1 Introduction

Bees are flying insects that belong to the taxonomic order Hymenoptera, the same as wasps and ants. While bees are the most diverse, abundant and dominant pollinator group (Potts et al., 2016), wasps, beetles, butterflies, moths, flies, bats, and birds participate as well in the pollination of many plants (Ollerton et al., 2011). Bees are responsible for much of the planet’s biodiversity and approximately 67% of the world’s fruit and grain production (Klein et al., 2006).

However, in recent decades, we witnessed a considerable decline of bees on Earth (Sánchez-Bayo and Wyckhuys, 2019; Potts et al., 2010). Several reasons contribute to the disappearance and even extinction of bees, including climate change, habitat loss, environmental pollution, pesticides, invasive species, and pathogens (Potts et al., 2016). Faced with this worrying scenario and due to the delay and ineffectiveness of palliative measures, scientists and lawmakers have demanded comprehensive and intensive monitoring of populations that promises to support the maintenance of biodiversity (Samways et al., 2020; O’Connor et al., 2019; Byrne and Fitzpatrick, 2009).

In this context, many studies have focused on measuring Wing-Beat Frequency (WBF) from sound, radar, or optics to develop intelligent methods for automatic detection, recognition, and monitoring of flying insects (Kawakita and Ichikawa, 2019; Parmezan et al., 2019; Van Roy et al., 2014; Batista et al., 2011). WBF is generally inversely proportional to the insect size, ranging from less than 10 Hz for large butterflies and moths to more than 1000 Hz for small flies. Insects of different body weight, such as a bee and a mosquito, have quite different WBF and can be distinguished simply by listening to the sounds they make. In addition to the size and bodyweight of the insect, WBF is affected by other factors like age, wing structure, metabolic status or feeding, and climatic-environmental conditions (Spiewok and Schmolz, 2006; Unwin and Corbet, 1984).

Relevant work in this research line includes that done by Goyal and Atwal (1977), who used an oscilloscope to estimate the WBF of two bee species. The frequencies of Apis cerana and Apis mellifera were, in this order, 306 Hz and 235 Hz for workers and 283 Hz and 225 Hz for drones. From a stroboscopic analysis, Witherell et al. (1977) measured the WBF values of workers A. mellifera, which was about 206.1 Hz. Unwin and Corbet (1984) went further, consistently describing the relationship between temperature and WBF of three bee species: Tetragonisca angustula, Bombus pratorum, and Bombus pascuorum. In the referred study, thermocouples measured temperatures, and a tachometer captured the flight data. Harrison et al. (1996) demonstrated that the rise in temperature from 20–40 °C caused substantial reductions in metabolic heat production and WBF in A. mellifera bees during hovering, agitated, or loaded flight. Golding et al. (2001) reported that the WBF of A. mellifera overlaps with that of Eristalis tenax (Diptera), ranging from 150 to 200 Hz. Hedenström et al. (2001) found an increase in WBF and the lift coefficient from bumblebees Bombus terrestris after having their wings cut off. Spiewok and Schmolz (2006) concluded that both temperature and light influence European hornets’ flight performance, Vespa crabro. Besides, the researchers found that flight speed regulation under different environmental conditions is sex-specific. The study conducted by Van Roy et al. (2014) showed, based on optical signatures, that the WBF of B. terrestris and Bombus ignitus are significantly different and that the bumblebees with larger wings had a lower WBF. Potamitis and Rigakis (2015) used an optoelectronic sensor to capture the WBF of some insects, including workers of A. mellifera. All measurements were performed in a controlled laboratory environment of 25 °C and 55% humidity. The study reaffirmed that insect sounds are generally fingerprints of species and can be used efficiently for insect recognition. More recently, Miller-Struttmann et al. (2017) employed an acoustic technique to evaluate the relationship between the first harmonic of the characteristic frequency (flight buzz) and bee functional traits that impact pollination success. The authors found that the flight buzz was correlated with traits known to influence pollination effectiveness, explaining 30–52% of the variation in body size and tongue length of workers and queens of Bombus balteatus and Bombus sylvicola.

Although much effort has already been made to characterize the WBF of bees and wasps, most of the published studies have been performed in controlled laboratory settings, considering a reduced number of species and small variation in temperature and humidity (Potamitis and Rigakis, 2015; Moore et al., 1986).

Given that the study of the influence of environmental variables on the WBF of hymenopterans is scarce and that quantitative research on the activity of these insects in their natural habitat is a challenging task, the present paper analyzes how changes in temperature and humidity affect the behavior and WBF of selected flying insects. The bees and wasps considered here are eusocial, i.e., they live in colonies composed of distinct castes, including queens, workers, and males. Nurse, guard, and forager are, in this order, some of the functions that worker bees of many species and Epiponini wasps perform throughout their life stages (Canevazzi and Noll, 2011; Michener, 2007).

We have collected flight data noninvasively under field conditions in two Brazilian cities using a low-cost optical sensor, which our research group at the University of São Paulo has developed. On this basis, our study presents four major contributions: (i) in addition to temperature and humidity variables, we collected WBF data from seven bee species—A. mellifera, Lestrimelitta limao, Nannotrigona testaceicornis, Plebeia droryana, Scaptotrigona bipunctata, T. angustula, and Trigona spinipes—, and two wasp species—Polistes canadensis and Polybia paulista. The data analysis showed, for each insect species, the presence of two distinct groups, one comprising of individuals whose flight frequency reached about 258 Hz and the other containing individuals whose flight frequency reached around 502 Hz; (ii) we identified a correlation between the studied environmental variables and the WBF of the hymenopteran insects. Generally speaking, in environments with higher temperatures, we observed higher values of WBF, while in conditions with higher humidity, we found lower values of WBF; (iii) we statistically showed that the bee and wasp WBF are significantly different given distinct temperature and humidity levels; (iv) we also described and discussed the flight activity of each species to understand their respective biological cycles.

This work offers a systematic perspective towards a better theoretical understanding of variations in the WBF of insects. From the practical standpoint, the study builds base components for (real-time) identification of insects, which can be used for census purposes to know what insects occur in which places at what times, as well as estimation of abundances and monitoring of population dynamics (Conrad et al., 2007; Thomas, 2005). Our findings can provide useful information for biologists/entomologists interested in the behavior of these species and engineers working on the development of new tools for real-time monitoring of agricultural and natural ecosystems.

2 Material and methods

2.1 Optical sensor

The data addressed in this paper were generated by a low-cost optical sensor that measures insects’ information during flight. Our research group has developed such a device since 2011 (Batista et al., 2011). It constitutes an essential component for building intelligent electronic traps with the aid of machine learning solutions to selectively capture only certain species, such as disease vectors and agricultural pests (Souza et al., 2020; Maletzke et al., 2018; Souza, 2016; Silva et al., 2015; Souza et al., 2013).

In Figure 1, we introduce the main components of the optical sensor and illustrate how it works. The central part of the device consists of a 3D-printed square piece with two parallel mirrors face-to-face (80 mm length × 80 mm width × 40 mm height). An infrared LED attached to one side of the centerpiece uses the mirrors to create an infrared light window captured by a phototransistor installed on the opposite side. The infrared light bounces back and forth between the mirrors until it reaches the phototransistor. When a flying insect crosses the light window, its wings and body partially occlude the light, causing small variations captured by the phototransistor as an audio signal. The device associates each audio record with environmental variables, including temperature, humidity, air pressure, and luminosity, measured by external sensors. The optical sensor also incorporates a Bluetooth wireless link for real-time data transmission and can be powered by electrical plugs or batteries with 24-h autonomy.

Figure 1.
figure 1

Main components of the optical sensor used to collect data from flying insects. (a) Side view. (b) Top view.

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Figure 2(a) presents an example of data generated by the sensor given the crossing of a stingless bee T. angustula. The data correspond to a short length signal, 0.2 s in total, mostly composed of low-level background noise and a brief period of 0.08 s with high amplitude variation. This wide-amplitude oscillation refers to the exact moment that the insect flies across the infrared light.

Figure 2.
figure 2

Example of data generated by the optical sensor. (a) Audio signal. (b) Spectrum.

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From the recorded audios, it is possible to extract information that can be employed to characterize different species and describe their behavior over time. Among the most useful information, we highlight the WBF. Such information is directly related to the fundamental frequency and can be found through the analysis of the audio in the frequency domain representation (spectrum) (Zölzer, 2008), as portrayed in Figure 2(b). In this illustration, the WBF of T. angustula bees is 453Hz. Other relevant features besides the WBF include the location, shape, and amplitude of the first harmonics.

2.2 Data collection

We conducted the data gathering in the southern Brazilian cities of Quatiguá (23°33’57.7” S, 49°54’38.9” W) and Tomazina (23°36’59.8” S, 50°00’09.5” W), State of Paraná. These cities’ subtropical climate is similar to some regions of the United States and Europe, with frosts occurring in the winter months (July–August) when temperatures can fall below freezing. The summers, in turn, are always hot and rainy with temperatures soaring as high as 32 °C.

The data acquisition lasted about two months (October–November 2017) and, during this period, we registered—from the insect passages through the optical sensors—temperatures ranging from 16 to 44 °C with relative humidity fluctuations between 24 and 100%. Figure 3 shows the values of these environmental variables over the data collection days in the two Brazilian cities.

Figure 3.
figure 3

Temperature and humidity levels observed over the data gathering days in the two Brazilian cities.

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In a meliponary located in Quatiguá, we collected data from five bee species: A. mellifera, N. testaceicornis, P. droryana, S. bipunctata, and T. angustula. Also, in Quatiguá, but now considering two farms in the region, we acquired data from L. limao bees and P. paulista wasps. In remote rural areas of Tomazina, we collected data from T. spinipes bees and P. canadensis wasps. We chose these seven bee species and these two wasp species since they are commonly observed in Brazil’s countryside. As we had a colony of each species, we placed our sensors at the colonies’ entrance and performed the data acquisitions individually for each species.

Figure 4 summarizes the setup of our data gathering. In Figure 4(a), we can see some of the various wooden containers hosted in the meliponary in Quatiguá. Each of these boxes houses a beehive. Figure 4(b) exposes the entrance of a colony with T. angustula bees. In general, such an entry corresponds to a cylinder or funnel built of wax and resin by bees. We installed the sensors at the beehive entrances, as exhibited in Figs. 4(c)–(d) for T. angustula and Figs. 4(e)–(f) for A. mellifera and L. limao, respectively. We incorporated a 100-mm-length paperboard cylinder onto the front of some sensors, e.g. Figure 4(f), to shield the phototransistors from external lights. When ambient light falls directly on the phototransistor, it saturates, and only the low-frequency portion of the signals is detected. We also had to adapt our sensors to be used via batteries in isolated regions, such as the rural areas of Tomazina. For example, Figure 4(g) shows a nest of T. spinipes bees, while Figure 4(h) exposes the sensor coupled to a large waterproof box placed over the said beehive. Figure 4(i) exhibits the colony of P. paulista wasps, and Figure 4(j) shows how we installed the sensor on the nest of these wasps. Figure 4(k) exposes the sensor coupled to the entry of the hive of P. canadensis wasps. We sent two individuals of each insect to professional taxonomists for identification. Figure 4(l) presents the bees and wasps analyzed after being deposited on Eppendorf tubes containing 70% ethyl alcohol.

Figure 4.
figure 4

Data gathering overview.

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Table I lists the primary information about data acquisition. In this table, for each insect, the following is described: species, place of the data collection, period we acquired data, number of individuals recorded after the data preprocessing, and insect image.

Table 1 Information from the data gathering
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2.3 Data preprocessing and statistical analysis

To analyze the relationship between environmental variables and the WBF of bees and wasps, we extracted for each audio signal—a passage of one insect through the optical sensor—the fundamental frequency from the spectrum and related them to the temperature and humidity values registered during the data gathering.

We must point out that the light window created by the sensor is very thin. Most of the passages through it last for a tenth of a second, which reduces the probability of having two or more signals simultaneously. Our study did not try to identify and separate multiple passage signals; it counted them as a single one. Silva et al. (2015) provide additional information about the detector responsible for identifying, from continuous recording, the events of interest and separating them from background noise.

Compared with other devices that can be used to measure the WBF of flying insects, e.g. microphones, our optical sensor is entirely “deaf” to interference from external sound sources, including bird vocalizations, frog calls, human voices, and traffic sounds. Other factors, however, can cause the sensor to record unwanted noises. It can happen in scenarios where the sensor is susceptible to rain, ant attack, or electrical interference.

To avoid any noise and build a high-quality dataset, we preprocessed the data in two steps. Firstly, we removed all audio signals longer than 1 s or with a fundamental frequency lower than 100 Hz and greater than 1000 Hz. Secondly, we performed a similarity search for each species separately, consisting of computing the average Euclidean distances between each audio signal acquired and ten audio signals with well-defined patterns, previously chosen manually and taken as reference samples. The data were then sorted according to such a metric, and, for each species, we discarded approximately 40% of the audio signals with the longest average distances to the reference signals. This was done to get rid of possible external noise or occasional bypass of other species.

Figure 5 shows the preprocessed data from T. angustula bees. Each small circle in this scatter plot represents a worker; the temperature and WBF variables describe the workers. Having observed that the data visually falls into two groups, with each group’s instances showing a linearly increasing trend, we decided to study each group separately. Presumably, each group represents a different role in the colony. To divide individuals into groups, we fitted regression lines to the data using Ordinary Least Squares procedure (Chatterjee and Hadi, 2012).

Figure 5.
figure 5

Scatter plot for temperature and WBF variables considering T. angustula bees.

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We analyzed the relationship between WBF and the environment within each group within each species. We applied the two-sample non-parametric Kolmogorov-Smirnov test, with a confidence interval of 99% (p-value < 0.01), to confront flight data in different ranges of temperature and humidity. The test allows us to compare two data samples and determine if they came from the same distribution (Lopes, 2011).

The flight activity patterns were assessed employing circular statistics, which are suitable for analyzing data that are directional and expressed in degrees or are cyclic/periodic in time, such as months, weeks, days, and hours. For each species with flights spread over 24 hours, we estimated the circular mean—the direction of the resultant vector or mean activity peak—, the mean resultant length R̄—a measure of (angular) dispersion analogous to the variance, but interpreted in the opposite sense—, the circular standard deviation, and the bootstrap 99% confidence interval for the mean direction. We also applied three circular statistical non-parametric tests assuming a level of significance of 0.01 for p: (i) Rao’s spacing test to verify whether the pattern departed from random; (ii) Wallraff test to determine in terms of angular dispersion if the flight activity of Group A exhibited synchronicity with that of Group B; and (iii) Mardia-Watson-Wheeler test to discover whether the pattern showed temporal distributions similar to those of the other species.

In this way, we analyzed the data from all the Hymenoptera insects investigated in this work, except for P. canadensis wasps. We gathered 229 audio signals of this species, a considerably small dataset compared with the number of records collected for the other insects (Table I). Although the amount of data obtained for P. canadensis is mostly explained by the number of individuals that make up the colony—about 15 individuals per nest—, it was insufficient for the study designed here.

3 Results

Figure 6 presents WBF distribution plots for the eight hymenopterans taking into account data acquired from 25 to 27 °C. Within each identified group A and B, we can see that while there is a clear separation between the data distributions of some species—e.g., P. paulista vs. A. mellifera—there is a tight overlap in the data distributions of other species—e.g., P. paulista vs. T. spinipes.

Figure 6.
figure 6

Density functions fitted to the WBF histograms across temperatures from 25 to 27 °C for the two investigated groups. (a) Group A and (b) Group B.

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Figure 7 graphically shows the relationship between the environmental variables, i.e., temperature and relative humidity, and the WBF of seven bee species and one wasp species. We empirically decided the ranges of the environmental variables so that the variation of the data within each one is small. This figure also illustrates the flight activity of each of the eight hymenopteran insects.

Figure 7.
figure 7

Influence of temperature (left) and humidity (middle) on the WBF and the observed flight activity (right) for seven bee species and one wasp species.

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On the left side of Figure 7, we display violin plots that describe the probability density of the WBF data at seven temperature ranges. This representation uses three markers: a circle, which symbolizes the average WBF value; a rectangle indicating the interquartile range of the data; and a straight line, which connects the averages (circles) and reflects the WBF behavior as a function of temperature. We differentiated Group A from Group B for each species using the colors light blue and dark blue, respectively. Following this same line of reasoning, the violin plots in the middle of Figure 7 depict the WBF development over seven humidity ranges. An exception occurs in the data from the bees N. testaceicornis: we did not register individuals of this species when humidity exceeded 90%. Finally, on the right side of Figure 7, we present the histograms that cover the flight activity of the insects. In these plots, the bars correspond to the number of individuals recorded at a particular time of day. Through these histograms, it is possible to see the exact time of day when the species are more or less active.

The results arranged in the first two columns of Figure 7 show that the environmental variables affect the WBF of Hymenoptera insects. The main patterns are: the higher the temperature, the higher is the WBF; and the higher the humidity, the lower is the WBF. To statistically demonstrate that our WBF data are significantly different given distinct environmental conditions, we applied the Kolmogorov-Smirnov test with p < 0.01 (Table II).

Table 2 Summary of the statistical comparisons of the WBF at different temperature (T) and humidity (H) ranges. For each group within each insect species, and interval of T and H, we display the WBF average in Hz followed, in parentheses, by its standard deviation.
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In Table II, for each insect species and investigated group, we statistically compared the data according to two scenarios: (i) WBF gathered over a temperature range from 21 to 23 °C vs. WBF collected over a temperature range from 33 to 35 °C; and (ii) WBF gathered over a relative humidity range from 45 to 55% vs. WBF collected over a humidity range from 75 to 85%. In the first scenario, we focus on comparing the flight frequencies covered by the two extreme ranges of temperature exhibited in Figure 7. In the second scenario, we fixed the ambient temperature at 25, 27, or 28 °C to compare WBF from two relatively distant humidity ranges. With a constant temperature and varied humidity, we isolate the ambient temperature’s influence on the flight frequencies.

As we can see in Table II, considering at least one group within each species and regardless of the scenario, all the WBF data compared showed statistically significant differences (✓), except for bees A. mellifera, N. testaceicornis, and T. spinipes.

Figure 8 shows the rose diagrams representing the flight activity distributions of the hymenopterans throughout the day. Solid, dotted, and dashed arrows indicate the mean activity peak (circular mean) at the level of species and groups A and B, respectively. The arrows’ length is related to the circular statistic R̄ (mean resultant length). Straight lines point to the hour corresponding to the species’ flight activity peaks identified from the circular densities (Table I of the supplementary material). In the histograms of Figure 7, we can visually identify the flight activity peaks of groups A and B by species.

Figure 8.
figure 8

Flight activity patterns. Solid arrows match the species mean, and arrow length is proportional to the degree of clustering around the mean. Dotted and dashed arrows denote, in this order, the means of groups A and B. Straight lines indicate the local maximums in the circular density at the species level. (a) A. mellifera, (b) L. limao, (c) N. testaceicornis, (d) P. droryana, (e) S. bipunctata, (f) T. angustula, (g) T. spinipes, and (h) P. paulista

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The circular statistics allowed us to detect unimodal, Figs. 8(a), (c) and (e)–(g), and bimodal, Figs. 8(b), (d) and (h), flight activity patterns (Rao’s spacing test: p < 0.01). Groups A and B presented asynchronous flight activity in five species (Wallraff test: p < 0.01): A. mellifera, L. limao, N. testaceicornis, P. droryana, and P. paulista. All eight species exhibited propensities to specific flight activity patterns (Mardia-Watson-Wheeler test: p < 0.01). Table III provides, for each insect species, the following flight activity information: mean resultant length (R̄), circular mean (μ), circular standard deviation (σ), and bootstrap 99% Confidence Interval for the mean (99% CI). This table also contains the average temperature and relative humidity observed within the circular mean’s confidence interval and the respective average flight frequencies of individuals from groups A and B; standard deviations are in parentheses. The circular statistics at the level of groups A and B did not differ substantially from those listed at the species level in Table III. For this reason, they are only reported in the supplementary material: Tables II and III.

Table 3 Results of descriptive circular statistics and their interaction with variables of ambient and WBF
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The information in Table III demonstrates that relative humidity decreased with increasing temperature, which varied on average from 25 to 30 °C during the average flight activity peaks (μ). In such periods, the hymenopterans reached two-thirds of the maximum WBF recorded in each group-species.

4 Discussion

WBF is one of the major components of the aerodynamic system of flying insects. According to researches (Spiewok and Schmolz, 2006; Unwin and Corbet, 1984) and based on our previous experiments involving mosquitoes (Souza et al., 2020; Maletzke et al., 2018; Reis et al., 2018; Souza et al., 2013), environmental variables such as temperature, humidity, and time of day, which is related to luminosity, are responsible for changing the flight behavior of insects as well as their level of activity. However, detailed information on the impact of these environmental variables on the WBF of many bee and wasp species is still scarce in the literature. The present study aims to fill this gap by quantifying the influence of different factors on insects’ flight from the order Hymenoptera.

Our results revealed, for each hymenopteran insect, the presence of two distinct groups (Figure 6). Group A comprises individuals that have a greater body weight than individuals from Group B. As the head, body, and wings of individuals from Group B are relatively smaller, they showed a higher WBF than individuals from Group A. The first part of this statement is a fact; the second part is supported by our own investigations and those of other authors (Grüter et al., 2017; Sauthier et al., 2017; Santoyo et al., 2016; Van Roy et al., 2014; Garcia and Noll, 2013; Spiewok and Schmolz, 2006; Elekonich and Roberts, 2005; Robinson, 1992; Unwin and Corbet, 1984), as well as by our original inductive exercise.

Although further studies are needed to clarify the differences between groups A and B, we have some basis for speculating that individuals in these groups are: (i) workers which received larger larval provisions (Group A) vs. workers that received smaller larval provisions (Group B); or (ii) guards (Group A) and foragers (Group B) in the case of stingless bees, and older workers (Group A) and mid-age workers (Group B) in the case of A. mellifera bees and P. paulista wasps.

For stingless bees, our second hypothesis suggests that the WBF of guards—workers tasked with cooling and defending the hive—are higher than the WBF of foragers—workers responsible for collecting nectar, pollen, resins, and water. This assumption is supported by the premise that guards have a higher body weight than foragers, such as observed for more than ten species, including the six stingless bees studied here (Grüter et al., 2017). Both guards and foragers are active throughout the day. Still, guards usually hover near the colony entrance, which would explain the large number of records of these individuals by our sensor.

Concerning A. mellifera bees and P. paulista wasps, our second hypothesis implies that older workers flap wings at a lower frequency than mid-age workers. Such a hypothesis is in line with Sauthier et al. (2017) and Robinson (1992), who reported that guarding tasks precede foraging activities in honey bees, and with Garcia and Noll (2013), who observed changes in the body weight, the salivary gland and the mandibular gland that were associated with age in the Epiponini P. paulista.

It is clear that the bigger the insect and its wings, the lower the fundamental frequency (WBF), as it will take longer for the larger wings to complete a movement cycle. Besides the age of the insect, its body weight and the structure and length of its wings, other factors such as metabolic status and climatic-environmental conditions are responsible for altering the WBF (Santoyo et al., 2016; Van Roy et al., 2014).

We identified an inclination in the relationship between the studied environmental variables and the WBF of different Hymenoptera insects. As we can see from most of the violin plots arranged in the first column of Figure 7, the higher the air temperature, the higher the WBF. In contrast, as we can see from most of the violin plots organized in the second column of Figure 7, the higher the relative humidity, the lower the WBF.

For some mosquito species like Aedes albopictus, Aedes aegypti, and Anopheles aquasalis, we observed temperature also has a direct influence on the data, increasing the WBF. However, there is no clear evidence that humidity at constant temperatures has any visible effect on the fundamental frequency of such insects (Souza et al., 2020; Maletzke et al., 2018).

Analyzing the relation temperature vs. WBF in Figure 7, it is possible to notice an increasing trend in the data of all species except A. mellifera and N. testaceicornis. The Africanized bees presented constant WBF with rising ambient temperature. Such behavior is similar to that reported in Soltavalta (1963), who found that flight tones of A. mellifera are independent of temperature. For N. testaceicornis bees, our results suggest that the flight frequency of this insect is changed only at high temperatures (≥ 33 °C). Considering the seven bee species and all seven temperature ranges, the lowest WBF came from Group A of T. spinipes—drifting from 154.29 (26.14) to 176.13 (26.08) Hz. On the other hand, Group B of T. angustula obtained the highest WBF—drifting from 393.58 (52.39) to 501.83 (12.90) Hz. Group A of the P. paulista wasp exhibited WBF in the interval of 128.74 (14.77) to 147.43 (14.13) Hz, while Group B showed WBF in the range of 243.31 (33.33) to 273.42 (23.58) Hz.

The results discussed so far are supported by research showing that WBF and flight metabolic rate increase with air temperature in flying insects (Souza et al., 2020; Unwin and Corbet, 1984). In this scenario, a large insect flying in low temperature may increase the WBF to raise its thoracic temperature, thereby improving flight efficiency. Consequently, the correlation between temperature and WBF variables decreases for larger insects; in very large insects, such a relationship may even become negative (Spiewok and Schmolz, 2006; Peat et al., 2005; Harrison et al., 1996; Spangler and Buchmann, 1991; Unwin and Corbet, 1984). For example, studies with solitary bees and bumblebees reported a WBF decrease with rising temperature (Spangler and Buchmann, 1991; Unwin and Corbet, 1984). Differently, some social hymenopterans such as A. mellifera have been shown to control their WBF regardless of ambient temperature levels (Soltavalta, 1963). Furthermore, for several bee species, it has been observed that the thoracic temperature of males is typically higher than of females (Coelho, 1991).

Examining the relation humidity vs. WBF in Figure 7, it is possible to see a decreasing trend in the data of both groups from the bees N. testaceicornis, P. droryana, S. bipunctata, and T. angustula, and the wasp P. paulista. Individuals from the species A. mellifera, L. limao, and T. spinipes displayed WBF averages reasonably balanced given the increase of the air humidity, with some slight variations in their values. Regarding the seven bee species and all seven humidity ranges, the lowest WBF came from Group A of T. spinipes—drifting from 151.30 (31.01) to 157.76 (26.53) Hz. In contrast, Group B of T. angustula achieved the highest WBF—drifting from 500.02 (22.41) to 397 (65.38) Hz. Group A of the P. paulista wasp presented WBF in the interval of 126.89 (14.83) to 144.55 (15.44) Hz, while Group B exhibited WBF in the range of 240.99 (35.94) to 270.39 (25.03) Hz.

In addition to visually showing that environmental variables impact the WBF of some bees and wasps, we statistically compared the flight data of the insects at distinct temperature and humidity ranges (Table II). Considering at least one group within each species and both explored scenarios in Table II, the only hymenopterans whose wing-beat presented no statistically significant differences were A. mellifera and N. testaceicornis, when compared data measured in the temperature ranges of 21–23 °C and 33–35 °C, and T. spinipes, when compared data acquired in the humidity ranges of 45–55% and 75–85% at a fixed temperature of 25 °C. We suspect that A. mellifera bees cannot control their WBF at different humidity levels as they do at different temperature rates. As relative humidity increases at a constant temperature in the scenario under consideration, the rate of heat production per wing-beat and the wing-beat frequency are proportionally reduced in order only to produce sufficient heat for thoracic temperature maintenance (Elekonich and Roberts, 2005). The flight frequencies of N. testaceicornis did not change significantly with increasing ambient temperature. Also, individuals of this species appear to be inactive when the humidity is above 90%. At 25 °C, relative humidity had no influence on the WBF of T. spinipes. We tried to fix other temperatures so that it was possible to analyze flight samples of this stingless bee within the same humidity ranges as in Table II, but there was not enough data to do so.

The periods of activity/inactivity of an animal is associated with its circadian rhythm. In this context, we portray the flight activity patterns of the studied species in Figure 7 (linear data) and Figure 8 (circular data). Unlike mosquitoes, which tend to be more agitated at dawn and/or dusk, Hymenoptera insects showed to be active outside the colony during 7:00–20:00. We verified that A. mellifera and N. testaceicornis bees are most active in the late morning and early afternoon (11:00–14:00), achieving peak concentrations around 12:17; individuals from the species S. bipunctata, T. angustula, and T. spinipes work outside the nest more in the afternoon (12:00–16:00) with flight activity peaks close to 13:36, 14:41, and 12:45, respectively; L. limao and P. droryana bees as well as P. paulista wasps are reasonably agitated at about 11:55 and more active in the late afternoon (16:00–19:00), reaching peak concentrations before nightfall (18:22).

Our circular analysis also revealed that flight activity patterns are statistically distinct between species and significantly asynchronous between groups A and B for A. mellifera, L. limao, N. testaceicornis, P. droryana, and P. paulista. Concerning bees, we registered a higher number of individuals from Group A than individuals from Group B. For the P. paulista wasps, we did not find a significant variation in the proportion between individuals from Group A and individuals from Group B.

We must emphasize that temperatures around 27.5 °C were observed along the flight activity peaks—straight lines in Figure 8—, which in turn occurred between late morning and mid-afternoon and, for three species, also before dusk. During these peaks and during the mean flight activity peaks, where the temperature varied on average from 25 to 30 °C (Table III), the insects reached two-thirds of the maximum WBF recorded in each group-species. Most importantly, these temperatures are within the range considered optimal for foraging, which is approximately between 20 to 30 °C. The maximum WBF occurred about 15:30, where the ambient temperature exceeded 30 °C.

As far as we know, no other study of comparable size has explored in such detail the relationship between the temperature and humidity variables and the WBF of hymenopteran species, aggregating information about the biological cycle of these insects. In addition to hel** biologists/entomologists interested in understanding the behavior of such species, our findings will help engineers build, or even enhance, insect flight data-based models. In real-time scenarios, models will be able to embed rules to adapt themselves to changes in temperature and humidity (Žliobaitė et al., 2016).

5 Limitations

The hymenopterans investigated in this paper emit an acoustic signal formed by frequencies harmonically related to the fundamental frequency, which here corresponds to the WBF and is also known as the first harmonic. Harmonics are elements of a distorted periodic waveform where frequencies are positive integer multiples of the fundamental. For example, if the fundamental frequency or first harmonic is 200 Hz (200 × 1), the second harmonic is 400 Hz (200 × 2), the third harmonic 600 Hz (200 × 3), and so on.

Automatic fundamental frequency estimation remains a challenging topic in the field of audio signal processing. While few methods are suitable for one domain, many do not work well for other domains. Besides, a detector’s accuracy is generally proportional to the quality/complexity of the signal (Gerhard, 2003).

During the design of this study, we evaluated three different algorithms to compute the WBF: one based on time-domain, i.e., the YIN method (De Cheveigné and Kawahara, 2002), and the other two founded on frequency-domain that consider respectively the spectrum and cepstrum representations (Zölzer, 2008). Such algorithms are based on peak detection and, therefore, susceptible to errors. One of these errors is taking the second harmonic as WBF because it has a peak of greater amplitude, or the first harmonic is not well represented. Although we have avoided such false positives as much as possible by discarding audio signals with low confidence peak detection, this issue is a limitation of this work.

According to our experiments in uncontrolled environments, YIN is as good as the spectrum-based detector in the face of clear signals. YIN is the best candidate for data with not very defined patterns; it has a confidence threshold that can be used as a criterion for audio signal selection. The cepstrum-based detector appears to be more sensitive than the other two methods, as it often identified peak values outside the range defined for the flight frequencies. The supplementary material shows ten signals of each species, five from Group A and five from Group B, which we chose at random using the YIN confidence threshold. For each audio signal, we exhibited the spectrum along with the estimated WBF. The flight frequencies vary around 100–580 Hz, depending on the species, body weight, and sex, and are affected by distinct factors such as climatic-environmental conditions.

6 Conclusion

Understanding the relationships between insect wing-beat frequency and environmental conditions is not only of fundamental interest from the biological perspective. Such understanding is critically necessary for develo** non-invasive species monitoring techniques, which could help estimate insects’ occurrence and their relative abundances in real time.

In this study, we collected a reference dataset to identify seven bee species and two wasp species at varying natural environmental conditions. We extracted distinct patterns of wing-beat frequency for each species and showed that the wing-beat frequency for most investigated species strongly depends on temperature and humidity.

Our analysis concludes that it is possible to distinguish species and body weight groups within each species from wing-beat frequency signals. The practical development of a computational diagnostic methodology for real-time operation remains the subject of future work.