Functional rarefaction: estimating functional diversity from field data

Studies in biodiversity-ecosystem function and conservation biology have led to the development of diversity indices that take species' functional differences into account. We identify two broad classes of indices: those that monotonically increase with species richness (MSR indices) and those that weight the contribution of each species by abundance or occurrence (weighted indices). We argue that weighted indices are easier to estimate without bias but tend to ignore information provided by rare species. Conversely, MSR indices fully incorporate information provided by rare species but are nearly always underestimated when communities are not exhaustively surveyed. This is because of the well-studied fact that additional sampling of a community may reveal previously undiscovered species. We use the rarefaction technique from species richness studies to address sample-size-induced bias when estimating functional diversity indices. Rarefaction transforms any given MSR index into a family of unbiased weighted indices, each with a different level of sensitivity to rare species. Thus rarefaction simultaneously solves the problem of bias and the problem of sensitivity to rare species. We present formulae and algorithms for conducting a functional rarefaction analysis of the two most widely cited MSR indices: functional attribute diversity (FAD) and Petchey and Gaston's functional diversity (FD). These formulae also demonstrate a relationship between three seemingly unrelated functional diversity indices: FAD, FD and Rao's quadratic entropy. Statistical theory is also provided in order to prove that all desirable statistical properties of species richness rarefaction are preserved for functional rarefaction.     

Strength and physical fitness predict the perception of looming sounds

Listeners consistently perceive approaching sounds to be closer than they actually are and perceptually underestimate the time to arrival of looming sound sources. In a natural environment, this underestimation results in more time than expected to evade or engage the source and affords a “margin of safety” that may provide a selective advantage. However, a key component in the proposed evolutionary origins of the perceptual bias is the appropriate timing of anticipatory motor behaviors. Here we show that listeners with poorer physical fitness respond sooner to looming sounds and with a larger margin of safety than listeners with better physical fitness. The anticipatory perceptual bias for looming sounds is negatively correlated with physical strength and positively correlated with recovery heart rate (a measure of aerobic fitness). The results suggest that the auditory perception of looming sounds may be modulated by the response capacity of the motor system.     

Penetration of radioactive sodium and chloride into cerebrospinal fluid and aqueous humor

1. Experiments were performed on six dogs to determine the rate of penetration of Cl(33) and Na(24) across the blood-aqueous humor and blood-cerebrospinal fluid barriers after intravenous injection of the radioactive ions. The radioactivity measurements were made with an immersion type of Geiger-Müller counter. 2. The concentrations of the labelled ions in the anterior chamber and the cisterna magna increase slowly to approach that of plasma. The rate of penetration k is calculated from a simple exponential equation with the half-value interval t(0.5) or the time required for the labelled-ion concentration in the fluid to reach 50 per cent of that of plasma. The average t(0.5) for Cl(38) and Na(24) in aqueous humor are 34.3 +/- 9 and 27.3 +/- 9 minutes, respectively, while those for cerebrospinal fluid are 90 +/- 6 and 95 +/- 6 minutes, respectively. 3. A study of the radioactivity in plasma was made to determine the per cent remaining after a steady state was reached. By means of this determination the sodium and chloride space was calculated to be 33 +/- 5 per cent.