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The attachment site of ticks has been studied in the context of both animal and human tick preference. In Oklahoma, a study of horses indicated that A. americanum preferentially bites the inguinal area, while I. scapularis and D. albipictus, the moose-tick, primarily bite the chest and axillary region, with D. albipictus often being found on the back18. A survey of dogs and cats across the US identified a similar distribution of ticks on dogs, with the attachment being most common on the abdomen, axillary and inguinal regions. However, this was species-specific with D. variabilis preferring the head and neck specifically19. Cats were more successfully parasitized by I. scapularis which preferred the head and A. americanum, which preferred the tail and perianal region19. This is similar to a study of tick distribution on wild black bears (Ursus americanus) in Pennsylvania, indicating that the primary tick present was I. scapularis and that the greatest numbers were found in association with the ears and muzzle20. In these cases, the ability for ticks to attach to specific areas is most likely a result of the grooming habits and abilities of the animals in question.Studies of anatomical region preference in humans also reported tick bite-site specificity associated with particular tick species. For example, in Korea, H. longicornis was determined to prefer abdomen and lower extremities (33%) and the abdomen/inguinal area (26.4%)21, which is a behavior similar to that of A. americanum observed here. Although H. longicornis is present in New York1, insufficient numbers were detected to draw definitive conclusions about its biting preference here. Additionally, a study in England (I. ricinus) reported that tick bites were most common in the legs (50%) of adult humans, but in the head and necks of children (43%)22, a differentiation that our survey does not at this time include. A similar phenomenon was observed in Russia, where tick bites were most common on the head and neck of all individuals (39.2%), but were much more common in children (84.9%)23. This study determined that the bite-site of single tick bites that resulted in infection with the Tick-Borne Encephalitis virus (TBEV) were associated with lethal outcomes if the bites were located on the head, neck, arms or axilla, while less lethality was associated with bites to the lower limbs and groin. This is most directly analogous to the transmission of DTV by I. scapularis, suggesting that bite site may have a similar relationship to disease outcomes in the related North American pathogen/vector pair.Under normal circumstances, ticks exist in sylvatic cycles with specific host preferences based on the tick species and life stage, with spillover to humans occasionally occurring for species with generalist feeding habits. Therefore, the feeding behaviors of ticks are variable, and this influences the ways that the ticks interact with humans.Ixodes scapularis is less specific in host-site preferenceThe primary life stages of I. scapularis that bite humans include nymphs and adult females, although males may also be found on humans. The body segment preference of I. scapularis is less specific than for D. variabilis, which prefers the head, and A. americanum, which prefers the thighs and pelvic region. Ixodes scapularis is primarily found on the central trunk, including the groin/pelvic region, the abdomen, the thoracic region, and the head/neck. This varies between the life stages, with more adults found in the thoracic/abdominal region of the body and nymphs being more commonly found on the arms and legs. This is partly due to the substantial size difference between adult and nymph/larval I. scapularis, with larvae being almost imperceptible and nymphs having a total body length of two to four millimeters. This results in nymphs/larvae being much more difficult to see, allowing them to more readily attach to the most visible portions of the human body while adults are restricted mostly to areas covered by clothing and hair.The presence of ticks on the head and neck indicates that I. scapularis tends to climb, although not with the preference for hair observed with D. variabilis. They appear to spend substantial time moving on the host, a period where they can be removed easily without having had a chance to potentially transmit pathogens by biting. On deer, this corresponds to a preference to move toward the neck and ears where the ticks are more difficult to dislodge24,25. On humans, it results in wide distribution across the whole body with less location specificity than other ticks.In addition to body region and life stage identification, I. scapularis ticks were also screened for several pathogens to determine if infection status influences host site preference. Anaplasma phagocytophilum, B. microti, and other pathogens (DTV and B. miyamotoi) did not influence the body segment the ticks chose to feed. However, in ticks infected with B. burgdorferi, a statistically significant change in the distribution of tick bites marked by an increased report of tick bites in the midsection and a decreased tick bites in the arms, legs, and head. While this may suggest a change in tick behavior/fitness in response to infection, it may also relate to the differences in infection rates of adult and nymph/larval ticks. Larvae, having never fed, are not infected with B. burgdorferi, and the rate of infection in nymphs is lower than that of adults1. Nymphs are less likely to be infected and are more likely to attach to the arms and legs, which is a potential source of the observed difference in infection rates. However, it remains unclear why this is not observed for the other pathogens that follow the same trend of increased infection rate in adult versus nymph/larval ticks.Bacterial and protozoal agents transmitted by I. scapularis take several hours for an infectious dose to be transmitted26,27,28. Therefore, prompt detection and removal of ticks is important for preventing tick-borne disease. Furthermore, understanding where the ticks attach allows them to be more easily detected, and also assists in preparing protective clothing for individuals entering tick-endemic areas. Additionally, knowing the biting location of I. scapularis could aid in detecting potential erythema migrans, a skin condition that occurs at the point of B. burgdorferi infected tick exposure in about 80% of cases29, which is highly diagnostic for both Lyme disease and STARI, which is transmitted by A. americanum.
Amblyomma americanum prefers the thighs and groin of subjectsAmblyomma americanum, the lone star tick, is present throughout the southern portion of New York and is particularly dominant on Long Island1. This species is relatively large, fast, and aggressive, feeding on various animals, including deer, medium-sized animals, and birds30. As a generalist feeder, both adult and nymph/larval A. americanum often bite humans in endemic areas. This experiment identified six larvae, 107 nymphs, and 48 adult A. americanum from human sources. The dominance of nymph submissions is likely due to the large size of the tick, making nymphs and adults easier to spot in more visible areas.In terms of body segment location, all life stages of A. americanum were most often found in the thigh/groin/pelvic region. Considering that most humans encounter ticks while walking through vegetation, the ticks most likely first adhere to the legs and move upward before biting. In this case, the ticks bite rapidly instead of ascending in large numbers to the torso or head. This area is also almost invariably covered in relatively tight-fitting clothing. The closeness of the fabric may also assist in inducing the ticks to feed by slowing their ascent and creating contact to induce biting.While it does not transmit the same range of pathogens as I. scapularis, A. americanum is still a medically significant species. This species can transmit Ehrlichia chaffeensis and E. ewingii31,32, which are at present rare in New York, but are likely to increase as more A. americanum becomes established. Amblyomma americanum is also associated with Southern Tick-Borne Rash Associated Illness (STARI)11, a disease of unknown etiology that has previously been observed in New York33 and with galactose-alpha-1,3-galactose (alpha-gal) allergy, a reaction to the tick’s saliva that can result in a long term, potentially serious allergic sensitivity to the consumption of red meat. While the attachment time required to transmit or induce these pathogens is still unclear, prompt detection and removal of the tick is still recommended. Knowing the approach of the tick and where it is likely to be found improves this process.Additionally, it is unclear if the results observed for A. americanum also apply to the related A. maculatum, the vector of Rickettsia parkeri, a cause of spotted fever. These ticks have been observed in the southernmost portions of New York with a high infection rate with R. parkeri34. Since early R. parkeri infection may result in a visible eschar, understanding where the eschar is most likely located can be critical for rapid diagnosis before the onset of severe disease symptoms. Considering the similarities in behavior between the two Amblyomma species, it may have similar preferences to A. americanum. Other escharotic diseases, such as F. tularensis, may also be present and linked to a tick with a highly dissimilar segment preference. The location of the escar itself, therefore, may be at least partially diagnostic for specific pathogens. However, at present, the sample size within this community engaged passive surveillance program is too small to assess its biting behavior in detail.
Dermacentor variabilis exhibits preference for the human headIn this study, D. variabilis was almost exclusively encountered in its adult life stage. This indicates that while the adult ticks are generalist feeders that may bite humans, the nymph and larval stages are not and have much greater host specificity, either feeding exclusively on a specific type of animal or being restricted to the vicinity of animal burrows. The exact identity of the preferred larval and nymphal host of D. variabilis in New York could not be determined from these data, but is presumed to be one or several rodent species, lagomorph, or mesocarnivore with broad distribution across the eastern United States.Additionally, D. variabilis was unique among the three species of ticks studied here. It had a strong bias toward the head and neck of human hosts, as opposed to a higher preference for the midsection and pelvis/groin with I. scapularis and especially A. americanum. This is clear evidence of climbing behavior, tending upward, but is also indicative of a strong preference for dense hair. In contrast to I. scapularis and A. americanum, D. variabilis in its adult stage is less likely to feed on deer35,36, with a preference for canids36, hence its colloquial name as the “American dog tick”. Hair provides the ticks with the same benefits as feeding on canids. It protects them from being immediately detected and removed, obscuring them until they can feed extensively. This can be of potential medical consequence in the case of tick paralysis, a condition of flaccid paralysis associated with the bite of Dermacentor spp. ticks30. In such cases, prompt removal of the tick is critical for treatment. Therefore, understanding its most likely location can be useful for removal of the tick before the onset of the condition, diagnostically to confirm the presence of the tick, or during treatment to ensure its removal. Considering that the tick will most likely be adult, it should be relatively obvious with careful observation.Limitations of this studyThe data described in this manuscript derived from a set of ticks submitted by general public, with site location from a questionnaire completed upon tick submission. While speciation and pathogen testing were performed under laboratory conditions, the public completed the initial survey and is therefore subject to a level of inherent error and ambiguity. In the context of this study, this mainly concerns whether the body location submitted concerns an attachment or a tick that is still crawling over the potential host in preparation for biting. The term “attachment” may be colloquially interpreted as to contain both categories, or a person can potentially be mistaken about the state of the tick. While ticks filled with blood have fed, the situation is more indeterminate for short-duration attachments where the ticks have not yet begun to engorge. This may introduce some level of error from ticks found on a body segment that were not, at the time of collection, attached. However, the data are overall still useful for predicting the most likely location where ticks of specific species can be found on a person. Studies with test subjects and ticks under controlled conditions may assist in elucidating this matter further. Additionally, this data set was compiled without regard to gender and age group. This data was not collected with this version of the questionnaire; therefore, the tick attachment cannot be stratified by any demographic parameters of tick submitters. More

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Study systemOur focal ecosystem is in Selvíria, state of Mato Grosso do Sul, Brazil ((hbox {20}^{circ }) (22′) (41.86”) S, (hbox {51}^{circ }) (24′) (58.90”) W), on a property owned by the São Paulo State University (UNESP). The location covers 350 ha of pasture composed of liverseed grass (Urochloa decumbens). The native vegetation was removed, pasture areas were implemented, and livestock was introduced in the 1970s, maintaining this configuration during the following 50 years. The climate of this area is categorized as equatorial savanna, with dry periods concentrated mostly during the winter, from April to August. During our sampling period (from November 23th, 1989, to November 19th, 2015), no vermifuges and insecticides that could affect negatively the community of dung beetles associated with cow pads were used1.The native dung beetle community at this site is composed of dwellers and tunnelers. Dwellers comprise the Aphodiinae subfamily, whereas all the tunnelers belong to the Scarabaeinae subfamily31. In total, there were eight species classified as dwellers (Ataenius crenulatus, A. picinus and Atanius aequalis-platensis grouped as one species, Blackburneus furcatus, Genieridium bidens, Labarrus pseudolividus, Nialaphodius nigrita and Trichillum externepunctatum) and ten native tunnelers (Ateuchus nr. puncticollis, A. vividus, Canthidium nr. pinotoides, Dichotomius bos, D. semiaeneus, D. sexdentatus, Ontherus appendiculatus, O. dentatus, O. sulcator). These species were chosen for our study because, as the invasive tunneler D. gazella (also from the Scarabaeinae subfamily), they all co-occur in pasture and exploit the same resource (cow pad)32. The initial establishment of D. gazella caused the loss of most of the native tunnelers from the community, with the invader becoming the overwhelming representative of the functional group, and an initial decrease of abundance for dwellers. Differently from native tunnelers, however, dwellers were able to recover their number a few years after invasion (Fig. 1a, Fig. S1).As reported in1, the abundance of dung beetles was significantly affected by both local minimum temperature and relative humidity. The influence of these two factors is expected, as they determine egg and larval survival and development of dung beetles. For example, because dung beetles are poikilotherms, environmental temperature is key to their development and fecundity33. One of the main dweller species, Labarrus pseudolividus, is widely found in locations with temperature averages ranging between (hbox {12},^{circ }hbox {C}) and (hbox {18},^{circ }hbox {C})34, making it tolerant to colder local temperatures. On the other hand, for D. gazella the lower developmental threshold is (hbox {15.5},^{circ }hbox {C}) (individuals cannot survive below this temperature), and the optimum temperature for population growth is (hbox {28},^{circ }hbox {C})35. For both groups, physiological growth and reproduction rates are maintained even when outside temperatures are close to the lower developmental threshold; dwellers, for example, live inside the dung pile, where temperature is higher and less variable than outside36,37. However, while tunnelers oviposit deep in the soil to protect the eggs, warmer and drier conditions reduce dweller egg viability on dung piles since they are exposed38. Low humidity conditions lead to drier dung and can cause egg and insect dessication. In addition, dwellers from our focal system have Palearctic evolutionary origins39; D. gazella’s natural distribution ranges from central to southern Africa40, presenting high physiological plasticity that allows it to tolerate high temperatures and low relative humidity better than other tunneler species41.Functional-group data collection and community structure characterizationDung beetles were collected once a week in a black-light flight intercept trap42, which guarantees the collection of coprophagic beetles. During all collection periods, climate variables were also collected from a meteorological station located within 2 km of our collecting site. See1 for the complete description of the collection process and database. For our purposes, we retained the species, number of individuals per species, and climate variables for each week sampled (Supplementary Information, SI, Figs. S1–S2).We focused first on the weekly abundance data, which we needed to process in order to avoid spurious results in our analyses stemming from the measurement protocol. Specifically, we filtered out seasonal low values associated with sampling in the coldest periods, when few beetles are captured because the reduced activity in all functional groups restricts their spatio-temporal distribution43. Including such samples would not be representative of the community and could bias the analysis since we are investigating community composition (i.e. proportions, very sensitive to low sampling). Thus, we considered only samples with a total number of beetles (that is, summing up all groups together) higher than the value of the median of all data, a conservative threshold that retains observations that allow for as much representation of the community as possible. As will become evident in the Results section and Supplementary Information, less conservative choices for the threshold did not alter our main conclusions.Following Mesquita -Filho et al.1, we categorized all sampled species into either dwellers or tunnelers. D. gazella is a tunneler and, as explained above, the native tunneler species experienced massive declines in abundance after its establishment, leaving D. gazella as almost the single representative in the tunneler functional group during the period of observation1. Thus, given the sharp contrast in community composition, we also separated the data into before and after invasion using to that end the 200th week, when D. gazella was first observed at the study site (September 11th, 1993, starting date for what we will call “after invasion”, our focal period henceforth).To describe community functional composition (i.e. system state) through time, we derived a normalized functional group ratio. First, because the abundance of each functional group spanned up to four orders of magnitude, we performed a logarithmic transformation of the number of captured insects from each group i, (log _{10}(N_{i}+K)), following  Yamamura44. Here, we chose (K=1), but the value of K did not alter our results qualitatively. In addition, the original data showed random mismatches in the phenology of each group, which gave the wrong impression of extreme short-term shifts in functional group dominance within the community. To avoid such artifacts, we used nonparametric local regression (LOESS)45 to smooth the dynamics of each group46. For this smoothing, we employed the loess function in the R software 3.6.147 with a smooth parameter equal to 0.25, but other moderate values (or an optimal value calculated with Bayesian inference by the R function optimal_span) did not alter our conclusions. Finally, we extracted back from the smoothed curve the number of beetles within each functional group to calculate the fraction (f_{dwell}) that measures the relative abundance of dwellers:$$begin{aligned} f_{dwell} = frac{N_D}{N_D+N_T} end{aligned}$$
(1)
where (N_D) corresponds to the number of dwellers per week and (N_T) corresponds to the number of native tunnelers (for the period before invasion), or only the number of D. gazella observed per week (after invasion), using their corresponding smoothed curves. Including also native tunnelers after invasion did not alter our conclusions.Climate driverWe devised a single climatic driver variable that merges the weekly measurement of temperature and relative humidity over the years, abiotic factors key to the survival and reproduction of both groups (see above). We first converted minimum temperatures and relative humidity to normalized climate variables using a min-max normalization (a feature scaling that uses the total range of temperatures or relative humidity, respectively, as normalization factor):$$begin{aligned} T = frac{T_{week} – T_{min}}{T_{max}-T_{min}};;,~ ~ ~ ~ ~ ~ RH = frac{RH_{week} – RH_{min}}{RH_{max}-RH_{min}};;, end{aligned}$$
(2)
where T corresponds to the normalized temperature, (T_{week}) is the weekly temperature, and (T_{max}) and (T_{min}) are the absolute maximum and minimum temperatures observed during the whole sampling period, respectively. We used a similar notation for relative humidity, RH. Based on the information above regarding beetle response to climate, the merged climate factor c was defined as the relationship:$$begin{aligned} c = frac{T}{RH};;, end{aligned}$$
(3)
for (RHne 0). That is, higher temperatures and/or drier conditions (expected to favor D. gazella) lead to higher values for c. On the other hand, lower temperatures and/or more humid conditions (expected to favor dwellers) imply lower values for c. Intermediate values of c can represent either moderate or extreme values for both T and RH.Identifying ecological states and quantifying resilienceWith our (f_{dwell}) data as an index of community composition (i.e. system state), we calculated kernel density functions to interpolate a continuous probability distribution of the relative fraction of dwellers in the community, (p_{n}(f_{dwell})) (function density, R software 3.1.647) for a given range of climatic driver c values. We grouped the (f_{dwell}) data using ranges for c of size 0.4, to ensure a significant amount of weekly samples that allowed for the reconstruction of these probability distributions (see Table S1, first column). Note that bins with extreme values showed few data points (see first and last rows in Table S1), and thus were rejected to prevent misleading results due to reduced sampling. Also note that, for the density function, we used the default Gaussian kernel with a smoothing bandwidth adjusted to be (50%) larger than the default value (“adjust” argument set to 1.5). This conservative choice aims to reduce the effect of the different sampling across c bins and to ensure that differences among distributions across c values are not the result of spurious sampling noise.Further, we transformed the kernel density function:$$begin{aligned} V(f_{dwell}) = -ln (p_{n}(f_{dwell})) end{aligned}$$
(4)
This (V(f_{dwell})) function, called potential (e.g.48), shows by design well-defined minima for the most frequently observed values of (f_{dwell}) (i.e. configurations most frequently observed for the community, which conform the modes of the probability distribution) in a given group of data. At these points, the potential exhibits a change of trend from decreasing to increasing, and therefore its derivative shows a change of sign. Eq. (4), thus, provides a simple criterion to identify possible system states, which is a reason why potentials have been used extensively across disciplines49,50,51. Nonetheless, because the position of extrema is invariant under the transformation, using probability distributions instead would not alter our conclusions.Representing the potential obtained from all the (f_{dwell}) system states associated with a same range of climatic driver c values allowed us to identify stable community configurations associated with a specific climate. The comparison of the potentials obtained for different c ranges enabled the description of how the community changed in response to climatic variation. The location of the minima revealed which states were stable for a given value of the climatic driver; the presence of two minima, then, flagged the existence of bistability (i.e. two different community compositions possible for the same c value).These minima are materialized as wells in the potential’s landscape, which provides an easy way to understand the concept of stability: the dynamics of the system for the given value of the driver will eventually “fall” into a well (either a state dominated by dwellers or a state dominated by tunnelers), with the shape of the well (e.g. its depth) determining how difficult it is for the system to “escape” that state. Therefore, the area inside a well provides quantification of the tendency of a system to stay in that specific state, i.e. the resilience of the associated ecological state or how strong a perturbation has to be to move the system from such an ecological state to another2,3,50,51,52,53. Thus, in addition to number and location of wells, measuring their associated area allowed us to further characterize the resilience of the community. To this end, we first set a visualization window common to all potentials. Specifically, we plotted the potentials within a range for the vertical variable (the potential, V) given by ([-1.5,1.5]); the horizontal variable (fraction of dwellers, (f_{dwell})) is by definition bounded between 0 and 1. For potentials that showed one single well, the area of the well was measured as the area above the potential curve within this visualization window. For potentials that showed two wells (bistability), we measured the value of the potential at the local maximum separating the two wells, and established that value as the upper (horizontal) line closing the area of each well. To ensure all cases were comparable and eliminate any arbitrariness of the choices above, we expressed resilience as a relative area; in other words, we further normalized the well area by the total area across wells for that potential, which means that any single-well case will show a resilience (or relative area) of 1, and the resilience of the two wells when there is bistability adds up to 1.Figure 1Left: Community composition by functional group for all weeks of observation1. Green represents dwellers, blue represents tunnelers, and orange represents the invader D. gazella. Right: Sketch of responses of the community composition to the climatic driver (i.e. phase diagram) expected from the physiological and behavioral characteristics of the functional groups in the community as described in text: linear (red), or non-linear but monotonic without (blue) or with (brown) hysteresis.Full size imageIdentifying ecological transitionsMeasuring a state variable, (f_{dwell}), and a driver, c (order and control parameter, respectively, in the jargon of regime shift theory), allowed us to study how their observed behavior over time materializes in a driver-state relationship (the so-called phase diagram) defining the possible shifts in dominance (i.e. regime shifts) that the community may undergo as climate changes12. The non-monotonic temporal behavior of the components of the order parameter (i.e. dwellers and tunneler availability) and the components of the control parameter (i.e. temperature and relative humidity) makes it difficult to predict the shape of the phase diagram, and therefore whether we can expect alternative stable states in the focal example. For such cases, the dominance of the dung beetle community could (1) shift in a linear fashion toward the functional group favored by climatic conditions; (2) shift between functional groups in non-linear threshold response to climatic conditions without hysteresis; or (3) shift between functional groups in non-linear threshold response to climatic conditions with hysteresis –and thus showing bistability (see Fig. 1b, or12). Other possibilities, e.g. a non-linear shift between functional groups where one group is favored at intermediate climatic conditions12 are discarded as the invader is better suited for warmer and drier conditions. To evaluate which of these possibilities occurred, we represented (f_{dwell}) as a function of c, as well as the location of the minima shown by the potentials above. In addition to the emerging shape of this relationship, this plot can reveal the presence of alternative stable states if two or more different points occur for the same value of the control parameter, c. More

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General methodological approachTo examine if larvae utilize external cues (i.e., oriented movement) to swim in a directional manner (i.e., significant mean vector length), we develop two complementary analyses that compare the empirically observed directional precision (i.e., mean vector length) with the null distribution expected under a strict use of internal cues (i.e., unoriented movement). The empirically observed directional precision is quantified as the mean vector length (R) of larval bearings (θ) (Fig. 2a), herein ({hat{R}}_{theta }). The angular differences between consecutive bearings, herein turning angles (Fig. 2a; Δθt = θt-θt-1), are used to generate two null distributions of Rθ expected under the unoriented movement of Correlated Random Walk (CRW; ({R}_{{theta }_{0}})), based on the two analyses: Correlated Random Walk-von Mises (CRW-vm) and Correlated Random Walk- resampling (CRW-r), described below. The first is theoretical and is based on a von Mises distribution of simulated Δθ (Fig. 2b, c); the second is empirical, and is based on resampling the Δθ within each trial (Fig. 2d, e). These two analyses are complementary because the first can generate an unlimited number of trajectories but is based on a theoretical distribution rather than on observations, whereas the second is based on a finite number of observations. In addition to these two main analyses, we apply a third analysis, the Correlated Random Walk-wrapped Cauchy, herein CRW-wc, which is similar to CRW-vm, with the only difference of using wrapped Cauchy distribution instead of von Mises. The reason for applying CRW-wc is that it was shown to represent well animal movement in some cases33. Notably, we consider the simple cases of undirected movement pattern with a turning angle distribution centered at 0 (CRW), testing if the mean vector length of the trial’s sequence is higher than that expected under CRW. If true, that would be an indication for a directed movement pattern (i.e., BRW or BCRW), or an indication for more complex behaviors (discussed in Supplementary note 4).Statistics and reproducibilityQuantitative analyses are applied to directional trials, i.e., larval bearing sequences ((hat{theta })) that are significantly different from a uniform distribution based on the Rayleigh’s test8 (p  81, 162, 270). Trials with Nobs higher than the maximal Nobs were trimmed to contain the maximal Nobs per species, retaining the later-in-time data. For the scuba-following trials, the number of observations had to be Nobs  > 20 due to the sensitivity of the analysis to a low number of observations. In other words, a low number of observations limits the capacity of the quantitative analyses to distinguish between oriented and unoriented movement patterns (see Supplementary note 3, Supplementary Figure S3). Importantly, both methods were shown to be robust in terms of artifacts and biases55,56, and have been tested together demonstrating high consistency in larval orientation results16,48.Each orientation trial includes a sequence of larval swimming directions, termed bearings (θ) (Fig. 2a). For the DISC trials, θ are the cardinal directions of larval positions within the DISC’s chamber55. The angular differences between θ of consecutive time steps (t) are defined as Δθ (Δθt = θt-θt-1), such that for every θ sequence of a given length (N), there is a respective Δθ sequence of length N-1 (Fig. 2a). Directional precision with respect to external and internal cues is computed as the mean vector length of bearings (Rθ) and of turning angles (RΔθ), respectively54. Values of mean vector length (R) range from 0 to 1, with 0 indicating a uniform distribution of angles and 1 indicating that all angles are the same.We used two quantitative approaches to examine if larvae exhibit oriented movement: the Correlated Random Walk- von Mises and Correlated Random Walk- wrapped Cauchy (CRW-vm and CRW-wc) analyses and the CRW resampling (CRW-r) analysis. Both types of analyses are based on the assumption that trajectories of animals that strictly use internal cues for directional movement are characterized by a CRW pattern. Hence, their capacity for directional movement is exclusively dependent on the distribution of their turning angles (Δθ)57. In contrast, for an external-cues orienting animal, for which movement directions are correlated with an external fixed direction, the mean vector length of the observed bearings, ({hat{R}}_{theta }), is expected to exceed that of a CRW, ({R}_{{theta }_{0}})6. Both analyses compare ({hat{R}}_{theta }) against the expected ({R}_{{theta }_{0}}), but the first type computes ({R}_{{theta }_{0}^{{vm}}})and ({R}_{{theta }_{0}^{{wc}}})using theoretical von Mises and wrapped Cauchy distributions of Δθ, and the second type computes ({R}_{{theta }_{0}^{r}}) by producing 100 new θ sequences per individual trial (larva) by multiple resampling-without-replacement of the Δθ.A key principle for both analyses types stems from the fact that the mean vector length of bearings (Rθ) is inherently dependent on the mean vector length of turning angles (RΔθ)28. In other words, an animal with a high capacity for unoriented directional movement, i.e., a narrow distribution of Δθ, is likely to yield a high Rθ, even if it makes absolutely no use of external cues for oriented movement. Hence, in both analyses ({hat{R}}_{theta }) is gauged against a distribution of ({R}_{{theta }_{0}}), given its respective mean vector length of turning angles ({hat{R}}_{triangle theta }). The open-source software R58 with the package circular59 is used for all analyses in this study.Correlated Random Walk-von Mises (CRW-vm)In this analysis, we first generate the directional precision (R), expected for unoriented CRW movement using the theoretical von Mises distribution (({R}_{{theta }_{0}^{{vm}}})). The CRW bearings sequences (({theta }_{0}^{{vm}})) are generated by choosing a random initial bearing, followed by a series of Nobs-1 turning angles (({triangle theta }_{0}^{{vm}})) in bearing direction; drawn at random (with replacement) from a von Mises distribution (Nrep = 1000). The length of ({theta }_{0}^{{vm}}) sequence is according to the number of observations in our four types of experimental trials: Nobs = 21 for the scuba-following, and 90, 180 and 300 for the DISC (Table 1). The directional precision of the von Mises distribution is dependent on the concentration parameter, kappa. Kappa values ranging from 0 to 399 are applied at 1-unit increments to cover the entire range of directional precision from completely random (kappa = 0), to highly directional (kappa = 399). Next, the directional precision of the bearings (Rθ) and the turning angles (RΔθ) are computed for each simulated sequence of θ (Fig. 2a–c).These respective pairs of values (RΔθ, Rθ) provide the basis for generating the expected relationship between ({R}_{{theta }_{0}^{{vm}}}) and ({R}_{{triangle theta }_{0}^{{vm}}}). Then, for any given kappa value, the following quantiles are computed: 5th, 10th, 20th,….,90th, and 95th (grey vertical distributions in Fig. 2c). Next, smooth spline functions are fitted through all respective quantiles, generating the ({R}_{{theta }_{0}^{{vm}}})quantile contours, which represent the null expectation under CRW. This expected (RΔθ, Rθ) correspondence creates a phase diagram (Fig. 2c), based on which the observed θ patterns are gauged. The procedure is repeated four times to match the among-study differences in the number of θ observations per trial (i.e., Nobs = 21, 90, 180, and 300; see Table 1).To examine if the observed larval movement patterns differ from those expected for unoriented movement (CRW-vm), we compute RΔθ and Rθ for each individual trial (({hat{R}}_{triangle theta }) and ({hat{R}}_{theta })). We then place these values in the phase diagram and examine their positions with respect to ({R}_{{theta }_{0}^{{vm}}}) (Fig. 2c). Larvae with ({hat{R}}_{theta }) substantially higher than ({bar{R}}_{{theta }_{0}^{{vm}}}), are considered to have a higher tendency for a straighter movement than expected under CRW, suggesting oriented movement such as BRW and BCRW (Fig. 2b, c)6,28. Larvae with ({hat{R}}_{theta }) values substantially below ({bar{R}}_{{theta }_{0}^{{vm}}})indicate irregular patterns such as a one-sided drift (right or left). A larva is considered directional if the bearing sequence ((hat{theta })) is significantly different from a uniform distribution based on the Rayleigh’s test (p  More

Scientists with visible and invisible disabilities take on adversity, helping themselves and others.Shigehiro Namiki always wanted to study insects. After his PhD research at the University of Tsukuba, he was a postdoctoral fellow, then a staff scientist at Janelia Research Campus. Among his projects, Namiki worked with others on a method to analyze how the few so-called descending neurons in fruit flies control a wide range of movements and behavior. These neurons run from the brain to the ventral nerve cord and branch out to circuits that control the insect’s neck, legs and wings. More