### Landscape ecology *on-chip*

Patchiness introduces a critical length scale in the landscape [22]. This determines the existence of fugitive strategies [26] which specialize in scramble competition for vacancy as opposed to excelling at interference competition within patches. To be or not to be a fugitive strategy? This is the core of the competition-colonization (CC) trade-off. This dichotomy is sketched in Fig. 1D, a relationship [27] linking competition (\(\omega\)) and colonization (\(\beta\)) abilities with \(\alpha\) indicating its strength (see Additional file 1: Table S1 for symbols),

$$\begin{aligned} \omega = e^{-\alpha \beta }. \end{aligned}$$

(1)

If patchiness exists, *E. coli* and *P. aeruginosa* can be positioned along this space of differentiation. The strategy of *E. coli* corresponds to a *fast* colonizer (higher \(\beta\)) and *P. aeruginosa* to a *superior* competitor (higher \(\omega\)). On the contrary, if the habitat is not patchy, the dichotomy vanishes and so do these phenotypes. To imitate the patchy nature of microbial habitats [28], we used microfabrication [29] to generate landscapes (see Additional file 1: Table S2 for glossary) where arrays of habitat patches are connected by corridors [24]. We fabricated 85 repetitions of a patch-corridor motif (Fig. 1A and Additional file 1: Fig. S2A) giving rise to a one dimensional crystal-like array of microhabitat patches (MHPs). For comparison, we made “flat landscape” environments which consist of a single, long MHP making up a strip-like habitat.

In these devices, we performed invasion-competition experiments using time-lapse microscopy of fluorescently labeled (RFP–GFP and GFP–RFP) co-cultures of wild-type strain pairs (*E. coli*–*P. aeruginosa*, shown here as magenta–green) to study ecological succession as the community develops over 48 hours (see Additional file 1: Table S3 for strains). We initiated the system with each species invading from opposite sides and recorded images in 10-min intervals (alternative initial conditions were also considered, see Additional file 1: Fig. S3 and Additional file 2: Supplementary Note 1). Local, within MHP (spatial index *k*), occupancy was calculated for both *P. aeruginosa*, \(P_k(t)\), and *E. coli*, \(E_k(t)\), for all images (time index *t*). Figure 1F shows *P. aeruginosa* fractional occupancy dynamics, \({\Theta }(t)\), calculated as an ensemble average by combining the data of 72 patchy landscapes (24 experiments containing 3 landscapes each). Community dynamics can be broken down in three stages: (i) a quick colonization by *E. coli* followed by (ii) an increasing domination by *P. aeruginosa* reaching a relative occupancy of \({\Theta } \sim 0.8\) 12 h after inoculation and (iii) a steady relaxation to a more moderate, albeit still *P. aeruginosa* dominated, coexistence; \(\Theta \rightarrow 0.65\). This is in striking contrast with results in well-mixed flasks where a steady increase in *P. aeruginosa* fractional abundance \(\theta (t)\) was observed (Fig. 1E).

### Population waves and monoculture metapopulations

Bacterial waves have been described since the seminal work of Adler [30] and their existence is a robust and integral part of bacterial dispersal [15, 24, 25, 30,31,32]. They are the product of interactions between attractant fields and the chemotactic behavior of individuals [30, 33]. These interactions lead to directional persistence in the swimming patterns of cells [15]. Waves drive quorum sensing [32] guided by the topology of the habitat [31]; thus, we expect them to set the conditions for coexistence (Fig. 1F). Previous work on monocultures colonizing similar landscapes has shown that after initial colonization by waves [25], bacteria develop into metapopulations [24]. Here, we link these waves to a mechanism promoting biodiversity by allowing persistence of a fugitive strategy [26].

In Fig. 1C, we show that in well-mixed monocultures *E. coli* is faster than *P. aeruginosa* at exiting lag-phase. This difference may be interrelated to wave formation and propagation. As the bacteria expand their range, waves experience diffraction [25] and produce a complex phenotype of patch colonization and local extinction (see Additional file 1: Fig. S4 for monoculture dynamics in patchy landscapes for each species). Some cells keep traveling with the wave from patch to corridor (*sensu* [15]) while others leave the pack to recruit and localize. This spatio-temporal pattern is a phenotype which bacteria regulate endogenously. Cells not traveling in waves can be both motile or aggregate at multiple scales [24] into non-motile clusters which are highly dynamic. Contrary to the work of Livingston and collaborators [12], which studied co-cultures of *P. aeruginosa* strains in well-mixed well plates and where dispersal was imposed in an exogenous fashion by cross-inoculation, here two species of bacteria are free to exhibit a wave-based range expansion. Can we still, in agreement with [12] and contrary to what we see in isolated well-mixed environments without cross-inoculation (Fig. 1E), observe coexistence?

### In spatial competition, pioneering *E. coli* colonizes first

Following the inoculation of the patchy device inlets (left *P. aeruginosa*, right *E. coli*) initial colonization by pioneer cells of *E. coli* occurs by a low density fast traveling \(\alpha\)-wave *sensu* van Vliet et al. [25] (Fig. 2A, left panel). Passing through the landscape this \(\alpha\)-wave leaves a low density population spanning the first four patches (\(k=1\cdots 4\)) at \(\tau _1 = 8\) hours. In Fig. 2B we show a zoomed-in view for four time points \(\tau _j\). By \(\tau _2 = 15\) hours division and recruitment have increased *E. coli* density reaching 35% of local occupancy (Fig. 2C, *top panel*). At this point, the first *P. aeruginosa* cells enter patches 1 and 2 (Fig. 2A, right panel). Shortly after (\(\tau _3 = 20\) h), its local occupancy \(P_1(\tau _3)\) begins to increase (Fig. 2C, *bottom panel*). At this stage, cells can be planktonic (free swimming) or sessile (aggregated). Subsequently, the aggregation phase progresses towards its climax; a MHP full with biofilm [14].

Aggregation events are crucial as they enhance localization of the superior competitor diminishing the connectivity of the landscape up to the point of complete fragmentation in some cases. As we show in Fig. 2B, at time \(\tau _3\) hours *P. aeruginosa* has successfully invaded the first patch where it coexists with *E. coli* at high local occupancy (\(P_1(\tau _3)\approx\) 50%). Due to the aggregation event of *E. coli* visible by \(\tau _2\) at the corridor between patches \(k=1\) and \(k=2\), *P. aeruginosa* occupancy is limited dramatically (\(P_k(\tau _3)\) for \(k=2\cdots 4\)). Eventually *P. aeruginosa* manages to penetrate the corridor and invade at time \(\tau _4 = 22\) hours when all four patches host a population with significant occupancy (\(P_k(\tau _4) > 0.3; k=1\cdots 4\)). After 36 hours *P. aeruginosa* dominates the landscape (Fig. 2D) with local occupancy around 70% compared to 30% reached by *E. coli* (Fig. 2C). Results obtained from all patchy landscapes (\(N=72\)) give rise to an ensemble average showing that statistically *P. aeruginosa* coexist with *E. coli* in the long term (\(\Theta \rightarrow 0.65\); Fig. 1F). While, in well-mixed experiments (Fig. 1E) *P. aeruginosa* always wins (\(\theta \rightarrow 1\)) after 36 h, when starting from 1:1, 10:1, 1:10 *P. aeruginosa* to *E. coli* ratios (Additional file 1: Fig. S2B).

###
*P. aeruginosa* invades later but outcompetes *E. coli* locally

After initial colonization by *E. coli*, we see a clear pattern of ecological succession, where *P. aeruginosa* enters the habitat as a densely-packed front which advances and disperses through the patchy landscape (Fig. 2A). *P. aeruginosa* occupancy (\(P_k(t)\); Fig. 2D, *right panel*) demonstrates a textbook example of Skellam’s “Malthusian population in a linear habitat” [34]. This is considerably different to the fugitive dynamics (*sensu* [26]) of *E. coli* occupancy (\(E_k(t)\); Fig. 2D, *left panel*) as can be appreciated in Fig. 2D. Here, we compare local occupancy \(P_k(t)\) and \(E_k(t)\) for all patches (\(k=1\cdots 85\)), as well as their landscape averages (\(\bar{E}(t) =(1/85)\sum _k E_k(t)\) and \(\bar{P}(t) =(1/85)\sum _k P_k(t)\); thick color curves in the foreground) before and after \(t=15\) h. As *P. aeruginosa* advances, *E. coli* retreats its range of high occupancy while keeping less localized and less dense fluctuating sub-populations. These local community dynamics (Fig. 2B) are observed repeatedly, following a classical ecological succession depicted in Fig. 3E, where local species composition flows through the following states: (*i*) *E. coli* early colonization, (*ii*) expansion by recruitment, (*iii*) competition with invading *P. aeruginosa*, and eventually (*iv*) replacement by *P. aeruginosa*.

Considering all patches (\(\forall k_s\)) in all landscapes (indexed by *s*), the long-term pattern of local community structure can be appreciated. In Fig. 2E, we show that, in the long term, the most frequent (\(\approx 1000\) occurrences) states observed fall within three classes: (*i*) fully occupied patches 100% dominated by *P. aeruginosa*, i.e., succession climax, point (0, 0.5); (*ii*) fully occupied patches 100% dominated by *E. coli*, point (1, 0.5); and (*iii*) extremely low density patches 100% dominated by *E. coli*, point \((1,\epsilon \rightarrow 0)\). Intermediate occurrences (\(\approx 100\)) correspond to patches with high levels of occupancy, \(Z_{k_s}>0.5\), that are mostly dominated by *P. aeruginosa*, \((1 - \Theta _{k_s})\le 0.5\), or to patches highly dominated by *E. coli*, \((1 - \Theta _{k_s}) \rightarrow 1\), showing all levels of occupancy, \(0.5> Z_{k_s} > \epsilon \rightarrow 0\). All other states are rare with less than \(\approx 10\) occurrences among 5100 sampled MHPs. To understand this long-term statistical pattern further, we look at the transient dynamics.

In Fig. 3A, for each landscape *s*, we plot *E. coli* fractional occupancy averaged over the whole landscape as a function of time binned hourly. For each binned time point \(\tau '_j\) plotted, there are \(\sim 400\) landscape configurations, with a total of \(\sim 19,000\) configurations over 48 hours. Early on (\(\tau \le 6\) h), most occurrences (\(\approx 100\)) correspond to early colonization by *E. coli*, \((1-\Theta _s) = 1\). The second level of occurrences (\(\approx 80\)) within this early period corresponds to the initial incursion of *P. aeruginosa* which is delayed respect to *E. coli* but which nevertheless later dominates, \((1-\Theta _s) = 0\). Immediately after (\(6 < \tau \le 12\)), we see that the peak of occurrences (\(\approx 100\)) has shifted from being dominated by *E. coli* to now being dominated by *P. aeruginosa*. If we consider how occurrences distribute over the plot, we can distinguish clear trajectories of replacement. During the final phase (\(24 < \tau \le 48\)), most (65%) landscapes are dominated by *P. aeruginosa*. The three curves overlayed on Fig. 3A represent three landscapes shown as kymographs in Fig. 3B. Such paths correspond to: (*i*) a case where *E. coli* dominates, \((1-\Theta _{{s}_1}) > 0.5\), due to fragmentation of the spatial distribution of *P. aeruginosa*; (*ii*) a *P. aeruginosa* dominated case where *E. coli* is mostly excluded, only coexisting in low numbers, \((1-\Theta _{{s}_2}) \rightarrow 0\); and (*iii*) a case where *E. coli* persists at significant levels, \((1-\Theta _{{s}_3}) \rightarrow 0.25\).

In Fig. 3C (and Additional file 1: Fig. S5A,B), we show a kymograph where competitive pressure by *P. aeruginosa* affects the dynamics of *E. coli*. Between \(12<t<18\) h, a wave of *P. aeruginosa* “chases” a wave of *E. coli*. At time \(\tau _1\) *E. coli* gets trapped at patch \(k=34\) encountering a ’wall’ of *P. aeruginosa* in patch \(k=33\) leading to succession (Fig. 3D).

As in all experiments, what is reproduced here is the general pattern of *E. coli* colonizing first followed by *P. aeruginosa* out-competing *E. coli* locally and sometimes globally. Coexistence of alternative local community states can be observed even in adjacent patches as a consequence of stochasticity. In most experiments however, there is remarkable determinism, which emerges as the statistical pattern we can appreciate in Fig. 3A when considering the temporal ordering of events of high occurrences (\(\approx 100\)). At multiple scales we see the heuristic pattern of ecological succession depicted in Fig. 3E.

### Aggregation-induced fragmentation promotes coexistence

An important driving force for coexistence in patchy landscapes is habitat modification by *E. coli* aggregating in corridors which can disrupt later arrivals. Fragmentation events act as priority effects changing the course of succession (Fig. 3A, B). In some instances it is a momentary delay in the expansion of *P. aeruginosa*, in other cases it offers *E. coli* significant extra time and space (gap structure; Additional file 1: Fig. S5C-E) isolated from competition. An example of this can be seen in the left most kymograph of Fig. 3B where *E. coli* dominates, \((1-\Theta _{s_1}) > 0.5\). Micro-colonies in the corridors have a jamming effect, illustrated in Fig. 1B, where competitive interactions are localized. In extreme cases this turns into fragmentation and the superior competitor is unable to overcome this barrier. The barrier is sometimes broken by de novo waves which can penetrate the competitor’s territory. Such an event can be seen in the right most kymograph in Fig. 3B. Here, a wave of *P. aeruginosa* collides at time \(t = 20\) h with *E. coli* aggregated at the corridor located between patches \(k=74\) and \(k=75\). This interaction can be appreciated post-collision in Fig. 4B. The wave of the superior competitor (green), is first unable to penetrate the territory held by *E. coli* (magenta) and reflects back as well as diffracting (*sensu* [25]), giving rise to a *P. aeruginosa* sub-population localized at MHP number 74. From this sub-population *P. aeruginosa* periodically emits new waves of subsequently higher cell numbers which eventually percolate through the barrier. Such wave invasions into hostile territory are reminiscent of *E. coli* expansion into landscape ecotopes with high concentration of antibiotics [35] and highlights the importance of waves for bacterial fitness.

To test if patchiness facilitates priority effects, we ran experiments in “flat” non-patchy landscapes and compared them to experiments in patchy ones which were started from the same cultures (\(n = 3\)). Coexistence was also observed in flat landscapes despite the fact that *E. coli* micro-colonies are unable to fragment the landscape. Here, coexistence is due to the emergence of a neutral ecology where species reach a similarly high level of long-term (\(t^* \gg 30\) h) average occupancy, \(\langle \bar{E}(t^*)\rangle _{\textrm{flat}} \approx \langle \bar{P}(t^*)\rangle _{\textrm{flat}}\) (Fig. 4H). In contrast, in the patchy system we see significantly different levels of long-term average occupancy, \(\langle \bar{E}(t^*)\rangle _{\textrm{patchy}} \ll \langle \bar{P}(t^*)\rangle _{\textrm{patchy}}\) (Fig. 4G).

In Fig. 4E, we show a *P. aeruginosa* (green) expansion front invading a patchy landscape and displacing *E. coli* (magenta) contrasting the result for a flat landscape (Fig. 4F), where we see a fast traveling wave of *P. aeruginosa* in coexistence with *E. coli*. This wave does not leave localized sub-populations behind as is the case for waves in patchy landscapes (Fig. 4E), but a rather homogeneous distribution of cells which after 36 hours show only minor long-term averaged occupancy differences (Fig. 4H). Contrary to patchy landscapes, the flat landscape has no intermediate patch scale and produces no separation between local population growth and landscape-scale range expansion.

From additional flat landscape experiments (6 devices, 18 landscapes), a statistical comparison was made regarding the spatial correlations between *P. aeruginosa* and *E. coli* using Pearson coefficient. For patchy landscapes, data was partitioned between patches and corridors for all 72 landscapes, thus rendering \(n = 6120\) pairs of both *P. aeruginosa* and *E. coli* pixel occupancy for each ecotope. Similarly, for flat landscape data, 85 virtual patch and corridor masks were generated *sensu* [36] rendering \(n = 1530\) replicates, see Fig. 4A.

When comparing virtual and real patches in the flat and patchy landscapes, respectively, we observe a near neutral, but slightly positive correlation describing average interactions (Fig. 4C). While virtual patches show less variance and no significant skew, the real patch distribution demonstrates a clear positive skewness. This suggests a disproportionate number of competing—co-localized— cells in patchy landscapes compared to flat landscapes.

Comparing the distributions of virtual and real corridors, differences become qualitative (Fig. 4D). For virtual corridors we see no significant correlation response with a slightly larger variance than that found for the virtual patch distribution. This is expected, as the smaller region masked by the virtual corridor permits more stochasticity. Remarkably, we found a bi-modal distribution for real corridors. The second peak emphasizes the significance of interactions at corridors, highlighted by the different dynamics (Fig. 4E, F). Analysis of micro-colony sizes in patchy versus flat landscapes provides further evidence for the relaxation of the competitive hierarchy in flat landscapes (Additional file 1: Fig. S6).

### A spatial model of the CC trade-off

The competition-colonization (CC) trade-off [37] has been proposed to explain coexistence in a number of diverse ecosystems, from the intertidal zone [38] to grasslands [39] and coral reefs [40]. Inspired by our empirical observations, we developed a spatially-explicit stochastic model. We incorporate a localized mixed state where both species can occupy a common site at the same time with the condition they are locked into an interference competition program. While locked in this state, no dispersal takes place, only competitive lottery.

We consider sites on a lattice representing a local community: vacant (state 0), occupied by competitor (state 1), colonizer (state 2), or both (mixed state \(*\)). State transitions are sketched in Fig. 5A where interactions occur in a local neighborhood (See 5 and Additional file 2: Supplementary Notes 2 and 3). We performed numerical studies and explored the parameter space \([(1-\Delta \beta ) \times \gamma ]\) representing differences in colonization ability \((1-\Delta \beta )\) and priority effects \(\gamma\) (Fig. 5 and Additional file 1: Fig. S7).

In Fig. 5B, we show our model’s long-term colonizer fractional occupancy \((1-\tilde{\theta })\) with nearest neighbor interactions. We recognize three phases: (I) a *scramble* phase, where only the colonizer survives; (II) a *coexistence* phase, where both persist; and (III) an *interference* phase, where the competitor wins. In Fig. 5, we show three patchy landscapes congruent with the *coexistence* (Fig. 5D) and *interference* (Fig. 5E) phases of our model. Fixing the value representing colonization differences, \((1-\Delta \beta )= 0.8\), we can think of individual experiments as different scenarios of priority effects changing stochastically. Using a value \(\alpha =4\) with a 20% difference (\(\Delta \beta _0=0.2\)) in dispersal ability (70% chances of losing interference competition; \(\eta (0.2)=0.698\)), in Fig. 5C, we show the average dynamics of colonizer fractional occupancy for different scenarios of priority effects (see Additional file 1: Fig. S7C-F for other values of \(\alpha\)). Notice the importance of parameter \(\gamma\) in determining trajectories of competitive replacement as well as long-term patterns of dominance (phases). For a 20% decrease in cross-colonization rate due to priority effects (\(\gamma = 0.8\)), we obtain a scenario within the *interference* phase (Fig. 5G), and the competitor pushes the colonizer off the landscape (Fig. 5E). Decreasing \(\gamma\) further results in another scenario we observed in experiments (Fig. 5D); *E. coli* persists due to the blockage of patch-corridor interfaces. Such scenario occurs for parameter \(\gamma = 0.3\) where simulations lay within the *coexistence* phase (Fig. 5F). A stochastic process \(\gamma _t\) would account for trajectories like the ones in Fig. 3A.

For no priority effects (\(\gamma =1\)), we distinguish two critical values \(\Delta \beta ^*\) and \(\Delta \beta ^{**}\) delimiting the three phases at the top of Fig. 5B: (i) If the difference in colonization ability is large, \(1> \Delta \beta >\Delta \beta ^*\), the system is in the *scramble* phase; (ii) if the difference is of intermediate magnitude, \(\Delta \beta ^*> \Delta \beta > \Delta \beta ^{**}\), the system is in the *coexistence* phase; and (iii) if small differences are considered, \(\Delta \beta ^{**}>\Delta \beta \ge 0\), the system is in the *interference* phase. When no differences exist, \(\Delta \beta =0\), there is *neutral* coexistence as the lottery has no bias (\(\eta =0.5\)) regardless of the trade-off strength \(\alpha\). The nearly neutral case (\(\Delta \beta \cong \epsilon \ne 0 : \epsilon \rightarrow 0\)) allows us to appreciate the role of \(\gamma\) which induces fragmentation and leads to an extinction threshold at \(\gamma _c\).

Scanning along a transect \((1-\Delta \beta _0) = 0.8\) across the phase space varying \(\gamma\) from no priority effects (\(\gamma =1\)) to full cross colonization inhibition (\(\gamma =0\)) in Fig. 5B, we traverse two transitions between phases: (i) a boundary between *interference* and *coexistence* and (ii) *coexistence* and *scramble*. Thus, at intermediate values of priority effects, we can expect coexistence for a pair of strategies with a small difference in colonization, \(0<\Delta \beta _0 < 0.3\). The sequestration from colonization, produced by localization of the interference interaction, has a critical role in modulating coexistence. This result is congruent with our finding that *E. coli* coexist with *P. aeruginosa* by a localization and fragmentation mechanism, thus highlighting the importance of priority effects occurring at the corridors.