Complexity vs linearity: relations between functional traits in a heterotrophic protist

Abstract

Background: Functional traits are phenotypic traits that affect an organism's performance and shape ecosystem-level processes. The main challenge when using functional traits to quantify biodiversity is to choose which ones to measure since effort and money are limited. As one way of dealing with this, Hodgson et al. (Oikos 85:282, 1999) introduced the idea of two types of traits, with soft traits that are easy and quick to quantify, and hard traits that are directly linked to ecosystem functioning but difficult to measure. If a link exists between the two types of traits, then one could use soft traits as a proxy for hard traits for a quick but meaningful assessment of biodiversity. However, this framework is based on two assumptions: (1) hard and soft traits must be tightly connected to allow reliable prediction of one using the other; (2) the relationship between traits must be monotonic and linear to be detected by the most common statistical techniques (e.g. linear model, PCA).

Results: Here we addressed those two assumptions by focusing on six functional traits of the protist species Tetrahymena thermophila, which vary both in their measurement difficulty and functional meaningfulness. They were classified as: easy traits (morphological traits), intermediate traits (movement traits) and hard traits (oxygen consumption and population growth rate). We detected a high number (> 60%) of non-linear relations between the traits, which can explain the low number of significant relations found using linear models and PCA analysis. Overall, these analyses did not detect any relationship strong enough to predict one trait using another, but that does not imply there are none.

Conclusions: Our results highlighted the need to critically assess the relations among the functional traits used as proxies and those functional traits which they aim to reflect. A thorough assessment of whether such relations exist across species and communities is a necessary next step to evaluate whether it is possible to take a shortcut in quantifying functional diversity by collecting the data on easily measurable traits.

Keywords: Functional traits; Linearity assumption; Soft/hard traits framework; Tetrahymena thermophila; Trait relations.

Fig. 1

Four scenarios illustrating a spectrum of possible relations between hard and soft traits: A This non-monotonic relationship allows prediction of the hard trait using the soft one, but not through a simple linear method. B An example of a monotonic relation, where the two traits are linearly related on a portion of their variation domain, only allowing accurate predictions of one trait by the other (either way) on this part. C The traits are here linearly related, but reliable predictions cannot be achieved because of the high standard error. D The ideal linear, strong and monotonic relationship needed for PCA and correlations. Thus, one can use a trait as a proxy for another one only if there is a well-known relationship that is correctly estimated, implying (1) the knowledge of the form of the relationship between the two traits, (2) a relationship where the values of one trait change with the values of the other (i.e. no constant values of one trait as the other one is changing) because such a relation prevents prediction on one of the traits and (3) a standard error on the model parameter small enough to give a reliable prediction

Fig. 2

Overview of the relations between the selected functional traits of T. thermophila cells. Arrows indicate how each trait affects the other ones, with a black arrow indicating an expected positive relation, a grey arrow for a negative one, and a dotted grey arrow for relations that can vary based on the environment. Each trait is colored based on its measurement difficulty with (1) green for easy, (2) yellow for intermediate, and (3) black for hard

Fig. 3

Pairwise relations among the six functional traits measured for the 40 T. thermophila strains. Each dot represents the average value of all replicates at the strain level, the blue line a linear model, and the red curve a GAM. Both are represented with their respective 95% confidence interval. Above every graph is displayed the deviance explained (D.exp) by each model. When displayed, the non-linear GAM is significantly better than the linear model (e.d.f. > 1). Otherwise, the non-linearity did not improve the model fit, both models remaining linear and identical (hence the same D.exp), and on the graph only the linear model is displayed

Fig. 4

PCA analysis performed on the six functional traits (averaged at the strain level) for the 40 T. thermophila strains. The left panels represent the distribution of the strains along dimensions 1 and 2 (A) and along dimensions 1 and 3 (C). The numbers in (A) and (C) stand for the labels of the strains. The right panels represent the associated correlation circles along the first and second dimensions (B) and the first and third dimensions (D). The arrows assess the representativity of the traits on the considered dimensions, with the closer the arrow is to the edge of the circle, the better the trait is represented. The functional traits are colored based on their measurement difficulty