The feeding behaviour of specialist butterflies may be affected by the mechanical and chemical characteristics of the tissues of their host-plants. Larvae of the butterfly, Battus polydamas archidamas feed only on Aristolochia chilensis, which contains aristolochic acids. We studied the oviposition pattern of adults and the foraging of larvae of B. polydamas archidamas over time in relation to variations in hardness of the substrate and concentration of aristolochic acids in different plant tissues. We further tested the effect of two artificial diets containing different concentrations of aristolochic acids on larval performance. B. polydamas archidamas oviposited mostly on young leaves and the larvae fed on this tissue until the second instar. Third instar larvae fed also on mature leaves and fourth and higher instars fed also on stems. Young leaves are softer and contain higher concentrations of aristolochic acids than mature leaves, and stems are both harder and contain a high concentration of aristolochic acids. Larvae reared on artificial diets containing a high concentration of aristolochic acids suffered less mortality and were heavier than those reared on a diet with a lower concentration of aristolochic acids, which suggests they are phagostimulatory. A strategy of host use regulated by aristolochic acid content and tissue hardness is discussed.
In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l \hspace{4.44443pt}(\@mod \; k)$ for which $ap + b$ is squarefree.
We consider positional numeration system with negative base −β, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β>1 of polynomials x2−mx−n, m≥n≥1, and show that in this case the set Fin(−β) of finite (−β)-expansions is closed under addition, although it is not closed under subtraction. A particular example is β=τ=12(1+5–√), the golden ratio. For such β, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (−τ)-integers coincides on the positive half-line with the set of (τ2)-integers.