[Coral-List] Contrast curve: a modern tool for comparing ecological metrics along gradients

Kayal Mohsen mohsen_kayal at yahoo.fr
Sat Sep 19 06:44:04 EDT 2015

Dear community,
I would like to draw your attention to some new developments in statistics that are improving our ability to compare quantitative data along continuous gradients, estimate divergence thresholds, and test hypotheses. I believe this should widely benefit investigations in Ecology given our common interests in the relationships between variability in species performances and diverse explicative ecological gradients.
The new method is a semi-parametric approach called contrast curve, and is based on a combination of Generalized Linear Mixed-effect Models (GLMMs) and penalized splines to account for multiple sources of complexity in data as often met in empirical ecology (repeated observations on study subjects, multiple subjects showing distinguished responses within the different groups compared, unbalanced designs, non-linearity in the relation between explicative and response variables, etc.).
In few words, the contrast curve method allows comparing two response curves along a continuous gradient and identifying the domains of significant difference. Its applications in Ecology are diverse, such as comparing metrics of species performances (eg, abundance, growth, survival, etc.) across time, space, or any ecological gradient describing the state of the organism (eg, size, age, weight) or its environment (temperature, pH, intensity of a given stress, etc.). In comparison, previous methods would only provide comparisons in slope and intercept of linear models estimated from such data, or require partitioning the explicative gradient into a number of subjective classes that are then treated as categorical.
The outline of the method and its benefits for ecological investigations are introduced in Box 2 of a paper that is published in this month’s volume of the journal Ecological Complexity (www.sciencedirect.com/science/article/pii/S1476945X15000793). For those with limited resource, an opened-access version is available on my RG portal (www.researchgate.net/profile/Mohsen_Kayal).
Beyond describing the new approach, the paper is focused on a large empirical study of coral population dynamics based on the estimation of coral performance in the different demographic processes as observed on the reef. Variation in each demographic process is related to the size of individual colonies or populations, and compared among dominant taxa using the introduced contrast curve approach. Observations are highly replicated in order to capture natural variability, and the complexity of the coral study model is highlighted. The use of the modern statistics to account for multiple sources of variability in data is also described.
Overall the paper is quite complex and multi-component, given the new approach and the target of capturing within a single study the different demographic processes and comparing them among taxa (see synthesis in Figure 5). For example, this allowed identifying opposing density-dependent patterns in recruitment among coral taxa, and different use of clonal fragmentation and fission-fusion processes in population maintenance. For a more simple illustration of application of the contrast curve approach in Ecology, Figure 3 in Jahangir’s study compares coral photosynthesis across positive versus negative temperature deviation (https://peerj.com/articles/1062/).
Many of us are interested in quantifying the effects of ecological gradients on species performances. In this purpose, we spend hours performing precise measurements in the field or in laboratory. One concern in analyzing such data is about using most appropriate statistics that avoid/limit rounding the edges when estimating the resulting patterns and testing hypotheses. The contrast curve is one step forward in this direction.
Reference: Kayal M, Vercelloni J, Wand MP, Adjeroud M (2015) Searching for the best bet in life-strategy: A quantitative approach to individual performance and population dynamics in reef-building corals. Ecological Complexity 23, 73-84.
________________________________Dr Mohsen Kayal (PhD)Bren School of Environmental Science & ManagementUniversity of California, Santa BarbaraCA 93106-5131, USAwww.researchgate.net/profile/Mohsen_Kayal

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