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We observed a clear reduction in the acoustic activity of sperm whales and beaked whales during the period when sonar signals were recorded at Station 5, indicating that whales ceased foraging in this area while military sonars were in use. The acoustic detection rate of sperm whales returned to pre-exercise baseline levels within the days following the CF16 exercise, while the observed reduction in beaked whale acoustic activity was more prolonged. Detection rates of Cuvier’s beaked whale clicks remained low throughout the 8-day period immediately following the exercise, and UMBW clicks were largely absent during this period. This study is observational and limited to showing correlation rather than cause and effect; nonetheless, these results are consistent with previous experimental research on the responses of beaked whales to simulated and real military sonars and suggest that whales were disturbed from normal foraging behaviour and likely displaced from the affected area during the CF16 exercise.The scale and duration of sonar use recorded during this study provides important context for the observed results. Much of the experimental work conducted to date on the responses of beaked whales and other odontocetes to sonar has involved controlled exposure experiments using animal-borne tags to record the fine-scale movements and acoustic behavior of individuals, allowing responses to be examined on the scale of minutes to hours e.g.,7,8,10. Experimental exposures to simulated sonar signals lasting approximately 15–30 min have elicited pronounced avoidance responses in Blainville’s beaked whales7, Cuvier’s beaked whales8, Baird’s beaked whales16, and northern bottlenose whales9,10. Generally, these studies were focused on the onset of the response and did not always assess the duration over which altered behaviour continued. However, the absence of foraging behaviour for several hours following exposure was noted in some cases, and focal animals performed sustained directed movement away from the exposure location during this time, covering distances of up to tens of kilometers10. In broader-scale studies examining responses of Blainville’s beaked whales to real multi-ship naval training operations on the Atlantic Undersea Test and Evaluation Center (AUTEC) in the Bahamas, displacements of up to 68 km were observed, lasting 2–4 days before whales returned to foraging in the area where they were exposed7,28. In the present study, the duration of naval sonar activity recorded during the CF16 exercise was considerably more prolonged, with bouts of sonar continuing for up to 13 consecutive hours and occurring repeatedly over an 8-day period. Although we can only make inference on species-level rather than individual-level responses based on the absence of clicks in our recordings, it is plausible that military sonar activity at this scale led to wide spatial avoidance of the affected area over an extended period.The absence of sperm whale click detections in the Station 5 recordings for 6 consecutive days during the CF16 exercise is notable; few prior studies have demonstrated sustained changes in foraging behaviour or substantial displacement of sperm whales following sonar exposure. Behavioural response studies conducted in northern Norway using controlled experimental exposures showed varying responses by sperm whales, which included changes in orientation and direction of horizontal movement, changes in acoustic behaviour, and altered dive profiles23. Exposure to lower frequency sonar signals in the 1–2 kHz range generally prompted stronger responses, including a reduction in foraging effort or transition from a foraging to non-foraging state, while exposure to higher frequency sonar signals in the range of 6–7 kHz did not appear to trigger changes in foraging behaviour21,29. More recently, Isojunno et al.30 quantified the responses of sperm whales to continuous and pulsed active sonars, and found that sound exposure level was more important than amplitude in predicting a change in foraging effort. We were not able to investigate differential responses to frequency or other sonar characteristics in this study, due to the observational nature of the study and the absence of sperm whale clicks throughout most of the exercise period. Likewise, we cannot exclude the physical presence of ships, aircraft, and submarines in the area or additional types of noise produced during maneuvers as potential factors contributing to the cessation of sperm whale and beaked whale click production and foraging behaviour.The observed changes in acoustic activity were more easily quantified for sperm whales than for beaked whales, due to higher baseline hourly presence of sperm whale clicks in the recordings. Sperm whales produce powerful echolocation clicks throughout their foraging dives, which can be recorded at ranges of 16 km or more31, and a single individual foraging in the vicinity of a hydrophone may be detected continuously throughout multiple dive cycles. Our analysis was based on sperm whale click detections that met a threshold signal-to-noise ratio (SNR), and the results therefore provide a minimum estimate of sperm whale presence in the vicinity of the recorder. Reporting results at the level of hourly presence rather than the number of individual click detections largely mitigated the effects of excluding low-SNR clicks recorded at greater distances from the hydrophone or during higher ambient noise conditions. Likewise, the presence of sperm whales on an hourly time scale is not likely to be substantially underestimated when recordings are collected using a low duty cycle32. By contrast, beaked whales produce echolocation clicks at higher frequencies and lower source levels, with highly directional beam patterns33. These clicks are likely only detected at ranges of up to approximately 4 km when the whale is oriented toward the hydrophone, and at lesser distances when clicks are received off-axis34. As a result, there is greater variability and lower baseline detection rates of beaked whale clicks on fixed passive acoustic recorders, which reduces statistical power to assess temporal changes in acoustic activity. Moreover, the duty-cycled recording schedule used at Station 5 provided only 65 s of high-frequency data 3 times per hour, and the presence of beaked whales is likely to be underestimated by this duty cycle, with potentially greater underestimation of Mesoplodont species compared to Cuvier’s beaked whales35.Continuous recordings were collected at the East Gully and Central Gully recording sites, but included only partial temporal coverage of the exercise period and no pre-exercise baseline data. No comparable recordings were available from these locations in a prior or subsequent year to form a control dataset. As a result, we were not able to use these datasets to assess changes in acoustic activity associated with the CF16 exercise. A slight decrease in hourly presence of northern bottlenose whale clicks in the Central Gully recordings occurred on September 19th–20th, 2016; however, we are aware that an oceanographic research vessel was coincidentally in the area deploying scientific instrumentation in close proximity to the Central Gully recording site on these dates, creating an additional source of potential disturbance. Despite these limitations, we included an analysis of the recordings collected at the East and Central Gully sites for two reasons: first, to provide perspective on the geographic extent over which activities associated with the CF16 exercise occurred; and second, to illustrate the diversity in beaked whale species composition at different locations across the region. Analysis of the recordings for sonar signals revealed that higher levels of sonar activity occurred near the Station 5 recording site than near the East or Central Gully locations. Due to the distance between recording sites and the timing of the sonar signals recorded, it appears that the recorded sonar signals came from multiple source locations over the duration of the exercise. Recordings from Central Gully contained the fewest sonar signals and lowest measured received levels, likely due to the deliberate avoidance of the Gully MPA and surrounding area by exercise participants during CF16. The Gully was established as an MPA in 2004, and is one of three adjacent canyons on the eastern Scotian Shelf currently designated as critical habitat areas for the endangered Scotian Shelf population of northern bottlenose whales36. The Station 5 recording site was located approximately 300 km to the southwest, and experienced higher levels of naval sonar activity during CF16. However, none of the locations were chosen specifically to monitor CF16, and we do not have access to information on the general exercise areas used, specific locations of naval vessels, submarines, or aircraft participating in the CF16 exercise, or the source levels of transmitted sonar signals. Due to the opportunistic nature of the recordings, the received levels of sonar signals measured at Station 5 likely do not represent the highest sound levels introduced into the marine environment during the CF16 exercise.Unlike many areas where behavioural responses to sonar are commonly studied, there are no instrumented naval training ranges off eastern Canada, and cetaceans inhabiting this region are unlikely to be accustomed to regularly hearing naval active sonars. Other than during the CF16 exercise, sonar signals were not noted during a large-scale analysis of cetacean call occurrence and soundscape characterization in 2 years of recordings collected at Station 5 and numerous other passive acoustic monitoring sites off eastern Canada26. Exposure context and familiarity with a signal may be important factors influencing an individual’s response to acoustic disturbance15. Experimental research on Cuvier’s beaked whales near a U.S. naval training range located off southern California demonstrated possible distance-mediated effects of sonar exposure, with more pronounced behavioural responses occurring with closer source proximity, even when received levels from the closer source were likely lower than those from more distant, high-powered sonar transmissions, which did not elicit as strong a response15. The movement and predictability of the sound source as well as the timing and duration of sonar transmissions may also be important factors influencing the behavioural response15. Whales inhabiting waters off southern California are likely habituated to hearing distant sonar due to routine naval training activities occurring on the range. Conversely, Wensveen et al.10 found that northern bottlenose whales in the eastern North Atlantic exhibited similar responses to simulated sonar signals played at various distances up to 28 km, suggesting that they perceived this novel stimuli as a potential threat even from a distance and at relatively low received levels. Bernaldo de Quiros et al.5 hypothesized that beaked whales not regularly exposed to active sonar signals may respond more strongly, both physiologically and behaviourally, which poses a concern for a region where military training activities involving the use of sonar are relatively infrequent, but occur periodically in the form of large-scale exercises involving the extensive use of active sonars and creating significant potential for acoustic disturbance.Behavioural disturbance due to anthropogenic noise may have energetic, health, and fitness consequences for deep-diving odontocete species. Disruption of normal diving patterns creates energetic costs due to the significant investment in each dive and the reduction of time available for prey intake when foraging dives are interrupted. Recent studies on the functional relationship between beaked whales and deep-sea prey resources suggest that certain characteristics of prey, including minimum size and density thresholds, are required for beaked whales to successfully meet their energetic needs12,37. While the distribution and characteristics of deep-sea prey are challenging to study and largely unknown in most regions, considerable environmental heterogeneity may be present, causing the quality of foraging habitat to vary significantly over even small horizontal scales12,37. This patchiness in habitat quality has important implications for behavioural disturbance, as even short-term displacement from high-quality habitat areas can affect the fitness of individuals and potentially lead to population-level consequences13.In addition to the consequences of sublethal disturbance, it is important to note that the likelihood of observing more acute impacts of exposure to naval active sonar, including injuries or fatalities, is extremely low in offshore regions. Individual and mass strandings of beaked whales and other cetaceans associated with military activities have typically been documented on oceanic islands with populated coastlines1,3,6. Factors affecting the probability that cetacean carcasses will wash ashore include buoyancy and decomposition rates in local water conditions, oceanic surface currents, the topography of coastlines, and the location of habitat relative to shore6. Off Nova Scotia, potential beaked whale and sperm whale habitat (consisting of water depths greater than 500 m) is located more than 100 km from the coastline, and injuries or fatalities occurring in deep water habitat in this region are unlikely to result in observed strandings. Stranding incidents involving sperm whales and beaked whales have been reported in Nova Scotia, but the cause of mortality is usually unknown38. Cetacean mortality is highly underestimated even in the aftermath of catastrophic events such as large oil spills39, and a lack of observed injuries or mortalities following offshore military activities should not be construed as evidence that no direct or immediate harm was caused.This study offered a unique opportunity to use existing passive acoustic monitoring (PAM) data to assess disturbance of poorly-known odontocete species during a real-world, large-scale military sonar exercise in a region where military sonar use at this scale is relatively uncommon. Ideally, a PAM study designed to examine disturbance in this context would collect continuous rather than duty-cycled recordings, and include ample baseline data surrounding the period of interest as well as in prior and subsequent years. Additionally, multiple acoustic sensors arranged in a dense array surrounding exercise locations would provide further insight into the spatial context of exposure and patterns of disturbance. Despite the data limitations in the present study, our results demonstrate that changes in odontocete foraging behaviour associated with acute, large-scale disturbance may be evident in PAM data even at low duty cycles. The nature of the observed effect (e.g., temporary disruption of foraging, spatial displacement, or more acute injury or distress) remains unknown, as do the number of individuals affected and the longer-term health and fitness implications. Broader baseline data on species occurrence and an improved understanding of species’ ecology and habitat use in the region are necessary for making informed mitigation decisions, allowing key habitat areas to be avoided, and understanding the impacts of naval active sonar exposure in this region on individuals and populations. More

This research focuses on the quantitative and qualitative analyses of cyanobacteria and microalgae present in rainfall during the summer phytoplankton bloom season of August–September 2019. In addition, a continuous episode of rainfall over several days was selected to demonstrate the washout process of microorganisms from the air with rain.Quantity of cyanobacteria and microalgae washed out with rain during the growing seasonCurrently, there is a growing number of scientific articles on cyanobacteria and microalgae in the atmosphere8. Unfortunately, there is a reference methodology for efficiently counting the microorganisms present in the air or in rainfall. A popular method for quantifying cyanobacteria and microalgae in the air is to show the number of taxa found in the collected samples after growth6,31,42,43,44,45,46. In this study, a total of 16 taxa of airborne cyanobacteria and microalgae were found in the samples. In the rainwater samples obtained during the summer of 2019, 11 taxa of cyanobacteria and microalgae were distinguished. The green algae in the rainwater samples included Bracteacoccus sp., Oocystis sp., Coenochloris sp., Chlorella sp., and Chlorococcum sp., while the cyanobacteria included Leptolyngbya sp., Pseudanabaena sp., Synechococcus sp., and Synechocystis sp. In addition, Chrysochromulina sp., which belongs to Haptophyta, was observed.Other studies recorded the presence of several to several dozen taxa in the air6,31,42,43,44,45,46. Certainly, a number of factors, starting with atmospheric conditions and ending with physical and chemical parameters of the surrounding waters, influence the diversity of cyanobacteria and microalgae in the atmospheric air. Analyzing global trends, only cyanobacteria have been found in the atmosphere of every region of the world31. However, according to Dillon et al.47, cyanobacteria have been detected in clouds at variable abundances between ~ 1% and 50% of the total microbial community. Xu et al.48 found that cyanobacteria constituted only 1.1% of the total bacterial community in clouds. It needs to be highlighted that there is still a lack of research available to provide this type of information for rainfall samples.For the period from July to September 2019, the results showed that the number of cyanobacteria and microalgae cells present in rainfall varied over time (Fig. 1) and ranged between 100 cells L–1 and 342.2 × 103 cells L–1. From July to the end of August, the cell number was relatively low, ranging from 100 cells L–1 to 28.6 × 103 cells L–1. This variability was related to the change in the biomass of blue green algae in the Gulf of Gdańsk (Table S2; Fig. 1). Therefore, this research also shows the close relationship between the processes taking place in the Baltic Sea and the presence of cyanobacteria and microalgae in the atmosphere. As the biomass of cyanobacteria in the Baltic Sea increased, the number of cyanobacteria and microalgae cells in the rainfall samples also increased (***p  More

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A theoretical framework of interacting bacterial strainsOur mathematical model was motivated by experimental assays used to establish colony biofilms where the founding inoculum is placed on the surface of solidified nutrient agar. Within the inoculum footprint, individual (or small clusters of) bacteria settle at random locations and grow over time into a mature structured macroscale community (Fig. 1A). In the mathematical model, all the founding cells are assumed to have identical properties. However, to track the dynamics of biofilm growth we divided the founding cells into two groups, denoted by ({B}_{1}) (shown in magenta) and ({B}_{2}) (shown in green) (Fig. 1B). Note that we refer to ({B}_{1}) and ({B}_{2}) as strains for brevity, even though they represent two isogenic cell lineages that express different fluorescent proteins in a single-strain biofilm (Fig. 1A). In our theoretical framework, biofilm dynamics were reduced to the fundamental processes of local growth and spatial spread (more details below), which provided a species-independent representation of dual-strain biofilm growth. Suitably nondimensionalised (see Section S3), the model is given by$$frac{partial {B}_{1}}{partial t}=nabla cdot left({Id}left(1-left({B}_{1}+{B}_{2}right)right){nabla B}_{1}right)+{B}_{1}left(1-left({B}_{1}+{B}_{2}right)right),$$$$frac{partial {B}_{2}}{partial t}=nabla cdot left({Id}left(1-left({B}_{1}+{B}_{2}right)right)nabla {B}_{2}right)+{B}_{2}left(1-({B}_{1}+{B}_{2})right),$$
(1)
where, the variables ({0le B}_{1}left({{{{{boldsymbol{x}}}}}},tright),{B}_{2}left({{{{{boldsymbol{x}}}}}},tright)le 1) denote the scaled densities of each strain, respectively at time (t, > ,0) (one nondimensional time unit corresponding to approx. 2.9 h) and at spatial position ({{{{{boldsymbol{x}}}}}}in Omega) (one nondimensional space unit corresponding to approx. 0.15 mm). The spatial domain (Omega ={{{{{{boldsymbol{x}}}}}}in {{mathbb{R}}}^{2}:{||}{{{{{boldsymbol{x}}}}}}{||}le R}) is a two-dimensional disk, representing the biofilm growth medium (Fig. 1C). This simplification provided a significant reduction in computational cost and was motivated by an analysis of a previously published data set, in which we found a two-order of magnitude difference between biofilm diameter and biofilm thickness in B. subtilis NCIB 3610 [27]. The model is therefore unable to explicitly resolve density distributions along the vertical axis, for example, layering of subpopulation caused by gradients in environmental conditions [28,29,30] or topographical features such as ‘wrinkles’ [31]. However, it is fully capable of capturing overlap between subpopulations that are below the environmental carrying capacity and thus can track spatio-temporal coexistence. Moreover, as we show below, we find strong agreement between data obtained from two-dimensional in silico biofilms and data gathered from laboratory grown biofilms, which further supports the model simplification.Fig. 1: Experimental and modelling set-up.A An example of the experimental assay. Founder cells carry either a constitutively produced copy of GFP (green) or mTagBFP (magenta). The bacteria were mixed in a 1:1 ratio and images taken after 24 h and 72 h of incubation. The number of founder cells was approx. 10 CFUs. The scalebars are 5 mm long. B An example realisation of the mathematical model. In the right-hand plots green and magenta are used to differentiate two subsets of the initial patches ((t=0), top) and their subsequent development ((t=25), bottom). Black areas indicate the computational domain, (varOmega). The plot of initial condition is a blow-up of the centre of the whole domain. The scalebars represent 7 nondimensional space units. C Schematic of model initial condition. Initial populations (filled coloured circles) are placed in ({varOmega }_{0}), a small subdomain of the whole computational domain (varOmega) (both centred at the origin (O)).Full size imageThe initial conditions of the theoretical framework were motivated by the random positions at which bacteria settle on the agar within the inoculum footprint (Fig. 1A). In our theoretical framework, we represented the experimental inoculum footprint by a small disk ({Omega }_{0}=left{{{{{{boldsymbol{x}}}}}}in Omega :{||}{{{{{boldsymbol{x}}}}}}{||} ; < ; {R}_{0}right}) in the centre of the computational domain (Fig. 1C). We modelled the random deposition of bacteria by randomly placing ‘microcolonies’ within ({Omega }_{0}) at nodes of a triangulated spatial mesh of linear geometric order, used in the application of a finite element method to numerically solve the model equations (Fig. 1B, C). Each initial microcolony was assumed to only contain one strain and to be at carrying capacity (i.e., ({B}_{1}=1) or ({B}_{2}=1) within each microcolony). Unless otherwise stated, we used an even number ((N)) of initial microcolonies and assigned exactly (N/2) to each strain at random. At spatial locations other than the assigned microcolonies, both densities were set to zero.The size of a spatial mesh element used in the model (approx. (0.008{m}{m}^{2}) in experimental parameters) was much larger than that of a single bacterial cell. This means that the initial conditions represented the experimental assays shortly after inoculation (typically after 24 h of incubation), at which time each bacterium (or small cluster of bacteria) had formed a distinct, spatially separated microcolony. Hence, the number of in silico microcolonies, (N,) represented the number of bacteria used in the initial inoculum. Resolving the initial data at this spatial scale allowed analysis for founder densities (0le Nle 824). Using a selected set of values from that range was sufficient to capture clear trends (see below). The range covers biologically relevant founder densities, which generate mature colony biofilms with broadly similar morphologies (Supplementary Fig. S1). Additionally, to verify whether the observed trends could be extrapolated to (N ; > ; 824), we represented high founder densities by piecewise spatially homogeneous initial conditions ({B}_{1}={B}_{2}=0.5) in ({Omega }_{0}) and ({B}_{1}={B}_{2}=0) otherwise.The strains were assumed to grow logistically, with growth being limited by the total population, which could not exceed unity (after nondimensionalisation). Moreover, spatial propagation was described by diffusion as is common [32]. However, in our model, we employed a diffusion coefficient that decreased with increasing population size. This density dependence prevented merging of initially separated founding patches in the model and was invoked to capture experimental observations that indicated such colonies abut rather than merge on meeting [33, 34]. The indicator function ({Id}=1) if ({B}_{1}+{B}_{2}le 1) and ({Id}=0) otherwise guaranteed nonnegativity of the diffusion coefficients; this constrained the model to the physically relevant case and moreover ensured numerical stability during simulation.Finally, we defined the competitive outcome score (for ({B}_{1})) of the interaction to be the relative mass of strain ({B}_{1}) i.e., ({B}_{1}^{Omega }/({B}_{1}^{Omega }+{B}_{2}^{Omega })) at the chosen end point ((t=T)) of our model simulation, where$${B}_{i}^{Omega }:={int }_{Omega }{B}_{i}({{{{{boldsymbol{x}}}}}},T){{{{{rm{d}}}}}}{{{{{boldsymbol{x}}}}}},,i=1,2.$$The competitive outcome score lies in the interval (left[{{{{mathrm{0,1}}}}}right]) with the value 0.5 signifying a 1:1 ratio between the strains. Note that we could swap the indices without loss of generality to equivalently define the competitive outcome to be the relative mass of strain(,{B}_{2}) at the chosen end point.Low founder densities yield large variability in competitive outcomesIn the absence of spatial dynamics, the mathematical model predicted that the ratio between both strains would always remain constant (left(frac{d}{{dt}}big(frac{{B}_{1}}{{B}_{2}}big)=0right)) and therefore that the competitive outcome would be determined by the initial ratio. To test whether such a relationship continued to hold in the full, spatially extended system, we examined data from simulations over a test range of initial founding cell densities. The initial strain ratio was selected to be 1:1 for each test.Model simulations using homogeneous initial conditions (representing high founder densities) consistently resulted in a competitive outcome score of 0.5 (i.e., strains in 1:1 ratio) with the strains remaining homogeneously distributed in space across the colony (Fig. 2A, Supplementary Movie S1). By contrast, independent model realisations using a specified number of microcolonies placed at randomly chosen locations representing low (({N}=6)) and intermediate (({N}=824)) founder densities, revealed significant variation in competitive outcome (Fig. 2B, C, Supplementary Movies S2 and S3). To explore this observed variability in more detail, we employed a Monte Carlo approach. For each fixed founder density (N) within the selected set, 1000 independent model realisations were conducted. Data from these simulations revealed that the competitive outcome score for each founder density was normally distributed with mean 0.5. The standard deviation was relatively large for low founder densities ((N={{{{mathrm{4,6,8,10}}}}})) and decreased with further increases in (N) (Fig. 2D). (Note the small standard deviation for (N=2); see supplementary information for a discussion of this special case). Finally, our model predicted significant changes in the spatial organisation of the two strains within the biofilm in response to changing founder density, consistent with previous studies [14]. For high founder densities, isogenic in silico strains were predicted to coexist homogenously (Fig. 2A). However, as the founder density was decreased (decreasing (N)), homogeneous coexistence was gradually replaced by the formation of spatial sectors dominated by one strain or the other. Full segregation occurred for low founder densities (Fig. 2B, C).Fig. 2: Spatial structure and variability in competitive outcome depend on founder density.A–C Example model realisations for different founder densities. All plots show the system’s initial conditions ((t=0)) and the outcomes after 25 time units. Plots visualising the systems’ states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}); plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. A The outcome of simulations initialised with piecewise spatially homogeneous populations representing high founder density. The ‘Merged’ image channel shows both strains (grey colour corresponds to overlap); the ({B}_{1})(green) and ({B}_{2}) (magenta) channels only show single strain filters of the plot. B The range of outcomes observed for low founder density (number of initial cell patches ({N}=6)). C The range of outcomes for intermediate founder densities ((N=824)). In (B, C) only the ‘Merged’ channel is shown. D Variability in competitive outcome increases with decreasing founder density. Each boxplot contains data from 1000 model realisations. Blue and red boxplots correspond to the founder densities in B and C, respectively.Full size imageAccess to free space determines competitive outcomeNext, we attempted to uncover the mechanism(s) by which low founder densities drive variability in competitive outcome. Motivated by [14], we first tested whether the initial separation between initial microcolonies of different types was the simple determinant. We did not find this to be the case for isogenic strain pairings in the mathematical model (Supplementary Fig. S2).As an alternative, we hypothesised that a microcolony surrounded by others may have little impact on competitive outcome as its contribution to biofilm growth would be ultimately limited. On the other hand, microcolonies located close to the boundary of the biofilm inoculum would be free to expand radially and thus could make a more significant contribution to the competitive outcome (for an example timelapse video see Movie S3). Hence, we explored whether competitive outcome was correlated to a strain’s potential for radial expansion beyond the inoculum. To do so, we assumed the potential for radial expansion to be solely determined by the geographical locations of a strain’s initial microcolonies. We then defined an appropriate score for this potential as follows. First, a circle was drawn that enclosed the initial microcolonies. Second, each point on the circle was associated with the nearest microcolony and assigned to that strain. Third, the total arc length on the circle associated with each strain was computed. Finally, the access to free space score (AFS score) for strain ({B}_{1}), denoted AFS1, was then computed as the ratio of the total arc length associated with ({B}_{1}) to the circumference of the circle. Therefore, (0le {{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{1}le 1) quantified strain ({B}_{1})’s hypothesised potential to contribute to radial biofilm expansion. It is straightforward to confirm that the AFS score for strain ({B}_{2}), ({{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{2}=1-{{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{1}). See Section S4.2 and Supplementary Figs. S3 and S4 for a mathematically rigorous definition of the AFS score.We explored the utility of the AFS score using (N=6) and (N=824) as representatives of low and intermediate founder cell densities, respectively. We increased the number of model realisations to 5000 for each of the selected values of N to ensure improved accuracy of our data analysis. The AFS score was then calculated for each of the 10,000 initial conditions (see examples Fig. 3A, B). On completion of each simulation, the corresponding competitive outcome score was computed. Analysis of these model data confirmed that the AFS score accurately predicts competitive outcome: for each fixed founder density, the AFS score unfolds the variation shown in Fig. 2D, yielding a positive, linear relationship between AFS1 and competitive outcome for ({B}_{1}) (Fig. 3C, D). For each of the selected values of (N), initial configurations of microcolonies with a low AFS1 score predictably generated a low competitive outcome for ({B}_{1}). Correspondingly, initial configurations with a high AFS1 score predictably generated a high competitive outcome for ({B}_{1}). The slope of this linear relationship provided a deterministic quantification of the variability of competitive outcomes for a given founder density (cf. Fig. 3C, D, Supplemental text).Fig. 3: Access to free space determines competitive outcome.A, B Example model realisations for different founder densities. All plots show system initial conditions ((t=0)) with the reference circle used to compute the AFS score (the circle is rescaled for visualisation purposes) and outcomes after 25 time units. The founder densities are (N=824) and (N=6) in A and B, respectively. Plots visualising system states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}); plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. C, D The relation between the AFS score ({AF}{S}_{1}), and competitive outcome is shown for intermediate founder density ((N=824)) and low founder density ((N=6)) in C and D, respectively. Data were obtained from 5000 model realisations and cover the continuum of ({AF}{S}_{1}). The observed probability density function for AFS is shown (circular markers); along with the density function of a fitted normal distribution ((mu approx 0.5,sigma approx 0.10) in C, (mu approx 0.5,sigma approx 0.16) in D) (solid line). E The relation between the standard deviations of the AFS score ({AF}{S}_{1}) and the competitive outcome. Each data point (circle) represents a different founder density and contains information from 1000 model realisations.Full size imageWe subsequently established that the predictive power of the AFS score was maintained across the range of founder densities considered in the model. Additionally, the variation in the AFS score was shown to decrease with increasing founder density (cf. Fig. 3C, D). Further, we revealed strong correlation between variation in AFS score and variation in competitive outcome (Fig. 3E). Therefore, for increasing founder density, the observed decrease in variation in competitive outcome can be directly attributed to the decrease in variation in the AFS score.Dual strain single-isolate biofilm assays confirm modelling hypothesesNext, we aimed to test the hypotheses put forward by the mathematical model. We selected an isogenic pair of Bacillus subtilis strains derived from isolate NCIB 3610 that constitutively produced the green fluorescent protein GFP (NRS6942, shown in green, Table S1) and the blue fluorescent protein mTagBFP (NRS6932, shown in magenta, Tables S1 and S2), respectively. In line with the modelling assumption, the isolates were mixed in a 1:1 ratio at a defined initial cell density (we used an OD600 of 1) and this cell culture was serially diluted prior to inoculating the colony biofilms (Section S7). Thus, biofilms were inoculated using ~106 CFUs and dilutions in 10-fold increments to order 1 CFU. For each founder density, 12 technical replicates were performed to provide a meaningful sample size, and the experiment was repeated on three independent occasions. We used a non-destructive colony biofilm image analysis approach, to measure the relative mass (and hence the competitive outcome) of the two isogenic strains at 24 h, 48 h, 72 h after inoculation (see Section S10). We confirmed that the output from the image analysis correlated well with data generated by disruption of the colony biofilm and analysis of the relative strain proportions determined using single cells analysis by flow cytometry (Fig. 4A) (see also [35]). The mTagBFP labelled strain consistently performed marginally worse than the GFP labelled competitor at high founder densities in co-culture, which suggests some impact on competitive fitness (Fig. 4B, C). To allow comparison with results from the mathematical model, we denoted the mTagBFP (NRS6932, shown in magenta) and GFP (NRS6942, shown in green) strains as ({B}_{1}) and ({B}_{2}), respectively, with associate AFS scores AFS1 and AFS2Fig. 4: Experimental data confirm modelling hypotheses.A Comparison of image analysis with flow cytometry. A scatter plot comparing measurements of relative density of the mTagBFP-labelled strain obtained from image analysis and flow cytometry is shown. Each data point corresponds to one biofilm, which was imaged before being analysed by flow cytometry. The data contains measurements taken from all strain pairs, all founder densities, and all time points. The solid blue line shows the identity (x=y), with the coefficient of determination being ({R}^{2}=0.91). B Example images of single-strain biofilms consisting of GFP (green(,{B}_{1})) and mTagBFP (magenta, ({B}_{2})) labelled copies of 3610. Taken after 72 h of incubation and shown for two different founder densities (scalebar 5 mm). C Strain density data. Competitive outcome measurements taken after 24 h, 48 h and 72 h of biofilm incubation. Plotted are technical repeats from one biological repeat of the experiment. The full data set is presented in Fig. S5A. D Example visualisations of AFS score calculations. Three example biofilms images at 24 h (left), 48 h (middle) and 72 h (right). The strains are as described in B. Images at 24 h show the reference circle used for the AFS1 score. E The relationship between AFS1 and competitive outcome for ({B}_{1}). AFS was calculated from images taken at 24 h, and competitive outcome for ({B}_{1}) after 48 h (left, (n=30)) and 72 h (right, (n=25)). The linear correlation coefficient (rho) is indicated.Full size imageOur experimental analysis proved consistent with the model predictions. High founder densities resulted in a broadly homogenous distribution of both strains over the footprint of the biofilm, while low founder densities led to a high degree of spatial segregation of the strains within the mature biofilm (Fig. 4B, see also [14]). Additionally, analysis of experimental data confirmed that variability in competitive outcome increased with decreasing founder density (Fig. 4B, C, Supplementary Fig. S5A). For founder densities equivalent to (sim)103 to (sim)106 CFUs, the competitive outcome was consistent across each set of technical replicates. By contrast, for founder densities equivalent to (sim)1 to (sim)102 CFUs, the competitive outcome was variable across each set of technical replicates. We noted that variability in competitive outcome, at all initial founder densities, was marginally amplified over time.We assumed the process of repeated dilution and selection of the inoculum volume may not guarantee an exact cell count and/or initial strain ratio of 1:1 at lower founder densities. Indeed, for low founder densities after 24 hrs incubation, we observed inconsistencies in the number and ratio of CFUs deposited (Supplementary Fig. S5B). We therefore considered whether these inconsistencies in the biofilm inocula contributed to the observed variability in competitive outcome. To explore this in more detail, we first implemented a combinatorial ‘cell picking’ model that mathematically simulated the process of selecting the small inoculum volume from a larger cell culture (see Section S4.3). This process identified a threshold of ({sim} {10}^{2}) CFUs below which variability in cell number and/or strain ratio could measurably deviate from their intended values in our experimental assay. Above this threshold, the combinatorial argument predicted limited deviation from the intended values (Supplementary Fig. S6A). Coupling these theoretical predictions with our experimental observations (Supplementary Fig. S5B), we concluded that any observed variability in competitive outcome cannot be a consequence of a measurable deviation in the inoculum composition for colony biofilms founded with (sim {10}^{2}) CFUs or higher.We next wanted to determine whether the predictive power of the AFS score could be used to connect experimental initial configurations of the bacteria with the observed competitive outcome. To do this accurately, we required that the founding bacteria remained spatially separated as small colonies until an image was taken at 24 h (the earliest imaging time-point, see Fig. 4D). Therefore, we only used founder densities lower than 102 CFUs. However, the above noted inconsistencies in initial strain ratios and cell counts at these densities raised the question of whether AFS could still accurately predict competitive outcome. To test this, we repeated our Monte Carlo simulations of (1) in which the number of initial microcolonies for each strain was drawn using the combinatorial cell picking model, rather than being a fixed number and in a 1:1 ratio. Analysing the resulting simulation data for model (1) confirmed that the predictive power of the AFS score was robust to any ‘naturally-occurring’ variation in the initial strain ratio (Supplementary Fig. S6B). Correspondingly, our analysis of the experimental data revealed a strong correlation between a strain’s AFS score and the competitive outcome measured at 48 h and 72 h after incubation (Fig. 4E).A modelling framework for non-isogenic strainsWe have established that for isogenic strains, the initial configuration of founding bacteria determines the competitive outcome in a ‘race for space’ and that the AFS score can accurately predict which strain will dominate. A natural question that follows is what would happen if this race for space was influenced by antagonistic interactions such as killing or growth inhibition. Therefore, we considered the effect of introducing a local (e.g., contact-dependent or short-range non-contact dependent) antagonistic mechanism that causes a reduction in strain net growth. In an extension of our theoretical framework (1), constants describing the ratios between the strains’ maximum growth rates in the absence of competition ((r)), diffusion coefficients ((d)) and competition coefficients ((c)) were introduced to allow for the possibility of differences in strain properties. This resulted in the following system obtained after a suitable nondimensionalisation (see Section S3):$$frac{partial {B}_{1}}{partial t}=nabla cdot left({Id}left(1-frac{{B}_{1}+{B}_{2}}{k}right){nabla B}_{1}right)+{B}_{1}left(1-frac{{B}_{1}+{B}_{2}}{k}right)-{B}_{1}{B}_{2},$$$$frac{partial {B}_{2}}{partial t}=nabla cdot left({Id}cdot dleft(1-frac{{B}_{1}+{B}_{2}}{k}right)nabla {B}_{2}right)+{{rB}}_{2}left(1-frac{{B}_{1}+{B}_{2}}{k}right)-c{B}_{1}{B}_{2}.$$
(2)
Here, the indicator function ({Id}=1) if ({B}_{1}+{B}_{2}le k) and ({Id}=0) otherwise, where k is the nondimensional carrying capacity. To start, strains were assumed to possess identical growth dynamics in the absence of competitors (i.e., r (=1,{d}=1)), but to significantly differ in their ability to negatively impact the competitor strain. For the simulations we set (c=0.2) representing a five-fold difference in competition strength, with ({B}_{2}) being the more effective competitor. A linear stability analysis of model [4] confirmed that in this case and for a homogeneous initial distribution of the strains in a 1:1 ratio, ({B}_{2}) wins the interaction. For this reason, we therefore refer to ({B}_{2}) as the (intrinsically) stronger strain and to ({B}_{1}) as the (intrinsically) weaker strain in the following.The assumption of identical growth dynamics allowed us to focus on the impact of antagonistic interactions on competitive outcome. We anticipated that this assumption was unlikely to hold for non-isogenic strains in experimental settings and therefore we examined (as will be discussed later) the impact of changes to the parameters (r,{d}) and (c). Subsequently, we showed the effect of such parameter variation to be limited.Spatial segregation induced by low founder densities enables coexistenceIn the context of local antagonistic interactions, low founder densities were expected to offer protection for the weaker strain by driving spatial segregation and the formation of enclaves. Test simulations supported this hypothesis. Model realisations with high (spatially uniform initial conditions) and intermediate ((N=824)) founder densities consistently led to competitive exclusion of the weaker strain (Fig. 5A, B, Supplementary Movies S4 and S5), while model realisations with low founder densities ((N=6)) resulted in coexistence with the strains being spatially segregated (Fig. 5C). Once established during early stages of the model simulation, spatial segregation was conserved. However, the stronger strain continually invaded its competitor’s clusters along strain-to-strain interfaces and eventually took over the biofilm centre. Simultaneously, the weaker strain enlarged its sectors due to unimpeded growth on the biofilm edge. Coexistence, as measured by competitive outcome was achieved by a balance of these processes (Supplementary Movie S6).Fig. 5: Modelling data for a non-isogenic strain pair with local antagonistic interactions.A–C Example model realisations for high (A), intermediate (B) and low (C) founder density are shown. A the Merged image channel shows both strains (grey colour corresponds to overlap), the ({B}_{1}) and ({B}_{2}) channels only show single strain filters of the plot. In B, C only the Merged channel is shown. Plots visualising system states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}) and the circles used to calculate the AFS scores around the initial conditions are not to scale. Plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. D The relation between founder density and competitive outcome. Each boxplot contains data from 1000 model realisations. E The relation between the AFS score ({AF}{S}_{1}), and competitive outcome for one fixed founder density ((N=6)). Data were obtained from 5000 model realisations and covers the continuum of ({AF}{S}_{1}). The observed probability density function for AFS is shown (circular markers); the density function of a fitted normal distribution ((mu approx 0.5,sigma approx 0.16)) as a solid line.Full size imageLow founder densities generated significant variation in competitive outcome (Fig. 5C). In particular, outcomes were observed for which the weaker strain ({B}_{1}) coexisted with, and could even outperform, the stronger strain ({B}_{2}). To better understand the impact of founder density, we performed Monte Carlo simulations with 1000 independent model realisations for each founder density (N) in our test range. Data from these simulations revealed both the mean and variation of competitive outcome for the weaker strain increased with decreasing founder density (Fig. 5D).Access to free space determines competitive outcome for low founder densitiesThe mathematical model consistently predicted competitive exclusion of the weaker strain at intermediate and high founder densities (Fig. 5A, B). Hence, in these cases, the AFS score no longer provided a meaningful predictor of competitive outcome. Rather, the model predicted the outcome to be dominated by the local antagonisms. However, as detailed above, low founder densities ((N) = 6) resulted in a highly variable competitive outcome and therefore we explored whether the AFS score remained an accurate predictor in this case. The simulation data confirmed that for this fixed number (N), the AFS score remained capable of accurately unfolding the observed variation in competitive outcome (Fig. 5E). Thus, initial strain configurations with a low AFS1 predictably generated a low competitive outcome for ({B}_{1}). The reciprocal was also maintained where initial strain configurations with high AFS1 predictably generated high competitive outcome for ({B}_{1}). As for isogenic strains, this relationship was found to be linear with the slope providing a measure of the deterministic range of competitive outcomes for a given founder density. The relationship between AFS and competitive outcome was again shown to be robust to natural variation in the initial strain ratio inherent in low founding cell densities (Supplementary Fig. S6C).Our mathematical model predicted that coexistence remained possible over a range of maximum growth rates, (r) (within a two-fold difference between dimensional strain growth rates in the absence of competition), diffusion coefficients, (d) (within a three-fold difference between dimensional diffusion coefficients), and most surprisingly, any values of the competition coefficient, (c) (Section S6 and Supplementary Fig. S7A–C). In particular, we showed that a strain required extreme competition efficiency ((c) very large) in order to compensate for being slower in growth ((d,r ; > ; 1)) (Supplementary Fig. S7D). Finally, the predictive power of the AFS score was preserved over the parameter range tested (Supplementary Fig. S7E, F).Dual-isolate biofilm assays – selection of a competition partnerTo experimentally test our model predictions, we needed to identify a suitable partner for NCIB 3610. We chose a Bacillus subtilis strain called NRS6153 (hereafter 6153). This selection was made because (i) 6153 is a genetically competent wild type strain with no known auxotrophies [36]); (ii) in liquid culture conditions the generation times of the two strains are within ~1.5-fold of each other (Fig. 6A); (iii) under biofilm conditions, single strain biofilms of both isolates have footprint sizes that are within (sim)2-fold of each other (Fig. 6B); (iv) across a broad range of founder densities, the competitive outcome of an isogenic pairing of 6153 isolates in a colony biofilm is broadly similar to that of an isogenic pairing of 3610 strains, albeit with more variability in the competitive outcome at the 72-h time point for high founder densities (cf. Fig. 4C (Supplementary Fig. S5A) and Fig. 6C (Supplementary Fig. S8A)); (v) when a colony biofilm is founded at high density with marked strains of 3610 and 6153 starting at an initial 1:1 ratio, 6153 is consistently outcompeted by 3610 (and hence defines 3610 as the stronger strain in the context of this study) (Fig. 6D); and (vi) using an antibiosis halo formation assay, interrogation of the interaction between 3610 and 6153 showed no evidence of contact-independent growth inhibition (Fig. 6E). In combination, these data allow us to infer that the mode of competition during co-culture in the colony biofilm is locally antagonistic.Fig. 6: Selection of a competitive strain.A Growth curves of 3610 (black) and 6153 (grey) in MSgg cultures at 30 °C. The three lines shown for each isolate represent separate biological repeats. B Biofilm footprint area of single-strain 3610 and 6153 biofilms. Data from 18 and 16 biofilms are shown for the 24 h and 48 h timepoint, respectively. C Competitive outcome data from colony biofilm assays of isogenic 6153 biofilms are shown after 24 h, 48 h and 72 h of incubation. Plotted are the technical repeats from one biological repeat. The full data set is presented in Supplementary Fig. S8A. D Flow cytometry data of mixed biofilms grown for 24, 48, and 72 h at 30 °C on MSgg media. Isolate names followed by ‘g’ represent strains constitutively producing  GFP, (green on the graph). Isolate names followed by ‘b’ indicate strains constitutively producing mTagBFP, (magenta on the graph). Three biological and three technical replicates were performed for each strain mix and timepoint and all data points are shown. The error bars represent the mean standard deviation. E Halo formation assays on MSgg agar plates at 24 h of growth. Strains producing mTagBFP (magenta) and GFP (green) are shown.Full size imageDual-isolate biofilm assays confirm modelling hypothesesWe performed dual strain biofilm assays competing 3610 and 6153 over a wide range of founder densities. These competitive assays confirmed the modelling prediction that in biofilms inoculated at low founder densities, coexistence within a non-isogenic strain pair is enabled by spatial segregation (Fig. 7A). Under such conditions, the intrinsically weaker strain (6153) formed spatial sectors and thus was able to coexist with the stronger strain (3610) through spatial segregation (Fig. 7A, B). In contrast, and again as predicted by the mathematical model (and reported during the selection of strain 6153 as a competition partner), for biofilms inoculated at high founder density, 3610 competitively excluded 6153 (Fig. 7A, B, Supplementary Fig. S8B). Finally, a computation of AFS scores based on images taken after 24 h of incubation showed strong correlation between a strain’s AFS score and its competitive outcome after both 48 h and 72 h of incubation for both 6153 alone and when in co-culture with 3610 (Supplementary Figs. S9 and 7C).Fig. 7: Experimental data for a non-isogenic strain pair with local antagonistic interactions.A Example dual-strain biofilms (3610 labelled with GFP (green), 6153 labelled with mTagBFP (magenta)). Images taken after 72 h of incubation for two different founder densities. Scalebars as in Fig. 2. B Competitive outcome data for 3610 in the 3610/6153 pair after 24 h, 48 h and 72 h of biofilm incubation. Plotted are technical repeats from one biological repeat of the experiment. The full data set is presented in Supplementary Fig. S8B. C The relationship between AFS and competitive outcome for 6153. AFS1 was calculated based on images taken after 24 h of biofilm incubation, and competitive outcome after 48 h (top, ({n}=22)) and 72 h (bottom, (n=17)).Full size image More

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