Introduction

In the fleeting weeks of their lifespan, female mosquitoes engage in a sequence of crucial behaviors—mating, blood-feeding, and egg-laying—to ensure successful reproduction. Marked progress has been made regarding the specific cues and associated neurosensory systems that allow mosquitoes to precisely locate a host (reviewed in Coutinho-Abreu, Riffell, and Akbari 2022) or an oviposition site (Afify and Galizia 2015), yet we have a limited understanding of the factors that dictate the timing of these behaviors. Mosquito do not engage in specific behaviors uniformly over time, yet behaviors rather concentrate at specific periods of the day—usually before sunset for Aedes species (Zahid et al. 2023) and after sunset for Anopheles (Kenea et al. 2016) and Culex species (Duffield 2024). The timing of blood feeding, for instance, is typically estimated using the “Human Landing Catch” assay, in which an individual records mosquito landings on their own body over time (for example in (Captain-Esoah et al. 2020). Although this field method accounts for relevant environmental variations and human cues, it is very labor intensive and complicates the isolation of specific factors that determine timing of host-seeking behavior. Laboratory experiments conducted in the absence of human cues but with periodic light cycles have shown that mosquitoes display rhythmic activity patterns (Jones, Hill, and Hope 1967; Taylor and Jones 1969), mirroring observations from field studies. Like in other insects, these behaviors are governed by an internal circadian rhythm, modulated by environmental cues like sunlight, but can also persist without them. At the molecular level, circadian rhythms in mosquitoes are regulated by clock genes, such as period and timeless, which control proteins driving daily activity cycles (Duffield 2024).

Historically, the characterization of circadian rhythms in mosquitoes was made possible by remarkably simple behavioral assays. These methods included using microphones to record the flight activity of individual mosquitoes (M. Jones 1964) and infrared beams to measure walking activity in narrow tubes (e.g. Newman, Anderson, and Goldberg 2016; Ajayi et al. 2024). While these assays have provided valuable insights, they are inadequate for comprehensive flight activity monitoring. Typically, measurements span only a few hours to days and focus on basic indicators like “active” or “not active,” and, importantly, severely restrict mosquito movement. Consequently, these methods do not allow quantification of rhythmic behaviors involving flight, such as sugar feeding, host-seeking, or egg-laying.

While assays to longitudinally monitor the activity of mosquitoes are limited, various recent studies have used high-resolution video recording with multiple cameras to track 3D mosquito flight. In conjunction with machine vision techniques, these approaches typically allow for detailed analysis of flight-based behaviors such as swarming (Cavagna et al. 2023), escape from predators (Cribellier et al. 2024), or navigating toward human cues (van Breugel et al. 2015). However, these setups are costly and generate vast amounts of data (Spitzen and Takken 2018), making them suitable for short-term (typically several minutes), high-resolution monitoring but inappropriate for long-term tracking over weeks. To date, no setup has been optimized to monitor the activity of freely flying of mosquitos over long periods of time.

Nevertheless, robustly recording and analyzing mosquito flight activity over several weeks is meaningful for several reasons: it allows measuring the effects of physiological processes like pathogen infection or blood ingestion that have long-lasting impacts, and it establishes a foundation to examine the complex interplay between flight activity and specific behaviors such as host-seeking or oviposition. Furthermore, long-term monitoring could enable comparative studies to better understand genetic factors driving variability between closely related species or strains. Additionally, this approach could be valuable for studying and quantifying behavioral adaptations in response to public health interventions such as insecticide treatments. With these goals and applications in mind, we sought to construct a low-cost open-source setup to monitor the flight activity of mosquitoes over weeks and enable quantification of specific behaviors like sugar-feeding and host-seeking.

Here we report “BuzzWatch”, an open-source hardware platform and computational pipeline to measure and analyze the rhythmic behavior of mosquitoes over weeks. Alongside this manuscript, we offer tutorials on constructing the setup and analyzing the data on a dedicated wiki page, and a graphical user interface to facilitate mosquito tracking from video footage and to perform multi-scale analysis from mosquito tracks. These resources will ensure reproducibility and promote consistent data exploration across different experiments and laboratories. In this work, we focus on Aedes aegypti, the primary vector of many arboviruses, and present four independent case studies, that collectively demonstrate the extensive capabilities of BuzzWatch:

1. Mapping natural variation in the daily rhythm of Aedes aegypti colonies, revealing a distinct signature distinguishing native and invasive populations.

2. Quantifying the long-term impact of physiological (ingestion of a blood-meal) or environmental changes (modification of the light cycle) on mosquito activity patterns, highlighting aspects of their phenotypic plasticity.

3. Measuring responses to repeated pulses of host cues, uncovering consistent differences between responses during night and day times.

In this work, we use the term ‘daily rhythm’ as an umbrella term to describe the observable patterns of mosquito behavior over a 24-hour period, acknowledging that these patterns may include both internal circadian influences and external environmental factors.

Results

An open platform to continuously monitor mosquito flight activity over weeks

To monitor mosquito behavior over weeks, we designed a dedicated hardware and software platform, constructed from readily available and low-cost materials and open-source methods to monitor the activity of populations of 40-60 adult mosquitoes (Fig.1A).

Figure 1.

Hardware: continuous monitoring of flight activity

We constructed a 15 × 15 × 15 cm transparent cage to house mosquitoes, allowing them to rest, fly, and sugar feed at any time (Fig.1B). The cage includes a sugar feeder supporting a population of 40 to 60 mosquitoes to thrive without human intervention for weeks, provided that the cage is placed in an environment with appropriate temperature and humidity conditions. The cage, sugar feeder, and supporting structural elements are constructed out of acrylic using a laser cutter, facilitating easy reproduction and modification. We designed and tested several versions of the setup, which can be placed in either a climatic room or a climatic controlled environment where temperature, humidity, and lighting are externally controlled (Fig.S1E,F), or in a custom-built environment where artificial daylight intensity is directly controlled by an RGB LED array connected to a Raspberry Pi (Fig.S1C,D).

We use the Raspberry Pi single board computer and associated Pi Camera mounted beneath the cage as a cost-effective means to record flight activity for weeks (Fig.1B, Fig.S1). Infrared illumination and a long-pass filter facilitate video acquisition independent of environmental lighting conditions without impacting mosquito behavior (infrared wavelengths do provide limited cues to mosquitoes (Zermoglio et al. 2017; Muir, Thorne, and Kay 1992). In balancing the quality of video acquisition required for the detection and tracking of flying mosquitoes with the reliability and storage capacity over weeks, we chose to record at a “low” resolution of 650×650 pixels at a relatively high frame rate of 25 frames per second. This allows all mosquitoes within the cage to be visible and enables reliable tracking of flying mosquitoes (Fig.1D). Recordings result in week- or month-long movies (segmented into 20-minute videos) of 40-60 freely behaving mosquitoes in a cage.

The list of parts and technical information necessary to construct the set-up are briefly described in the Methods section (Table 2) and extensively documented in a dedicated “wiki” website with step-by-step illustrated guides (Fig.1C, https://theomaire.github.io/buzzwatch/construct.html). The total cost of materials for one complete set-up is around 150-300euros per cage (see Table 2)), making it affordable for laboratories to build several replicas.

Table 1.

Table 2.

Software: Tracking and measuring mosquito flight activity

We developed a dedicated Python pipeline to extract and analyze the flight activity of mosquitoes captured during month-long recordings, which can be used as a command line tool or through a dedicated graphical user interface facilitating detailed analysis (Fig.1C). With its straightforward design and virtually no user input required, our pipeline using parallel computing typically processes 20-minute videos in 1-5 minutes, enabling the analysis of one week’s data in 10 hours on a standard laptop computer.

Leveraging the observation that every alive mosquito moves at least once per day, we create background images devoid of alive mosquitoes by averaging 100 frames over a span of 33 hours (see Fig.S2). Averaged images facilitate daily counting of the number of dead mosquitos to estimate the number of alive mosquitos at any time over a 30-day experiment. We employed computer vision methods to detect centroids of mosquitoes (Fig.1D middle, Fig.S2A).

We refined the greedy centroid tracking algorithm to efficiently classify individual mosquitoes as resting or flying. This classification allows robust quantification of population level activity patterns and metrics such as the fraction of flying mosquitoes at any given time (Fig.1E) and observe the longitudinal dynamics of rhythmic patterns over long timescales (Fig.1F). We furthermore extract the 2D projection of the 3D flight trajectories of mosquitoes (Fig.1D right, Fig.S2B,C,D,E). While 2D projection underestimates flight speed by a factor of (assuming isotropic movement in a 3 dimensions, see Supplementary text1) this approximation does not affect the quantification of population level activity patterns and metrics such as the fraction of flying mosquitoes or the duration of individual flight bouts. Describing mosquito flight behavior in detail is complex, yet simply knowing when a mosquito starts or stops flying can provide significant biological insights as initiating flight is typically the first step towards behaviors such as sugar feeding or host seeking.

In Fig.1D-I, we present an example dataset for the continuous 32-day monitoring of 40 non-blood-fed Ae. aegypti females. For this experiment (and all other if not specified otherwise), we used a 24-hour cycle consisting of 12 hours of light and 12 hours of darkness, with a smooth dimming transition between the light and dark. According to the Zeitgeber convention, ZT0 marks the beginning of the increase in light intensity (artificial ‘sunrise’), and ZT12 marks the end of the decrease in light intensity before complete darkness (artificial ‘sunset’).

Consistent with previous studies on Ae. aegypti locomotor and flight activity (Taylor and Jones 1969), we observed two peaks of flight activity: a smaller peak following “sunrise” (ZT0) and a more pronounced peak before “sunset” (ZT12) (Fig.1E). During the night and midday flight activity is low and Ae. aegypti females are generally resting. At the peak of activity, only about 10% of mosquitoes are flying at any moment, while nearly all fly at least once during the evening peak (Fig.S4). We focus on the instantaneous fraction flying, as it offers a robust measure indicative of the transition between resting and flying. In addition to the fraction of flying mosquitoes, a population measure, we also quantified several features of individual flight trajectories, including the duration of flight, the duration of resting, and the 2D projection of instantaneous/average flight speed (Fig.S2; Fig.S3). By monitoring a group of 40 mosquitoes for several weeks, an experiment typically yields around 10,000 flight trajectories, which form a solid basis to compute robust distributions of the different flight statistics (Fig.1G).

Multiscale analysis from seconds to weeks

With datasets capturing flight activity at sub-second resolution over weeks, we were able to perform nuanced statistical analyses across multiple time scales—from mere seconds to entire days (Fig.1G-I). These rich data facilitate the examination of three key forms of variability: between individual flight trajectories (Fig.1G); variation during the day (24 hours), quantified by averaging the data over multiple days to discern daily rhythmic patterns and day-to-day variations in mosquito activity (Fig.1H); and across consecutive days (or parts of the day) to understand longitudinal trends over weeks (Fig.1I). For the fraction of flying Ae. aegypti, we observed that the daily activity pattern remained remarkably similar over 32 days (Fig.1H top). However, we observed an increase in peak activity in the evening over the course of the experiment, while the morning peak started to decrease after 20 days. This dual pattern of consistent daily rhythms coupled with gradual changes over weeks portrays the flight activity rhythm of mosquito as a complex behavioral trait, which emerges from the interplay between robust internal regulation and nuanced physiological changes.

Next, we repeated the multi-scale analysis on different behaviors or flight features such as sugar-feeding activity, flight duration, and flight speed. To estimate sugar-feeding behavior, we compared mosquito presence on the sugar-feeder to that on a control area, establishing a “sugar feeding index” (Fig.S3A-D). This method revealed increased presence on the sugar-feeder around the evening peak (ZT10-ZT12), suggesting increased sugar feeding (Fig.S3D). Compared to the instantaneous fraction flying, we observed a less pronounced pattern for sugar feeding index throughout the day, significant variation between days, and no discernable trend over long time-scales (Fig.S3E). Similarly, for flight duration and speed, no distinct daily or long-term pattern emerged (Fig.S3F-G), indicating high stability of these behavioral features in the absence of external perturbation.

The data presented above demonstrate that BuzzWatch provides a robust and efficient way to quantify the multiscale temporal dynamics of mosquito flight activity patterns over weeks. Using the dedicated python GUI app and guidelines from the wiki, all analysis and plots can be reproduced with a few clicks. Having established the method using Ae. aegypti maintained in a stable environment and isolated from host cues, we next sought to uncover the relative contribution of genetic, physiological, and environmental factors to the daily flight activity rhythm of mosquitoes.

BuzzWatch uncovers intra-species variation in the daily rhythm of flight activity

Having demonstrated our method using a single Ae. aegypti mosquito cohort, we sought to probe the range of natural variability mosquito may display, from species to sub-species, colonies, and individual replicate populations.

Monitoring nocturnal and diurnal species

We first compared the activity patterns of Ae. aegypti to a closely related mosquito species, Aedes albopictus and a more distant species Anopheles stephensi (Fig.2A). As expected, we observed major differences in both the timing and amplitude of activity throughout the day, An. stephensi was mostly active during the night, whereas Ae. aegypti and Ae. albopictus were completely inactive at night. On the other hand, closely related species like Ae. aegypti and Ae. albopictus have a globally similar timing of flight activity, yet Ae. albopictus showed much higher total activity. These results demonstrate that our platform is compatible with a large variety of different mosquito species and recovers the known difference between key species.

Figure 2.

Mapping the behavior of 10 geographically diverse Ae. aegypti colonies to investigate sub-species differences

We investigated differences among populations of the same species by examining 10 laboratory colonies of Ae. aegypti isolated from different geographical locations (Noah H. Rose et al. 2020), representing two subspecies: the native African subspecies Aedes aegypti formosus (Aaf) and the globally invasive subspecies Aedes aegypti aegypti (Aaa), which specializes in biting humans and breeding in human habitats (Fig.2B). The human-adapted Aaa subspecies diverged from its African ancestor around 5,000 years ago (Noah H Rose et al. 2023) and spread out of Africa during the Atlantic slave trade (Powell and Tabachnick 2013). While genetic signatures of Aaa adaptation to human habitats are emerging (Lozada-Chávez et al. 2025), observed behavioral differences between the two subspecies remain largely restricted to host preference (McBride 2016). This panel of colonies provides an ideal testbed to quantify potentially subtle behavioral differences between Ae. aegypti subspecies under consistent conditions. We monitored 40 mosquitoes from each colony over 10 days and performed multiscale analyses of flight behavior. All colonies exhibited the characteristic “Aedes aegypti” pattern with subtle, colony-specific variations (Fig.2D). To quantify differences at colony and subspecies levels, we developed two complementary statistical approaches: a local “interval-based” method using generalized mixed models and a global “pattern-based” method employing dimensionality reduction.

Interval-based approach reveals that Aaa are more active than Aaf during midday

For the local interval-based approach, we divided the 24-hour day into one-hour intervals and applied a generalized linear mixed model (GLMM) to each interval to analyze the average fraction of mosquitoes flying. In these models, subspecies was a fixed effect, replicate cage was a random effect, and individual days were treated as different realizations of the same variable (see methods). For each test, we report the z-score and p-value comparing Aaa and Aaf based on the time of day (Fig.2C). Aaa flew significantly more during midday (p-value < 0.01) and somewhat less during the night (p-value < 0.05), with no difference observed during morning or evening activity peaks.

We repeated this analysis for additional behaviors like sugar feeding, flight duration, and speed as described above. We developed “barcode plots” (generated automatically within the GUI app) that summarize all behavioral statistics stratified by hour, showing significant z-scores (p-value < 0.05) across all time intervals and variables (Fig. 2E). Aaa colonies exhibited increased sugar feeding activity, flight speed, and flight duration compared to Aaf. Despite significant changes at certain times, the actual differences were modest except for midday (ZT2-ZT10)flying fractions and flight duration, where differences were clearly larger than colony-level variation (Fig.S5). We further examined these two variables averaging over the same interval (ZT2-ZT10) for each colony (Fig.2F) and found a moderate positive correlation (ρ = 0.51), linking longer flights to increased flying percentages.

To explore differences within subspecies, we compared specific Ae. aegypti colonies using GLMM (KUM and RAB for Aaf; KPP and PHN for Aaa) finding small but significant variations in flight activity. For example, the PHN colony was more active at night than KPP, while RAB was more active between ZT3-ZT9 than KUM (Fig.S6A,B). These differences may reflect local adaptation of each population to specific environmental conditions.

Pattern-based approach confirms difference between Aaa and Aaf colonies

In addition to our GLMM analysis, we employed dimensionality reduction to uncover broader patterns in daily flight activity. Unlike GLMM, which analyzes each hour independently, dimensionality reduction captures patterns based on relative changes throughout the day. We used principal component analysis (PCA) to transform high-dimensional flight statistics into a low-dimensional space. Briefly, each day is represented as a ‘day vector,’ capturing 96 features related to the average, minimum, maximum, and standard deviation of flight activity across 1-hour intervals. PCA embeds these day vectors in two dimensions, revealing global patterns in mosquito flight activity. This approach produced distinct clusters for Aaa and Aaf colonies (Fig.2G), indicating global differences in their daily activity rhythms. We applied linear discriminant analysis to the PCA-reduced data (Fig.2H), identifying midday activity (ZT2-ZT10) as the key differentiator between the subspecies (Fig.2I), aligning with the results of our interval-based GLMM approach (Fig.2C).

Applying the local interval-based, and global pattern-based approach to quantify and visualize the activity patterns of all (sub)species, provides a comprehensive perspective on how daily rhythms vary across species, subspecies, and colonies, highlighting the integrated nature of these patterns (see Fig.S6D).

These two methods enable us to compare behavioral variables such as flight activity, sugar feeding, and flight duration within a unified framework, refining our hypotheses about observed differences. Notably, both techniques showed that human-adapted Aaa populations exhibit higher midday flight activity (ZT2-ZT10), a period typically marked by low activity in Aedes aegypti. Comparisons involving sugar feeding and flight duration, along with daily correlations, suggest that increased midday activity may be due to higher overall metabolism rather than specific circadian rhythm regulation.

Quantifying the impact of physiological and environmental perturbations

Next, we investigated the impact of physiological and environmental perturbations on daily rhythms. Outside the laboratory, adult mosquitoes typically experience significant and complex changes in their surrounding environment and physiological states through natural behaviors like blood-feeding, or external perturbations like light pollution.

BuzzWatch provides an ideal framework to quantify the flight behavior of mosquitoes for several days or weeks before and after a given perturbation, with the potential to reveal long-term consequences. To demonstrate this idea, we present two examples of such “perturbation experiments”: one where we monitor the impact of ingesting a blood meal, and another where we examine the impact of an increase in day length.

Blood feeding has a long-term impact on activity patterns

We explored how a blood meal affects the daily rhythm of female mosquitoes. We tracked the activity of blood-fed female mosquitoes and non-fed controls over 19 days (Fig.3A). Consistent with previous studies (for instance in (Lima-Camara et al. 2014)), blood-feeding caused a 2-day period of strongly reduced activity. Beyond this period, we used the interval-based GLMM approach to analyze the impact of blood feeding on flight activity over the period 3-12 days post blood meal (days 10-19) (Fig.3B). Compared to the control, blood-fed mosquitoes showed a slight decrease in activity after the morning peak (ZT1-ZT5) and an increase in activity before the evening peak (ZT10-ZT11) (Fig.3C). There were no significant changes in overall flying time, sugar feeding, flight duration, or speed, suggesting subtle rhythm changes rather than major physiological shifts.

Figure 3.

To assess the stability of these changes, we expanded our statistical approach, using a 5-day moving window instead of a fixed 10-day period. Each row in the heatmap shown in Figure 3D represents the median day of the window, with columns showing hourly intervals. This analysis confirms that the observed behavioral changes were stable over the 10 days after blood ingestion, with no decrease or increase in the magnitude of the change over time (Fig.3E). These findings indicate that, after a brief period of rest, blood ingestion has a moderate but persistent effect on mosquito flight activity patterns.

Next, we examined whether egg-laying could reverse these stable changes in flight activity patterns. Without an oviposition site, as was the case in the previous experiment, females may retain eggs which could explain the subtle yet long-lasting effect on mosquito behavior. To test that hypothesis, we allowed blood-fed females to lay eggs over a period of 6 days, measured their activity for the next 10 days and compared this to blood-fed females that did not have access to an oviposition site (Fig.3F, and Fig.S7A). We observed that egg-laying altered flight patterns in subsequent days, with increased activity from ZT2-ZT4 and decreased activity from ZT8-ZT12 (Fig.3G). Remarkably, this pattern mirrors changes seen after blood ingestion. Comparing the effects of blood feeding and egg-laying over the same time intervals, shows that evening flight changes were reversed, while morning changes were only partially reversed (Fig.3H). This suggests that egg-laying after blood feeding partially returns the mosquito to its original pre-blood-feeding activity pattern.

Complex response to photoperiod change

By feeding on humans, species like Ae. aegypti can be exposed to artificial light that may disrupt the natural rhythmic patterns shaped by sunlight which evolved over millions of years (Taylor and Jones 1969; Baik et al. 2020; Rund et al. 2020). An unanswered question is the extent of their phenotypic plasticity, specifically how quickly they adapt to these changes. As a proof of concept, we used BuzzWatch to simulate a shift from a “natural” 12-hour light/12-hour dark cycle, typical of rural areas near the equator, to a 20-hour light/4-hour dark cycle, simulating the photoperiod of urban areas. We monitored mosquitoes for 12 days under the natural cycle, then switched to the urban cycle for 10 more days (Fig.4A). After the change, mosquitoes changed from a two-peak activity rhythm (4B) to a pattern with three or four peaks (4C), illustrating their phenotypic plasticity. Among the three peaks, two clearly matched the start (ZT0) and end of the light period (ZT20), whereas an additional peak was observed around ZT14 (ZT10 in previous 12L-12D regime), not corresponding to any of the former or new light-dark transitions (Fig.4C; Fig.4D second row). Using GLMM analysis, we found that increased daylight significantly altered flight activity and reduced flight speed and duration, yet did not affect sugar feeding (Fig.4D).

Figure 4.

Beyond these immediate changes, we investigated finer behavioral shifts on longer time scales. Initially, total flight activity surged after the photoperiodic change but gradually returned to levels similar to the previous regime within 6-7 days (Fig.4E). This suggests a gradual, week-long adjustment during which mosquitoes redistribute their flight activity. To explore this further, we applied the global dimensionality reduction analysis by comparing 9 days in each photoperiod (Fig.4F). We observed a clear separation along a first axis (close to component one), corresponding to major changes in flight rhythm already detected by GLMM approach (Fig.4G-H red line). Surprisingly, in both photoperiod regimes, days structured themselves along a second axis (close to component two). Over time, days gradually move upwards along this second axis in the 12L-12D regime and downwards in 20L-4D regime (Fig.4F). The second axis (blue line in Fig.4H) primarily reflects changes in total activity (as seen in Fig.4E), alongside subtle adjustments in flight rhythm. A complete absence of rhythm change would appear as a flat blue line in Fig.4H. A possible interpretation is that mosquitoes initially aligned with the 12L-12D cycle retain a “memory” of it, before gradually shifting under new conditions.

Overall, this study revealed two aspects of the plastic response of mosquitoes to photoperiodic change: rapid rhythm changes within 1-2 days, and slower, refined adjustments over weeks. These results underscore the complex temporal aspect of phenotypic plasticity of mosquito flight behavior in response to environmental changes.

Measuring the response to pulse of host-cues at different times of the day

Next, we used our platform to quantify mosquito responses to short pulses of host cues. Previously, we measured “spontaneous” flight activity without host cues. While it is unclear if this is driven by a quest for hosts, increased activity may certainly contribute to host-seeking by raising the chances of encountering a host or detecting its cues. However, when mosquitoes are inactive, such as at night or midday (Fig.1D), their response to host cues is uncertain. Here, we focused on CO₂ and heat for their consistency and reproducibility (Sorrells et al. 2022; McMeniman et al. 2014). We designed a system controlled by a Raspberry Pi board to deliver controlled pulses of CO₂ and heat at user-defined intervals. This system includes a CO₂ canister, a “gas mixing” chamber with a solenoid valve, an air pump, and a Peltier module to heat a small area of the cage (Fig.5A). We observed that 30 seconds of CO₂ followed by 4.5 minutes of heat effectively attracted mosquitoes for several minutes. While pulse parameters can be adjusted, we used this 5-minute sequence consistently and refer to it as a “single host-cue pulse.”

Figure 5.

Response to a single pulse of host cues

Starting with a “single pulse” experiment, we examined mosquito responses to CO₂ and heat. We quantified the fraction of flying mosquitoes and their distribution over several surfaces (heated, sugar-feeder, and controls, see Fig.5B-C). Immediately after the pulse, flight activity surged, slowly decreasing over several minutes (Fig.5B top). Mosquitoes quickly gathered at the heated area, while other areas showed no change, or a reduction in occupancy (Fig.5B middle). While not encompassing the full complexity of blood feeding behavior, this experiment shows that monitoring mosquito distribution over time reliably quantifies responses to host cues serving as a proxy for host-seeking behavior (Supp. Movie 1, mosquito inserting their proboscis through the acrylic holes in response to the heated surface).

Host-seeking response at different times of the day

We asked how the response to pulses of host cues varied throughout the day. As previously observed, in the absence of host cues Ae. aegypti flight activity is virtually absent during midday and nighttime (Fig.2, Fig.5D). To explore if Ae. aegypti responds to host-associated cues during these apparent “resting” times, we tested four stimulations daily at ZT-8, ZT-4, ZT4 and ZT8 over nine days to quantify the behavioral response (Fig.5D). We stimulated triplicate cages containing 40 Ae. aegypti females with this pulse regime, measuring total flight activity and attraction to the heated surface (as in Fig.5B). We analyzed peak responses in a 10-minute window after the pulse, smoothing data with a 1-minute average (Fig.5F). Responses were consistent for a given time of day, differed greatly between day and night, and varied minimally within those periods (Fig.5E-F). Flight activity and attraction were 2-3 times higher during the day (Fig.5E). Importantly, even at night 10% of mosquitoes showed increased activity in response to the stimulus, a level of activity comparable to the evening peak without stimuli. However, nighttime attraction to heat was modest, sometimes similar to control surface fluctuations, unlike daytime responses.

By expanding BuzzWatch with a module to consistently deliver host-associated cues, we showed that strength of the responses to CO₂ and heat varies throughout the 24-hour cycle, yet responses are consistent across days at specific times. Even at times when mosquitoes typically rest, they respond measurably to stimulation, although Ae. aegypti’s host-seeking response is approximately twice as high during the day compared to night. This suggests that the host-seeking response is heavily influenced by circadian rhythms, in ways that cannot be solely explained by baseline flight activity. This proof of concept demonstrates that BuzzWatch can effectively characterize mosquito responses to host cues.

Discussion

BuzzWatch establishes a novel approach to longitudinally study multi-scale temporal aspects of mosquito flight activity. We developed a comprehensive methodological pipeline that encompasses designing cages, setting up mosquito recordings, automatically extracting flight tracks from video footage, and analyzing these tracks to effectively quantify mosquito activity over weeks in a tightly controlled, user-defined environmental setting. BuzzWatch enables researchers to gather longitudinal, rich population-level datasets, allowing comprehensive analyses of mosquito daily rhythm, phenotypic plasticity, and responses to environmental cues.

Flight is fundamental to initiating key behaviors in adult mosquitoes, such as sugar feeding, host seeking, mating, and oviposition. Monitoring such behaviors over weeks presents the challenge of tracking flight effectively. Previous studies used high-precision multi-camera 3D flight tracking to characterize short-term mosquito flight behaviors such as attraction to human cues during host-seeking and environmental interactions (Gupta et al. 2024) (van Breugel et al. 2015). However, sophisticated multi-camera setups are not used to characterize behaviors over longer periods of time as it would quickly generate impractical amounts of data requiring massive computational resources for analysis. The complexity of multi-camera 3D tracking setups furthermore requires specific laboratory expertise and considerable financial resources. While obtaining high-resolution tracking data of the intricate 3D maneuvers characteristic of mosquito flight is essential in some contexts, a wide variety of behaviors can be assessed without this level of detail. With BuzzWatch, we therefore opted for the approach of using a single low-cost camera to monitor flight behaviors of cohorts of mosquitoes, and developed analysis tools to extract key behavioral metrics from movies spanning hundreds of hours. While the full 3D flight track is reduced to a 2D projection in our setup, it allows accurate long-term assessment of activity patterns, sugar feeding behavior, responses to host cues, and certain flight statistics. The BuzzWatch setup is low-cost and can be constructed from readily available materials, making it a scalable approach to run several month-long replicate experiments in parallel, a capacity that is out of reach for current multi-camera 3D flight tracking setups.

In contrast to camera-based approaches that monitor freely flying mosquitoes, tube-based locomotor activity monitoring systems like the commonly used Drosophila Activity Monitor (DAM) (Chiu et al. 2010) use motion induced beam breaks to quantify activity. These systems, and camera-based derivatives (e.g. (Sondhi et al. 2022) and Araujo, Guo, and Rosbash 2020), are easy to set up and compatible with monitoring mosquitoes over several days. However, activity in these systems is only detected when a moving insect blocks a light beam (likely underestimating true activity, see (Keleş et al. 2025)). The obtained data is therefore limited to counting “active” versus “inactive” states while not providing locomotion statistics (e.g. duration and speed of movement), nor do they provide insight regarding when an insect visits a specific area of interest such as a sugar feeder, or a surface presenting host-associated cues. These assays furthermore typically constrain animals in narrow tubes or 24-well plates, severely restricting movement and preventing flight, fundamental to many mosquito behaviors. Compared to multi-camera 3D flight tracking approaches on the one hand, and beam-block activity monitors on the other, BuzzWatch provides an affordable and scalable alternative for accurate long-term activity monitoring of cohorts of freely flying mosquitoes, and assessment of key behaviors such as responses to host cues, and sugar feeding. BuzzWatch incorporates a comprehensive downstream pipeline to rigorously analyze mosquito behavior across multiple timescales. To empower researchers to rigorously test hypotheses using advanced statistical tools, we provide an extensive GUI application that facilitates statistical analysis, enabling reproducible comparisons between different conditions and investigating emerging patterns in temporal data. We implemented two complementary approaches: a local “interval-based” analysis using GLMMs and a global “pattern-based” analysis using dimensionality reduction techniques. With BuzzWatch we establish an integrated open-source hardware and software pipeline from cage design to statistical analysis of behavior. While we optimized each step for our studies, we adopted a modular and flexible approach using generic and low-cost parts to enable adoption and adaptation by others.

Origins and implication of changes in mosquito flight-activity patterns

By comparing diverse populations of Ae. aegypti, we found that the Aaa subspecies exhibits more midday flight activity and increased sugar feeding compared to the Aaf subspecies. All experimental colonies had been maintained in laboratory conditions for only 15-30 generations (see Table1 and supplementary file 1). Previous studies on rhythmic activities used older lab colonies of Aaa, complicating direct comparisons (Ajayi et al. 2024). Known differences between Ae. aegypti subspecies include higher susceptibility to arbovirus infection for Aaa (Aubry et al. 2020) and increased preference for human blood meals and human-associated oviposition sites (Powell and Tabachnick 2013; McBride 2016). Our data suggest that higher midday flight activity of Aaa reflects longer flights and increased sugar feeding, indicating possible physiological differences. Whether this behavior is directly related to the adaptation of Aaa to human habitats remains to be investigated. To gain more insight into the origin of the changes in flight rhythm, future research could leverage genomic data comparing multiple Aaa and Aaf populations (Lozada-Chávez et al. 2025) to identify genes associated with flight rhythm or metabolic differences. It would be interesting to investigate whether the higher midday flight activity of Aaa translates into elevated response to host-cues during midday. Indeed, recent studies show that temporal patterns of locomotor activity and host-seeking response are determined by genetic factors in Ae. aegypti (Dong et al. 2024).

BuzzWatch and phenotypic plasticity in mosquitoes

In response to physiological changes, like blood ingestion, and environmental shifts, such as a sudden photoperiod increase, we observed a rapid initial shift in behavior followed by subtle long-term adjustments or stability. Further research is needed to determine if these findings reflect the general robustness and plasticity of mosquito behavior in changing environments. Specifically, BuzzWatch is a potent tool for addressing public health issues linked to mosquito phenotypic plasticity. Indeed, as major vectors of human pathogens, Ae. aegypti and Anopheles mosquitoes are often exposed to control measures like insecticides and traps. Several field studies have reported behavioral shifts that enable mosquitoes to escape these control measures, threatening their long-term efficacy (Carrasco et al. 2019). To understand how such “behavioral resistance” to interventions evolves, it is crucial to determine whether these traits are constitutive or induced (i.e., phenotypically plastic). We foresee BuzzWatch as a promising tool to rigorously quantify behavioral resistance to interventions like insecticides and shedding light on its origins.

Ae. aegypti and Anopheles mosquitoes also face pathogen infections over approximately two weeks, during which pathogens replicate and spread through the organism. The long-term effects of these infections, especially regarding arboviruses (Maire, Lambrechts, and Hol 2024), remain unclear. The BuzzWatch platform could be instrumental in tracking the flight behavior of Plasmodium- and arbovirus-infected mosquitoes in the weeks following an infectious blood meal.

Overall, BuzzWatch represents a significant advancement in the study of mosquito behavior, providing an integrated, open-source platform that enhances our understanding of phenotypic plasticity and adaptive responses and holds promise for contributing to effective public health strategies in combating mosquito-borne diseases.

Methods

Cage design and fabrication

Cages were created from acrylic (Richardson) using a laser cutter (Trotec Speedy 300). Cage designs were adapted from boxes created using boxes.py (https://boxes.hackerspace-bamberg.de/). Cage parts and supports were either glued with commercial superglue or with dichloromethane-based acrylic adhesive (Acrodis, Sunclear ref029019). Three millimeter thick acrylic was used for all cage parts, except for the perforated side windows covering the sugar feeders which were made out of 1.5 mm thick acrylic in order to allow mosquito to easily reach the sugar cotton by inserting their proboscis through 1 mm diameter holes. For the raspberry pi camera to record mosquito activity, transparent acrylic has to be used for the bottom part of the cage. For all the other parts, either transparent or white diffusive acrylic can be used to improve image quality. In order to create a uniform visual background, white paper was placed on top of the cage. An infrared LED light source (Andoer IR49S LED, usb-c powered) was placed 20 cm above each cage, to ensure constant and homogenous lighting for video recording independent of variable visible light intensities. A Raspberry PI V2 NOIR 8MP camera was placed 20 cm below each cage to record the activity of all mosquitoes within the cage. Camera focus was adjusted manually so that the both the bottom and the top of the cage were equally sharp, to minimize bias in tracking mosquitoes located at different distances from the camera. A 850 nm infrared long-pass filter (Thorlabs FEL0850) was placed in front of the camera lens so that the camera sensor only received infrared light, blocking all visible wavelengths. This assures that background image intensity and contrast remain constant throughout the days, facilitating analysis. See the BuzzWatch website for design files and extensive tutorial on construction. Four cages were placed in an enclosure (600mm*750mm*750mm) constructed from 3 mm white opaque acrylic and aluminum rail profiles (see Fig.S1). Two RBG LEDs strips connected to a Raspberry Pi (NeoPixel RGB 1m 60 LEDs ADA1138) were installed inside the container to control the daylight cycle. A python script using the neopixels module controlled the light intensity of all LEDs in the strip, according to a pre-defined day/night cycle with 3-hour gradual dimming. Temperature, Humidity sensors (DHT11) as well as a light sensor (TSL2591) were placed inside the container for continuous logging.

Video recording and storage

Each camera was connected to a Raspberry Pi 4B+ micro-computer, which was programmed to automatically record videos in h264 format. Videos were stored in 20-minute segments on the micro-SD card. Cron scheduling rebooted the Raspberry Pi automatically every 12 hours, converted the h264 files on the SD card to mp4 format, and transferred all mp4 files to an external SSD. Video recording settings were manually adjusted before the start of recording using the Python pirecorder module (Jolles 2020) interface and kept constant during the experiment. A Python script utilizing the pirecorder module handled the recording and conversion to .mp4. At the conclusion of the experiment, all .mp4 videos (approximately 200-400 GB) were transferred to a server or a local workstation for analysis. An example image of the SD-card with all settings is available for download.

BuzzWatch GUI app for mosquito tracking and data analysis

We developed a cross-platform graphical user interface app in Python to streamline both the tracking of mosquitoes and the subsequent analysis of mosquito behavior.

Mosquito tracking

Our analysis pipeline employs standard computer vision techniques, such as background subtraction and thresholding, to segment mosquitoes from the cage background. A clean background image is generated by averaging 100 frames from 100 consecutive 20-minute videos, spanning over 30 hours, ensuring no mosquitoes are visible in the background image. This clean background is crucial as mosquitoes typically move at least once within 24 hours. Two distinct parallel operations are performed to track resting and flying mosquitoes. Resting mosquitoes are identified by subtracting the background from all frames, followed by blob detection to segment and track centroids. A greedy algorithm processes these centroids to form tracks of resting mosquitoes, capturing both stationary and slow-moving individuals. For flying mosquitoes, the previous frame is subtracted—a standard motion detection method—followed by segmentation and centroid tracking optimized for flying mosquitoes. A custom algorithm links tracks of resting and flying mosquitoes to identify take-off and landing events. The algorithm performs a local search to find matching pairs, assuming spatial proximity between the end of a resting track and the start of a flight track for take-off events, and vice versa for landings. This bootstrapping procedure is iterated five times to enhance matching accuracy, an minimize identity swaps. Importantly, identity swaps do not compromise the extraction of population-level variables, such as the fraction of mosquitoes flying or resting on specific surfaces, such as sugar feeders. Final mosquito tracks are stored as pickle files for each analyzed video, containing coordinate data and IDs for 40 mosquitoes at 25 frames per second, with file sizes typically ranging from 20–30 MB.

Data analysis, exploration, and visualization

Unless specified otherwise, for all population level data (fraction flying; fraction sugar feeding) we applied the same normalization procedure: time-series were resampled to 1-minute intervals, normalized by the total number of alive mosquitoes, and smoothed by a 20-minute rolling window. For the “day-relative fraction flying” we further normalized by the sum of the fraction flying over a given day from 0h00 to 23h59 (area under the curve).

Interval-based GLMM analysis

To assess the impact of various conditions on mosquito activity at specific times of the day, we employed a generalized linear mixed model (GLMM). We divided each day into short time intervals (e.g., 20 minutes) and calculated the average value of mosquito activity variables within these intervals, such as the average proportion of mosquitoes flying between 12:00 and 12:20. The model is formulated as follows:

Where:

• Y_ij represents the outcome for the i-th observation within the j-th experiment.

• β₀ is the intercept, representing the baseline level of activity.

• β₁ ×Condition_ij denotes the fixed effect of the condition being tested (e.g., blood-fed vs. non-blood-fed).

• u_j is the random intercept for the j-th experiment, modeled as u_j ~ 𝒩 (0, σ_u), accounting for variability between replicates.

• ϵ_ij is the residual error, assumed to be ϵ_ij ~ 𝒩 (0, σ²).

This model does not explicitly account for specific day-to-day effects; values from different days are treated as separate realizations of the same statistical variable. Each mosquito activity variable for each time interval is modeled independently, meaning cross-correlations between time intervals or effects spanning different intervals are not directly addressed.

To define and fit each Generalized Linear Mixed Model (GLMM), we used the Python module MixedLM from statsmodels.regression.mixed_linear_model, with method = ‘lbfgs’, maxiter = 500, and used the summary output to extract the coefficient, standard error, p-value, and z-score (and confidence interval). The z-score is defined as the coefficient divided by its standard error.

As an example, for Fig. 2 and the Ae. aegypti sub-species analysis, the GLMM is formulated as follows:

where:

• β₀ is the intercept,

• β₁ × (1_Aaa/Aaf) represents the fixed effect,

• u_j is the random effect,

• ϵ_ij is the residual noise.

Pattern-based dimension reduction analysis

To compare activity patterns between days, replicates, or conditions, we used dimensionality reduction. As for the GLMM model, we divided each day into non-overlapping intervals of one hour (interval can be changed in the GUI). Each day was represented as a high-dimensional vector consisting of 96 features, detailing the average, minimum, maximum, and standard deviation of flight activity variables for each 1-hour interval. We referred to these as “day-vectors”. To facilitate comparison between different day vectors, we normalized the data for mean and standard deviation (across the ensemble of day vectors considered) and applied dimensionality reduction using principal component analysis (PCA) (in the GUI app one can alternatively use UMAP or t-SNE). This allowed us to visualize day-vectors in a 2D space, where the two axes are the principal components capturing the greatest variance. Two day-vectors positioned closely in this reduced space indicate a “globally” similar daily activity pattern. Note that the relative positioning depends on the specific PCA axes that were computed. Importantly, PCA is independent of labels assigned to day-vectors (like different colonies). Therefore, to compare two groups of day-vectors, such as different subspecies, we applied Linear Discriminant Analysis (LDA) on the PCA-reduced coordinates. This identifies the axis that best separates the two groups. To interpret this separation, we back-transformed the LDA axis into time-of-day coordinates. This was possible because PCA axes are linear combinations of the original 96 dimensions. The relative contributions (weights) of each dimension were considered, and contributions were grouped by time intervals by selecting the highest contribution from the four statistics (average, min, max, and std) for each interval. This way, contributions can be represented as function of the time of day. This approach, using PCA-reduced space, offers a robust way to discern differences between groups by accounting for overall variance and structure among all day-vectors. This procedure can be applied to any PCA-derived axis, such as the first or second principal components, the LDA axis, or the axis orthogonal to the LDA axis, as illustrated in Fig.3G-H.

Mosquito rearing

The mosquito species/strains used in this study are described in Table 1. Ae. aegypti and Ae. albopictus mosquitoes were reared at Institut Pasteur. Eggs were hatched in dechlorinated tap water in a vacuum chamber for 45 minutes. Then 200 newly hatched larvae were transferred to a plastic tray filled with 1.5 liter water. Larvae were kept at 28°C, 40% relative humidity on a standard diet of fish food (Tetramin, Tetra). Fish food was added on the first day after hatching, and a second time after 3 days. After 6-7 days, pupae were collected in a 10cm wide, 15cm high plastic container with clean water and placed in BugDorm-1 cages (BugDorm) for adult emergence. Emergence cups were removed after 4 days. Adult Aedes mosquitoes were maintained at 28 ± 1^°C, 75% relative humidity, and a photoperiod of 12 hr light : 12 hr dark in 30 × 30 × 30 cm screened BugDorm-1 cages having continuous access to 10% sucrose, without separating males and females. Anopheles stephensi were reared at Radboudumc, Nijmegen under similar temperature, humidity, and diurnal cycle conditions, with continuous access to 5% glucose.

BuzzWatch experiment

Three to five days after emergence, Aedes mosquitoes were aspirated and knocked-down on ice for 10 minutes. Females were selected and counted in a petri dish on ice. Once all females were sorted in one petri dish, they were transferred inside an acrylic BuzzWatch cage that was immediately closed with screws. An. stephensi females were aspirated directly into the BuzzWatch cage. The sugar feeders were filled with cotton soaked with 10% sucrose solution, excess liquid was absorbed with paper and feeders were placed carefully on the side of each cage (Fig.S3), supported by elastic bands. Cages were placed inside the setup (Fig.S1) for recording.

Specific protocol Fig.1 and Fig.2

One cage containing 40 Ae. aegypti females strain KPP aged 3-5 days old was monitored for 32 days. A single sugar feeder was placed on the side of the cage and was changed weekly. One cage containing 40 Ae. aegypti females strain KPP aged 3-5 days old was monitored for 32 days. A single sugar feeder was placed on the side of the cage and was changed weekly.

Specific protocol Fig.3 blood feeding (see also Fig.S7 for egg-laying)

For the blood-feeding experiment, 4 cages each containing 40 Ae. aegypti KPP females aged 3-5 days old were monitored in parallel for 19 days. At day 6, all cages were removed from the recording platform and brought to the blood-feeding room for 1 hour (17h-18h). Rabbit blood was provided with a membrane feeder heated to 37C to Cage #1 and Cage #4; 39/40 (Cage#1) and 40/40 (Cage#4) mosquitoes engorged (verified by visual inspection). No blood was provided to control Cage #2 and #3. All 4 cages were returned to the BuzzWatch platform and recording resumed.

For the egg-laying experiment, mosquitoes were reared in large bug dorm cages with males and females together for 3-5 days. Females were then aspirated, kept on ice in a 4°C fridge for 10 minutes, and sorted with tweezers. Approximately 360 females were sorted into boxes (60 females per box) and maintained without sugar cotton overnight. The next day, all mosquitoes were offered a blood meal using a membrane feeder. Immediately after feeding, boxes were placed on ice for sorting. Well-fed females, distinguished by visible blood in the abdomen, were sorted and placed in small bug dorm cages (60 per cage). Cotton soaked with 10% sucrose was placed on top of each cage to allow sugar feeding while preventing egg laying on the cotton (which may occur if it is placed inside the cage). After two days, egg cups with absorbent paper (ref) were placed in two cages to allow egg-laying, while nothing was added to the control cages. After four more days, the egg cups were removed, and the cages were placed on ice in a 4°C fridge for 10 minutes. Forty females per cage were sorted, placed in a petri dish, and then transferred to a BuzzWatch cage. The sugar feeders were changed weekly week during the subsequent 21 days of continuous monitoring. Inspection of the sugar feeder cotton (placed behind a 1mm diameter and 1.5mm width acrylic pierced grid) showed no eggs, consistent with previous observations that mosquitoes do not lay eggs through these holes.

Specific protocol 4 light cycle change

Four cages each containing 40 Ae. aegypti KPP females aged 3-5 days old (from the same rearing batch, prepared as in protocol 1) were monitored in parallel for 23 days. At day 13, the light-cycle was changed from 12h light – 12 hours dark to 20 light – 4 hours dark. One sugar feeder was used per cage, changed weekly.

Specific protocol 5 host-seeking

A cage containing 40 Ae. aegypti KPP females aged 3-5 days old were prepared as in the Fig.1 protocol. After 5 days adaptation to the set-up, the cage was submitted to host-cue pulses for 5 minutes at 4 fixed times (ZT-8; ZT-4; ZT4 and ZT8) for 9 consecutive days. A sugar feeder was placed opposite to the host-cue delivery window, changed 1 day before the host-cue stimulation subsequently not replaced for 10 days. The experiment was repeated 3 times (different mosquitoes and different replicate cages).

Code and Data availability

Webpage with tutorials: https://theomaire.github.io/buzzwatch/

Graphical user app repository: https://github.com/theomaire/BuzzWatch_app_v2

Repository with all processed data to run analysis in the BuzzWatch analysis app :

Acknowledgements

We thank Catherine Lallemand (Pasteur) and Geert-Jan van Gemert (Radboud UMC) for assistance with mosquito rearing. We are grateful to all members of the Lambrechts and Hol labs for their insights and feedback during this project, and comments on the manuscript. We are grateful to Noah Rose, Carolyn McBride, Jewelna Akorli, Sampson Otoo, Joel Lutomiah, Rosemary Sang, Massamba Sylla, Martin Mayanja, Julius Lutwama, Alain Kohl, Alongkot Ponlawat, Veasna Duong, Claudia Romero-Vivas, Isabelle Dusfour, and Anubis Vega-Rúa, for their contributions in establishing the Ae. aegypti colonies. We thank members of the FabLab of Institut Pasteur for technical assistance with laser cutting acrylic and structural elements of the container.

Additional information

Funding

This work was supported by a VIDI (grant VI.Vidi.213.167) from NWO (the Dutch science foundation), a Radboudumc Hypatia Fellowship, the French Government’s Investissement d’Avenir program Laboratoire d’Excellence Integrative Biology of Emerging Infectious Diseases (grant ANR-10-LABX-62-IBEID), and the Inception program (Investissement d’Avenir grant ANR-16-CONV-0005). The study has received resources funded by the European Union’s Horizon 2020 research and innovation program under grant agreement No 731060 (Infravec2). T.M. was supported by a Pasteur-Roux-Cantarini postdoctoral fellowship.

Contributions

T.M : Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft.

Z.W. : Data curation, Formal analysis, Validation, Methodology (Performed experiments and analysis with Anopheles mosquitoes and helped with development of the method)

L.L. : Resources, Project administration, Writing - review and editing, Funding acquisition.

F.J.H. : Conceptualization, Investigation, Resources, Writing - original draft, Project administration, Funding acquisition.

Funding

Dutch Research Council (VI.Vidi.213.167)

Radboud University Nijmegen Medical Centre (Hypatia Hol)

Agence Nationale de la Recherche (ANR-10-LABX-62-IBEID)

Agence Nationale de la Recherche (ANR-16-CONV-0005)

European Commission

https://doi.org/10.3030/731060

Institut Pasteur (Pasteur-Roux-Cantarini postdoctoral fellowship)

Additional files

Supp. Movie 1

Supplementary text

Flight Speed from 2D vs 3D Trajectories

In our study, we analyze 2D flight trajectories of mosquitoes from BuzzWatch video recordings, which are projections of their actual 3D trajectories. This leads to an underestimation of the average flight speed as the displacement in the z-direction (perpendicular to the camera’s focal plane) is unaccounted for.

Assuming isotropic flight, where flight speed is uniformly distributed across the x, y, and z axes, we estimate that the 2D measured speed v_2D is related to the actual 3D speed v_3D by:

This conversion factor of derives from the geometric projection of a 3D vector onto a plane. To see that, let us consider a unit vector v in spherical coordinates with θ the polar angle and ϕ the azimuthal angle (https://en.wikipedia.org/wiki/Spherical_coordinate_system) :

When projected onto the xy-plane, the z-component is ignored, yielding:

The magnitude of this projection is:

To find the average projection length over all orientations, we integrate over the unit sphere. The elemental surface area in spherical coordinates is sin θ dθ dϕ. Thus, the average projection L_avg is:

Utilizing [, we find:

Evaluating from 0 to π:

The integration over ϕ results in 2π, thus:

Therefore, the average projection length of a unit vector onto a 2D plane is , supporting the conversion factor used.

Supplementary Figures

Figure S1.

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Figure S7.