing almost 10,000 coral species annotations, we show that the surface structure influences coral species richness (r2>50%) across the plane of geometric possibilities.

It remains to be seen how the geometric theory we present translates to other surface habitats, such as non-coral benthos or on land.  Nonetheless, our results demonstrate the key geometric constraints acting to shape structural complexity and provide a basis to better understand drivers of biological diversity and ecosystem function as surface habitats continue to rapidly change under climatic extremes.

2014 and 2017 orthomosaics show the impact from 4 years of consecutive disturbances at Lizard Island. Time-series: Damaris Torres-Pulliza

Sadly, the storm disturbance initially referred to in the PhD advertisement turned into back-to-back cyclones, followed by back-to-back coral bleaching events6.  Coral bleaching was reported once again in 2020.  This sequence of disturbances is among the most extreme on record and reflects a global trend towards a higher frequency of intensified climatic extremes with devastating compounding effects7.   We are hopeful that our approach allows us to understand the habitat consequences of these disturbances, as well as to predict recovery. 

Signs of coral recovery at Lizard Island (2019). Photo: Damaris Torres-Pulliza
Find out more here:
Damaris Torres-Pulliza, Maria A. Dornelas, Oscar Pizarro, Michael Bewley, Shane A. Blowes, Nader Boutros, Viviana Brambilla, Tory J. Chase, Grace Frank, Ariell Friedman, Mia O. Hoogenboom, Stefan Williams, Kyle J. A. Zawada and Joshua S. Madin (2020) A geometric basis for surface habitat complexity and biodiversity. Nature Ecology and Evolution, DOI: 10.1038/s41559-020-1281-8

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  1. Pizarro, O. et al.  A simple, fast, and repeatable survey method for underwater visual 3D benthic mapping and monitoring. Ecol. Evol. 7, 1770–1782 (2017).
  2. Magurran, A. & McGill, B. J. (eds) 2010, Biological diversity: frontiers in measurement and assessment. Oxford University Press, Oxford.  ISBN 978-0-19-958067-5. 
  3. Kovalenko, K. E. et al. Habitat complexity: approaches and future directions. Hydrobiologia 685, 1–17 (2012).
  4. Risk M. J. Fish diversity on a coral reef in the Virgin Islands. Atoll Res Bull. 153: 1-6 (1972).
  5. Friedman, A. et al. Multi-Scale Measures of Rugosity, Slope and Aspect from Benthic Stereo Image Reconstructions. PLoS ONE 7:e50440 (2012).
  6. Madin, J. S. et al. Cumulative effects of cyclones and bleaching on coral cover and species richness at Lizard Island. Mar. Ecol. Prog. Ser. 604, 263–268 (2018).
  7. IPCC, 2019: IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner H.-O et al. (eds.)].  September 2, 2019.

Header photo: Damaris Torres-Pulliza

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