Philippa Kaur

The experiments were approved by the French Ethics Committee in charge of Animal Experimentation (no.2019072411491441) and were in accordance with institutional and ARRIVE guidelines.Animal collection and husbandryIn May 2019, juvenile European sea bass, Dicentrarchus labrax (Linnaeus 1758) (6 months old, mass 5 g), were transferred from a fish farm (Turbot Ichtus, Trédarzec, France) to the Ifremer rearing facility (Plouzané, France). Fish were kept in a common tank for 5 months, maintained under a 12 L: 12 D photoperiod, and fed at satiety three times a week using commercial pellets (Neo Start, Le Gouessant, Lamballe, France).In October 2019, fish (n = 40) were anaesthetized (Tricaïne; 125 mg L−1), weighed (41.5 ± 1.8 g, MCE11201S-2S00-0, Sartorius, Göttingen, Germany), and implanted subcutaneously with an identification tag (RFID; Biolog-id, Bernay, France). The fish were then randomly allocated to ten replicate 400 L tanks supplied with open-flow, fully aerated seawater (oxygen saturation  > 95%, salinity 32 ppt), thermo-regulated during winter to avoid falling below 13 °C, and fed at satiety three times a week. Temperature was recorded weekly. To account for the potential effect of temperature variation over the duration of the trial (15.5 ± 0.5 °C, range: 13.1–17.9 °C) on growth, a correlations analysis was performed between temperature and specific growth rate (SGR). No statistical relationship was found between SGR and temperature (Spearman R2 = 0.060, P = 0.596). Additional fish (n = 40) were present in the tanks (final density: n = 8 per tank) for the need of another project.Growth measurementsBody mass (BM) was measured about every four weeks from October 2019 to June 2020. The fish were fasted for 48 h and anesthetized before each BM measurement (± 0.1 g). The specific growth rate (% day-1) was estimated as follows:$${text{Specific~Growth~Rate}} = ~frac{{ln left( {final~BM} right) – ln left( {initial~BM} right)}}{{{text{days~elapsed}}}} times 100$$In March 2020, a red muscle biopsy sample was collected from fish to measure the mitochondrial metabolic traits. Past growth was defined as specific growth rates before the analysis of mitochondrial metabolic traits (past specific growth rate, SGRpast). SGRpast were calculated using the BM at the muscle biopsy as the final BM and the BM at 7, 11, 16, and 20 weeks before the muscle biopsy as the initial BM (Fig. 1). Future growth was defined as specific growth rates after analysis of mitochondrial metabolic traits (future specific growth rates, SGRfuture). SGRfuture were calculated using the BM at 4, 8, and 12 weeks after the muscle biopsy as the final BM and the BM at the muscle biopsy as the initial BM. In European sea bass, most of the somatic growth occur within the first 3 to 5 years of life, so several months of growth measurement at the juvenile stage might be representative of the overall growth of the animal.Figure 1Experimental design. Juvenile European sea bass (n = 40) were weighted about every four weeks over a 32-week period. At week 20, a biopsy of red muscle was used for mitochondrial assay. Specific growth rates (SGR) were calculated relative to the time of the biopsy. Past growth rate corresponds to SGR calculated before the biopsy, and future growth rate corresponds to SGR calculated after the biopsy.Full size imageMuscle biopsy procedureMuscle biopsy was performed as a non-lethal means of sampling tissue for the mitochondrial assay while allowing us to determine future growth rate. Fish were anaesthetized with tricaine (as above), weighed (76.7 ± 3.6 g), and biopsied. A skin incision ( More

Study areaWe conducted field studies in both regions from August to March, each year from 2012 to 2016. In north India, we selected the two traditional breeding colonies of the Painted Storks, viz., the Delhi Zoo (28° 36′ N 77° 14′ E) and Keoladeo National Park (KNP) (27° 17′ N 77° 52′ E), Bharatpur, Rajasthan (Fig. 1). In the Delhi Zoo, close to the river Yamuna, the Painted Storks nest in the traditional heronries with other colonial nesters, Little Cormorant, Indian Cormorant, Black-headed Ibis, and Night Heron38. The KNP, a Ramsar site spread over 29 km2, situated at the confluence of the rivers Gambhir and Banganga on the western edge of the Gangetic basin, supports diverse fauna, flora, and a mosaic of habitats, wetlands, woodlands, scrub forests, grasslands, and heronries39. In 2013, we recorded 680 adults and 310 nests in the Delhi Zoo and 1584 adults and 430 nests of Painted Storks in the KNP.We selected the Vedanthangal Bird Sanctuary (VBS), the nesting colonies at Melmaruvathur Lake, and Koonthankulam Bird Sanctuary (KBS). The KBS & VBS are the newly declared Ramsar sites in Tamil Nadu, south India. The VBS (12° 32′ 02″ N and 79° 52′ 29″ E) is a 40.3-hectare community reserve effectively protected by the state Forest Department, Tamil Nadu, and Vedanthangal villagers40. It is the oldest breeding waterbird reserve in south India, located 85 km southwest of Chennai. More than 40 species of waterbirds, both residents and migrants, live here. Along with the other 17 heronry species, the Painted Storks build nests every year from November to April during its breeding season. The Painted Stork nesting colonies at Melmaruvathur Lake (12° 25′ 53″ N and 79° 49′ 36″ E) are about 20 km away from the VBS. Here, the Painted Storks build nests at 1.8–5 m above the water level, on trees of Acacia nilotica and Barringtonia acutangula on mounds surrounded by water41. In 2012, we recorded a total of 3185 nests in the VBS, with a maximum number of nests belonging to Spot-billed Pelican (1050 nests) followed by Painted Stork (550 nests), Asian Open-bill (770 nests), and others.Birds have been breeding in Melmaruvathur Lake since 2013, and we counted 80 nests of Spot-billed pelican, 45 nests of Oriental White Ibis, and 56 nests of Painted Stork during the winter of the year 2014. The Lake is spread over 0.19 km2 with islets (mounds) with four clusters of Acacia nilotica and Barringtonia acutangula trees. Rainwater and domestic sewage from the neighboring residential complex are the primary water source, and recreational boating attracts a large crowd visiting the Melmaruvathur temple41. KBS (8° 29′ 44″ N and 77° 45′ 30″ E) is about a 1.3 km2 protected area, declared a bird sanctuary in 1994 and an Important Bird Area40. It comprises Koonthankulam and Kadankulam irrigation tanks actively protected and managed by the local community. We noticed the frequent failures of breeding events due to water shortages related to monsoon failures in VBS and KBS. In 2015, we also observed Painted Storks’ breeding failure across northern India for unknown reasons; therefore, data could not be collected for those periods.Bioclimatic variablesWe obtained the bioclimatic variable, particularly temperature at 2 m height for all the four study sites, from the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) Prediction of Worldwide Energy Resource (POWER) Project funded through the NASA Earth Science/Applied Science Program. The monthly average data from 2010 to 2020 was downloaded from the POWER Project’s Hourly 2.0.0 version on 2022/01/04.Digital images of Painted Storks collected under field conditionsUsing Binoculars (Olympus 10X50), Digital Cameras (Canon 5D Mark III and Sony handy-cam), we monitored and recorded all active nests with juveniles and adult Painted Storks twice a week. The nests were on trees, 3–7 m in height, and chicks and adults were visible, which aided the photography. Nests were numbered for our records by taking note of tree branching patterns, the nest’s position on the tree, and other local identification marks. Numbering the nests helped us identify the individuals associated with a given nest and avoided re-recording the same individual (pseudoreplication). Storks show site fidelity42,43, and hence we assumed the same breeding pairs occupied the same nesting site.During the initial months of the breeding seasons, pairing and copulations of the breeding pairs could be readily noticeable. We took consecutive photographs when they were copulating at the nest. After disengagement following the copulation, the birds (male and female) standing side by side at the nest were also photographed. The first author noted all the relevant spatial orientations of males and females during each copulation event in the field notes. Thus nearly 100 copulations involving different individuals of the Painted Storks pair were photographed. To minimize measurement errors, we selected for further analysis only the images of males and females standing parallel and close to each other, perpendicular to the camera. Since we used the digital images of the free-living Storks, we did not have the freedom to choose all morphological features resulting in some missing values. Therefore, we selected a hundred and forty-eight individuals for the analysis from nearly 1500 localized adults. The technique has an efficiency of less than 10% of the population, more efficient than the traditional capture, measure, and release of individuals. Though many individuals were recorded, only a few were subjected to the analyses. Moreover from the digital images, not all the morphological characters of the individuals were measured. The birds’ orientation towards the camera assumes importance because the correct direction ensures maximum exposure of body parts in the picture. In many pictures, correct orientation was missing as the birds were behind other individuals or branches of the trees or leaves. Therefore, selecting the right digital image becomes crucial. Keeping all the above criteria, we filtered images that were later included in the analysis.Calibrations of subject-distance using Exif MetadataWe extracted the EXIF metadata from each JPEG image of Painted Stork. EXIF metadata includes the filename, type, date, and time of the image captured, image width and height in pixels, camera model, lens information, field of view, focal length, and subject-distance. The subject-distance (Painted Stork distance from the camera) being a critical variable and its Exif metadata were standardized with the following equation.$${text{Subject{-}distance}} = 0.7864 times {text{(EXIF subject{-}distance)}}^{{1.0301}}$$
(1)
Using the Eq. (1) derived from an earlier study5, we regressed actual subject-distance with the Exif subject-distance from the images. Then multiplying with the field of view, available as Exif metadata (angle of view) with standardized subject-distance (Eq. 1), the total image size (length and width) in metric units was estimated. We excluded the cropped or manipulated images because Image (size) estimation is possible only for the images coming straight from the camera with EXIF tags. The methodological details for calibration and estimation of in-situ measurements of the morphological variables are given in Mahendiran et al.5.Measurements of the morphological variablesWe created a TPS file for JPEG images of Painted Storks with the TPSUtility Program44. Using the TPS file in the TPSDig (v. 2.17) program44, we measured the selected characters (morphological variables) in pixels. Later, it was used along with the total image size to estimate the size of the specific morphological features in metric units, following Mahendiran et al.5. Ten different morphological variables were measured: Bill length (upper and lower mandible), tibia & tarsus length of both legs, distances among the ear, nostril and corners of the mouth, and body length. We estimated the dimensions of the rigid body parts, viz., bill length, tibia, and tarsus using the given methodology13,15,21. Bill length is the distance from the tip of the upper mandible to the beginning of skin corners near nostrils, the proximal end of the beak (marked as ‘a’ in Fig. 3); Tibia length is the distance from the joint of the tibia-tarsus to the feathers (marked as ‘b’ in Fig. 3); Tarsus length is the distance between the tibia-tarsus joint and foot (marked as ‘c’ in Fig. 3). We took measurements of each individual’s right and left legs and other characters, viz., inter-distances among the nostril, corner of the eye, corner of the mouth on each side (marked as ‘d’, ‘e’, ‘f’ in Fig. 3). Body depth is the distance from the base of the neck near the breast to the tip of the tail (marked as ‘g’ in Fig. 3).Data analysisWe performed the statistical analysis in R45, primarily through the nlme, ggbiplot, nnet, tidyverse, devtools packages. We did not have the freedom to measure a few morphological variables due to the problems mentioned above, which led to missing values in the datasets. We filled the missing values with the impute function using the R Core team45 through mice & VIM packages. When the missing values are high in numbers, we discard the data rather than use the impute function. Since almost about 70% of the lower mandible values were missing, we discarded them and ended up having only nine morphological variables in the final analysis. Moreover, the lower mandible is movable, with the mouth being open and closed, producing a considerable variation in measurements.We designed the matrix (Individuals × Region × Sex) representing the intraspecific variations concerning the region and sexes of Painted Storks46. The individuals are in rows (R), their region in column (C1), and sex in column (C2). We considered the regional variations as a sequence of the latitudinal gradient of the study sites. The values of the individuals (R) were the selected morphological variables. This matrix helped us investigate the critical questions relating to eco-geographic variations and sexual dimorphism.To determine whether temperature varied between study sites, we conducted a two-way ANOVA to analyse the effect of study sites (between North India (DZ & KNP) and South India (VBS & KBS)) and months of the year on the temperature at 2 m. For each character, Dimorphism Index (DI) was calculated as a mean value of female divided by the mean male, multiplied by 100, following the method of Urfi and Kalam15. We estimated the general body size of Painted Storks from the selected morphological variables through Principal Component Analysis (PCA) and tested hypotheses on Eco-geographic variations (Bergmann’s or Allen’s rules)2,47 and the sexual dimorphism15,48. The dimension reduction through PCA was carried out after the imputation as there were a few missing values. Body depth was omitted only for the principal component analysis due to many missing values. However, the values of all the characters are presented in the summary statistics in Table 1. The first principal component is characterized as a measure of size, and subsequent components describe various aspects of shape; therefore, it is considered a measure of general body size15,48,49. The PC1 indicated the body size variation, and PC2 revealed leg length variation (tibia and tarsus). We used nested ANOVA to test their body size variation between regions and sexes. The sexes nested within the region explained the eco-geographic rules and sexual selection patterns.Using a multinomial logistic regression model, we compared the Painted Storks’ northern male (NM), southern male (SM), and female (SF) with the reference category, northern female (NF). Then, we classified the data through multinomial log-linear and feed-forward neural network models. We predicted the Painted Stork’s region and sex using the Machine Learning (ML) algorithms through open-source software Waikato Environment for Knowledge Analysis (WEKA.3.9.5) implemented in Java50. WEKA has standard Machine learning/data-mining algorithms with pre-processing tools generating insightful knowledge from the Painted Storks’ morphological data.Using the R and Python interfaces, we used different ML software frameworks, libraries, and computer programs, viz., TensorFlow and Keras, and extensively explored the WEKA workbench environment to predict the sex and region of the Painted Stork. We used the k-fold cross-validation (k = 10) to avoid overlapping test sets, including splitting the data into k subsets of equal size, using each subset for testing and the remainder for training. We analyzed using the WEKA on a Lenovo ThinkPad P53s Mobile Workstation with the 8th Gen Intel® Core i7 @ 1.80 GHz processor, 48 GB DDR4 Memory, NVIDIA® Quadro® P520 with 2 GB GDDR5 Graphics. The performance criteria for all the eight models were assessed by using the Precision (TP/(TP + FP)), Recall (TP/(TP + FN)), Area under Curve (AUC) = (Sensitivity + Specificity)/2, Accuracy = (TP + TN)/(TP + TN + FP + FN), where TP, TN, FN and FP are the acronyms of true positive, true negative, false negative and false positive, respectively. We used the WEKA experimenter environment to test the statistical significance of the selected Machine Learning algorithms. We performed the Paired T-tester based on the number of correctly classified instances and areas under the curve. More

Case studyThe experimental setup for the field studies that provided the bacterial population and weather data used here was previously described by Belias et al. [9]. Briefly, baby spinach and lettuce plants were spray-inoculated with E. coli and S. enterica (Salmonella) onto field plots established in Davis, CA (University of California, Plant Sciences Field Research Facility); Freeville, NY (Homer C. Thompson Research Farm, Cornell University); and Murcia, Spain (La Matanza Research Farm). The spinach and lettuce varieties were selected based on their suitability for baby leaf production: lettuce var. Tamarindo, and spinach var. Acadia F1 and Seaside F1. Four replicate trials at different times of the regional growing season were carried out per location. The plants were spray-inoculated with a 104 CFU/mL cocktail of rifampin-resistant strains of commensal E. coli and attenuated S. enterica serovar Typhimurium (Salmonella), and samples were collected for bacterial cell quantification by plate counts on selective and differential media at 0, 4, 8, 24, 48, 72 and 96 h post-inoculation. Concurrent with leaf sample collection, weather variables (temperature, relative humidity (RH), solar radiation intensity, and wind velocity) were recorded hourly for the respective field locations. The hourly dew point (DP) was calculated as a function of both the hourly temperature and RH.Model for persister formation on plantsMathematical modeling to characterize the switch rate from a non-persister bacterial cell (hereafter termed “normal cell”) to a persister cell in the phyllosphere under laboratory conditions was performed as described in our previously published study [24]. Briefly, persister cell fractions were quantified in culturable EcO157 populations after inoculation onto young lettuce plants cultivated in plant growth chambers. Persister cells recovered from the lettuce phyllosphere were identified using the antibiotic lysing method [23]. The greatest persister fraction in the EcO157 population on lettuce in our laboratory investigation above was observed during population decline on leaf surfaces of plants left to dry after inoculation. Using mathematical modeling, we calculated the switch rate from an EcO157 normal to persister cell on dry lettuce plants based on these data [24]. Importantly, our laboratory conditions mimicked inoculation conditions in which E. coli arrived via water on leaves, the surfaces of which progressively dried like under prevailing weather conditions in the field.Based on the main dynamic observed in the field study data [9] and building on our previous study [24], we assumed that the total enteric pathogen population is composed of (i) non-persister (normal) cells consisting of two sub-populations, characterized by fast (n1) (CFU/100g) and slow (n2) (CFU/100g) decay, and (ii) the persister population, leading to the following model from Munther et al. [24]:$$frac{{dn_1}}{{dt}} = – theta _{n_1}n_1 – alpha _dn_1 + beta _dleft( {1 – sigma } right)hat p,$$
(1a)
$$frac{{dn_2}}{{dt}} = – theta _{n_2}n_2 – alpha _dn_2 + beta _dsigma hat p,$$
(1b)
$$frac{{dhat p}}{{dt}} = – mu _{hat p}hat p – beta _dhat p + alpha _dleft( {n_1 + n_2} right),$$
(1c)
$$n_1left( 0 right) = n_{10},n_2left( 0 right) = n_{20},, hat pleft( 0 right) = widehat {p_0},$$
(1d)
where (theta _{n_i})(1/h) is the death rate of the normal cells (subscript i = 1 for fast and i = 2 for slow), (hat p) (CFU/100 g) represents the persister cell population at time t (h), (mu _{hat p}) (1/h) reflects the persister population inactivation rate, αd (1/h) is the switch rate from normal to persister state, βd (1/h) is the switch rate from persister to the normal state, and σ ∈ (0,1) is a constant, describing the fraction of persister cells switching back to the normal, slowly decaying state. Equation (1a) and (1b) reflect the assumption that times between switching states are exponentially distributed, using the expected values (frac{1}{{alpha _d}}) (h) and (frac{1}{{beta _d}}) (h) of the respective distributions.Lacking data for potential persister populations from the field trials, we assumed the persister population is a fraction 1  > k  > 0 of the tail population, as observed in Munther et al. [24]. Regarding the model above, this implies that (hat p approx kn_2) for (t ge t^ ast), where (t^ ast approx frac{1}{{theta _{n_1}}}) (the time scale of survival for the fast-decaying population (n1)). In accord with bi-phasic decay, for (t ge t^ ast), the main dynamics for slow decaying population (n2) is dictated by (- theta _{n_2}n_2) in Eq. (1b). This suggests that the effective switch rates from n2 to (hat p) and from (hat p) back to n2 balance, so that (beta _dsigma hat p approx alpha _dn_2) in Eq. (1b). Following these ideas, we simplified the model in Eq. (1a)–(1d) to:$$frac{{dn_1}}{{dt}} = – theta _{n_1}n_1 – alpha _dn_1,$$
(2a)
$$frac{{dn_2}}{{dt}} = – theta _{n_2}n_2,$$
(2b)
$$frac{{dhat p}}{{dt}} = – theta _{hat p}hat p + alpha _dn_1,$$
(2c)
$$n_1left( 0 right) = n_{10},n_2left( 0 right) = n_{20},, hat pleft( 0 right) = widehat {p_0},$$
(2d)
where we ignored (beta _dleft( {1 – sigma } right)hat p) in (1a) since the decay rate ((theta _{n_1})) dominates. Also, by setting (theta _{hat p} = mu _{hat p} + beta _d(1 – sigma )), and using (beta _dsigma hat p approx alpha _dn_2), we obtained Eq. (2c). Furthermore, because (hat p approx kn_2) for (t ge t^ ast), (theta _{hat p} approx) (theta _{n_2}).In particular, the assumption that (hat p approx kn_2) for (t ge t^ ast) characterizes the switch rate from normal to persister cells, αd, as (alpha _d approx kalpha), where α is a hypothetical switch rate assuming that the population is composed only of fast decaying normal cells (n1) and a hypothetical persister cell population (p). In this case, the hypothetical population p starts small at (widehat {p_0}), initially increases due to switching from population n1 and then slowly decays as the n1 population is effectively inactivated (i.e., the tail of the total population is comprised entirely of p). From this perspective we utilized the following equations:$$frac{{dn_1}}{{dt}} = – theta _{n_1}n_1 – alpha n_1,$$
(3a)
$$frac{{dp}}{{dt}} = alpha n_1 – theta _pp.$$
(3b)
$$n_1left( 0 right) = n_0,, pleft( 0 right) = widehat {p_0},$$
(3c)
For mathematical justification regarding the relationship (alpha _d approx kalpha), please see the appendix (Supplementary Information).The utility of the relationship (alpha _d approx kalpha), is twofold. First, we used model fitting (Eqs. (3a)–(3c)) to determine α from the respective field study data [9]. Note that using Eqs. (3a)–(3c), we actually fit for (theta _{n_1}), θp, and α using the field study data [9]. Please reference the “model fitting procedure” section as well as the appendix for details concerning the unique determination of the aforementioned parameters, i.e., the practical identifiability of these parameters, and justification regarding the legitimacy of measured tail populations relative to the respective field trial data [9]. Second, because we wanted to examine Spearman’s correlations (corr) between αd and various weather factors, given a particular weather factor (vec w) across trials (i = 1, ldots ,n), let k be the maximum persister fraction (of the tail) across these n trials, that is, for each i, we have (alpha _{d_i} approx k_ialpha _i), so (alpha _{d_i} lesssim kalpha _i). Thus kαi represents the maximum persister switch rate for each trial i, and since corr((kvec alpha ,vec w)) =corr((vec alpha ,vec w)), we conducted the correlation analysis with the fitted α values in lieu of the actual persister switch rate αd.The assumptions behind our approach are summarized below:

A.

The tails of pathogen populations surviving on plants in the field study [9] are comprised of some fraction k ∈(0,1) of persister cells since their decay rate is quite small and they remain culturable.

B.

Because (alpha _d approx kalpha), we hereafter utilize α from model (3a)–(3c) as the representative persister switch rate.

C.

Given that the experimental context [24] for modeling persister switching occurred during population decline, we only employed trials from Belias et al. [9] that exhibited bi-phasic decay. Namely, we did not include trials in which significant bacterial growth was observed at the time scale of successive data points (the time scale in the field study is on the order of 4–16 h for the 1st day and then 24 h thereafter.)

D.

The switch rate from normal to persister cell is on average a monotonic function of some measure of environmental stress.

Based on assumptions A–D above, we applied the model (3a)–(3c) to published pathogen population size and weather data from four replicate trials in Spain, two in California, and one in NY [9]. More specifically, we fit model (3a)–(3c) to the respective population data in order to:

1.

determine values for the maximum switch rate α relative to the produce/bacteria type at the field scale,

2.

describe the correlative relationship between α and weather factors in the respective field trials.

Model fitting procedureIn model (3a)–(3c) above, we supposed dp/dtt = 0  > 0, i.e., we assumed that bacteria experience stress from the change in conditions from culture growth and inoculum suspension preparation to those on the plant surface and therefore, that persister formation increases in the phyllosphere immediately following inoculation. The report that EcO157 persister formation increases as early as 1 h after inoculation into leaf wash water [23], which could be considered as a proxy for the average oligotrophic environment that bacterial cells experience after spray inoculation onto leaves or through irrigation in the field, supports this assumption. To avoid identifiability issues between the initial persister population (widehat {p_0}) and α regarding the model fits above, we assumed that (widehat {p_0})= 1 ((widehat {p_0}) = 0 gives the same results). Thus, the initial persister population at inoculation is at its lowest, an assumption supported by Munther et al. [24], who observed an average fraction of EcO157 persisters of 0.0043% in the inoculum population. This imparts the largest possible switch rate, α, onto the population, corresponding to the largest and hence most conservative food safety risk.Let yk (CFU/100 g of produce) be the average bacteria population measurement at time tk (h) and let Pk,X (CFU/100 g of produce) represent the model prediction (total population) at time tk relative to the parameter vector (X = [ {theta _{n_1} , theta_p , alpha } ]^T). Following Eqs. (3a) and (3b), this means that ({{{{{{{mathrm{P}}}}}}}}_{k,X} = n_1left( {t_k,X} right) + p(t_k,X)). Since the population data spans multiple orders of magnitude, we calculated the residuals as (e_{k,X} = log _{10}y_k – log _{10}P_{k,X}). To determine the optimal model fit (see the appendix for details regarding a priori bounds on parameter ranges), we utilized the fminsearch function in MATLAB (MATLAB 2020b, The MathWorks, Inc., Natick, Massachusetts, United States) to determine the parameter vector X that minimizes the 2-norm of the following function F:$$| | Fleft( X right) | |_2 = left( {mathop {sum }limits_k e_{k,X}^2} right)^{frac{1}{2}}$$Correlation analysisTo provide a statistical foundation from which to relate the switch rate α and measured weather factors, we utilized Spearman and partial Spearman correlation. First, we calculated the Spearman correlation coefficients between α and each of the respective factors: 8-h average of temperature, RH, solar radiation, wind speed post-inoculation, and then we calculated the partial Spearman correlation coefficients for each respective weather factor, while controlling for the other three factors and simultaneously controlling for produce type (using lettuce =1 and spinach =0) (For details regarding why 8-h weather variables were used, see the “model fitting” subsection of the results.) The correlation coefficients were determined using the corr and partialcorr functions in MATLAB 2020b (The MathWorks, Inc., Natick, MA, USA). Considering the significant association of Salmonella α with RH and temperature, we also examined the correlation between α and dew point. Figure 1 presents a logical flow of the statistical analysis. Partial correlations with a P value of less than 0.05 were deemed significant. If the 8-h average of a weather factor exhibited a significant correlation with the switch rate, the 8-h minimum and range of the weather factor were also tested.Fig. 1: Logical flow diagram for statistical analysis.Factors in Step 1: UV (average ultraviolet radiation intensity), RH (average air relative humidity), Wind (average wind speed), and Temp (average air temperature). All weather data used in the statistical analysis were obtained over 8 h post-inoculation of E. coli and Salmonella onto lettuce and spinach leaves in the field.Full size image More

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