Does the abundance of hoverfly mimics (Syrphidae) depend on the numbers of their hymenopteran models ?

We tested the prediction that, if hoverflies are Batesian mimics, this may extend to behavioral mimicry such that their numerical abundance at each hour of the day (the daily activity pattern) is related to the numbers of their hymenopteran models. After accounting for site, season, microclimatic responses and for general hoverfly abundance at three sites in north-west England, the residual numbers of mimics were significantly correlated positively with their models 9 times out of 17, while 16 out of 17 relationships were positive, itself a highly significant non-random pattern. Several eristaline flies showed significant relationships with honeybees even though some of them mimic wasps or bumblebees, perhaps reflecting an ancestral resemblance to honeybees. There was no evidence that good and poor mimics differed in their daily activity pattern relationships with models. However, the common mimics showed significant activity pattern relationships with their models, but the rarer mimics did not. We conclude that many hoverflies show behavioral mimicry of their hymenopteran models.

The evolution of imperfect mimicry in hoverflies

Ideas about the evolution of imperfect mimicry are reviewed. Their relevance to the colours patterns of hoverflies (Diptera, Syrphidae) are discussed in detail. Most if not all of the hoverflies labelled as mimetic actually are mimics. The apparently poor nature of their resemblance does not prevent them from obtaining at least some protection from suitably experienced birds. Mimicry is a dominant theme of this very large family of Diptera, with at least a quarter of all species in Europe being mimetic. Hoverfly mimics fall into three major groups according to their models, involving bumblebees, honeybees and social wasps. There are striking differences in the general levels of mimetic fidelity and relative abundances of the three groups, with accurate mimicry, low abundance and polymorphism characterizing the bumblebee mimics: more than half of all the species of bumblebee mimics are polymorphic. Mimics of social wasps tend to be poor mimics, have high relative abundance, and polymorphism is completely absent. Bumblebee models fall into a small number of Muellerian mimicry rings which are very different between the Palaearctic and Nearctic regions. Social wasps and associated models form one large Muellerian complex. Together with honeybees, these complexes probably form real clusters of forms as perceived by many birds. All three groups of syrphid mimics contain both good and poor mimics; some mimics are remarkably accurate, and have close morphological and behavioural resemblance. At least some apparently 'poor' mimetic resemblances may be much closer in birds' perception than we imagine, and more work needs to be done on this. Bumblebees are the least noxious and wasps the most noxious of the three main model groups. The basis of noxiousness is different, with bumblebees being classified as non-food, whereas honeybees and wasps are nasty-tasting and (rarely) stinging. The distribution of mimicry is exactly what would be expected from this ordering, with polymorphic and accurate forms being a key feature of mimics of the least noxious models, while highly noxious models have poor-quality mimicry. Even if the high abundance of many syrphid mimics relative to their models is a recent artefact of man-made environmental change, this does not preclude these species from being mimics. It seems unlikely that bird predation actually controls the populations of adult syrphids. Being rare relative to a model may have promoted or accelerated the evolution of perfect mimicry: theoretically this might account for the pattern of rare good mimics and abundant poor ones, but the idea is intrinsically unlikely. Many mimics seem to have hour-to-hour abundances related to those of their models, presumably as a result of behavioural convergence. We need to know much more about the psychology of birds as predators. There are at least four processes that need elucidating: (a) learning about the noxiousness of models; (b) the erasing of that learning through contact with mimics (extinction, or learned forgetting); (c) forgetting; (d) deliberate risk-taking and the physiological states that promote it. Johnston's (2002) model of the stabilization of imperfect mimicry by kin selection is unlikely to account for the colour patterns of hoverflies. Sherratt's (2002) model of the influence of multiple models potentially accounts for all the patterns of hoverfly mimicry, and is the most promising avenue for testing.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).