On Information Rank Deficiency in Phenotypic Covariance Matrices

New insights into patterns of integration in the femur and pelvis among catarrhines

OBJECTIVES

Integration reflects the level of coordinated variation of the phenotype. The integration of postcranial elements can be studied from a functional perspective, especially with regards to locomotion. This study investigates the link between locomotion, femoral structural properties, and femur-pelvis complex morphology.

MATERIALS AND METHODS

We measured (1) morphological integration between femoral and pelvic morphologies using geometric morphometrics, and (2) covariation between femoral/pelvic morphologies and femoral diaphyseal cross-sectional properties, which we defined as morpho-structural integration. Morphological and morpho-structural integration patterns were measured among humans (n = 19), chimpanzees and bonobos (n = 16), and baboons (n = 14), whose locomotion are distinct.

RESULTS

Baboons show the highest magnitude of morphological integration and the lowest of morpho-structural integration. Chimpanzees and bonobos show intermediate magnitude of morphological and morpho-structural integration. Yet, body size seems to have a considerable influence on both integration patterns, limiting the interpretations. Finally, humans present the lowest morphological integration and the highest morpho-structural integration between femoral morphology and structural properties but not between pelvic morphology and femur.

DISCUSSION

Morphological and morpho-structural integration depict distinct strategies among the samples. A strong morphological integration among baboon's femur-pelvis module might highlight evidence for long-term adaptation to quadrupedalism. In humans, it is likely that distinct selective pressures associated with the respective function of the pelvis and the femur tend to decrease morphological integration. Conversely, high mechanical loading on the hindlimbs during bipedal locomotion might result in specific combination of structural and morphological features within the femur.

Can extreme climatic events induce shifts in adaptive potential? A conceptual framework and empirical test with Anolis lizards

Multivariate adaptation to climatic shifts may be limited by trait integration that causes genetic variation to be low in the direction of selection. However, strong episodes of selection induced by extreme climatic pressures may facilitate future population-wide responses if selection reduces trait integration and increases adaptive potential (i.e., evolvability). We explain this counter-intuitive framework for extreme climatic events in which directional selection leads to increased evolvability and exemplify its use in a case study. We tested this hypothesis in two populations of the lizard Anolis scriptus that experienced hurricane-induced selection on limb traits. We surveyed populations immediately before and after the hurricane as well as the offspring of post-hurricane survivors, allowing us to estimate both selection and response to selection on key functional traits: forelimb length, hindlimb length, and toepad area. The direct selection was parallel in both islands and strong in several limb traits. Even though overall limb integration did not change after the hurricane, both populations showed a non-significant tendency toward increased evolvability after the hurricane despite the direction of selection not being aligned with the axis of most variance (i.e., body size). The population with comparably lower between-limb integration showed a less constrained response to selection. Hurricane-induced selection, not aligned with the pattern of high trait correlations, likely conflicts with selection occurring during normal ecological conditions that favours functional coordination between limb traits, and would likely need to be very strong and more persistent to elicit a greater change in trait integration and evolvability. Future tests of this hypothesis should use G-matrices in a variety of wild organisms experiencing selection due to extreme climatic events.

An effect size for comparing the strength of morphological integration across studies

Understanding how and why phenotypic traits covary is a major interest in evolutionary biology. Biologists have long sought to characterize the extent of morphological integration in organisms, but comparing levels of integration for a set of traits across taxa has been hampered by the lack of a reliable summary measure and testing procedure. Here, we propose a standardized effect size for this purpose, calculated from the relative eigenvalue variance,V r e l $V_{rel}$ . First, we evaluate several eigenvalue dispersion indices under various conditions, and show that onlyV r e l $V_{rel}$ remains stable across samples size and the number of variables. We then demonstrate thatV r e l $V_{rel}$ accurately characterizes input patterns of covariation, so long as redundant dimensions are excluded from the calculations. However, we also show that the variance of the sampling distribution ofV r e l $V_{rel}$ depends on input levels of trait covariation, makingV r e l $V_{rel}$ unsuitable for direct comparisons. As a solution, we propose transformingV r e l $V_{rel}$ to a standardized effect size (Z-score) for representing the magnitude of integration for a set of traits. We also propose a two-sample test for comparing the strength of integration between taxa, and show that this test displays appropriate statistical properties. We provide software for implementing the procedure, and an empirical example illustrates its use.