Ecology

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Acoustic measurementsA set of acoustic echo sounder data was used to analyze fish density. This was collected within the Mycto-3D-MAP program using split-beam echo sounders at 38 and 120 kHz. The Mycto-3D-MAP program included multiple large-scale oceanographic surveys during 2 years and a dedicated cruise in the Kerguelen area. The dataset was collected during 4 large-scale surveys in 2013 and 2014, both in summer (including both northward and southward transects) and in winter, corresponding to 6 acoustic transects of 2860 linear kilometers (see Table 1 for more details). Note that all legs except summer 2014 (MYCTO-3D-Map cruise) were logistic operations, during which environmental in situ data (such as temperature or salinity profiles) could not be collected. The data were then treated with a bi-frequency algorithm, applied to the 38 and 120 kHz frequencies (details of data collection and processing are provided in37). This provides a quantitative estimation of the concentration of gas-bearing organisms, mostly attributed to fish containing a gas-filled swimbladder in the water column38. Most mesopelagic fish present swimbladders and several works pointed out that myctophids are the dominant mesopelagic fish in the region39. Therefore, we considered the acoustic signal as mainly representative of myctophids concentration. Data were organized in acoustic units, averaging acoustic data over 1.1 km along the ship trajectory on average. Myctophid school length is in the order of tens of meters40. For this reason, acoustic units were considered as not autocorrelated. Every acoustic unit is composed of 30 layers, ranging from 10 to 300 meters (30 layers in total).The dataset was used to infer the Acoustic Fish Concentration (AFC) in the water column. We considered as AFC of the point ((x_i), (y_i)) of the ship trajectory the average of the bifrequency acoustic backscattering of 29 out of 30 layers (the first layer, 0-10 m, was excluded due to surface noise) AFC quantity is dimensionless.As the previous measurements were performed through acoustic measurements, a non-invasive technique, fishes were not handled for this study.Table 1 Details of the acoustic transects analyzed.Full size tableRegional data selectionThe geographic area of interest of the present study is the Southern Ocean. To select the ship transects belonging to this region, we used the ecopartition of41. Only points falling in the Antarctic Southern Ocean region were considered. We highlight that this choice is consistent with the ecopartition of42 (group 5), which is specifically designed for myctophids, the reference fish family (Myctophidae) of this study. Furthermore, this choice allowed us to exclude large scale fronts (i.e., fronts that are visible on monthly or yearly averaged maps) which have been the subject of past research works43,44. In this way our analysis is focused specifically on fine-scale fronts.Day-night data separationSeveral species of myctophids present a diel vertical migration. They live at great depths during the day (between 500 and 1000 m), ascending at dusk in the upper euphotic layer, where they spend the night. Since the maximal depth reached by the echo sounder we used is 300 m, in the analysis reported in Figs. 2 and 3 we excluded data collected during the day. However, their analysis is reported in SI.1. A restriction of our acoustic analyses to the ocean upper layer is also consistent with the fact that the fine-scale features we computed are derived in this work by satellite altimetry, thus representative of the upper part of the water column ((sim 50) m). Finally, we note that the choice of considering the echo sounder data in the first 300 m of the water columns is coherent with the fact that LCS may extend almost vertically in depth even at 600 m depth45,46 and with the fact that altimetry-derived velocity fields are consistent with subsurface currents in our region of interest down to 500 m20.Satellite dataVelocity current data and Finite-Size Lyapunov Exponent (FSLE) processing. Velocity currents are obtained from Sea Surface Height (SSH), which is measured by satellite altimetry, through geostrophic approximation. Data, which were downloaded from E.U. Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu/), were obtained from DUACS (Data Unification and Altimeter Combination System) delayed-time multi-mission altimeter, and displaced over a regular grid with spatial resolution of (frac{1}{4}times frac{1}{4}^circ) and a temporal resolution of 1 day.Trajectories were computed with a Runge-Kutta scheme of the 4th order with an integration time of 6 hours. Finite-size Lyapunov Exponents (FSLE) were computed following the methods in14, with initial and final separation of (0.04^circ) and (0.4^circ) respectively. This Lagrangian diagnostic is commonly used to identify Lagrangian Coherent Structures. This method determines the location of barriers to transport, and it is usually associated with oceanic fronts9. Details on the Lagrangian techniques applied to altimetry data, including a discussion of its limitation, can be found in10.Temperature field and gradient computation The Sea Surface Temperature (SST) field was produced from the OSTIA global foundation Sea Surface Temperature (product id: SST_GLO_ SST_L4_NRT_OBSERVATIONS_010_001) from both infrared and microwave radiometers, and downloaded from CMEMS website. The data are represented over a regular grid with spatial resolution of (0.05times 0.05^circ) and daily-mean maps. The SST gradient was obtained from:$$begin{aligned} Grad SST=sqrt{g_x^2+g_y^2} end{aligned}$$where (g_x) and (g_y) are the gradients along the west-east and the north-south direction, respectively. To compute (g_x), the following expression was used:$$begin{aligned} g_x=frac{1}{2 dx}cdot (SST_{i+1}-SST_{i-1}) end{aligned}$$where the SST values of the adjacent grid cells (along the west-east direction: cells (i+1) and (i-1)) were employed. dx identifies the kilometric distance between two grid points along the longitude (which varies with latitude). The definition is analog for (g_y), considering this time the north-south direction and (dysimeq 5) km (0.05(^circ)).Chlorophyll field Chlorophyll estimations were obtained from the Global Ocean Color product (OCEANCOLOUR_ GLO_CHL_L4_REP_OBSERVATIONS_009_082-TDS) produced by ACRI-ST. This was downloaded from CMEMS website. Daily observations were used, in order to match the temporal resolution of the acoustic and satellite observations. The spatial resolution of the product is 1/24(^{circ }).Estimation of satellite data along ship trajectory For each point ((x_i), (y_i)) of the ship trajectory, we extracted a local value of FSLE, SST gradient, and chlorophyll concentration. These were obtained by considering the respective average value in a circular around of radius (sigma) of each point ((x_i), (y_i)) . Different (sigma) were tested (ranging from 0.1(^circ) to 0.6(^circ)), and the best results were obtained with (sigma =0.2^circ), reference value reported in the present work. This value is consistent with the resolution of the altimetry data.Statistical processingFront identification FSLE and SST gradient were used as diagnostics to detect frontal features, since they are typically associated with front intensity and Lagrangian Coherent Structures10. Note that the two diagnostics provide similar but not identical information. FSLEs are used to analyze the horizontal transport and to identify material lines along which a confluence of waters with different origins occur. These lines typically display an enhanced SST gradient because water masses of different origin have often contrasted SST signature. However, this is not a necessary condition. FSLE ridges may be invisible in SST maps if transport occurs in a region of homogeneous SST. Conversely, SST gradient unveils structures separating waters of different temperatures, whose contrast is often – but not always – associated with horizontal transport. Therefore, even if they usually detect the same structures, these two metrics are complementary. Frontal features were identified by considering a local FSLE (or SST gradient, respectively) value larger than a given threshold. The threshold values have been chosen heuristically but consistently with the ones found in previous works. For the FSLEs, we used 0.08 days(^{-1}), a threshold value in the range of the ones chosen in18 and47. For the SST gradient, we considered representative of thermal front values greater than 0.009({^circ })C/km, which is about half the value chosen in47. However, in that work, the SST gradient was obtained from the advection of the SST field with satellite-derived currents for the previous 3 days, a procedure which is known to enhance tracer gradients.Bootstrap method The threshold value splits the AFC into two groups: AFC co-located with FSLE or SST gradient values over the threshold are considered as measured in proximity of a front (i.e., statistically associated with a front), while AFC values below the threshold are considered as not associated with a frontal structure. The statistical independence of the two groups was tested using a Mann-Whitney or U test. Finally, bootstrap analysis is applied following the methodologies used in47. This allows estimating the probability that the difference in the mean AFC values, over and under the threshold, is significant, and not the result of statistical fluctuations. Other diagnostics tested are reported in SI.1.Linear quantile regression Linear quantile regression method48 was employed as no significant correlation was found between the explanatory and the response variables. This can be due to the fact that multiple factors (such as prey or predator distributions) influence the fish distribution other than the frontal activity considered. The presence of these other factors can shadow the relationship of the explanatory variables (in this case, the FSLE and the SST gradient) with the mean value of the response variable (the AFC). A common method to address this problem is the use of the quantile regression48,49, that explores the influence of the explanatory variables on other parts of the response variable distribution. Previous studies, adopting this methodology, revealed the limiting role played by the explanatory variables in the processes considered50. The percentiles values used are 75th, 90th, 95th, and 99th. The analysis is performed using the statistical package QUANTREG in R (https://CRAN.R-project.org/package=quantreg, v.5.3848,51), using the default settings.Chlorophyll-rich waters selection The AFC observations were considered in chlorophyll-rich waters if the corresponding chlorophyll concentration was higher than a given threshold. All the other AFC measurements were excluded, and a linear regression performed between the remaining AFC and FSLE (or SST gradient) values. The corresponding thresholds (one for FSLE and one for SST gradient case) were selected though a sensitivity test reported in SI.1. These resulted in 0.22 and 0.17 mg/m(^3) for FSLE and for SST gradient, respectively. These values are consistent among them and, in addition, they are in coherence with previous estimates of chlorophyll concentration used to characterise productive waters in the Southern Ocean (0.26mg/m(^3)52).Gradient climbing modelAn individual-based mechanistic model is built to describe how fish could move along frontal features. We assume that the direction of fish movement along a frontal gradient is influenced by the noise of the prey field (SI. 2). Specifically, we consider a Markovian process along the (one dimensional) cross-front direction. Time is discretized in timesteps of length (varDelta tau). We presuppose that, at each timestep, the fish chooses between swimming in one of the two opposite cross-front directions (“left” and “right”). This decision depends on the comparison between the quantity of a tracer (a cue) present at its actual position and the one perceived at a distance (p_R) from it, where (p_R) is the perceptual range of the fish. We consider the fish immersed in a tracer whose concentration is described by the function T(x).An expression for the average velocity of the fish, (U_F(x)), can now be derived. We assume that the fish is able to observe simultaneously the tracer to its right and its left. Fish sensorial capacities are discussed in SI.2. The tracer observed is affected by noise. Noise distribution is considered uniform, with (-xi _{MAX}{tilde{T}}(x_0-varDelta x)), the fish will move to the right, and, vice versa, to the left. We hypothesize that the observational range is small enough to consider the tracer variation as linear, as illustrated in Fig. S7 (SI. 3). In this way:$$begin{aligned}&{tilde{T}}(x_0+varDelta x)=T(x_0)+ p_R,frac{partial T}{partial x}+xi _1 \&{tilde{T}}(x_0-varDelta x)=T(x_0)- p_R,frac{partial T}{partial x}+xi _2 ;. end{aligned}$$In case of absence of noise, or with (xi _{MAX}p_R,frac{partial T}{partial x}). If (T(x_0+varDelta x) >T(x_0-varDelta x)) (as in Fig. S7), and the fish will swim leftward if$$begin{aligned} xi _1-xi _2 >2p_R,frac{partial T}{partial x}; . end{aligned}$$Since (xi _1) and (xi _2) range both between (-xi _{MAX}) and (xi _{MAX}), we can obtain the probability of leftward moving P(L). This will be the probability that the difference between (xi _1) and (xi _2) is greater than (2p_R,frac{partial T}{partial x})$$begin{aligned} P(L)&=frac{1}{8xi _{MAX}^2} bigg (2 xi _{MAX} – 2 p_R,frac{partial T}{partial x}bigg )^2\&=frac{1}{2} bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2 end{aligned}$$.The probability of moving right will be$$begin{aligned} P(R)&=1-P(L) end{aligned}$$and their difference gives the frequency of rightward moving$$begin{aligned} P(R)-P(L)&=1-2P(L)=1-bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2\&=frac{p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg ); , end{aligned}$$where the absolute value of (frac{partial T}{partial x}) has been added to preserve the correct climbing direction in case of negative gradient. The above expression leads to:$$begin{aligned} U_F(x)=frac{V p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg );. end{aligned}$$
(1)
We then assume that, over a certain value of tracer gradient (frac{partial T}{partial x}_{MAX}), the fish are able to climb the gradient without being affected by the noise. This assumption, from a biological perspective, means that the fish does not live in a completely noisy environment, but that under favorable circumstances it is able to correctly identify the swimming direction that leads to higher prey availability. This means that$$begin{aligned} p_R*frac{partial T}{partial x}_{MAX}=xi _{MAX},. end{aligned}$$
(2)
Substituting then (2) into (1) gives:$$begin{aligned} U_F(x)=V frac{frac{partial T}{partial x}}{frac{partial T}{partial x}_{MAX}}bigg (2-frac{big |frac{partial T}{partial x}big |}{frac{partial T}{partial x}_{MAX}}bigg );. end{aligned}$$
(3)
Finally, we can include an eventual effect of transport by the ocean currents, considering that the tracer is advected passively by them, simply adding the current speed (U_C) to Expr. (3).The representations provided are individual based, with each individual representing a single fish. However, we note that all the considerations done are also valid if we consider an individual representing a fish school. (U_F) will then simply represent the average velocity of the fish schools. This aspect should be stressed since many fish species live and feed in groups, especially myctophids (see SI.2 for further details).Continuity equation in one dimension The solution of this model will now be discussed. The continuity equation is first considered in one dimension. The starting scenario is simply an initially homogeneous distribution of fish, that are moving in a one dimensional space with a velocity given by (U_{F}(x)).We assume that in the time scales considered (few days to some weeks), the fish biomass is conserved, so for instance fishing mortality or growing rates are neglected. In that case, we can express the evolution of the concentration of the fish (rho) by the continuity equation$$begin{aligned} frac{partial rho }{partial t}+nabla cdot mathbf{j },=,0 end{aligned}$$
(4)
in which (mathbf{j }=rho ;U_{F}(x)), so that Eq. (4) becomes$$begin{aligned} frac{partial rho }{partial t}+nabla cdot big (rho ;U_{F}(x)big ),=,0;. end{aligned}$$
(5)
In one dimension, the divergence is simply the partial derivate along the x-axis. Eq. (5) becomes$$begin{aligned} frac{partial rho }{partial t}=-frac{partial }{partial x} bigg (rho ;U_{F}bigg ) end{aligned}$$
(6)
Now, we decompose the fish concentration (rho) in two parts, a constant one and a variable one (rho ,=,rho _0+{tilde{rho }}). Eq. (6) will then become$$begin{aligned} frac{partial rho }{partial t}=-U_Ffrac{partial {tilde{rho }}}{partial x}-rho frac{partial U_F}{partial x};. end{aligned}$$
(7)
Using Expr. (3), Eq. (7) is numerically simulated with the Lax method. In Expr. (3) we impose that (U_F(x)=V) when (U_F(x) >V). This biological assumption means that fish maximal velocity is limited by a physiological constraint rather than by gradient steepness. Details of the physical and biological parameters are provided in SI.6. More

Test surfacesWe used smooth and hairy, homogeneous and striped (with different widths of black and white stripes) test surfaces. In order to mimic the curved zebra back, all test surfaces had a convex cylindrical shape (length: 15 cm, radius: 7 cm). In the schlieren measurements (see subsection “Schlieren imaging”), the cylinder’s horizontal long axis was perpendicular (Supplementary Fig. S1A,B) or parallel (Supplementary Fig. S1C) to the collimated horizontal light beam illuminating the target area, while the stripes were perpendicular (Supplementary Fig. S1A) or parallel (Supplementary Fig. S1B) to the cylinder’s long axis. Supplementary Tables S1 and S2 list the patterns, colours and names of the 8 smooth and 10 hairy test surfaces. The smooth surfaces were composed of cardboard squares (15 cm × 15 cm) (Supplementary Fig. S2). The hairy surfaces were composed of cattle, horse and zebra hides glued by dextrin to a cylindrical (length: 15 cm, radius: 7 cm) gypsum base (Supplementary Fig. S3). Surfaces hsc1(7b7w)perp, hsc1(8b7w)par, hsc3(3b2w)perp and hsgc3(3s2L)perp were used to model that the black stripes of zebras could be separately erected, while the white remained flat7. No animals were killed, the horse and cattle hides were provided by Hungarian horse and cattle keepers, while the zebra hide was obtained from a Hungarian zoological garden.Thermography of lamplit test surfacesUsing a thermocamera (VarioCAM, Jenoptik Laser Optik Systeme GmbH, Jena, Germany, nominal precision of ± 1.5 K, with relative pixel-to-pixel precision  1 s. Since in the upper rectangular window of the filtered schlieren images the lifespan t of local minima of I(x) was very short, we performed statistics only for the lower rectangular window.For the statistical analysis of the characteristics of I(x) (Nmin, ΔI, dave) and air stream behaviour (t, dcovered, v, dmax, dse), we applied Principal Component Analysis (PCA) and fitted ellipses to component scores with 95% confidence interval. We applied Wilcoxon rank sum test with Bonferroni correction for the datasets. Because of the large sample size of the dataset Nmin, ΔI, dave—for smooth test surfaces 4475 observations per surface and for hairy test surfaces 5369 observations per surface—, the Wilcoxon rank sum test would result in highly significant differences for almost all comparisons15. Therefore, we used a Monte Carlo approach, where we randomly selected 250 (≈ 5% of the full dataset) samples, ran the Wilcoxon rank sum test with Bonferroni correction, recorded the results, repeated this 499 times (to have 500 runs) and finally the average of the results of the 500 runs was calculated. The data evaluation was made by our custom-written scripts in Python programming language. For statistical analyses we used the R statistical package 3.6.316.Disturbance caused by an artificial wind and a butterflyTo demonstrate the influence of very weak winds on the air streams above lamplit test surfaces, we blew air by a compressor with a press of 1.6 bar from 1.5 m above the following test surfaces: ss1(8b7w), hsz(8b7w)perp, hsh1(8b8w)perp and hhbc. The compressor tube ended in an air-blow gun. Before the measurements, the air pressure was 4 bar in the 3-litre compressor tank, and the regulator was set to 1.6 bar. The compressor was turned off prior to recording a given sequence and during the measurement the air-blow gun was used to generate horizontal “wind” until the pressure decreased to 1 bar (atmospheric pressure). The artificial wind speed created by the compressor was measured (with accuracy  More

Rearing methodologyEristalis flower flies were reared in laboratory conditions from egg clutches laid by wild-caught females in the summer of 2019 (see Supplementary Materials for detailed rearing methodology). Only flies that emerged on the same day were used in the experiments. An artificial diapause protocol (see Supplementary Materials for detailed protocol) was used to prolong the lifespan of lab-reared flower flies, as adult Eristalis flower flies in lab colonies have shorter lifespans than adult Eristalis flies in the wild48. Once the adult flies emerged, all siblings were placed in artificial diapause in a refrigerator and fed 10% sucrose ad libitum until the experiment began. These Eristalis flower fly rearing and artificial diapause protocols are a modification of previously published protocols48,49.Osmia lignaria (n = 50; Crown Bees, Woodinville, WA, USA) and Megachile rotundata (n = 50; Watts Solitary Bees, Bothell, WA, USA) were purchased and allowed to emerge in an incubator kept at 23 °C and 65% humidity. Bumble bees (Bombus impatiens) used as C. bombi source colonies or as uninfected sources of bees for the dose–response trials were purchased from Biobest (Biobest, Leamington, Ontario, Canada) and maintained in the lab by feeding sucrose and pollen from a mixture of honey bee-collected poly-floral pollen (Bee Pollen Granules, CC Pollen High Desert, Phoenix AZ, USA). To ensure the commercial colonies were free of parasites, we pulled 20 workers and screened them for parasites via microscopy. No parasites were found in any of the colonies used for the dose–response trials.Evaluating whether the European drone fly, Eristalis tenax, is a host of Crithidia bombi
After breaking artificial diapause, the E. tenax flower flies were allowed to groom, but not feed, for one hour. Each fly was then placed abdomen-first into a 1.5 mL microcentrifuge tube harness to collect defecation events (Supplementary Figure S5). The size of these tubes allowed the flies to feed comfortably, but the tubes were also tapered at the bottom, which prevented the flies from stepping in their feces. Holes were placed along the side of the tubes so the fly could respire. One large hole was placed on the lid of the tube so the fly could be inoculated directly with a pipette.Flies were randomly divided into treatment and control groups. E. tenax flies in a roughly 1:2 F:M sex ratio were used in both the treatment (n = 30) and control groups (n = 30), for a total of 60 replicates. The flies that emerged from the same egg clutch with this 1:2 F:M sex ratio were the only siblings that could accommodate the replicates needed for this experiment, which is why this sex ratio was used.The C. bombi inoculum was made fresh from infected B. impatens individuals the morning of the experiment using established protocols. Briefly, we dissected the gut of infected B. impatiens workers from a laboratory source colony that sustained a strain collected from wild B. impatiens workers from Massachusetts, USA (GPS coordinates: 42.363911 N, – 72.567747 W). We homogenized the bee guts in distilled water and diluted the mixture to 1280 C. bombi cells μL−1, which we then combined 1:1 with 30% sucrose solution for an inoculum of 640 cells μL−1, a standard inoculum concentration for infecting bumble bees with C. bombi35,50. Control groups were fed 5 μL of a 30% sucrose and blue dye (Butler Extract Co., Lancaster, PA, USA) that in pilot experiments was not found to influence host or parasite survival. Treatment groups were inoculated with 5 μL (3200 cells total) of C. bombi, 30% sucrose and blue dye solution. The number of cells used in the inoculum is similar to levels of C. bombi found in the feces of bumblebees with recently established infections37. Blue dye was used to better visualize when fecal events occurred and flies that did not drink the entire 5 μL inoculum were not used in the experiment.After feeding, the flies were monitored continuously until defecation occurred. As these flies recently emerged from artificial diapause and were starved pre-experiment, every hour post-inoculation the flies were fed a 30% sucrose and blue dye solution ad libitum to encourage defecation. Once a fly defecated, the feces were collected via pipette and diluted to a 10 μL solution with deionized water to observe and count parasites using Kova Glasstic slides. The fly was then placed in an individual 60 mL plastic portion cup with filter paper (Sigma–Aldrich, St Louis, MO, USA) and a 1.5 mL microcentrifuge tube feeder containing 500 μL of a 30% sucrose and blue dye solution for 10 days. Feeders and filter papers were replaced every 3 days to prevent mold growth. As C. bombi typically replicates in high numbers after 10 days in the guts of bumble bees51, both control and treatment flies were dissected and C. bombi gut counts were performed 10 days post-inoculation. Since actively swimming, and thus live, C. bombi is infective to susceptible bumble bee hosts35, only actively swimming C. bombi were counted. The fecal volume, dilution factor and counts of C. bombi were quantified for each individual fly to calculate the exact amount of C. bombi in the individual’s first defecation event.Dose–response dataCrithidia bombi inoculum was made from infected B. impatiens individuals the morning of each trial using the protocols described above, with two exceptions. First, the C. bombi strain was collected from wild B. impatiens workers from New York, USA (GPS coordinates: 42.457350, − 76.426907). Second, a range of serially diluted doses were used to inoculate uninfected B. impatiens workers. The doses were: 25,000 cells, 12,500 cells, 6250 cells, 3125 cells, 1563 cells, 781 cells, 391 cells, 195 cells, 98 cells, 49 cells, 24 cells, and 12 cells. To obtain these doses, we homogenized bee guts in distilled water and diluted the mixture to 5000 C. bombi cells μL−1 with 30% sucrose solution. Serial dilutions were then conducted with a 10% sucrose solution to ensure the same osmolarity of each inoculum.We conducted four replicate dose–response trials over a period of four weeks. Each week, five uninfected workers per dose from each of two colonies were administered 5 μL of C. bombi inoculum. The ten highest doses were administered for the first 2 weeks, and two additional doses (24 cells, and 12 cells) were added for the final 2 weeks. Inoculated bees were kept individually in vials and fed 30% sucrose ad libitum for 7 days at 23 °C and 65% humidity. After 7 days, the bees were dissected and C. bombi loads were quantified using a hemocytometer as described above. In addition, the right forewing was removed from each bee and marginal cell length was measured as a proxy for size52. In total, 220 bees were inoculated (20 replicates for each of the ten highest doses, 10 replicates for the two lowest doses).Defecation patterns on a shared floral resourceAll pollinators (O. lignaria, M. rotundata, E. arbustorum and E. tenax) were placed in individual 60 mL plastic portion cups lined with filter paper. Each pollinator received a 1.5 mL microcentrifuge tube feeder containing 500 μL of fluorescent dye via 2.5 g of fluorescent powder (Stardust Micas) dissolved into 500 mL 30% sucrose feeders to visualize fecal deposition on flowers. After 24 hours, filter papers were collected (for analysis of fecal volume and defecation frequency, see below) and a total of five, randomly selected pollinators of the same species were placed in 12 × 12 × 12″ mesh cages (Bioquip Products, Rancho Dominguez, CA, USA) containing inflorescences of similar sized Solidago dansolitum ‘Little Lemon’ goldenrod each replicate trial. Goldenrod was used in this experiment because both bees and flower flies were observed foraging on this abundant floral resource. Only pollinators with filter papers containing fluorescing defecation events were released in the mesh cages.All E. arbustorum cages (n = 10) contained 2:3 F:M sex ratios, except one cage contained a 3:2 F:M sex ratio. All E. tenax cages (n = 20) contained 3:2 F:M sex ratios, except four cages contained 2:3 F:M sex ratios. All O. lignaria cages (n = 10) contained 4:1 F:M sex ratios, except one cage contained a 3:2 F:M sex ratio. For the two fly species, sample sizes and F:M sex ratios were determined by the greatest, same-day sibling emergence. For O. lignaria, sample sizes and F:M sex ratios were determined by emergence availability. M. rotundata floral deposition data was not collected, as the F:M emergence was heavily skewed to males that did not interact with, and therefore defecate on, the flowers.After 24-hours, the pollinators were removed and the defecation events on the goldenrod from all cages were counted under a blacklight. The location of the defecation events on the goldenrod was recorded. The plant parts were divided into six categories: ‘inside’ the flower (inside the corolla), ‘outside’ the flower (surface of the corolla), on the sepal, on the bract (the leaflike structure beneath the flower), on the stem or on a leaf.Defecation frequency and fecal volumesThe diameter of the smallest and largest defecation events per filter paper was measured by a digital caliper and an average diameter was calculated from these two values for all pollinators. The average diameter of the defecation events was converted to an average volume (in μL) using a standard curve (Supplementary Figure S6; R2 = 0.99 for the calibration data). The collected fecal volumes defecated by control flies from the E. tenax inoculation experiment (see above) were compared to the average fly fecal volumes calculated here. This was done to analyze whether flies in a confined environment, where they were inoculated with C. bombi, defecated similar volumes to flies allowed to move freely in an individual cup, which the average volumes were estimated from. In addition, the number of defecation events (frequency) over a 24-hour period on the collected E. arbustorum (n = 46) and E. tenax (n = 100) filter papers were counted for each fly.Statistical analysesFor the E. tenax inoculation experiment, we evaluated the amount of C. bombi cells in the first defecation event using a negative binomial generalized linear model (GLM), with fly sex as predictor. We chose negative binomial over Poisson to account for overdispersion, which we evaluated using Pearson residuals. Significance of sex was evaluated using a likelihood ratio test (LRT).Data from the B. impatiens inoculation experiment were used to fit two dose–response curves, the first for infection probability, and the second for infection intensity among infected bees. Infection intensity was defined using the loads estimated from the hemocytometer. A bee was considered infected if the counts were nonzero. We first tested whether the dose ingested, wing length (as a proxy for body size) and the colony the bee came from affected its response. For infection probability, this was done using a GLM with log10(dose), colony, wing length and their interactions as predictors, and infection status as the Bernoulli response. For infection intensity, this was done using a linear model (LM) with the same predictors, and log10(intensity) as response, using only infected bees. Doses were log-transformed in accordance to how the experimental doses were varied, while intensities were log-transformed to achieve normality of the residuals. Significance of predictors were tested in accordance with the principle of marginality.While we found that wing length and colony were significant predictors, in practice the colony-specific response of a wild bee is unknown (since it would not have come from any of the experimental colonies), while the dependence on wing length is only useful in a size-based epidemiological model. Hence, we generated dose–response curves by marginalizing across colony and wing length. Finally, we tested whether linear relationships between the link function and log10(dose), assumed in LMs and GLMs, were sufficient to capture the shape of the dose–response curves, by fitting the data to shape-constrained additive models and then comparing AIC values53. SCAMs are generalized additive models (GAMs) on which additional constraints such as monotonicity have been imposed; being more flexible, they can better capture the shapes of the dose–response curves should the linear relationships be inadequate.We evaluated whether fecal volume depended on pollinator species and sex with a linear model (LM), fitted using weighted least squares to account for unequal variances between group (detected using Levene’s test). Since the transformation from diameter (of feces on filter paper) to volume introduced a noticeable skew to the distribution, we transformed the volume back to diameter and further performed a Box-Cox transformation to achieve normality54, which we verified using the Shapiro–Wilk and D’Agostino’s K2 test. The transformed volume was used as the response in the abovementioned linear model.For E. tenax, fecal volume was also manually collected from the 1.5 microcentrifuge tubes during the inoculations experiment. We compared the fecal volume from the two methods using a LM with method and fly sex as well as their interaction as predictors. Volumes were log-transformed to achieve normality, while the linear model was fitted using ordinary least squares since Levene’s test indicated no significant deviation from the assumption of equal variance.We evaluated whether defecation frequency depended on pollinator species and sex with a LM, again fitted using weighted least squares to account for unequal variances between groups. While two of the groups showed deviation from normality using the Shapiro–Wilk test, the deviations were only marginally significant and hence not expected to qualitatively affect the results55.Finally, we evaluated defecation patterns on goldenrod using a negative binomial GLM, with feces counts as the response, and pollinator species, plant location and their interaction as predictors. We did not use a mixed model with cage number as a random effect since there was only one count value per cage per location, so pseudo-replication was not an issue. Significance of predictors were evaluated using LRT in accordance to the principle of marginality56 (i.e., main effects were tested only when their interactions were insignificant and hence dropped). Post-hoc tests of pairwise contrasts with Tukey corrections were performed for predictors that were significant. We recognize that the principle sex ratio and its interactions with other predictors could also be included among the predictors; however, since each species had cages with predominantly one sex ratio (E. tenax 3F:2M; E. arbustorum 2F:3M; O. lignaria mix of 4F:1M and 5F:0M), this meant that species and sex ratios were highly correlated, making it impossible to separate their effects. Nonetheless, since female Eristalis flies do not provision their brood, the differences between sexes (e.g., time spent foraging on plants) may be less pronounced than in bees. More

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