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Modelling complex evolved food websOur interest here is to develop a conceptual comparison between the eigenvalue spectrum of a complex, evolved food web and a random matrix analog. We therefore focus on the widely-used generalised Lotka–Volterra equations for consumer-resource interactions. For simplicity, we further restrict to a single basic nutrient source, and require that species feeding on the basic nutrient source are never omnivorous31, e.g., plants do not consume other plants. The original Lotka–Volterra equations32,33 describe spatially and temporally homogeneous, consumer-resource relations. The generalised Lotka–Volterra equations34,35,36 can be used to describe the dynamics of larger, more complex food webs, and encode the dynamics of primary producers as$$begin{aligned} frac{dot{S_i}}{S_i} = k_i left( 1 – sum _{j=1}^{n_1} S_j right) – alpha _i – sum _{k=n_1+1}^{n} eta _{ki} S_k, end{aligned}$$
(1)
where (S_i), (iin {1,dots ,n_1}), denote the population densities of primary producers in units of biomass, normalised to the system carrying capacity and (n_1) denotes the total number of primary producers, (k_i >0) denote the growth rates of the corresponding primary producer (S_i), that is, the maximal reproduction rate at unlimited nutrient availability. We use (k_i=k) for all primary producers. The negative sum on the species (S_j) encodes logistic growth by accounting for nutrient depletion by all primary producers. For all other species, (S_k), (kin {n_1+1,dots ,n}) with n the total number of species in the food web, the equations read$$begin{aligned} frac{dot{S_k}}{S_k} = sum _{m=1}^{n} beta _{km}eta _{km} S_m – alpha _k – sum _{p=n_1+1}^{n} eta _{pk} S_p. end{aligned}$$
(2)
Here, (S_k) is again measured in units of normalised biomass. In Eqs. (1) and (2), (alpha _j >0) is the decay rate of a species (S_j), representing death not caused by consumption through other species. (eta _{ki}ge 0) is the link-specific interaction strength between consumer (S_k) and resource (S_i). On the RHS of either equation, note the final term representing the diminishing effects experienced by each resource species, which is caused by consumption. This term is mirrored by the first term in Eq. (2), which describes the strengthening effect on the consumer side. The coefficients (beta _{ki}le 1) encode link-specific consumption efficiency—that is, potentially incomplete use of energy removed from a resource species by its consumer. (beta _{ki}=1) would describe perfect consumption efficiency whereas in real food webs this value is estimated to lie considerably lower37. In our simulations we use (beta _{ki}=beta) for all interactions present.Equations (1) and (2) describe a simplified food web structure where consumption is modelled by the simple Holling type-I response38, where consumer resource fluxes scale proportional to the product of consumer and resource biomass density and there are no saturation effects. Moreover, Eqs. (1) and (2) assume that the food web is rigid in that species are incapable of adapting their consumption behaviour to changes within the food web, such as a decreasing population of resources or competition from an invasive species39. Yet, these equations allow for a coherent description of the energy fluxes between species and constitute an established framework for complex consumer-resource relations to evolve.To evolve food webs we simulate Eqs. (1) and (2) numerically. New species are added successively to an existing food web. We assume that invasion attempts occur on a slow timescale, such that equilibrium can be reached before the subsequent invasion attempt, though occasionally, the food web does not converge to its equilibrium state. After each invasion attempt the steady state species vector (mathbf {S^*}) is computed. In case of feasibility the eigenvalues of the community matrix are evaluated in order to determine the linear stability of the steady states. If feasibility is not obtained, that is, if (mathbf {S^*}) contain negative populations, Eqs. (1) and (2) are integrated numerically until extinctions occur and feasibility of the remaining species is reached (Details: “Materials and methods”). Examples of several invasion attempts are shown in Fig. 2.Figure 1Evolution of three food webs using different assembly rules. All main panels show decay rates of all species present plotted against invasion attempts, that is, evolutionary steps. The decay rates are plotted as (Delta alpha equiv alpha – alpha _{min}), where (alpha _{min}) denotes the lower limit on decay rates (compare: Table 1). The thin red line highlights the currently lowest producer decay rate. Grey symbols denote producers, yellow and magenta symbols denote consumers of one or two resources, respectively. Cyan symbols denote omnivores. (a) Food webs where only one resource per consumer is allowed, yielding a treelike food web without loops. (b) Consumers can have either one or two resources at the same trophic level. (c) Consumers are allowed one or two resources at any trophic level (lge 1). Note that both axes use logarithmic scaling. Insets: Normalised histograms of species richness, using all data. Note the logarithmic vertical axis scaling.Full size imageFigure 2Time series of a food web during several invasions. The panels (a–f) respectively correspond to invasion attempts 40312–40314, and 40316–40318 in Fig. 1c. Upper row: In each panel, orange circles and red “x”-symbols denote the invasive and extinct species, respectively. The vertical coordinate denotes trophic level, and node areas represent initial biomass densities. The green hexagon represents the basic nutrient source. (a) A species successfully invades the food web, but causes the extinction of two resident species, among these one of its own resources. (b) the invader is successful without causing any extinctions. (c) The invader is a primary producer and causes extinction of the invader from (b). (d) The invader replaces a resident species of same niche as the invader. (e) The invader is unsuccessful in invading the food web as it shares a niche with one of the resident species. (f) The invader is a primary producer and causes the extinction of three resident species, among these the primary producer with lowest decay rate, corresponding to largest intrinsic fitness, which is highlighted by the black arrow. Lower row: Time series corresponding to each of the food webs above, where time is measured in units of the inverse primary producer growth rate, (k^{-1}). Blue and orange lines represent resident and invasive species, respectively, as the new steady state is approached. The black line in the last panel represents the producer with lowest decay rate. Note the double-log axis scaling.Full size imageLoops profoundly impact food web evolutionTo make sure our results do not depend on the details of the invasion process we allow for several qualitatively distinct evolutionary processes: (i) treelike food webs, where each consumer has a single resource; (ii) non-omnivorous food webs with loops; (iii) omnivorous food webs. Loops are known to be relevant for sustained limit cycles and chaotic attractors, thus widening the range of dynamical properties. Indeed, we find treelike food webs to stand out in that fitness, measured by species decay rates, indefinitely increases in the evolutionary process (Fig. 1a, dotted red line), a finding consistent with the recent literature30. This indefinite fitness improvement hinges on the absence of network loops: a given primary producer can only be replaced by an invading primary producer of greater intrinsic fitness, that is, lower decay rate.Allowing for network loops, evolved food web do not show indefinite fitness improvement (Fig. 1b,c) and mean species richness somewhat decreases (Fig. 1, insets). All histograms show a systematic difference in odd and even species richness, with food webs of odd species richness being the most frequent. This tendency is most pronounced for treelike food webs. We interpret this as a manifestation of the requirement of non-overlapping pairing28. Treelike food webs are feasible and stable if every species in the food web can be coincidentally paired with a connected species or nutrient that is not part of another pairing. In food webs of even species richness the nutrient is never included in such a pairing. Food webs consisting of several smaller trees that are connected through the nutrient source are therefore only feasible if every tree satisfies this requirement individually. On the contrary, the nutrient is always included in a pairing in food webs of odd species richness, and therefore odd food webs are more likely to be feasible. To a lesser extent this tendency is also found in the histograms representing food webs with network loops. We interpret this as resulting from the fact that 40-60% of the food webs from simulations allowing network loops are in fact treelike.Why do loops counteract indefinite fitness improvement? This can be seen as a manifestation of relative, rather than absolute, fitness, where a species can consume two resources and thereby can help eliminate even primary producers of high intrinsic fitness (Fig. 1b,c). An example of this is illustrated in Fig. 2f), where the intrinsically fittest producer is a node in a food web loop, and is driven to extinction during the invasion of a producer with lower intrinsic fitness.The evolution of intrinsic fitness in Fig. 1 implies that allowing for interaction loops makes resident species more vulnerable to extinction during invasions, because parameters that characterise high intrinsic fitness before an invasion might characterise low intrinsic fitness during the invasion. This is supported by the cumulative distribution of resident times (Fig. S1a), where residence times in food webs with network loops fall off faster than the residence times in treelike food webs. In Fig. S1b we observe that in accordance with this, the distribution of extinction event size falls off faster for treelike food webs (Fig. S1b), where the extinction event size is measured relative to the total number of species (species richness) in the food web. Fig. S1b therefore implies that interaction loops make food webs less robust to invasions, as invasive species tend to create larger extinction events here than in treelike food webs. Finally, we find invasive species to have higher success rates when invading food webs with interaction loops, and the success rate is found to increase with (beta). In simulations with (beta =0.75) we observe 11.5%, 27.2% and 29.8% for treelike, non-omnivorous, and omnivorous food webs with loops, respectively. The implications of this are twofold. On one hand, it is easier to assemble feasible food webs when multiple resources and omnivory are allowed. On the other hand, these food webs are more susceptible to invasions and their resident species are more vulnerable. If a food web contains two-resource species, removal of one of the two resources of a species (S_i) by an invader can already lead to a cascading extinction of S, as exemplified by Fig. S2.Robustly bi-modal eigenvalue spectraWe now turn to the eigenvalue spectra of the evolved complex food webs, which we present as two-dimensional histograms in the complex plane (Fig. 3). Each simulation conducts (10^5) invasion attempts, yet the number of unique feasible food webs is considerably lower, that is, approximately equal to the aforementioned rates of successful invasions. Furthermore, the number of unique feasibly food webs drastically decreases with species richness. While the data shown represent relatively small networks, we find that key spectral features are very systematic as function of species richness. A generic feature is that spectra typically have many eigenvalues with small negative real parts. Further, the real parts scatter more and more closely at small negative values, as species richness increases beyond two. All spectra contain a considerable fraction of purely real eigenvalues, typically making up 15–30% of a spectrum.Figure 3Complex eigenvalue spectra of evolved food webs. Each panel represents the two-dimensional histogram in the complex plane. Species richness and invasion mechanism are as labelled in panels, that is, rows of panels represent treelike, non-omnivorous, and omnivorous food webs. Note that the colour scale is logarithmic, with green marking the areas with largest likelihood of eigenvalues (Details: “Materials and methods”). Eigenvalue spectra of omnivorous food webs of other species richnesses can be seen in Fig. S3.Full size imageThe origin of purely real eigenvaluesThe first column in Fig. 3 represents food webs with species richness two. These simple food webs only have one feasible configuration, namely that of one primary producer and one consumer. Any differences between spectra in the left column are therefore purely statistical. These food webs can be considered as isolated interactions between a consumer and its resource, hence the analytical eigenvalues of this food web can provide some insight on the dynamics underlying the eigenvalue spectra. From the analytical eigenvalues we obtain that an eigenvalue is purely real if the inequality$$begin{aligned} beta eta le frac{1}{2}left( gamma + sqrt{gamma ^2 + kgamma }right) , ,,,,,,,,text {with},, gamma equiv frac{alpha _2}{1-alpha _1/k}, end{aligned}$$
(3)
is fulfilled (Details: Sec. S3). Here, (alpha _1) and (alpha _2) are the decay rates of the resource and the consumer, respectively, and (beta eta) is short for (beta _{21}eta _{21}), the “consumption rate” of the consumer. (gamma) can be interpreted as the inverse intrinsic fitness of the food web.From feasibility, we have the additional requirement of (gamma < beta eta), hence, the consumer’s “consumption rate” is bounded also from below. As k decreases, the lower and upper boundaries on (beta eta) approach one-another until they are equal for (k=0). A food web with low producer growth rate is therefore likely to have complex eigenvalues. In the opposite limit, when (krightarrow infty), or equivalently (alpha _1 rightarrow 0), we see that (gamma) reduces to (alpha _2). In the first limit Eq. (3) reduces to (beta eta le infty) which will always be satisfied and all eigenvalues are therefore purely real in this limit. This corresponds to a food web where the consumer has infinite access to resources and there is no stress or constraints on the web that could cause oscillations. In the limit where (alpha _1 rightarrow 0), the eigenvalues pick up an imaginary component when (beta eta) is large compared to (alpha _2) and k. This occurs when the consumer population has a large intrinsic growth rate, thus heavily exploiting its resource.Overall, purely real eigenvalues characterise food webs where consumption of the resource is moderate compared to the intrinsic fitness of the resource. This corresponds to an over-damped limit where the consumer does not consume enough to cause any significant displacement of the resource population, hence a perturbation of the consumer population will not spread to its resource. For higher species richness the Jacobian quickly becomes too complicated to be solved analytically. Even so, we expect the dynamics between a consumer and its resources to be conceptually analogous, namely that “sustainable over-consumption” yields oscillating densities and complex eigenvalues.The set of smallest and largest real-valued eigenvalues is obtained when (beta eta) is only slightly larger than (gamma), hence barely satisfying the criterion of feasibility. The eigenvalues then reduce to (lambda _{pm } = -frac{k-alpha _1}{2} pm frac{k-alpha _1}{2}). (lambda _+) is always zero, that is, food webs of species richness two are always stable, and with our choice of parameters (lambda _- ge -0.95). We observe approximately the same range of real values in all numerical spectra of any species richness, thereby implying that the choice of parameters might be more important for the spectrum width than the structure of the food web.The overall shape is qualitatively similar for all food web structures (see: Fig. 3). Importantly, omnivorous spectra are the only ones to contain also eigenvalues with positive real part, that is, unstable eigenvalues. These food webs do therefore not converge to their equilibrium state after an invasion, but are displaying periodic or chaotic dynamics (Details: “Materials and methods”). The unstable eigenvalues are all barely larger than zero, hence hardly visible in Fig. 3. Interestingly, non-omnivorous food webs with network loops exhibit the same species richness and approximate connectivity as the omnivorous food webs, yet they do not yield unstable eigenvalues. The differences between treelike food webs and food webs with network loops discussed earlier must therefore be unrelated to the stability of the food webs, thus emphasising the difference between stability to perturbation of a given food web and its robustness to invasions. For omnivorous food webs the fraction of unstable eigenvalues increases with species richness and decreases with (beta). Intuitively, it seems reasonable that there is a relation between instability and low consumption efficiency. A species with a low consumption efficiency has to compensate by consuming more biomass, thereby putting more stress on its resources. Only for (beta =1) are there no unstable omnivorous eigenvalues.Figure 4Complex eigenvalue spectra of random matrices. Heat maps of eigenvalue spectra of random matrices, corresponding to the respective species richnesses shown in Fig. 3. Off-diagonal entries are drawn from a normal distribution with probability (p(N) = frac{N^2+21N-28}{9N(N-1)}) (Details: Sec. S5), and are otherwise set to zero. Diagonal elements are set to (-1).Full size imageWe now compare the evolved spectra (Fig. 3) to their random counterparts (Fig. 4). The diagonal entries represent self regulation of each species and are set to (d = -1). Off-diagonal entries are drawn from ({mathcal {N}}(0, 1)) with probability p(N), and are otherwise 0.$$begin{aligned} p(N) = frac{N^2+21N-28}{9N(N-1)}, ~~text {for } N >1, end{aligned}$$
(4)
where N is “species richness”, that is, the number of rows (or columns) of the matrix. This corresponds to the implemented connectivity in the simulation allowing network loops and omnivory, that is, the connectivity of omnivorous food webs given no extinctions occur (Details: Sec. S5). As predicted by spectral theory of random matrices, the spectra are centred around d on the real axis and approach a circular geometry as the size of the matrix increases. Already for (N=2) does the spectrum contain unstable eigenvalues. The fraction of unstable eigenvalues increases with N as the circle radius increases. Also for random spectra do we observe a large fraction of purely real eigenvalues. We attribute this to the small size of the matrices, being much smaller than the infinity limit for which the law was derived40.Figure 5Distribution of eigenvalues along the real axis. Normalised frequency distributions of eigenvalues along the real axis for all food web structures and random matrices for species richness (2-9). Eigenvalues representing food webs are taken from simulations using a range of values of (beta) (Table 1), since varying (beta) does not have significant effects on the real-part distributions (Details: Sec. S6). All distributions are scaled to start in (-1). Note the logarithmic vertical axis scaling.Full size imageFinally, we study the real-part frequency distributions of eigenvalues of all four types (treelike, non-omnivorous, omnivorous and random). The frequency distributions for species richness 2–9 can be seen in Fig. 5, where each distribution consists of data from various values of (beta) (see Table 1). In order to facilitate comparison of the functional form of the frequency distributions, rather than the range, the frequency distributions are scaled to be bounded by (-1) on the real axis, that is, we divide each data point by ((|min {x}|)^{-1}) where x is the data points of the distribution. Frequency distributions representing the evolved food webs follow approximately the same curve for a given species richness, and are distinctively different from the random matrices. As also seen in Fig. 3 omnivorous distributions are the only to extended to positive values for species richness greater than two.Once again, we observe quantitative differences between food webs with odd and even species richness: For odd species richness the distribution is bi-modal with a global maximum near (x=0) and a secondary maximum near the lower limit, that is (x=-1). For even species richness, the distribution is initially less strongly peaked. Yet, as species richness increases, a sharp peak emerges around (x = 0). The distribution thus becomes more similar to that of the food webs with an odd number of species.The intermediate part of the spectrum is increasingly depleted of eigenvalues at higher species richness. Comparing Fig. 5 with Fig. 3 we see that the left part of all distributions consists of purely real eigenvalues, whereas it is mostly complex eigenvalues that make up the global maximum near (x=0). This implies that perturbations can be divided into two main groups: perturbations from which the food web quickly returns to the respective steady state, and perturbations that induce oscillations from which the food web takes very long to recover. The peak consisting of purely real eigenvalues near (x=-1) does not change notably with species richness, indicating that, independent of species richness, food webs are robust to certain perturbations. In accordance with this we observe that food webs of all species richness usually return quickly to their steady states after an unsuccessful invasive species goes extinct. The main peak (near (x=0)) becomes both higher and narrower with increasing species richness, that is, the food webs become quasi-stable. In larger food webs there are more species that can be disturbed by a perturbation, which might prolong the effect of the perturbation, that is, push eigenvalues towards zero on the real axis. Overall, we thus find that the histogram of complex food webs becomes strongly bi-modal as food webs consisting of many species are approached in an evolutionary process, whereas random matrix spectra are consistently uni-modal. In Sec. S8–S9 we consider the robustness of the results in Fig. 5 by varying the parameter distributions and implementing Holling type-II response, respectively. More

RESEARCH HIGHLIGHT
29 August 2022

North America’s largest land mammal can double the diversity of native grasses through its grazing.

Home on the range: the American bison’s taste for prairie grasses helps to boost diversity of native flora (pictured, stiff goldenrod, Solidago rigida). Credit: Jill Haukos/Kansas State University

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Grazing animals can shape the grasslands they dine on by preferentially eating certain species, allowing other species to find a foothold. To quantify this effect, Zak Ratajczak at Kansas State University in Manhattan and his colleagues analysed 29 years’ worth of data from plots in an unploughed native tallgrass prairie in eastern Kansas1. Since 1992, the plots have been managed in one of three ways: year-round grazing by bison (Bison bison); seasonal grazing by cattle; or no grazing at all.

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doi: https://doi.org/10.1038/d41586-022-02332-4

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Fly population and maintenanceWe used an outbred population of Drosophila melanogaster established from 160 Wolbachia-infected fertilised females collected in Azeitão, Portugal54, and given to us by Élio Sucena. For at least 13 generations prior to the start of the experiments the flies were maintained on standard sugar yeast agar medium (SYA medium: 970 ml water, 100 g brewer’s yeast, 50 g sugar, 15 g agar, 30 ml 10% Nipagin solution and 3 ml propionic acid; ref. 61), in a population cage containing at least 5000 flies, with non-overlapping generations of 15 days. They were maintained at 24.3 ± 0.2 °C, on a 12:12 h light-dark cycle, at 60–80 % relative humidity. The experimental flies were kept under the same conditions. No ethical approval or guidance is required for experiments with D. melanogaster.Bacterial speciesWe used the Gram positive Lactococcus lactis (gift from Brian Lazzaro), Gram negative Enterobacter cloacae subsp. dissolvens (hereafter called E. cloacae; German collection of microorganisms and cell cultures, DSMZ; type strain: DSM-16657), Providencia burhodogranariea strain B (gift from Brian Lazzaro, DSMZ; type strain: DSM-19968) and Pseudomonas entomophila (gift from Bruno Lemaitre). L. lactis43, Pr. burhodogranariea44 and Ps. entomophila45 were isolated from wild-collected D. melanogaster and can be considered as opportunistic pathogens. E. cloacae was isolated from a maize plant, but has been detected in the microbiota of D. melanogaster46. All bacterial species were stored in 34.4% glycerol at −80 °C and new cultures were grown freshly for each experimental replicate.Experimental designFor each bacterial species, flies were exposed to one of seven treatments: no injection (naïve), injection with Drosophila Ringer’s (injection control) or injection with one of five concentrations of bacteria ranging from 5 × 106 to 5 × 109 colony forming units (CFUs)/mL, corresponding to doses of approximately 92, 920, 1,840, 9200 and 92,000 CFUs per fly. The injections were done in a randomised block design by two people. Each bacterial species was tested in three independent experimental replicates. Per experimental replicate we treated 252 flies, giving a total of 756 flies per bacterium (including naïve and Ringer’s injection control flies). Per experimental replicate and treatment, 36 flies were checked daily for survival until all flies were dead. A sub-set of the dead flies were homogenised upon death to test whether the infection had been cleared before death or not. To evaluate bacterial load in living flies, per experimental replicate, four of the flies were homogenised per treatment, for each of nine time points: one, two, three, four, seven, 14, 21, 28- and 35-days post-injection.Infection assayBacterial preparation was performed as in Kutzer et al.24, except that we grew two overnight liquid cultures of bacteria per species, which were incubated overnight for approximately 15 h at 30 °C and 200 rpm. The overnight cultures were centrifuged at 2880 × g at 4 °C for 10 min and the supernatant removed. The bacteria were washed twice in 45 mL sterile Drosophila Ringer’s solution (182 mmol·L-1 KCl; 46 mol·L-1 NaCl; 3 mmol·L-1 CaCl2; 10 mmol·L-1 Tris·HCl; ref. 62) by centrifugation at 2880 × g at 4 °C for 10 min. The cultures from the two flasks were combined into a single bacterial solution and the optical density (OD) of 500 µL of the solution was measured in a Ultrospec 10 classic (Amersham) at 600 nm. The concentration of the solution was adjusted to that required for each injection dose, based on preliminary experiments where a range of ODs between 0.1 and 0.7 were serially diluted and plated to estimate the number of CFUs. Additionally, to confirm post hoc the concentration estimated by the OD, we serially diluted to 1:107 and plated the bacterial solution three times and counted the number of CFUs.The experimental flies were reared at constant larval density for one generation prior to the start of the experiments. Grape juice agar plates (50 g agar, 600 mL red grape juice, 42 mL Nipagin [10% w/v solution] and 1.1 L water) were smeared with a thin layer of active yeast paste and placed inside the population cage for egg laying and removed 24 h later. The plates were incubated overnight then first instar larvae were collected and placed into plastic vials (95 × 25 mm) containing 7 ml of SYA medium. Each vial contained 100 larvae to maintain a constant density during development. One day after the start of adult eclosion, the flies were placed in fresh food vials in groups of five males and five females, after four days the females were randomly allocated to treatment groups and processed as described below.Before injection, females were anesthetised with CO2 for a maximum of five minutes and injected in the lateral side of the thorax using a fine glass capillary (Ø 0.5 mm, Drummond), pulled to a fine tip with a Narishige PC-10, and then connected to a Nanoject II™ injector (Drummond). A volume of 18.4 nL of bacterial solution, or Drosophila Ringer’s solution as a control, was injected into each fly. Full controls, i.e., naïve flies, underwent the same procedure but without any injection. After being treated, flies were placed in groups of six into new vials containing SYA medium, and then transferred into new vials every 2–5 days. Maintaining flies in groups after infection is a standard method in experiments with D. melanogaster that examine survival and bacterial load (e.g. refs. 22, 63, 64). At the end of each experimental replicate, 50 µL of the aliquots of bacteria that had been used for injections were plated on LB agar to check for potential contamination. No bacteria grew from the Ringer’s solution and there was no evidence of contamination in any of the bacterial replicates. To confirm the concentration of the injected bacteria, serial dilutions were prepared and plated before and after the injections for each experimental replicate, and CFUs counted the following day.Bacterial load of living fliesFlies were randomly allocated to the day at which they would be homogenised. Prior to homogenisation, the flies were briefly anesthetised with CO2 and removed from their vial. Each individual was placed in a 1.5 mL microcentrifuge tube containing 100 µL of pre-chilled LB media and one stainless steel bead (Ø 3 mm, Retsch) on ice. The microcentrifuge tubes were placed in a holder that had previously been chilled in the fridge at 4 °C for at least 30 min to reduce further growth of the bacteria. The holders were placed in a Retsch Mill (MM300) and the flies homogenised at a frequency of 20 Hz for 45 s. Then, the tubes were centrifuged at 420 × g for one minute at 4 °C. After resuspending the solution, 80 µL of the homogenate from each fly was pipetted into a 96-well plate and then serially diluted 1:10 until 1:105. Per fly, three droplets of 5 μL of every dilution were plated onto LB agar. Our lower detection limit with this method was around seven colony-forming units per fly. We consider bacterial clearance by the host to be when no CFUs were visible in any of the droplets, although we note that clearance is indistinguishable from an infection that is below the detection limit. The plates were incubated at 28 °C and the numbers of CFUs were counted after ~20 h. Individual bacterial loads per fly were back calculated using the average of the three droplets from the lowest countable dilution in the plate, which was usually between 10 and 60 CFUs per droplet.D. melanogaster microbiota does not easily grow under the above culturing conditions (e.g. ref. 42) Nonetheless we homogenised control flies (Ringer’s injected and naïve) as a control. We rarely retrieved foreign CFUs after homogenising Ringer’s injected or naïve flies (23 out of 642 cases, i.e., 3.6 %). We also rarely observed contamination in the bacteria-injected flies: except for homogenates from 27 out of 1223 flies (2.2 %), colony morphology and colour were always consistent with the injected bacteria (see methods of ref. 65). Twenty one of these 27 flies were excluded from further analyses given that the contamination made counts of the injected bacteria unreliable; the remaining six flies had only one or two foreign CFUs in the most concentrated homogenate dilution, therefore these flies were included in further analyses. For L. lactis (70 out of 321 flies), P. burhodogranaeria (7 out of 381 flies) and Ps. entomophila (1 out of 71 flies) there were too many CFUs to count at the highest dilution. For these cases, we denoted the flies as having the highest countable number of CFUs found in any fly for that bacterium and at the highest dilution23. This will lead to an underestimate of the bacterial load in these flies. Note that because the assay is destructive, bacterial loads were measured once per fly.Bacterial load of dead fliesFor two periods of time in the chronic infection phase, i.e., between 14 and 35 days and 56 to 78 days post injection, dead flies were retrieved from their vial at the daily survival checks and homogenised in order to test whether they died whilst being infected, or whether they had cleared the infection before death. The fly homogenate was produced in the same way as for live flies, but we increased the dilution of the homogenate (1:1 to 1:1012) because we anticipated higher bacterial loads in the dead compared to the live flies. The higher dilution allowed us more easily to determine whether there was any obvious contamination from foreign CFUs or not. Because the flies may have died at any point in the 24 h preceding the survival check, and the bacteria can potentially continue replicating after host death, we evaluated the infection status (yes/no) of dead flies instead of the number of CFUs. Dead flies were evaluated for two experimental replicates per bacteria, and 160 flies across the whole experiment. Similar to homogenisation of live flies, we rarely observed contamination from foreign CFUs in the homogenate of dead bacteria-injected flies (3 out of 160; 1.9 %); of these three flies, one fly had only one foreign CFU, so it was included in the analyses. Dead Ringer’s injected and naïve flies were also homogenised and plated as controls, with 6 out of 68 flies (8.8%) resulting in the growth of unidentified CFUs.Statistical analysesStatistical analyses were performed with R version 4.2.166 in RStudio version 2022.2.3.49267. The following packages were used for visualising the data: “dplyr”68, “ggpubr”69, “gridExtra”70, “ggplot2”71, “plyr”72, “purr”73, “scales”74, “survival”75,76, “survminer”77, “tidyr”78 and “viridis”79, as well as Microsoft PowerPoint for Mac v16.60 and Inkscape for Mac v 1.0.2. Residuals diagnostics of the statistical models were carried out using “DHARMa”80, analysis of variance tables were produced using “car”81, and post-hoc tests were carried out with “emmeans”82. To include a factor as a random factor in a model it has been suggested that there should be more than five to six random-effect levels per random effect83, so that there are sufficient levels to base an estimate of the variance of the population of effects84. In our experimental designs, the low numbers of levels within the factors ‘experimental replicate’ (two to three levels) and ‘person’ (two levels), meant that we therefore fitted them as fixed, rather than random factors84. However, for the analysis of clearance (see below) we included species as a random effect because it was not possible to include it as a fixed effect because PPP is already a species-level predictor. Below we detail the statistical models that were run according to the questions posed. All statistical tests were two-sided.Do the bacterial species differ in virulence?To test whether the bacterial species differed in virulence, we performed a linear model with the natural log of the maximum hazard as the dependent variable and bacterial species as a factor. Post-hoc multiple comparisons were performed using “emmeans”82 and “magrittr”85, using the default Tukey adjustment for multiple comparisons. Effect sizes given as Cohen’s d, were also calculated using “emmeans”, using the sigma value of 0.4342, as estimated by the package. The hazard function in survival analyses gives the instantaneous failure rate, and the maximum hazard gives the hazard at the point at which this rate is highest. We extracted maximum hazard values from time of death data for each bacterial species/dose/experimental replicate. Each maximum hazard per species/dose/experimental replicate was estimated from an average of 33 flies (a few flies were lost whilst being moved between vials etc.). To extract maximum hazard values we defined a function that used the “muhaz” package86 to generate a smooth hazard function and then output the maximum hazard in a defined time window, as well as the time at which this maximum is reached. To assess the appropriate amount of smoothing, we tested and visualised results for four values (1, 2, 3 and 5) of the smoothing parameter, b, which was specified using bw.grid87. We present the results from b = 2, but all of the other values gave qualitatively similar results (see Supplementary Table 2). We used bw.method = “global” to allow a constant smoothing parameter across all times. The defined time window was zero to 20 days post injection. We removed one replicate (92 CFU for E. cloacae infection) because there was no mortality in the first 20 days and therefore the maximum hazard could not be estimated. This gave final sizes of n = 14 for E. cloacae and n = 15 for each of the other three species.$${{{{{rm{Model}}}}}},1:,{{log }}left({{{{{rm{maximum}}}}}},{{{{{rm{hazard}}}}}}right), sim ,{{{{{rm{bacterial}}}}}},{{{{{rm{species}}}}}}$$Are virulence differences due to variation in pathogen exploitation or PPP?To test whether the bacterial species vary in PPP, we performed a linear model with the natural log of the maximum hazard as the dependent variable, bacterial species as a factor, and the natural log of infection intensity as a covariate. We also included the interaction between bacterial species and infection intensity: a significant interaction would indicate variation in the reaction norms, i.e., variation in PPP. The package “emmeans”82 was used to test which of the reaction norms differed significantly from each other. We extracted maximum hazard values from time of death data for each bacterial species/dose/experimental replicate as described in section “Do the bacterial species differ in virulence?”. We also calculated the maximum hazard for the Ringer’s control groups, which gives the maximum hazard in the absence of infection (the y-intercept). We present the results from b = 2, but all of the other values gave qualitatively similar results (see results). We wanted to infer the causal effect of bacterial load upon host survival (and not the reverse), therefore we reasoned that the bacterial load measures should derive from flies homogenised before the maximum hazard had been reached. For E. cloacae, L. lactis, and Pr. burhodogranariea, for all smoothing parameter values, the maximum hazard was reached after two days post injection, although for smoothing parameter value 1, there were four incidences where it was reached between 1.8- and 2-days post injection. Per species/dose/experimental replicate we therefore calculated the geometric mean of infection intensity combined for days 1 and 2 post injection. In order to include flies with zero load, we added one to all load values before calculating the geometric mean. Geometric mean calculation was done using the R packages “dplyr”68, “EnvStats”88, “plyr”72 and “psych”89. Each mean was calculated from the bacterial load of eight flies, except for four mean values for E. cloacae, which derived from four flies each.For Ps. entomophila the maximum hazard was consistently reached at around day one post injection, meaning that bacterial sampling happened at around the time of the maximum hazard, and we therefore excluded this bacterial species from the analysis. We removed two replicates (Ringer’s and 92 CFU for E. cloacae infection) because there was no mortality in the first 20 days and therefore the maximum hazard could not be estimated. One replicate was removed because the maximum hazard occurred before day 1 for all b values (92,000 CFU for E. cloacae) and six replicates were removed because there were no bacterial load data available for day one (experimental replicate three of L. lactis). This gave final sample sizes of n = 15 for E. cloacae and n = 12 for L. lactis, and n = 18 for Pr. burhodogranariea.$${{{{{rm{Model}}}}}},2 :,{{log }}({{{{{rm{maximum}}}}}},{{{{{rm{hazard}}}}}}), sim ,{{log }}({{{{{rm{geometric}}}}}},{{{{{rm{mean}}}}}},{{{{{rm{bacterial}}}}}},{{{{{rm{load}}}}}}),\ times ,{{{{{rm{bacterial}}}}}},{{{{{rm{species}}}}}}$$To test whether there is variation in pathogen exploitation (infection intensity measured as bacterial load), we performed a linear model with the natural log of infection intensity as the dependent variable and bacterial species as a factor. Similar to the previous model, we used the geometric mean of infection intensity combined for days 1 and 2 post injection, for each bacterial species/dose/experimental replicate. The uninfected Ringer’s replicates were not included in this model. Post-hoc multiple comparisons were performed using “emmeans”, using the default Tukey adjustment for multiple comparisons. Effect sizes given as Cohen’s d, were also calculated using “emmeans”, using the sigma value of 2.327, as estimated by the package. Ps. entomophila was excluded for the reason given above. The sample sizes per bacterial species were: n = 13 for E. cloacae, n = 10 for L. lactis and n = 15 for Pr. burhodogranariea.$${{{{{rm{Model}}}}}},3:,{{log }}({{{{{rm{geometric}}}}}},{{{{{rm{mean}}}}}},{{{{{rm{bacterial}}}}}},{{{{{rm{load}}}}}}), sim ,{{{{{rm{bacterial}}}}}},{{{{{rm{species}}}}}}$$Are persistent infection loads dose-dependent?We tested whether initial injection dose is a predictor of bacterial load at seven days post injection22,25. We removed all flies that had a bacterial load that was below the detection limit as they are not informative for this analysis. The response variable was natural log transformed bacterial load at seven days post-injection and the covariate was natural log transformed injection dose, except for P. burhodogranariea, where the response variable and the covariate were log-log transformed. Separate models were carried out for each bacterial species. Experimental replicate and person were fitted as fixed factors. By day seven none of the flies injected with 92,000 CFU of L. lactis were alive. The analysis was not possible for Ps. entomophila infected flies because all flies were dead by seven days post injection.$${{{{{rm{Model}}}}}},4:,{{log }}({{{{{rm{day}}}}}},7,{{{{{rm{bacterial}}}}}},{{{{{rm{load}}}}}}), sim ,{{log }}({{{{{rm{injection}}}}}},{{{{{rm{dose}}}}}}),+,{{{{{rm{replicate}}}}}},+,{{{{{rm{person}}}}}}$$Calculation of clearance indicesTo facilitate the analyses of clearance we calculated clearance indices, which aggregate information about clearance into a single value for each bacterial species/dose/experimental replicate. All indices were based on the estimated proportion of cleared infections (defined as samples with a bacterial load that was below the detection limit) of the whole initial population. For this purpose, we first used data on bacterial load in living flies to calculate the daily proportion of cleared infections in live flies for the days that we sampled. Then we used the data on fly survival to calculate the daily proportion of flies that were still alive. By multiplying the daily proportion of cleared flies in living flies with the proportion of flies that were still alive, we obtained the proportion of cleared infections of the whole initial population – for each day on which bacterial load was measured. We then used these data to calculate two different clearance indices, which we used for different analyses. For each index we calculated the mean clearance across several days. Specifically, the first index was calculated across days three and four post injection (clearance index3,4), and the second index was calculated from days seven, 14 and 21 (clearance index7,14,21).Do the bacterial species differ in clearance?To test whether the bacterial species differed in clearance, we used clearance index3,4, which is the latest timeframe for which we could calculate this index for all four species: due to the high virulence of Ps. entomophila we were not able to assess bacterial load and thus clearance for later days. The distribution of clearance values did not conform to the assumptions of a linear model. We therefore used a Kruskal-Wallis test with pairwise Mann-Whitney-U post hoc tests. Note that the Kruskal-Wallis test uses a Chi-square distribution for approximating the H test statistic. To control for multiple testing we corrected the p-values of the post hoc tests using the method proposed by Benjamini and Hochberg90 that is implemented in the R function pairwise.wilcox.test.$${{{{{rm{Model}}}}}},5:,{{{{{{rm{clearance}}}}}},{{{{{rm{index}}}}}}}_{3,4}, sim ,{{{{{rm{bacterial}}}}}},{{{{{rm{species}}}}}}$$Do exploitation or PPP predict variation in clearance?To assess whether exploitation or PPP predict variation in clearance we performed separate analyses for clearance index3,4 and clearance index7,14,21. As discussed above, this precluded analysing Ps. entomophila. For each of the two indices we fitted a linear mixed effects model with the clearance index as the response variable. As fixed effects predictors we used the replicate-specific geometric mean log bacterial load and the species-specific PPP. In addition, we included species as a random effect.In our analysis we faced the challenge that many measured clearance values were at, or very close to zero. In addition, clearance values below zero do not make conceptual sense. To appropriately account for this issue, we used a logit link function (with Gaussian errors) in our model, which restricts the predicted clearance values to an interval between zero and one. Initial inspections of residuals indicated violations of the model assumption of homogenously distributed errors. To account for this problem, we included the log bacterial load and PPP as predictors of the error variance, which means that we used a model in which we relaxed the standard assumption of homogenous errors and account for heterogenous errors by fitting a function of how errors vary. For this purpose, we used the option dispformula when fitting the models with the function glmmTMB91.$${{{{{rm{Model}}}}}},6 :,{{{{{{rm{clearance}}}}}},{{{{{rm{index}}}}}}}_{3,4},{{{{{rm{or}}}}}},{{{{{{rm{clearance}}}}}},{{{{{rm{index}}}}}}}_{7,14,21}, \ sim ,{{log }}({{{{{rm{geometric}}}}}},{{{{{rm{mean}}}}}},{{{{{rm{bacterial}}}}}},{{{{{rm{load}}}}}}),+,{{{{{rm{PPP}}}}}}+{{{{{{rm{bacterial}}}}}},{{{{{rm{species}}}}}}}_{{{{{{rm{random}}}}}}}$$Does longer-term clearance depend upon the injection dose?In contrast to the analyses described above, we additionally aimed to assess the long-term dynamics of clearance based on the infection status of dead flies collected between 14 and 35 days and 56 to 78 days after injection. Using binomial logistic regressions, we tested whether initial injection dose affected the propensity for flies to clear an infection with E. cloacae or Pr. burhodogranariea before they died. The response variable was binary whereby 0 denoted that no CFUs grew from the homogenate and 1 denoted that CFUs did grow from the homogenate. Log-log transformed injection dose was included as a covariate as well as its interaction with the natural log of day post injection, and person was fitted as a fixed factor. Replicate was included in the Pr. burhodogranariea analysis only, because of unequal sampling across replicates for E. cloacae. L. lactis injected flies were not analysed because only 4 out of 39 (10.3%) cleared the infection. Ps. entomophila infected flies were not statistically analysed because of a low sample size (n = 12). The two bacterial species were analysed separately.$${{{{{rm{Model}}}}}},7 :,{{{{{rm{CFU}}}}}},{{{{{{rm{presence}}}}}}/{{{{{rm{absence}}}}}}}_{{{{{{rm{dead}}}}}}}, sim ,{{log }}({{log }}({{{{{rm{injection}}}}}},{{{{{rm{dose}}}}}})),\ times ,{{log }}({{{{{rm{day}}}}}},{{{{{rm{post}}}}}},{{{{{rm{injection}}}}}}),+,{{{{{rm{replicate}}}}}},+,{{{{{rm{person}}}}}}$$To test whether the patterns of clearance were similar for live and dead flies we tested whether the proportion of live uninfected flies was a predictor of the proportion of dead uninfected flies. We separately summed up the numbers of uninfected and infected flies for each bacterial species and dose, giving us a total sample size of n = 20 (four species × five doses). For live and for dead homogenised flies we had a two-vector (proportion infected and proportion uninfected) response variable, which was bound into a single object using cbind. The predictor was live flies, and the response variable was dead flies, and it was analysed using a generalized linear model with family = quasibinomial.$${{{{{rm{Model}}}}}},8:,{{{{{rm{cbind}}}}}}({{{{{rm{dead}}}}}},{{{{{rm{uninfected}}}}}},,{{{{{rm{dead}}}}}},{{{{{rm{infected}}}}}}), sim ,{{{{{rm{cbind}}}}}}({{{{{rm{live}}}}}},{{{{{rm{uninfected}}}}}},,{{{{{rm{live}}}}}},{{{{{rm{infected}}}}}})$$Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

MaterialsStudy areaThe Sinbilawin town is located southeast of Dakahleia Governorate, Egypt. It is bounded to the east by the Timai El-Amded city, west by the Aga city, north by the Mansoura city and to the south by the Diarb Negm city. The Sinbilawin lies between 31° 27′ 38.07″ E longitude and 30° 53′ 1.55″ N latitude (Google Earth) (Fig. 1). The total area of Sinbilawin town is about 304.5 km2 with total cultivated area of Sinbilawin is about 64,362.28 Faddens5. The Sinbilawin town is characterized a flat land.Figure 1Map of the Sinbilawin city, 2015 (study area).Full size imageRice strawThe total area of rice crop in Egypt is 1,215,830 faddan and the production of rice is 4,817,964 tons. The average of productivity is 3.963 tons5. The total area of rice crop in Sinbilawin center is 34,078.12167 faddan and the production of rice straw is 148,376.1417 tons. The rice area map is shown in Fig. 2.Figure 2Rice area map.Full size imageDataGIS is a powerful tool which used for computerized mapping and spatial analysis. GIS is used in many applications such as geology, protection, natural resource management, risk management, urban planning, transportation, and various aspects of modeling in the environment. Also, it is using for decision making22. In this study GIS is used to select the best site to be suggested to collect the rice straw as shown in flowchart of Fig. 3.Figure 3Flowchart of rice straw collecting from Sinbilawin center.Full size imageSoftware programs

a.

Google Earth program
Google Earth combines the power of Google Search with satellite imagery, maps, Terrain and 3D buildings to put the world’s geographic information at your fingertips. It displays satellite images of varying resolution of the Earth’s surface, allowing users to see things like cities and houses looking perpendicularly down or at an oblique angle, with perspective23.

b.

Image Processing and Analysis Software (ENVI) program
It has been used to separate layers from the satellite image as layer of road, layer of urban, layer of canal and layer of sites to the rice crop planting. ENVI 5.6.2 Classic is the ideal software for the visualization, analysis and presentation of all types of digital imagery. ENVI Classic’s complete image-processing package includes advanced, yet easy-to-use, spectral tools, geometric correction, terrain analysis, radar analysis, raster and vector GIS capabilities, extensive support for images from a wide variety of sources, and much more24.

c.

GIS program
ArcGIS Desktop 10.1 will be using in the present study. It is the newest version of a popular GIS software which produced by ESRI. ArcGIS Desktop is comprised of a set of integrated applications. All figure numbers were created using GIS software.

Design a model for assembling rice strawArcGIS10.1 was selected in this study to design a model for selecting the suitable sites to collect rice straw amounts in Sinbilawin center. To achieve the former goal must be gotten the satellite images (landsat 8) for the province of Dakahleia and the Sinbilawin center. These images were called operation land imager (OLI). Thus, layers will be obtained from the satellite images such as water channels, drainages, urban areas, main and sub- roads, rice crop areas and sites. ENVI program has been used to separate layers and place it in a file which named (Shp. file) for easy insertion in ArcGIS10.1 program. In this present study, design a model will be done on the main layers which will be obtained from the satellite image as follows:

Location and the administrative limits of Dakahleia Governorate and Sinbilawin center.

The rice crop area and sites in Dakahleia governorate as the main layer.

Layer of rice area and their sites in Sinbilawin center. Sinbilawin center was selected in the study because it is cultivated largest rice area in Dakahleia and Dakahleia biggest governorate cultivates rice.

Layer of roads network in Sinbilawin center. The network of roads was included the main roads and submain to aggregation rice straw. Given the problems associated with transport cost, disposal, and issues that arise from inadequate agriculture crop residues management, the collect units become essential to be nearest of the network of road to facilitate the process of transportation and minimize cost.

Layer of the urban locations in Sinbilawin center. Crop residues collection sites have an enormous impact on urban in general due to contamination and fires. This study proposes the collecting rice straw sites not be near of the urban, because it causes many health problems for the population.

Layer of the canal locations in Sinbilawin center. Collecting rice straw sites must be nearest from the source of water as canal for safety, protect it from fire and important for any recycle operation.

Layer of the drain locations in Sinbilawin center. Also, drain is important as the source of water but less than canal.

Arc GIS 10.1 to select the suitable sites for assembling rice strawThree Scenarios were suggesting for completing the design of the modeling to select best sites for collecting rice straw. From the three scenarios wall be reached to the best collecting sites for rice straw in Sinbilawin center as follows:

The first scenario: Modeling for Sinbilawin center
In this case, modeling was running on the Sinbilawin center as the whole unit.

The second scenario: Modeling for the village in Sinbilawin center.
The Sinbilawin center consists of 97 villages and some other area surrounding. In this case, modeling was running on each village and each accessory in Sinbilawin center.

The third scenario: Modeling for the best site in each village in Sinbilawin center.
In this case, the modeling was running on each best site which located in each village (on the 97 sites in Sinbilawin center).

MethodsTo achieve the former objective in this study wall be done as follows:

Location and the administrative limits of Dakahleia Governorate and Sinbilawin center were uploaded as map by Google earth program.

The rice crop area and sites in Dakahleia governorate. The data of area and sites to rice crop in Dakahleia governorate were collected from the Ministry of Agricultural—Central Administration of Economy and Statistics as numerical data for each center in Dakahleia governorate. Map for Dakahleia governorate was obtained via satellite image from the Remote Sensing Authority.

Rice production (ton) = Cultivated area(fed)*Average production (4.354 ton/fed)5.

Total rice straw (ton) = Rice production (ton) / 2.5.

Satellite image layersAreas and sites of satellite layers for rice in Sinbilawin centerArea and sites of rice crop in Sinbilawin center as the database were obtained and collected Extraction layer from the Ministry of Agricultural. Central Administration of Economy and Statistics as numerical data for each village. Sinbilawin map as layer of molding was obtained via satellite image from the Remote Sensing Authority. It was used with ArcGIS 10.1 software to inference the sites and area of rice crop in the Sinbilawin center villages.Layer for the road network in Sinbilawin centerThe network of roads is very important factor and effective for collecting rice straw. The network roads map as the layer was extracted from satellite image via the Remote Sensing Authority. It was used with ArcGIS 10.1 software to inference the main and sub roads in the Sinbilawin center.Layer for the urban locations in Sinbilawin centerCrop residues collection sites have an enormous impact on urban general due to contamination, environmental pollution and fires, which are causing many health problems for the population. The urban map as the layer was extracted from satellite image via the Remote Sensing Authority. It was used with ArcGIS 10.1 software to appear all the urban sites in the Sinbilawin center.Layer for the water source in Sinbilawin centerRice straw collection sites must be nearest from the source of water as canal for safety and protect it from fire also water is very important for any recycle operation. The canal map as the layer was extracted from satellite image via the Remote Sensing Authority. It was used with ArcGIS 10.1 software to appear all source of water as canal in the Sinbilawin center.Layer for the drain locations in Sinbilawin centerThe drain is important as the source of water but less than canal. The drain map as the layer was extracted from satellite image via the Remote Sensing Authority. It was used with ArcGIS 10.1 software to appear all drain in the Sinbilawin center.ArcGIS 10.1 to select the suitable sites for collecting rice strawModeling was designed as shown in Fig. 4 to apply with the three scenarios.Figure 4Short form for modeling to select suitable sites to assembly rice straw.Full size imageFrom the three scenarios shall be reached to the best collecting sites for recycling rice straw in Sinbilawin center as follows:

The first scenario was running modeling for Sinbilawin center.

The second scenario was running modeling for the village in it.

The third scenario was running modeling for the best site in each village in it.

Different steps were running with modeling to select the best sites to assembly rice straw in Sinbilawin center: 1- Euclidean distance. 2- Reclassify (or changes). 3-Weighted overlay. Assuming common measurement scale and weights for each layer according to its importance as follows:—Roads 50%, Channels 40%, Urban 10% so that the total is 100%0.4- Select Layer by Location (Data Management). In this step, order of selecting layer sites was given through Arc tool box at ArcGIS10.1 for selecting sites through the Arc toolbox at ArcGIS10.1 software as follow: 1- Intersection with roads. 2- Intersection with canals water.Total cost of collecting rice strawTransportation for collecting crop residues is important factors because it affects the success or failure of crop residues utilization. GIS was used to determine suitable sites for collecting rice straw and converting it through given parameters as:

Total length of road (km).

Total weight of rice straw (ton).

Speed of tractor in sub roads (30 km/h)

Total time of transfer (h).

All experimental protocols were approved by Benha University Research Committee and all methods used in this study was carried out according to the guidelines regulations of Benha University. This work is approved by the ethic committee at Benha University. More