Tenacity and silk investment of two orb weavers: considerations about diversification of the Araneoidea

Orbiculariae consists of two major clades: the cribellate Deinopidea and the much more diverse ecribellate Araneoidea. It has been hypothesized that the higher diversity of Araneoidea is a consequence of the superiority of the viscid orb web. However, this explanation seems incomplete: for example, cribellate silk may perform better than viscid silk in some contexts. Here, we consider the hypothesis that the diversification of Araneoidea was facilitated by changes in microhabitat occupation behavior due to the cheaper viscid orb web. In the present work we investigate the idea that the reduction in site tenacity caused by the emergence of the viscid orb web has led to an increase in the exploration of different resources and to a greater diversification of the Arancoidea through the evolutionary time. To test this idea, we evaluated the response of one cribellate orb web spider (Zosis geniculata Olivier 1789, Uloboridae) and one ecribellate orb web spider (Metazygia rogenhoferi Keyserling 1878, Arancidae) to abrupt prey absence. The changes in site tenacity and the day-to-day investment in web silk were evaluated. Spiders with three-dimensional webs tend to exhibit greater site tenacity than spiders making orb webs. Zosis geniculata and M. rogenhoferi show similar site tenacity when prey is ample. When prey is unavailable, the tenacity of the cribellate species increases while the tenacity of the ecribellate remains unchanged, and the silk investment of both species decreases. However, this decrease in silk investment is more extensive in Z. geniculata. These results coincide with the idea that a less costly ecribellate orb web leads to a lower tenacity and suggest that more frequent microhabitat abandonment in a context of insect radiation (Neiptera) leads to more diverse and opportunistic exploration of microhabitats that, in the long term, may be one explanation for the greater Araneoidea diversification.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.