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Model frameworkThe capture-recapture model applied here is the hierarchical model for stratified populations proposed by Royle et al.48. The model aims to estimate local population size or community structure49 using capture-recapture data from multiple independent locations. In the following, we briefly describe the model in our context, including addressing heterogeneity in detection probability.Let us consider that we establish S independent camera stations in a survey area. Then, we install K camera traps at each station to monitor exactly the same focal area (totally S × K camera traps will be used). We assume that these camera traps detect animals within the focal areas NT times in total. For animal pass i (i = 1, 2, 3, …, NT), we will obtain (1) at the station where the animal is detected (hereafter station identity; gi), and (2) how many of the K cameras at the station were successful in detecting the animal pass (hereafter detection history; yi). The hierarchal capture-recapture model uses these two data, gi and yi.Let the number of the animal passes at station s be Ns (s = 1, 2, 3, …, S). Then, we assume that Ns follows a Poisson distribution with a parameter λ. In this case, the probability of passage i occurring at station s is expected to be (frac{lambda }{lambda times S}). Thus, station identity, gi, can be modelled as follows:$$g_{i} sim {text{ Categorical}}; left(frac{lambda }{lambda times S}right)$$
When the number of the animal passes at station s, Ns, may have larger variation than expected from the Poisson case, we may assume a negative binomial distribution model or may give a random effect to the parameter of the Poisson distribution at the camera station level.The detection history Y with elements yi can be modelled using a data augmentation procedure47. Specifically, the original detection Y is artificially augmented by many M – n passes with all-zero histories (i.e. not detected by any camera). The augmented data W with elements wi (y1, y2…yNT, 0, 0, … 0) will consist of the passage that occurred but was not detected by any camera (false zero), which occurs with probability ψ, and the passage that did not occur (structural zeros) with the probability 1 − ψ. A set of latent augmentation binary variables, z1, z2, … zM, is introduced, which denotes the false zero (z = 1) and the structural zero (z = 0). That is$$z_{i} sim {text{ Bernoulli }}left( psi right).$$The elements of the augmented data, wi, can be modelled conditional on the latent variables zi. There would be two alternative approaches to modelling the wi.The simplest one may regard wi as random binomial variables. That is$$w_{i} |z_{i} = , 1sim {text{ Binomial }}left( {K,p} right)$$When accounting for the heterogeneity of detection among animal passes, it can be accommodated using a beta distribution as follows;$$w_{i} |z_{i} = , 1sim {text{ Binomial }}left( {K,p_{i} } right)$$$$p_{i} sim {text{ Beta}}left( {alpha ,beta } right)$$The expected detection probability can be derived from (widehat{alpha }/(widehat{alpha }+widehat{beta })) and the correlation coefficients can be calculated by (1/(widehat{alpha }+widehat{beta }+1)).Alternatively, we can regard wi as a categorical variable that takes values from zero to K.$$w_{i} sim {text{ Categorical }}left( pi right)$$
where π is a probability vector of length K + 1. For simplicity, let us consider two camera traps installed at each station, and those cameras have equal detection probability. Then, wi can take either 0 (i.e. zi = 0 or both camera traps missed animals with conditional on zi = 1), 1 (i.e. only one camera trap detected animals with conditional on zi = 1), or 2 (i.e. both camera traps detected animals with conditional on zi = 1). Thus, when we define the probability that wi takes 0, 1, 2 with conditional on zi = 1, as φm (m = 1, 2, 3), the elements of π is equal to {zi × φ0 + (1 − zi)}, {zi × φ1}, {zi × φ2}, respectively.We then take different modelling approaches depending on whether detection probability among animal passes is heterogeneous or not. When two camera traps at a station detect animals independently with the same probability ρ, φ0, φ1, and φ2 can be expressed as a function of ρ, i.e. (1 − ρ)2, 2 × ρ × (1 − ρ)2, ρ2, respectively (Clare et al.47). On the other hand, when detections by the two camera traps are correlated, we need to estimate three real parameters φm that designate the probabilities of all outcomes wi|zi = 1. We assume that ρm follows the Dirichlet distribution with the parameter γm (m = 1, 2, 3). That is$$varphi_{m} sim {text{ Dirichlet}}left( {gamma_{1} ,gamma_{2} , , gamma_{3} } right)$$In this approach, the expected detection probability can be derived from ({widehat{varphi }}_{1}/2+{widehat{varphi }}_{2}) and the correlation coefficients can be calculated by ({widehat{varphi }}_{2}-{({widehat{varphi }}_{1}/2+{widehat{varphi }}_{2})}^{2}).Compared to the beta-binomial distribution approach, the approach using categorical-Dirichlet distribution might be more flexible in accommodating detection heterogeneity while it might be more challenging to estimate the model parameters. In either approach, the expected total number of animal passes can be expressed as (lambda times S). Thus, ψ can be fixed as follows:$$psi = frac{lambda times S}{M}$$For more details of the models, see Royle et al.48 and Clare et al.44.Testing the effectiveness of the hierarchical capture-recapture modelWe performed Monte Carlo simulations to evaluate the effectiveness of the hierarchical capture-recapture model. Because the model reliability has been confirmed well48, we here focused on the effects of heterogeneity in detection probability on the accuracy and precision of the estimates.We assumed that the number of detections by camera traps followed a negative binomial distribution with a mean of 5.0 and dispersion parameter 1.27, which derived the actual data on an ungulate in African rainforests34. We also assumed two camera traps each at 30 stations (i.e. 60 camera traps in total). We generated detection histories (i.e. the number of camera traps successfully detecting animals in each animal passage) using a beta-binomial distribution with the expected detection probability at 0.8 or 0.4. We varied the correlation coefficients (= 1/(α + β + 1)), from 0.1 to 0.5 in 0.1 increments. The scale parameters of the beta distributions for each scenario are shown in Table 1. Additionally, to determine the effects of sample sizes on the accuracy and precision of estimates, we increased the number of camera stations at 100. Since this setting requires much computation time, we only assumed a detection probability of 0.4 and a correlation coefficient of 0.3.We estimated the parameters of the hierarchical capture-recapture models assuming a beta-binomial distribution and a categorical-Dirichlet distribution using the Markov chain Monte Carlo (MCMC) implemented in JAGS (version 3.4.0) in all the simulations. We assumed that the number of animal passes followed a negative binomial distribution. For the model assuming a beta-binomial distribution, we transformed the scale parameters, α and β as p*phi and p*(1 − phi), respectively (p is an expected detection probability). Then we used a weakly informative prior (gamma distribution with shape = 10 and rate = 2) for phi and a non-informative uniform distribution from 0 to 1 for the detection probability49. For the model assuming a categorical-Dirichlet distribution, the Dirichlet prior distribution was induced by treating each γm ~ Gamma(1, 1) and calculating each probability by ({varphi }_{m}={{gamma }_{m}}/{sum }_{m=1}^{M}{gamma }_{m}) followingv and Clare et al.44. We generated three chains of 3000 iterations after a burn-in of 1000 and thinned by 5. The convergence of models was determined using the Gelman–Rubin statistic, where values  More

Timeseries imaging tracks gene expression in spatial systemsRecent studies have shown it possible to identify the members of microbial consortia as well as their gene expression within spatially-structured systems30,33,34. However, these methods capture data cross-sectionally and are unable to provide temporal insight into gene expression patterning as it emerges in these cell populations. To bridge this gap, we built a fluorescent imager inside an incubator (Supplementary Fig. 1). Our framework characterizes cellular growth and gene expression in spatially-structured environments with previously unattainable time-resolution and throughput. Fluorescently labeled cells are illuminated using LEDs connected to a custom-built control system (see methods). The images are background corrected and analyzed, tracking colony growth and gene expression information (Supplementary Figs. 2, 3) straight from the spatially-structured system.In our experiments, we utilized a dual-labeled P. aeruginosa PA14 strain harboring PBad-DsRed(EC2)35 driven by L-arabinose in the plate media, which cannot be metabolized by the cells36, and PrhlAB-GFP28,37. When grown in spatial structure, the constitutive expression of DsRed provided a measure of the local density of bacteria (Supplementary Fig. 4). In all our experiments, the dynamical expression of GFP, validated by RT-qPCR (Supplementary Fig. 5) (see methods), reported on the expression of rhlAB.Using these data, we were able to characterize how the surroundings experienced by these microbes influence the dynamics of their cooperative behavior directly in a spatially-structured setting.Rhamnolipid production differs in liquid and spatial environmentsRhamnolipids are necessary for cooperative swarming behavior in P. aeruginosa and for other traits related to virulence26. Rhamnolipids can be produced in liquid culture10,20,28,38, thus rhamnolipid production is often studied in detail there. Despite recent work indicating that gene expression related to quorum signaling systems in P. aeruginosa may differ in spatial structure29, no studies assess how downstream genes, such as rhlAB, may be affected in spatially-structured colonies. Given the relevance of these diffusible inputs to the rhlAB system, we hypothesized that there could be differences between gene expression patterns in liquid and spatial environments.We compared P. aeruginosa biomass growth and gene expression in the liquid and spatial environments (Fig. 1a). Liquid culture data was collected following prior methods28. To interrogate the spatial system, we used the protocol from the classic Colony Forming Unit (CFU) assay. Cells were seeded with extreme dilution and we observed the behavior of the resultant colonies (cCFUs) across time and within the random configurations generated.Fig. 1: Rhamnolipid production differs between liquid culture and surface-attached P. aeruginosa.a Cartoon depictions of liquid and spatially-structured environments used in this study. b Optical density timeseries describing P. aeruginosa growth in liquid culture. [Blue] Biomass growth without exogenous quorum signals. [Purple] Biomass growth with exogenous quorum signals. c DsRed fluorescent timeseries generated from a custom-built imager (Supplementary Fig. 1) and custom software (Supplementary Fig. 3) describing P. aeruginosa growth in colony forming units (CFU). [Blue] Biomass growth without exogenous quorum signals [Purple] Biomass growth with exogenous quorum signals added to the plate media. [Inset] Example plate showing colonies at 48 h. Scale bar 1 cm. d Promoter activity (left[frac{{dGFP}}{{dt}}cdot frac{1}{{{OD}}_{600}}right]) of PrhlAB with respect to culture growth rate (left[frac{d{{OD}}_{600}}{{dt}}cdot frac{1}{{{OD}}_{600}}right]). [Blue] without exogenous quorum signals [Purple] with exogenous quorum signals. e Promoter activity (left[frac{{dGFP}}{{dt}}cdot frac{1}{{DsRed}}right]) of PrhlAB with respect to CFU growth rate (left[frac{{dDsRed}}{{dt}}cdot frac{1}{{DsRed}}right]). [Blue] without exogenous quorum signals [Purple] with exogenous quorum signals provided in the plate media.Full size imageWe observed differences in growth between cells grown in liquid culture (Fig. 1b) and spatial structure (Fig. 1c) with the same media composition. The growth pattern observed in liquid culture recapitulates previously reported data22,28. In comparing WT growth (dark blue data in Fig. 1b, c) between environments, we observed that both achieve a period of exponential growth, followed by a period of slowed growth. This sub-exponential growth is prolonged and no period of biomass decay is observed in the spatially-structured environment during our observation window.Quorum signal perturbation has long been an experimental tool to determine if a phenotype is responsive to social signaling9,10. rhlAB gene expression in particular is known to be downstream of both the las and rhl quorum signal systems39,40. However, it has previously been shown that liquid culture perturbation with additional C4-HSL and 3-oxo-C12-HSL, the rhl and las quorum signal system auto-inducers respectively, do not illicit significant change in growth or PrhlAB dynamics in this strain of P. aeruginosa22. We replicated this liquid culture result (Fig. 1b, purple data). In the spatially-structured system, we performed this perturbation by including both quorum signal molecules in the plate media in the same concentration by volume as previously published22. This analysis was done using biological replicates with More

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