The design of the bronchial tree has largely been proposed as a model of optimal design from a physical-functional perspective. However, the distributive function of the airway may be more related to a geometrical than a physical problem. The bronchial tree must distribute a three dimensional volume of inspired air on a two dimensional alveolar surface, included in a limited volume. It is thus valid to ask whether an optimal bronchial tree from a physical perspective is also optimum from a (...) geometrical point of view. In this paper we generate a simple geometric model for the branching pattern of the bronchial tree, deducing relationships that permit estimation of the departures from the geometrical optimum of each bifurcation. We also, for comparative purposes, estimate the departures from the physical optimum. From the geometrical assumptions: i) a symmetrical dichotomic fractal design, ii) with minimum volume and iii) maximum dispersion of the terminal points; and several simulations we suggest that the optimality is characterized by a bifurcation angle Θ ∼ 60° and a length reduction scale γ = (1/2)1/3 = 0.7937. We propose distances from the physical and geometrical optimality defined as Euclidean distances from the expected optima. We show how the advanced relationships and the distances can be used to estimate departures from the optimality in bronchographs of four species. We found lower physical and geometrical departures in the distal zone than those of the proximal zones, as well as lower physical than geometrical departures from optimality. (shrink)

Many studies have attempted to assess the relative effects of different vectors of a disease on animal populations. To this end, three measures have been proposed: Vectorial efficiency, Vectorial capacity and recently Vectorial effectiveness (or Vectorial impact). In this study we relate these measures to derive some of their properties emphasising in the vectorial impact for its importance in both, population performance of parasites and the proportion of the prevalence of one parasite due to a given vector. We applied the (...) quantitative expressions advanced in this study to a simple Chilean example with one parasite (Trypanosoma cruzi), two vectors (Triatoma infestans and Mepraia spinolai) and one animal population (humans: Chagas's disease). (shrink)

The extreme sexual size dimorphism in spiders has motivated studies for many years. In many species the male can be very small relative to the female. There are several hypotheses trying to explain this fact, most of them emphasizing the role of energy in determining spider size. The aim of this paper is to review the role of energy in sexual size dimorphism of spiders, even for those spiders that do not necessarily live in high foliage, using physical and allometric (...) principles. Here we propose that the cost of transport or equivalently energy expenditure and the speed are traits under selection pressure in male spiders, favoring those of smaller size to reduce travel costs. The morphology of the spiders responds to these selective forces depending upon the lifestyle of the spiders. Climbing and bridging spiders must overcome the force of gravity. If bridging allows faster dispersal, small males would have a selective advantage by enjoying more mating opportunities. In wandering spiders with low population density and as a consequence few male–male interactions, high speed and low energy expenditure or cost of transport should be favored by natural selection. Pendulum mechanics show the advantages of long legs in spiders and their relationship with high speed, even in climbing and bridging spiders. Thus small size, compensated by long legs should be the expected morphology for a fast and mobile male spider. (shrink)