Philippa Kaur

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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

Study areaFigure 2 shows the location of the study area on a map of China generated by ArcGIS software. This study’s field experiments were carried out in the Shuanghe Town agricultural comprehensive water-saving demonstration area (40°42′ N; 107°24′ E), which is located in the middle reaches of the Hetao Irrigation Area of Inner Mongolia. The duration of the experimental process ranged from April in 2018 to October in 2020. The experimental area was characterized by a mid-temperate semi-arid continental climate. The average annual precipitation was determined to be 138 mm and the average evaporation was approximately 2332 mm. The majority of the rainfall was concentrated during summer and autumn seasons, and the accumulation of salt in the surface soil was considered to be serious in the spring and winter months. The average rainfall during maize growth period was 75.3 mm. The 0 to 40 cm soil layers in the experimental area were categorized as silty loam soil, with an average bulk density ranging from 1.42 to 1.53 g cm−3. A maize straw layer with a thickness of 5 cm was buried at a depth of 40 cm, and then the land was leveled. Also, in addition to autumn watering and spring irrigation procedures, water from the Yellow River was used three times for irrigation during the entire growth period of the maize crops. The adopted irrigation method belonged to border irrigation. Urea (46% N) were used as the fertilizer types.Figure 2The location of the study area.Full size imageField trials design and data collectionWe carried out experiment 1 from 2018 to 2019, and the data obtained were used for model training and to determine the hyper-parameters. The experimental design is shown in Table 1. The PNN model trained from the data obtained in experiment 1 predicted the optimal range of irrigation amount and nitrogen application rate (N rate) for each growth period of maize. In these ranges, the soil organic matter and total nitrogen could be kept above 20 g/kg and 1.6 g/kg, respectively, the soil salt content was less than 2 g/kg, and the pH value was between 6.5 and 7.5. In order to verify the accuracy and feasibility of the range of irrigation and nitrogen application simulated by PNN, the field experiment 2 was set in 2020 based on the range simulated by PNN and to evaluate the fitting degree between measured and simulated values of soil indicators under the same amount of irrigation and nitrogen application. The experimental design is shown in Table 2.Table 1 Experimental 1 design scheme.Full size tableTable 2 Experimental 2 design scheme.Full size tableThe experimental design were repeated for three times. The plot area of each treatment measuring 8 × 9 = 72 m2. The surrounding area was separated using 1.2 m buried polyethylene plastic film, and 30 cm was left at the top to prevent fertilizer and water from flowing into each other. The field management process was consistent with that used by the local farmers. The film width of maize was 1.1 m, with each film covering two rows. The plant spacing was approximately 45 cm, and the row spacing was 35 cm. In addition, the planting density of the maize was 60,000 plants/hm2.During the entire growth period of the maize crops, soil samples were collected from the 0 to 20 cm, 20 to 40 cm, 40 to 60 cm, 60 to 80 cm, and 80 to 100 cm soil layers using a soil drill and a three-point method was adopted. The soil samples were stored at 4 °C for the determination of total nitrogen, organic matter, total salt content, and pH values. The total nitrogen, organic matter, total salt content, and pH were determined using a KDN-AA double tube azotometer, MWD-2 microwave universal digestion device, TU1810PC ultraviolet–visible spectrophotometer, and a TU18950 double beam ultraviolet–visible spectrophotometer, respectively.Soil parameters measured include organic matter (SOM), total nitrogen (TN), Salt and pH. The data set includes pre-irrigation and post-irrigation reports from 2018 to 2020. Statistical parameters regarding the soil data are shown in Table 3.Table 3 Various meteorological variables and their descriptive statistics.Full size tableThe dataset obtained in Experiment 1 in 2018 to 2019 was 2490 rows in size, the 80/20 principle was used to data into training, and testing sets were required for ML modeling; 80% of data were employed for model training, while the remaining 20% were used for testing. Specifically, the data corresponding to the treatments with the nitrogen application rate (N rate) of 75 kg/hm2 (N3) in all the treatments (W1N3, W2N3, W3N3) were used as the test set, and the data of the other treatments were used as the training set. The training set was used to initiate ML parameter training. Subsequently, The test set was employed to assess the model. The dataset size in 2020 was 1080 rows, which was used to verify ML modeling.Figure 3 shows the changes of soil indexes over time for each treatment in the field test (take the 0–40 cm soil in the main distribution area of maize roots as an example). There are differences under the influence of different irrigation amounts. When irrigation is 90 mm, soil SOM is 13.25% and 7.00% higher than 60 mm and 120 mm, and soil TN is 4.59% and 6.50% higher than 60 mm and 120 mm, respectively. The soil Salt was 23.30% lower than 60 mm, and the pH was 4.16% and 4.36% lower than that of 60 mm and 120 mm, respectively. It can be seen that irrigation of 90 mm is more favorable for increasing soil SOM and TN contents and reducing soil salinity and alkalinity. Soil SOM and TN contents were the highest at n 75 kg/hm2, which were 4.38% and 8.34% higher than those at N = 93.3 kg/hm2, respectively. Soil Salt was the lowest at N = 60 kg/hm2, which was 3.02% lower than those at N = 75 kg/hm2, with a small gap with other levels. In conclusion, nitrogen application of 75 kg/hm2 was beneficial to increase soil organic matter and nitrogen content, and nitrogen application of 60 kg/hm2 was beneficial to controlling soil salt content.Figure 3Changes in soil organic matter, total nitrogen, salinity, and pH under different treatments over time (a case study of 2019).Full size imageMachine learning (ML) models used for irrigation and nitrogen application strategiesFive ML frames were used to estimate the irrigation and N rate. These models are preference Neural Network (PNN), Support Vector Regression (SVR), Linear Regression (LR), Logistic Regression (LOR), and traditional BP Neural Networks (BPNN). Among them, the prediction effects of linear, Poly, and rbf kernel functions are respectively tried in SVR framework. The torch framework was used to train and test machine learning models in Python.Development of preference neural networkModel frameworkThe preference neural network (PNN) which was proposed for the first time in this study was a typical deep learning model. PNN can be regarded as an approximate natural function in order to describe the complete dependence of the soil fertility indexes, including the effects of soil total nitrogen, organic matter, total salt content, and pH values on irrigation and nitrogen applications. More specifically, PNN has the ability to optimize the function by constructing the mapping y = f (x, θ) and learning parameter θ.First, the input end of PNN model was defined as matrix X ∈ ℝn×d (in which n is the sample size, n = 2490; and d is the dimension of each input vector, d = 6), where {xi} i=1, …, n ∈ X represents the vectorized set of total nitrogen, organic matter, salt content, and pH used for measuring the soil fertility, as well as the nitrogen application and irrigation durations (expressed by days after sowing). At the same time, the output end of the model was defined as the matrix Y ∈ ℝn×2, which represented the levels of the irrigation and nitrogen fertilizer applications. The goal of the proposed PNN model was to learn the fixed mapping Y′ = f (X; θ) ⇒Y through the given input matrix X, where θ is the well optimized learnable parameters which can be obtained via PNN training. Meanwhile, the predicted value Y′ will infinitely approach the measured value Y. The structure and the algorithm of this study’s PNN model is shown in Fig. 4 and Table. 4.Figure 4Schematic diagram for the PNN structural connections. In the figure, it can be seen that when each input vector passed through each layer of the PNN, it is first multiplied by the Hadamard product of the weight matrix and preference value matrix for the purpose of obtaining a weight matrix with preference properties. After the matrix was activated by the Relu Function, Batch Normalization Module Methods and the Dropout Module were used for random suspension and normalization processing, and the input of the next layer was obtained.Full size imageTable 4 Algorithm of Preference neural network.Full size tableLayer-by-layer affine transformationA good definition of the affine transformation of the information flow between layers is considered to be the key to neural network model training. Generally speaking, the learnable parameter θ of each layer of a model includes the weight parameter w and the preference parameter b. The hidden representation hl of the l-th layer in PNN is defined as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{mathrm{T}}{W}_{l}+{b}_{l}$$
(1)

where Wl and bl represent the learnable weight and bias variables of the l layer, respectively, and hl-1 is the hidden representation of the upper layer. Therefore, when l = 1, then h0 = X.In the present study, using the hierarchical update rules, a given input data stream was allowed to pass through each hidden layer with intermediate operations, and then finally reached the output end.Preference structureThe correlation between different production behavior factors (e.g., irrigation levels) and different natural factors (e.g., soil organic matter) differs in agricultural production. However, the traditional fully connected neural network has the characteristic that nodes of one layer are fully connected with all nodes of subsequent layers, resulting in the neurons between production behavior factors and natural factors with very weak correlation still all being connected. Conversely, connections between neurons corresponding to factors with solid correlations are not strengthened.Therefore, in this study the preference value module was specially developed. By first calculating the correlation and significance between different production behavior factors (irrigation amount, N rate) and different soil fertility factors (organic matter, total nitrogen, total salt and pH), the preference value between the above two types of variables was calculated, and the preference matrix was constructed. Then the Hadamard product of the weight matrix and preference matrix was used to realize the artificial intervention and guidance to the neural network’s learning process.In order to reduce the adverse impact of non-normality of data on correlation analysis as much as possible, this study rank-based inverse normal (RIN) transformations (i.e., conversion to rank score) methods were used to normally process the data28. The RIN transformation function used here is as follows:$$f(x)={Phi }^{-1}left(frac{{x}_{r}-frac{1}{2}}{n}right)$$
(2)

where Φ–1 is the inverse normal cumulative distribution function, and n is the sample size.The normal cumulative distribution function is represented as follows: for discrete variables, the sum of probabilities of all values less than or equal to a, and its formula is as shown below:$${F}_{X}(a)=P(Xle a)$$
(3)
The RIN normalized conversion values meet the requirements of normal distribution, Pearson correlation analysis and t-test can be directly performed, and the formula used was as follows:$$r(X,Y)=frac{mathrm{Cov}(X,Y)}{sqrt{left(mathrm{Var}left[Xright]mathrm{Var}left[mathrm{Y}right]right)}}$$
(4)

where r (X, Y) is the Pearson Correlation Coefficient, Var [X] is the variance of X, and Var [Y] is the variance of Y, Cov (X, Y) is the covariance of X and Y, which represents the overall error of the two variables. The t-test is performed on the normalized data after rank-based inverse normal (RIN) transformation method, and the formula is as follows:$$t=sqrt{frac{n-2}{1-{r}^{2}}}$$
(5)

where n is the number of samples, and r represents the Pearson Correlation Coefficient. Preference value is the concentrated embodiment of correlation and significance between variables, and the calculation formula is as follows:$${PV}_{ij}=frac{r({X}_{i},{Y}_{j})}{{P}_{ij}+e}$$
(6)

where PVij represents the preference values between the variables Xi and Yj, Xi represents the ith production behavior factor (e.g., irrigation amount), and Yj represents the jth soil fertility factor (e.g., soil organic matter content), ({P}_{ij}) is obtained by looking up the table based on the t, and e is a constant, taking 0.001 in order to prevent the denominator of the formula from being 0.In order to make the preference values of the various indicators in the same order of magnitude more stable, the preference values were normalized:$${PV}_{normal}=pm frac{left|{PV}_{i}-{PV}_{avg}right|}{sqrt{frac{sum_{i=1}^{N}{({PV}_{i}-{PV}_{avg})}^{2}}{N-1}}}$$
(7)

where N represents the number of variables related to the experimental treatments, PVi -PVavg takes the absolute value, while the positive or negative values of the PVnormal were determined by the positive or negative values of the correlation r.The PNN integrated the preference matrixes into the neural network structures by identifying the Hadamard products of the learnable weights between the preference matrixes and the input and output data. By referring to Eq. (1) in the hierarchical affine transformation, the preference constraint of PNN could be expressed as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{T}{W}_{l}odot P+{b}_{l}$$
(8)

where P is the preference matrix calculated by Eq. (8), and ⊙ represents the Hadamard product of the corresponding elements of the matrix. The structure of preference neural network and preference value are shown in Figs. 5 and 6.Figure 5Schematic diagram of the preference connection structures of the preference neural networks. The depth of the network detailed in the figure only illustrates the preference connection structure (for a better demonstration), and does not indicate the depth of the PNN used in the experiment.Full size imageFigure 6PVnormal between production behavior factors and natural factors. Since soil depth, days, irrigation amount and N rate were all artificially set variables, and there was no objective correlation in the data set. Therefore, the preference values among these variables were default e = 0.001.Full size imageHyper-parameters of PNNWe conducted experiments on the datasets with varying the hyper-parameters (such as the number of PNN layers and hidden layers, the number of nodes in each layer, learning rate, dropout rate and batch size) to understand that how the Hyper-parameters impact on the performance of PNN.We select the activation function and learning rate by referring to the neural network structure commonly used in similar fields (1 hidden layer and 64 hidden nodes)29,30. It is found that ReLU has better performance than other activation functions (sigmoid, tanh). The performance is best when the learning rate is around 0.005. It is generally believed that neural networks with more hidden layers are able, with the same number of resources, to address more complex problems31, but excessively increasing network depth will easily lead to overfitting32. Since there is no direct method to select the optimal number of hidden layers and nodes33, this study first calculated the structure of one hidden layer and 64 nodes in each layer, and found that the combined effect was poor (R2 of irrigation and nitrogen application were 0.3971 and 0.4124, respectively). Therefore, the trial-and-error method is adopted. The number of hidden layers starts from 1 and is incremented by 1 to test the maximum number of 10 hidden layers. The number of nodes in each layer were tested with a maximum number of 100 hidden neurons, starting with 5 and increasing by 5.We found that when the number of hidden layers of PNN exceeds 6, and the number of nodes in each layer exceeds 65, the performance will drop significantly. The reason behind this phenomenon could be the current dataset size is insufficient for larger scale of the PNN model. In the consideration of that the size of new dataset we can obtain very year is similar to the current dataset size, we believe that current hyper-paramter settings of PNN is in a reasonable condition.After that, the number of layers was fixed as 6, and the number of nodes in each layer were tested 10 times with 60 as the starting point and 1 as the increment, we found that when the number of nodes was 64, the improvement of the fit degree was no longer noticeable. On this basis, we changed different activation functions and learning rate again, and found that PNN still has the best performance when the activation function is ReLU and the learning rate is 0.005. Then, different batch sizes and dropout rates were tried. The two parameters had weaker effects on the performance than the other parameters, and the performance was optimal at 256 and 0.1, respectively.The hyper-parameters include:

1.

number of PNN layers;

2.

number of hidden layers;

3.

types of activation function;

4.

percentage of dropout;

5.

learning rate;

6.

loss function;

7.

optimizer;

8.

batch size;

9.

number of epochs;

10.

number of workers.

The ideal PNN structure for the study comprises these layers:

1.

number of PNN layers is 8;

2.

number of hidden layers is 6;

3.

Fully connected layers with 64 nodes and ReLU activation function

4.

dropout with 0.1.

5.

the learning rate is 0.005;

6.

loss function is Huber Loss Methods (HLM);

7.

optimizer: ADAM;

8.

epochs is 500;

9.

the batch size is 256;

10.

number of workers is 6.

Hyper-parameters of other modelsLR algorithms and LOR do not have hyper-parameters that need to be adjusted. A part of the hyper-parameters of the SVR model was determined by referring to Guan Xiaoyan’s research34, and a part of the hyper-parameters of the BPNN model was determined by referring to Gu Jian’s research27. RMLP takes the same hyperparameters as PNN. The hyperparameters of SVR and BPNN models are shown in Table 5.Table 5 Hyper-parameters of other model.Full size tableModel performance evaluationThe proposed PNN model was trained and validated using the field measured data from 2020 and the performance achievements of PNN were evaluated by the root mean square errors, mean square errors, and mean absolute errors as follows:$$RMSE=sqrt{frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{n}}$$
(9)
$${R}^{2}=1-frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{iavg})}^{2}}$$
(10)
$$MAE=frac{{sum }_{i=1}^{n}left|{y}_{ipre}-{y}_{iavg}right|}{n}$$
(11)
Model multidimensional fertility targetsThe soil fertility grade classification of soil organic matter, soil total nitrogen content and salt content in this study was based on the soil fertility grade classification results by the Agriculture and Animal Husbandry Bureau of Bayannur City, along with the local standard Technical Specifications for the Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), as the shown in Tables 6 and 7.Table 6 Soil organic matter and Soil total nitrogen degrees.Full size tableTable 7 Grading of the salinization degrees.Full size tableIn the evaluation system of soil fertility referencing the Technical Specifications for Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), the pH was divided into four grades according to the membership degrees of the land productivity evaluations, as detailed in Table 8.Table 8 pH grading degrees of the cultivated land.Full size tableBased on the classification standard of soil fertility obtained by the Bureau of Agriculture and Animal Husbandry of Bayannur City, when the farmland soil is at the high fertility level, the soil organic matter and total nitrogen content should be more than 20 g/kg and 1.6 g/kg, respectively. Soil salt content was less than 2 g/kg. Meanwhile, the pH value is kept between 6.5 and 7.5. More

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Study sites and study designThe study was performed in the frame of a dog ecology research project, with details on the study locations published elsewhere15,42,43. For the current study, five study sites located in Indonesia and Guatemala were included. Site selection was carried out by each country’s research team, taking into consideration rural and urban settings, as well as differing expected number of dogs present at each location. The Indonesian study sites were semi-urban Habi and rural Pogon, in the Sikka regency, at the eastern area of Flores Island (Supplementary Fig. 6). In Guatemala, the study sites were Poptún (urban setting), Sabaneta and La Romana (both rural settings), located in the Guatemalan department of Péten, in the northern part of the country (Supplementary Fig. 7). Data were collected during May to June 2018 in Guatemala and from July to September 2018 in Indonesia.In each location, a 1 km2 area was predefined using Google Earth within which the study took place. The 1 km2 area was chosen because of the research goals of another part of the project, investigating the contact network of the dogs15. Within these areas, the teams visited all dog-owning households. In each household, the study was presented to an adult of the family, who was then asked if they owned a dog and if they were willing to participate in the study. After the dog owner’s oral or written consent was granted, a questionnaire was answered, and the dogs collared. The handling of the dogs was performed by a trained veterinarian or a trained veterinary paramedic of the team.The questionnaire data was collected through interviews with the dog owners. Multiple dogs per household could be included as multiple entries in the questionnaire. The detailed questionnaire contains information on the household location, dog demographics (age, sex, reproductive status) and management (dog’s purpose, origin, confinement, vaccination status, feeding and human-mediated transportation within and outside the pre-determined area).All dogs of a household fulfilling the inclusion criteria were equipped with a geo-referenced contact sensor (GCS) developed by Bonsai Systems (https://www.bonsai-systems.com), containing a GPS module and an Ultra-High-Frequency (UHF) sensor for contact data recording43,44. GCS devices report a 5-m maximum accuracy, a run-time of up to 10 years, can store up to 4 million data points and carry a lithium-polymer-battery (LiPo). For this study, only GPS data were analysed. The GCS were set to record each dog’s geographical position at one-minute intervals. Dogs remained collared for 3 to 5 days with the duration of the data collection being limited by the device’s battery capacity, as batteries were not re-charged or changed during the study. Throughout the time of recording, date, hour, GPS coordinates and signal quality (HDOP) raw data were collected by the GPS module and amassed into the workable databases.Exclusion criteria were dogs of less than four months of age (since they were not big enough to carry a collar), sick dogs and pregnant bitches (to avoid any risk of stress-induced miscarriages). Reasons for non-participation of eligible dogs included dog owner’s absence, dog’s absence, inability to catch the dog, and refusal of participation by the dog owner. In addition, dogs foreseen for slaughtering within the following four days were excluded in Indonesia to ensure data collection for at least four to five days. All dogs included in this study were constantly free roaming or at least part-time (day only, night only and for some hours a day). Human and/or animal ethical approval were obtained depending on the country-specific regulations. All the procedures were carried out in accordance with relevant guidelines. Ethical clearance was granted in Guatemala by the UVG’s International Animal Care and Use Committee [Protocol No. I-2018(3)] and the Community Development Councils of the two rural sites, which included Maya Q’eqchi’ communities45. In Indonesia, the study was approved by the Animal Ethics Commission of the Faculty of Veterinary Medicine, Nusa Cendana University (Protocol KEH/FKH/NPEH/2019/009). In addition, dogs that participated in the study were vaccinated against rabies and/or dewormed to acknowledge the owners for their participation in the study.Data cleaningData were stored in an application developed by Bonsai Systems compatible with Apple operating system (iOS iPhone Operating Systems), downloaded as individual csv file for each unit, and further analysed in R (version 3.6.1)46.The GPS data were cleaned based on three automatised criteria. First, the speed was calculated between any two consecutive GPS fixes, and fixes with speed of  > 20 km/h were excluded, given the implausibility of a dog running at such speed over a one-minute timespan47. It is noteworthy that car travel causes speeds over 20 km/h. However, as we were interested in analysing the dog’s behaviour outside of car transports, removing these fixes was in line with our objectives. Second, the Horizontal Dilution of Precision (HDOP), which is a measure of accuracy48 and automatically recorded by the devices for each GPS fix, was used to exclude fixes with low precision. According to Lewis et al.49, GPS fixes with HDOP higher than five were excluded, which deleted 1.3% of data in Habi, 2.2% in Pogon, 3.3% in Poptún, 1.8% in La Romana and 2.1% in Sabaneta. Third, the angles built by three consecutive fixes were calculated for each dog. When studying animals’ trajectories as their measure of movement, acute inner angles are often connected to error GPS fixes50. The fixes having the 2.5% smallest angles were excluded, to target those fixes with highest risks of being errors, while balancing against the loss of GPS fixes due to the cleaning process. With the exclusion of the smallest angles, 2.6% of data were deleted in Habi, 3% in Pogon, 2.9% in Poptún, 2.6% in La Romana and 2.7% in Sabaneta. After the automatised cleaning was concluded, 18 obvious error GPS fixes (unachievable or inexplicable locations by dogs) still prevailed in the Habi dataset and were manually removed.Habitat resource identification and calculation of terrain slopeTo analyse habitat selection of the collared FRDD, resources were delimited by a 100% Minimum Convex Polygon (MCP) including all cleaned GPS fixes per study site, using QGIS51 (Fig. 1).Figure 1GPS fixes plotted over a Google satellite imagery layer with its respective outlined computed Minimum Convex Polygon (MCP) delimitating the habitat available for the study population in: (a) Habi; (b) Pogon; (c) Poptún; (d) La Romana and (e) Sabaneta. Source QGIS (version 3.4 Madeira, http://qgis.org), map data: Google Satellite.Full size imageResources were defined by taking into consideration the following criteria: resources are (i) likely to impact upon movement patterns of dogs, (ii) identifiable by landscape satellite topography, and (iii) chosen considering information on relevant gathering places for FRDD observed by the field teams. Three resources were disclosed in all study sites: buildings, roads and vegetation coverage. All habitat relevant resources were manually identified within the available area (MCP) in QGIS using satellite imagery. All building-like structures were identified using vector polygons and summed under the layer “buildings”. Roads were identified and manually traced using vector lines in all sites, except in Poptún where the roads were automatically traced using an OpenStreetMap road layer of the area (https://www.openstreetmap.org/export). A buffer vector polygon was generated to encompass the full potential width of the roads, with a 5 m width in Habi and Poptún (semi-urban and urban site) and a 2 m width in Pogon, La Romana and Sabaneta (rural sites). In Habi, a “beach” layer was defined by generating a five-meter buffer from the shoreline in both directions using a vector polygon. The layer “sea” was defined as the vector polygon resulting from the difference between the MCP sea outer limit and the beach buffer polygon. Vegetation coverage was distinct between study sites with sparse vegetation and bushes present in all sites except Pogon, and dense forest-like vegetation present in La Romana and Pogon. These two types of vegetation were defined as “low” and “high vegetation”, respectively. In Habi and La Romana, “low” and “high vegetation”, respectively, were manually identified using vector polygons and summarised under the respective layers. Finally, open field in Habi, high vegetation in Pogon and low vegetation in Poptún, La Romana and Sabaneta were the last vector layers to be established since they represented the difference between all other polygon vector layers and the MCP total area. After all resource vector polygons had been created, an encompassing vector layer was generated by merging all resource polygon vectors for final resource classification (Fig. 2). As part of the resource classification in Habi, the airport terminal and runaway as well as waterways enclosed in the MCP area were identified but excluded from the analysis.Figure 2(a) Habi, (b) Pogon, (c) Poptún, (d) La Romana and (e) Sabaneta Habitat classification vector layers. The different habitat resources, identifiable by colour, were merged to create the comprehensive Habitat classification vector. In the Indonesian sites (a, b) and Guatemalan sites (c–e) buildings are coloured red, vegetation low in Habi, Poptún, La Romana and Sabaneta is coloured light green, vegetation high in Pogon and La Romana dark green, roads black, beach yellow, sea dark blue, airport grey, waterways light blue and open field light orange. The airport area (gray) and waterways (light blue) in Habi were not classified as separate habitat layers and were excluded from further analysis. Source QGIS (version 3.4 Madeira, http://qgis.org), map data: Google Satellite.Full size imageAfter the construction of the habitat resource layers, all GPS fixes were assigned to the respective resource they were located, using the QGIS join attributes by location algorithm. Fixes located exactly on the MCP border in Indonesia were not classified automatically and had to be manually classified to the respective resource.In non-flat topographies (all locations expect Habi) we tested the hypothesis of whether the steepness would influence the dogs’ movement patterns. The degrees of slope were calculated using a 30-m raster-cell resolution (STRM 1-Arc Second Global, downloaded from the United States Geological Survey (USGS) Earth Explorer, https://earthexplorer.usgs.gov/). The slope was assigned by the QGIS join attributes by location algorithm to each GPS fix.Statistical analysisTo quantify habitat selection in each study site, we compared resources used by the dogs with the resources available, according to Freitas et al.52. Adapting the methodology applied by O’Neill et al.18, the observed number of GPS fixes for each dog was used to generate an equivalent number of locations that were randomly distributed within the MCP area using the Random points in layer bound vector tool from QGIS. For example, if dog “D300” had 100 recorded GPS fixes, 100 random points were generated within the MCP of the respective study site and assigned to “D300”. Random points were then assigned to the respective resources and slope of that location, as previously done with the observed GPS fixes. Using this approach, the habitat resources used by each dog could be compared to the available resources in the respective study site, using a regression model.Observation independence is a fundamental presupposition of any regression model. However, the spatial nature of the point-referenced data permits perception of spatial dependence. In our dataset, spatial autocorrelation was proven for all study sites using the Moran’s I test. Therefore, we applied a spatial regression model, which takes into consideration spatial autocorrelation while exploring the effects of the study variables. A mixed effects logistic regression model accounting for spatial autocorrelation was created to quantify the effect of variables on used (i.e. observed GPS fix) versus available (i.e. randomly generated GPS fixes) resources, using the fitme function in the spaMM package in R53,54. The model’s binary outcome variable was defined as either observed (1) or random (0) GPS fix, i.e. the dog being present or absent from a position. The explanatory variable was the resource classification with “buildings”, “roads”, “low vegetation”, “beach”, “sea” and “open field” as levels in Habi; “buildings”, “roads” and “high vegetation” in Pogon; “buildings”, “roads”, “low vegetation” in Poptún and Sabaneta; and “buildings”, “roads”, and “high” and “low vegetation” in La Romana. Different habitat resources were used interchangeably as reference level. In all study sites except Habi, the slope was included as an additional explanatory variable. As observations were not evenly distributed in time, with less observations recorded towards the end of the study, a variable ”hour” was added as an additional continuous fixed effect.Each observed GPS fix was assigned to the hour of its record, with the earliest timestamp registered in each study site being assigned the hour zero. The randomly generated points were randomly assigned to an hour within the determined time continuum of the observed GPS fixes. As our focus was investigating habitat selection at a population-level, we assumed there was no within-dog autocorrelation (space/time) and each dog was independent and exhibited no group behaviour38. Still, to partially account for spatial autocorrelation of each dog’s household, the random effects included in models were defined as each dog’s household geographical location recorded during fieldwork by a GPS device. The restricted maximum likelihood (REML) through Laplace approximations, which can be applied to models with non-Gaussian random effects55, and the Matérn correlation function were used to fit the spatial models with the Matérn family dispersion parameter ν, indicator of strength of decay in the spatial effect, was set at 0.554. More

Study area descriptionYangtze River Basin is situated in central China (Fig. 1). Its geographical coordinates are between 30° 48′ 30″–31° 02′ 30″ N and 112° 48′ 45″–113° 03′ 45″ E. Taizishan is located in the transition zone between the north and south of China, with an altitude of 403–467.4 m. It belongs to the subtropical monsoon humid climate zone and has obvious karst landforms. The farm area is 7576 hectares, the forest coverage rate is 82.0%, and the vegetation is mainly Masson pine, fir, and various broad-leaved tree species. Increased forest coverage reduces sediment production30. The soil is mainly viscous yellow–brown soil and loess parent material. Rain is concentrated in summer, with an average annual rainfall of 1094.6 mm and an average annual temperature of 16.4 °C. Rainfall-related flood risk increased in the Yangtze River Delta in recent years31.The study was based in a Pinus massoniana forest in the Taizishan forest farm of Hubei Province. The Pinus massoniana (Masson pine) is a common species distributed in Central China.Figure 1Geographic location of the study area. Maps were generated using ArcGIS 10.8 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageExperiment designWe chose the Pinus massoniana forest with 47a in the study area as the research object. In the typical Pinus massoniana forest, the separate layers of litter (semi-decomposed and non-decomposed layers) were collected from several 1 m × 1 m quadrat and placed in grid bags. The litter of the semi-decomposed layer have no complete outline, and the color was brown. As the litter leaves of the completely decomposed layer are powdery and are combined with the soil layer, this layer is difficult to collect. Before testing, it was necessary to clean the soil off the pine needles and then allow the litter to dry naturally. The characteristics of the semi-decomposed and non-decomposed litter layers are shown in Table 1. The soil samples need to be dried and screened by 10 mm. When filling the soil trough, every 0.1 m of soil thickness was one layer, for a total of four layers (0.4 m). The characteristics by soil particle sizes are different (Fig. 2). The soil samples were dried naturally, crushed, and then sieved. The soil trough (2 m long, 0.5 m wide and 0.5 m deep) was filled to have a bulk density of 1.53 g·m−3. In this process, an appropriate amount of water was sprinkled on the surface of each soil layer to achieve a soil moisture content consistent with the surrounding, undisturbed, or natural, state. The simulation experiment was conducted in the Jiufeng rainfall laboratory at Beijing Forestry University, China. We used a rainfall simulation system (QYJY-503T, Qingyuan Measurement Technology, Xi’an, China) used a rotary downward spray nozzle. The system is able to simulate a wide range of rainfall intensities (10 to 300 mm h−1) using various water pressure and nozzle sizes controlled by a computer system.Table 1 Characteristics of the non-decomposed and semi-decomposed layers of Pinus massoniana litter.Full size tableFigure 2Soil particle composition of study area soil layers.Full size imageAccording to the results of the field forest investigation, the litter was covered with the experimental treatments shown in Table 2. The treatments mass coverage of non-decomposed litter layer was named as follows: N1 denoted litter mass coverage 0 g·m−2, N2 was ‘the non-decomposed litter mass coverage 100 g·m−2’, N3 was ‘the non-decomposed litter mass coverage 200 g·m−2’, and N4 was ‘the non-decomposed litter mass coverage 400 g·m−2’, N5 was ‘the semi-decomposed litter mass coverage 100 g·m−2’, N6 was ‘the non-decomposed litter mass coverage 100 g·m−2 and the semi-decomposed litter mass coverage 100 g·m−2’, N7 was ‘the non-decomposed litter mass coverage 200 g·m−2 and the semi-decomposed litter mass coverage 100 g·m−2’. N2, N3 and N4 were the undissolved state of litter layer, and N4 (non-decomposed state, ND), N7 (initial stage of litter decomposition, ID), N6 (middle stage of litter decomposition, MD) and N5 (final stage of litter decomposition, FD) respectively represent different stages of litter decomposition.Table 2 The experimental design of this study.Full size tableAccording to the rainfall in the Taizishan area of Hubei Province, erosive rainfall and extreme rainstorms were selected as the research conditions. Summer rainfall events occur mainly in the summer in this area, and a rainfall intensity of 60 mm·h−1 was the most common erosive rainfall intensity. Under extreme weather conditions, the rainfall intensity can reach up to 120 mm·h−1. Our experiments were conducted with 60 and 120 mm·h−1 rain intensities with a rainfall that lasted 1 h. According to the field investigation data of forest land, this area is a low mountain and hilly area with a slope mostly between 5° and 10°. Therefore, 5° and 10° were selected for the slope treatments in this study. The combination of slope and rainfall intensity was named as follows: T1 denoted ‘Slope 5° and rainfall intensity 60 mm·h−1’, T2 was ‘Slope 10° and rainfall intensity 60 mm·h−1’, T3 was ‘Slope 5° and rainfall intensity 120 mm·h−1’, and T4 was ‘Slope 10° and rainfall intensity 120 mm·h−1’. With two rainfall intensities, two slopes, seven litter coverage gradient and two repetitions combined, this study had a total of 56 rainfall events.Experimental procedureBefore the test, the soil samples were wetted for 10 h and then drained for 2 h to eliminate the effect of the initial soil moisture on the soil detachment measurement. When the simulated rainfall started, all the runoff and sediment produced from plot were collected every 5 min in the first 10 min, and then collected once every 10 min during the subsequent 50 min. At the same time, runoff velocity, depth and temperature were measured and vernier calliper (accuracy 0.02 mm) respectively.The overland flow velocity was measured using dying method (KMnO4 solution)32. After judging the flow pattern, we confirmed the correction coefficient K value (in laminar flow state, K = 0.67; transition flow state, K = 0.70; turbulent flow state, K = 0.8). The average velocity of overland flow was obtained by multiplying the correction coefficient K and the instantaneous velocity. Runoff depth was measured using vernier calliper (accuracy 0.02 mm). Runoff temperature was measured using thermometer. When the rainfall experiment finished, the collected runoff samples were measured volumetric cylinder and then settled for at least 12 h. The clear water was decanted, and the samples were put into an oven to dry for 24 h under 105 °C. The sediment sample was dried and weighed with an electronic scale.Calculation of hydrodynamic parametersOverland flow has the characteristics of a thin water layer, large fluctuations of the underlying surface, and unstable flow velocity. At present, most scholars use open-channel flow theory to study overland flow33,34. In open-channel flow theory, the Reynold’s number (Re), Froude constant (Fr), flow index (m), resistance coefficient (f), and soil separation rate (({D}_{r})) are the basic parameters of overland flow dynamics, through Reynold’s number (Re), Froude constant (Fr), flow index (m) can distinguish flow patterns. Re is calculated as:$$Re=Rcdot V/nu ,$$where Re is the Reynolds number of the water flow, which is dimensionless, and can be used to judge the flow state of overland flow. When Re ≤ 500, the flow pattern is laminar; when 500   5000, the flow pattern is turbulent. R is the hydraulic radius (m), which is generally replaced by flow depth as measured by a vernier calliper (accuracy 0.02 mm). (V) is the average velocity (m·s−1); (nu) is the kinematic viscosity coefficient (m2·s−1), and the calculation formula is (nu) = 0.01775·10−4·(1 + 0.0337 t + 0.00021 t2), where t is the test overland flow temperature35.Fr is the Froude constant, which is the ratio of the inertial force to gravity and can be used to distinguish overland flow as rapid flow, slow flow, or critical flow. When Fr  1, the fluid is rapid flow.Fr is calculated as:$$Fr=V/sqrt{gcdot R},$$where (Fr) is the Froude constant of the water flow, which is dimensionless; (V) is the average velocity (m·s−1); g is the acceleration of gravity and has a constant value of 9.8 m·s−2; R is a hydraulic radius (m), and is generally replaced by flow depth as measured by a vernier calliper (accuracy 0.02 mm).Regression fitting is made for runoff depth (h) and single width flow (Q). The runoff depth equation for slope is as follows:$$h=k{q}^{m},$$where q is the single width flow (L·m−1·s−1); h is the depth of water on the slope (m); and m is the flow index, which reflects the turbulent characteristics of the flow state. The larger m is, the more energy the flow consumes in the work of resistance. The comprehensive index (k) reflects the characteristics of the underlying surface and the water viscosity of the slope flow. The larger k is, the stronger the surface material of the slope works on the flow.The resistance of overland flow reflects the inhibition effect of different underlying surface conditions on the velocity of overland flow. The Darcy–Weisbach formula is widely used in research because of its two advantages: applicability and dimensionlessness under laminar and turbulent flow conditions36,37.The resistance coefficient (f) is calculated as follows:$$f=8cdot gcdot Rcdot J/{V}^{2},$$where the resistance coefficient f has no dimension; g is the acceleration of gravity and is always 9.8 m·s−2; R is a hydraulic radius (m), generally replaced by flow depth measured by a vernier calliper (accuracy 0.02 mm); (V) is the average velocity (m·s−1); and J is the hydraulic gradient, which can be converted by the gradient in a uniform flow state and is generally replaced by the sine value of the gradient.Shear stress ((tau)) is the main driving force that affects the stripping of soil particles from the surface soil38. Shear stress is calculated as:$$tau =rcdot gcdot Rcdot J,$$where (tau) is the shear force of runoff (Pa); and r is the density of water and sediment concentration flow (kg·m−3). This study used a muddy water mass and volume ratio in the unseparated state to calculate the density of water and sediment concentration flow.Flow power (W) is the runoff power per unit area of water and refers to the power consumed by the weight of water acting on the riverbed surface to transport runoff and sediment. W is calculated as:$$W=tau cdot V,$$where W is the flow power (N·m−1·s−1); and (tau) is the shear force of runoff (Pa).Soil separation rate (({D}_{r})) refers to the quality of soil in which soil particles are separated from the soil per unit time. The calculation formula is as follows:$${D}_{r}={W}_{d}-{W}_{w}/tcdot A,$$where ({D}_{r}) is the rate of soil separation (kg·m−2·s−1); ({W}_{w}) is the dry weight of soil before the test; ({W}_{d}) is the dry weight of soil after the test, measured by the drying method (kg); t is the scouring time (s); and A is the surface area of the soil sample (m2). More

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