Divisibility sequences of polynomials and heights estimates

In this note we compute a constant $N$ that bounds the number of non--primitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram--Mah{\'e}--Silverman--Stange--Streng, 2012, and we show that the constant can be chosen independently of the specific point and to some extent of the specific curve, as predicted in loc. cit.Comment: to appear in New York Journal of Mathematic

Increased copulation duration before ejaculate transfer is associated with larger spermatophores, and male genital titillators, across bushcricket taxa

Copulation duration varies considerably across species, but few comparative studies have examined factors that might underlie such variation. We examined the relationship between copulation duration (prior to spermatophore transfer), the complexity of titillators (sclerotized male genital contact structures), spermatophore mass and male body mass across 54 species of bushcricket. Using phylogenetic comparative analyses, we found that copulation duration was much longer in species with titillators than those without, but it was not longer in species with complex compared with simple titillators. A positive relationship was found between spermatophore size and copulation duration prior to ejaculate transfer, which supports the hypothesis that this represents a period of mate assessment. The slope of this relationship was steeper in species with simple rather than complex titillators. Although the data suggest that the presence of titillators is necessary to maintain long copulation prior to ejaculate transfer, mechanisms underlying this association remain unclear

Testing the Efficacy of Global Biodiversity Hotspots for Insect Conservation: The Case of South African Katydids

The use of endemism and vascular plants only for biodiversity hotspot delineation has long been contested. Few studies have focused on the efficacy of global biodiversity hotspots for the conservation of insects, an important, abundant, and often ignored component of biodiversity. We aimed to test five alternative diversity measures for hotspot delineation and examine the efficacy of biodiversity hotspots for conserving a non-typical target organism, South African katydids. Using a 1° fishnet grid, we delineated katydid hotspots in two ways: (1) count-based: grid cells in the top 10% of total, endemic, threatened and/or sensitive species richness; vs. (2) score-based: grid cells with a mean value in the top 10% on a scoring system which scored each species on the basis of its IUCN Red List threat status, distribution, mobility and trophic level. We then compared katydid hotspots with each other and with recognized biodiversity hotspots. Grid cells within biodiversity hotspots had significantly higher count-based and score-based diversity than non-hotspot grid cells. There was a significant association between the three types of hotspots. Of the count-based measures, endemic species richness was the best surrogate for the others. However, the score-based measure out-performed all count-based diversity measures. Species richness was the least successful surrogate of all. The strong performance of the score-based method for hotspot prediction emphasizes the importance of including species’ natural history information for conservation decision-making, and is easily adaptable to other organisms. Furthermore, these results add empirical support for the efficacy of biodiversity hotspots in conserving non-target organisms

Functional equivalence of grasping cerci and nuptial food gifts in promoting ejaculate transfer in katydids.

The function of nuptial gifts has generated longstanding debate. Nuptial gifts consumed during ejaculate transfer may allow males to transfer more ejaculate than is optimal for females. However, gifts may simultaneously represent male investment in offspring. Evolutionary loss of nuptial gifts can help elucidate pressures driving their evolution. In most katydids (Orthoptera: Tettigoniidae), males transfer a spermatophore comprising two parts: the ejaculate-containing ampulla and the spermatophylax-a gelatinous gift that females eat during ejaculate transfer. Many species, however, have reduced or no spermatophylaces and many have prolonged copulation. Across 44 katydid species, we tested whether spermatophylaces and prolonged copulation following spermatophore transfer are alternative adaptations to protect the ejaculate. We also tested whether prolonged copulation was associated with (i) male cercal adaptations, helping prevent female disengagement, and (ii) female resistance behavior. As predicted, prolonged copulation following (but not before) spermatophore transfer was associated with reduced nuptial gifts, differences in the functional morphology of male cerci, and behavioral resistance by females during copulation. Furthermore, longer copulation following spermatophore transfer was associated with larger ejaculates, across species with reduced nuptial gifts. Our results demonstrate that nuptial gifts and the use of grasping cerci to prolong ejaculate transfer are functionally equivalent

Versatile Aggressive Mimicry of Cicadas by an Australian Predatory Katydid

Background: In aggressive mimicry, a predator or parasite imitates a signal of another species in order to exploit the recipient of the signal. Some of the most remarkable examples of aggressive mimicry involve exploitation of a complex signal-response system by an unrelated predator species. Methodology/Principal Findings: We have found that predatory Chlorobalius leucoviridis katydids (Orthoptera: Tettigoniidae) can attract male cicadas (Hemiptera: Cicadidae) by imitating the species-specific wing-flick replies of sexually receptive female cicadas. This aggressive mimicry is accomplished both acoustically, with tegminal clicks, and visually, with synchronized body jerks. Remarkably, the katydids respond effectively to a variety of complex, species-specific Cicadettini songs, including songs of many cicada species that the predator has never encountered. Conclusions/Significance: We propose that the versatility of aggressive mimicry in C. leucoviridis is accomplished by exploiting general design elements common to the songs of many acoustically signaling insects that use duets in pairformation. Consideration of the mechanism of versatile mimicry in C. leucoviridis may illuminate processes driving the evolution of insect acoustic signals, which play a central role in reproductive isolation of populations and the formation of species

The Signaller's Dilemma: A Cost–Benefit Analysis of Public and Private Communication

Understanding the diversity of animal signals requires knowledge of factors which may influence the different stages of communication, from the production of a signal by the sender up to the detection, identification and final decision-making in the receiver. Yet, many studies on signalling systems focus exclusively on the sender, and often ignore the receiver side and the ecological conditions under which signals evolve.We study a neotropical katydid which uses airborne sound for long distance communication, but also an alternative form of private signalling through substrate vibration. We quantified the strength of predation by bats which eavesdrop on the airborne sound signal, by analysing insect remains at roosts of a bat family. Males do not arbitrarily use one or the other channel for communication, but spend more time with private signalling under full moon conditions, when the nocturnal rainforest favours predation by visually hunting predators. Measurements of metabolic CO(2)-production rate indicate that the energy necessary for signalling increases 3-fold in full moon nights when private signalling is favoured. The background noise level for the airborne sound channel can amount to 70 dB SPL, whereas it is low in the vibration channel in the low frequency range of the vibration signal. The active space of the airborne sound signal varies between 22 and 35 meters, contrasting with about 4 meters with the vibration signal transmitted on the insect's favourite roost plant. Signal perception was studied using neurophysiological methods under outdoor conditions, which is more reliable for the private mode of communication.Our results demonstrate the complex effects of ecological conditions, such as predation, nocturnal ambient light levels, and masking noise levels on the performance of receivers in detecting mating signals, and that the net advantage or disadvantage of a mode of communication strongly depends on these conditions