Despite Batesian mimicry often eliciting predator avoidance, many Batesian mimics, such as some species of hoverfly (Syrphidae), are considered to have an “imperfect” resemblance to their model. One possible explanation for the persistence of apparently imperfect mimicry is that human perceptions of mimicry are different from those of natural predators. Natural predators of hoverflies have different visual and cognitive systems from humans, and they may encounter mimics differently. For example, whilst humans often encounter hoverflies at rest on vegetation, or in photographs or textbooks, where they are typically viewed from above, natural predators may approach hoverflies from the side or below. To test how viewing angle affects the perception of mimicry, images of mimetic hoverflies and their models (wasps and bees) were shown from different angles in an online survey. Participants were asked to distinguish between the images of models and mimics. The results show that the viewing angle does affect perceived mimicry in some species, although it does not provide a complete explanation for the persistence of imperfect mimicry in nature. The effect is also highly species-specific. This suggests that to better understand how selection has shaped mimetic accuracy in hoverflies and other taxa, further study is required of the viewing angles that predators utilize most commonly in nature.

Insect specimens and photography

Insect specimens were collected between June 2020 and August 2021 from various locations in the East Midlands (UK), using a hand net. Species were selected opportunistically from those that were most abundant at our field sites. Specimens were euthanized by freezing at -18°C for approximately 30 minutes. They were then pinned through the thorax and positioned into a natural-looking posture before drying for 6-24 hours. Specimens were suspended, with the anterior uppermost, on a motorized turntable (Syrp Genie II), positioned against a white background, and lit indirectly using two LED panel lights (22W, 5600K; Pixapro, Brierley Hill, UK). They were photographed using a DSLR camera (Canon EOS 600D) and macro lens (Tamron SP 90mm) with F20, 1/6s exposure, and ISO400. Each specimen was photographed from nine different viewing angles – three different vertical camera positions (vertical angle) at each of three equally spaced turntable orientations (rotational angle) (Figure 1).

Photos of three specimens of each of 10 different species were selected for this study. We identified the three most abundant aposematic Hymenoptera at our field sites as the most plausible “model” species for hoverfly mimics: Vespula vulgaris, Vespula germanica, and Apis mellifera. The species were divided into a wasp group and a bee group. The wasp group consisted of the two common wasp species (V. vulgaris and V. germanica), three wasp mimics (Epistrophe grossulariae, Helophilus pendulus, and Sericomyia silentis), and a control non-mimetic fly (Mesembrina meridiana). E. grossulariae and H. pendulus are both considered accurate mimics of Vespula species when observed from a dorsal view (Dittrich et al., 1993; Leavey et al., 2021). The accuracy of S. silentis has not been assessed. The bee group consisted of the honeybee, A. mellifera, two bee mimics (Eristalis pertinax and Eristalis tenax), and a control non-mimetic fly (Cheilosia albitarsis). Eristalis species have been shown to be very inaccurate mimics of Vespula species when viewed dorsally (Dittrich et al., 1993), but the accuracy of their mimicry of Apis has not been quantified. The choice of which control non-mimetic fly was included in each group was arbitrary. A different control non-mimetic fly was included in each group so that all species were encountered the same number of times by each participant (see below).

Survey

A survey was coded using RStudio (R Core Team, 2019) using the shiny (Chang et al., 2022), shinyjs (Attali, 2021), shinycssloaders (Sali and Attali, 2020) and rdrop2 (Ram and Yochum, 2020) packages and deployed on the shinyapps.io server (Posit Software, 2022). Upon opening the survey, the user was allocated at random to the bee or wasp group and a single vertical angle and rotational angle combination (from the nine demonstrated in Figure 1). The user was given information explaining how to complete the survey (Figure S1), shown a “model photo” (of a specimen that was not included in the question set) of either Apis mellifera or Vespula germanica (depending on which group had been selected) from the selected viewing angle, and told which model type (“bee” or “wasp”) the photo showed.

The user was then shown the rest of the photos in the group from the selected viewing angle. For the wasp group, participants were shown 18 photos in a random order (three specimens of six species) and asked the question, “Is this a wasp?”. For the bee group, participants were shown 12 photos in a random order (three specimens of four species) and asked the question, “Is this a bee?”. For each image, the participants were asked to select an answer (either “Yes” or “No”) and then were told if they were correct or incorrect. This allowed participants to continue to learn what the images showed throughout the survey. Once all images in the first model group had been shown, the participant was shown the model photo for the other group from the same viewing angle and told which model type it showed. Participants were then asked to classify the images of the species in this group in the same manner as the previous group. The participants were not given a time limit to answer individual questions or complete the survey overall. Once all 30 questions had been asked, the participant was thanked for taking part and shown their overall score.

The link to this survey was sent out to various student and staff email lists at the University of Nottingham, as well as to members of the public via social media. Participants completed the survey using their own device, meaning that display types/resolutions and viewing distances varied. One hundred and forty-six responses to the survey were received. Due to the random allocation to each treatment, the number of participants allocated to each treatment varied from 9 to 20 (N for each treatment: high dorsal = 9, high ventral = 17, high side-on = 19, mid dorsal = 16, mid ventral = 20, mid side-on = 18, low dorsal = 18, low ventral = 11, low side-on = 18).

Statistical analysis

Statistical analysis was carried out using R version 4.3.1 (R Core Team, 2019). A set of nested Generalized Linear Mixed Effects models (GLMMs) was fitted to the entire data set using the glmmML function (Broström, 2022). The response variable was whether the image was correctly classified, and binomial errors were assumed. The participant ID and insect specimen were fitted as random effects. The species, vertical angle, rotational angle, and question number were fitted as fixed effects. The order in which the questions were asked was centered around zero, with values ranging from -14.5 to 14.5. Another fixed effect called group order was fitted to account for whether the questions were asked in the first or second species group. The question number and group order were included in the models to determine if learning occurred across the question set. All two-way interactions between these fixed effects were included in the maximal model. Preliminary inspection of the data suggested there was not a strong three-way interaction between species, vertical angle, and rotational angle.

To determine the best model to describe the data, a model selection process was followed as in Symonds and Moussalli (2011) and Smolis et al. (2023). The dredge function from the MuMIn package (Barton, 2023) was used to fit models with every combination of the fixed effects and their two-way interactions and compare them using the corrected Akaike information criterion (AICc) to find the best model. ΔAICc (the difference in AICc between the best model and model i) and the AICc weight (ωi) were calculated by the dredge function. The accumulated AICc weight (acc ωi) was calculated and used to determine the 95 % confidence set of models. The evidence ratio (ER) was calculated using the equation: 

ER = exp( − 1/2 ∆AICc_best) / exp(−1/2 ∆AICc_i) 

(from Symonds and Moussalli (2011)), where is the ΔAICc value for the best model, so is equal to zero. The predictor weight was calculated for each predictor by summing the weights of the models in which they were included. In preliminary analysis, we encountered convergence errors for some statistical models, owing to the near-perfect recognition of images of the control (non-mimetic) species, and one of the A. mellifera specimens. To avoid this problem, these images were removed from the dataset before conducting the final analysis.