One of the central aims of ecology is to identify mechanisms that

maintain biodiversity1,2. Numerous theoretical models have

shown that competing species can coexist if ecological processes

such as dispersal, movement, and interaction occur over small

spatial scales1–10. In particular, this may be the case for nontransitive

communities, that is, those without strict competitive

hierarchies3,6,8,11. The classic non-transitive system involves a

community of three competing species satisfying a relationship

similar to the children’s game rock–paper–scissors, where rock

crushes scissors, scissors cuts paper, and paper covers rock. Such

relationships have been demonstrated in several natural systems12–

14. Some models predict that local interaction and dispersal

are sufficient to ensure coexistence of all three species in

such a community, whereas diversity is lost when ecological

processes occur over larger scales6,8. Here, we test these predictions

empirically using a non-transitive model community containing

three populations of Escherichia coli. We find that

diversity is rapidly lost in our experimental community when

dispersal and interaction occur over relatively large spatial scales,

whereas all populations coexist when ecological processes are

localized.

Microbial laboratory communities have proved useful for studying

the generation and maintenance of biodiversity15–17. In particular,

communities containing toxin-producing (or colicinogenic) E.

coli have been the centre of much attention from both theoretical

ecologists3,6,8,18–20 and microbiologists21–27. Colicinogenic bacteria

possess a ‘col’ plasmid, containing genes that encode the colicin (the

toxin), a colicin-specific immunity protein (which renders the cell

immune to the colicin) and a lysis protein (which is expressed when

the cell is under stress, causing partial cell lysis and the subsequent

release of the colicin)26,27. In general, only a small fraction of a

population of colicinogenic cells will lyse and release the colicin27.

Colicin-sensitive bacteria are killed by the colicin but may occasionally

experience mutations that render them resistant to the colicin.

The most common mutations alter cell membrane proteins that

bind or translocate the colicin23,24,26,27. In some cases, the growth rate

of resistant cells (R) will exceed that of colicinogenic cells (C), but

will be less than the growth rate of sensitive cells (S). This occurs

because resistant cells avoid the competitive cost of carrying the col

plasmid21,22,26,27 but suffer because colicin receptor and translocation

proteins are also involved in crucial cell functions such as

nutrient uptake21,23,24,26,27. In such cases, S can displace R (because S

has a growth-rate advantage), R can displace C (because R has a

growth-rate advantage) and C can displace S (because C kills S).

That is, the C–S–R community satisfies a rock–paper–scissors

relationship.

Using a modification of the lattice-based simulation of Durrett

and Levin6, we theoretically explored the role of the spatial scale of

Figure 1 Predictions of the lattice-based simulation (see Box 1). a, b, Snapshots of the

lattice in a simulation with a local neighbourhood at times 3,000 (a) and 3,200 (b). The

unit of time is an ‘epoch’, equal to 62,500 lattice point updates (an epoch is the average

turnover of any given lattice point in the 250 £ 250 grid). The strains are colour-coded as

follows: C is red, S is blue and R is green; empty lattice points are white. c, The complete

community dynamics for the same simulation run. d, Community dynamics for a

simulation with a global neighbourhood. The abundances in c and d are log transformed.

When the abundance of a strain goes to zero, we represent this event with a diamond on

the abscissa of the relevant graph at the relevant time. For a–d we used the following

parameters: D C ˆ 1/3, D S,0 ˆ 1/4, D R ˆ 10/32, and t ˆ 3/4 (see Box 1).

e, Sensitivity of qualitative dynamics to changes in a subset of parameter values. For the

(t,D R) values plotted, the greyscale indicates the number of ‘local’ simulated runs (out of

10) in which coexistence occurred for at least 10,000 epochs, with the lighter area

indicating a higher probability of coexistence. For all simulations, we require DS;0 ,

DR ,DC ,DS;0‡t

1‡t ; which (at least for the mixed system) ensures that S displaces R, R

displaces C, and (if C has sufficient density) C displaces S.

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ecological processes in our C–S–R community (see Box 1). When

dispersal and interaction were local, we observed that ‘clumps’ of

types formed (Fig. 1a). These patches chased one another over the

lattice—C patches encroached on S patches, S patches displaced R

patches and R patches invaded C patches (Fig. 1a, b). Within this

fluid mosaic of patches, the local gains made by any one type were

soon enjoyed by another type. The result of this balanced chase was

the maintenance of diversity (Fig. 1c). However, this balance was

lost when dispersal and interaction were no longer exclusively local

(that is, in the ‘well-mixed’ system—see Box 1). In the mixed

system, continual redistribution of C rapidly drove S extinct, and

then R outcompeted C (Fig. 1d). Durrett and Levin6 describe a

qualitatively similar effect of spatial scale in their model of

colicinogenic, sensitive, and ‘cheater’ strains (where a cheater was

defined as a strain producing less colicin at a lower competitive

cost).

When ecological processes were local in the simulation, coexistence

occurred over a substantial range of model parameter values

(Fig. 1e), suggesting that the result was not very sensitive to the

specific choice of parameter values. In the case of the mixed system,

coexistence never occurred for the region of parameter space shown

in Fig. 1e. In agreement with Durrett and Levin6, our simulation

results suggested that three strains with the abovementioned nonhierarchical

relationship could coexist when dispersal and interaction

are local, whereas one strain excludes the others when the

community is well mixed.

To test this conclusion, we used three strains of the bacterium E.

coli: a colicin-producing strain (C), a sensitive strain (S), and a

resistant strain (R), which satisfied a rock–paper–scissors competitive

relationship (see Methods). We placed the C–S–R community

in the following three environments: (1) ‘Flask’ (a well-mixed

environment in which dispersal and interaction are not exclusively

local); (2) ‘Static Plate’ (an environment in which dispersal and

interaction are primarily local); and (3) ‘Mixed Plate’ (an environment

intermediate between these two extremes).

For the Flask environment, the bacteria were grown in shaken

flasks containing liquid media. We transferred an aliquot of the

community to fresh media every 24 h. In the Static Plate environment,

the bacteria were grown on the surface of solid media in

Petri plates. Every 24 h, we pressed each plate onto a platform

covered with a sterile velveteen cloth and then placed a fresh plate

on the velvet. This method transferred a small sample of the

community and allowed the transferred sample to retain the spatial

pattern that developed on the previous plate. The Mixed Plate

environment was identical to the Static Plate environment, except

that at each transfer the fully-grown community plate was pressed

on the velvet several times, each time rotated at a different angle

(see Methods).

Figure 2a shows that C, S and R strains were maintained at high

densities in the Static Plate environment throughout the experiment.

Photographs of the plates show the spatial pattern that

developed over the experiment (Fig. 3a). The pink and yellow interstrain

boundaries in Fig. 3b show clearly that R chased C, and C

Figure 2 Community dynamics in the experimental treatments: a, Static Plate; b, Flask;

and c, Mixed Plate. Dashed lines indicate that the abundance of the relevant strain has

decreased below its detection limit. Data points are the mean of three replicates, and bars

depict standard errors of the mean. Consecutive data points are separated by 24 h,

approximately 10 bacterial generations.

Figure 3 Time series photographs of a representative run of the Static Plate environment.

We initiated the plate environments by depositing small droplets from pure cultures in a

hexagonal lattice pattern, where the strain at each point was assigned at random. a, The

changing spatial configuration of the experimental community is shown in this first panel

of photographs. Patches inhabited by C cells were less dense and consequently easily

distinguished from S and R patches. The dense growing ‘spots’ that appear inside the C

clumps were determined to be resistant cells generated de novo from S cells. An empty

layer existed between C clumps and S clumps, where diffused colicin had prevented the

growth of S cells, but where C cells had not yet colonized. The border between C and R

lacked this empty layer. b, ‘Chasing’ between clumps is highlighted in this second panel.

The letters giving the initial spatial distribution of the strains are preserved for reference.

The borders between C and S are coloured in yellow and the borders between C and R in

pink.

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chased S, respectively. It was not possible to see S chasing R, because

these two strains grew to comparable densities. However, the S

density did not consistently decrease over time (Fig. 2a),

suggesting that S did indeed chase R. Thus, coexistence did not

result from absolute spatial isolation of the three strains. As can be

seen in Fig. 3, interaction (for example, competition and killing)

occurred at the boundaries between the strains. These results

support the prediction that balanced chasing in a spatially structured,

non-hierarchical community may result in the maintenance

of diversity.

The results for the Flask environment are shown in Fig. 2b. In

contrast to the Static Plate environment, both S and C dropped

below their detection limits before the study was completed. The

difference in dynamics between the Flask and Static Plate environments

did not merely reflect differences between liquid culture

and surface growing conditions. Simply mixing the surface growing

community at each transfer event (that is, our Mixed Plate

environment) produced dynamics very similar to those in the

Flask environment (Fig. 2c). Thus, it appears that dispersal and

interactions must be local for coexistence to occur in this

community.

To explore the robustness of our results, we repeated the experimental

work described above using different initial spatial configurations

and starting strain frequencies (see Methods). In the

cases considered, we observed dynamics very similar to those

observed in our original experiment—that is, chasing of types,

coexistence of all three types for at least 66 generations when

ecological processes were localized, and displacement of S and C

and persistence by R when processes were not localized (data not

shown). These observations suggested that our results were not due

to the particular starting conditions chosen in our initial

experiments.

The work described here lies at the crossroads of two recent trends

in the study of biodiversity. The first is increasing interest in the role

of the spatial scale of ecological processes2,4,9,17. It has been shown

theoretically that simply allowing interaction and dispersal to occur

locally can promote diversity within a community2,4–9,11. Our

experimental results confirm these predictions. The second trend

concerns the role of non-hierarchical competitive relationships3,6,11,28,29.

Recent theory suggests that the number of species

coexisting on a limited number of resources can be astonishingly

high when there are non-hierarchical relationships among the

species28,29. Our study system represents a very simple non-transitive

triplet: a game of rock–paper–scissors. Our experimental results

are consistent with the prediction that non-hierarchical competitive

relations can promote diversity. However, in our case, the localization

of ecological processes is also necessary.

Localized processes may be important for coexistence in other

natural communities as well. For many relatively sessile organisms

such as plants, some marine invertebrates and the microbial

constituents of biofilms, dispersal and interaction tend to occur

over small spatial scales. Communities with such organisms may

also exhibit non-transitive relationships. For instance, if one species

produces a toxin (a widespread phenomenon, occurring in many

species of plants30, marine invertebrates13, fungi30, and essentially

every major bacterial lineage27) there will be the potential for nontransitivity.

This can occur if toxin production is costly, both

sensitive and resistant species exist, and costs associated with

resistance are less than those associated with toxin production.

However, the relative magnitude of these costs will be critical to the

prospects for coexistence. Specifically, if the costs of resistance or

allelopathy are either too great or too small, the community can

collapse, even if the members maintain a non-transitive relationship

(for example, see the dark portions of Fig. 1e). If the relative costs

in our experimental community are representative of those in

natural communities, then we might expect the scale of ecological

processes to determine the likelihood of biodiversity maintenance

in vegetation with allelopathic plants, coral reefs with toxic sessile

invertebrates, and microbial communities with antibiotic-producing

microbes. Such communities may be ideal systems to study

further the role of local dispersal and interaction in species

coexistence. A

Methods

The experimental system

We used the E. coli colicin E2 system: strains BZB1011 (S), E2C-BZB1011 (C), and E2R-

BZB1011 (R). C was marked with resistance to T6 coliphage and S with resistance to T5

coliphage. Other than the non-conjugative col plasmid and markers, C was isogenic to S. R

bacteria were generated by selecting marked S mutants able to grow in the presence of the

colicin24. All types were counted by selective plating, with S counted by subtraction.

Periodically, we checked the markers by verifying that T6-resistant bacteria produced

colicin E2 and that T5-resistant bacteria did not.

Determining strain relationships

The relative fitnesses of the strains were determined by growing two competing strains

in pairwise competition, both in 10 ml Luria–Bertani (LB) liquid culture and in 4 ml of

soft agar on the surface of agar plates. The fitness (w) of strain x relative to that of

strain y is

w…x; y† ˆ

ln…xF=x0†

ln…yF=y0†

where x0 and y0 are initial densities and xF and yF are densities after 24 h of growth.

We found w(R,S) ˆ 0.59 ^ 0.097 and w(R,C) ˆ 1.91 ^ 0.399 in the liquid culture

environment and w(R,S) ˆ 0.73 ^ 0.142 and w(R,C) ˆ 1.90 ^ 0.230 on the plates. We

did not compute w(S,C) in either environment, but we observed that the colicin produced

by strain C effectively kills S cells (for example, spotting colicin on a S lawn gives large clear

plaques). Thus, C kills S, S outgrows R, and R outgrows C.

Tracking community dynamics

In the Static Plate environment, the bacteria grew on the surface of 4ml of soft LB agar,

which had been poured onto a plate with a hard LB agar base. To initialize a plate, 15 ml

droplets of pure culture were placed in a 31-point hexagonal lattice (Fig. 3a). The droplet

pattern was generated by randomly assigning the identity of the strain at each lattice point

according to the probability distribution: Pr{C} ˆ 0.25, Pr{S} ˆ 0.5, and Pr{R} ˆ 0.25.

After 24 h of growth at 37 8C, we pressed a fully grown plate on a platform covered with

velvet. Then three fresh plates were pressed on the velvet, taking care to preserve

orientation. The first plate was used for counting strain densities after the next day’s

growth. This was done by scraping off the soft agar layer with the bacterial community into

Box 1

Lattice-based simulation

We embedded our virtual C–S–R community in a 250 £ 250 regular

square lattice with periodic (or ‘wrap-around’) boundaries. To start the

simulations shown in Fig. 1, every lattice point was randomly and

independently assigned one of the following states: occupation by a C, S

or R cell or the ‘empty state’. We used an asynchronous updating

scheme, which consisted of sequentially picking random focal points

and probabilistically changing their states. The state transition

probabilities of a focal point depend both on its current state and the

states of points within its neighbourhood. The size of a neighbourhood

represents the spatial scale of ecological processes. To explore the role

of spatial scale, we simulated our community using two different

neighbourhood sizes. The ‘local’ neighbourhood consisted of the eight

lattice points directly surrounding a focal point; in such a case,

interaction (that is, killing and competition for space) and dispersal (that

is, ‘birth’) are local. The ‘global’ neighbourhood consisted of every point

in the grid outside of a focal point; in this case, interaction and dispersal

are no longer exclusively local, and the community behaves like a wellmixed

system. For either neighbourhood, if an empty lattice point is

selected for updating, the probability that it is filled with a cell of type i

(with i [ {C,S,R}) is given by f i, the fraction of its neighbourhood

occupied by strain i. If an occupied lattice point in state i is selected, it

is killed with probabilityDi. AlthoughDC andDR are fixed values,DS is

not; it is equal to DS,0 ‡ t (fC), where DS,0 is the probability of death of

an S cell without any neighbouring C cells, and t measures the toxicity

of neighbouring C cells.

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10 ml of saline, vortexing the mixture for several seconds, and then following standard

selective plating protocol. The second plate was used for propagating the community (that

is, for pressing on the velvet after the next day’s growth). The third plate was photographed

(see Fig. 3).

The Mixed Plate environment was identical to the Static Plate environment described

above with the following exception: at each transfer, the fully-grown plate was (1) pressed

lightly on the velvet, (2) turned clockwise at a randomly chosen angle and pressed a second

time, (3) turned randomly counter-clockwise and pressed a third time, and (4) turned

randomly clockwise and pressed a fourth time. The fresh plates were then pressed on the

velvet to initiate this ‘mixed up’ sample.

Our Flask environment was a 125 ml flask with 33.75 ml of LB broth shaken at

125 rev min21 at 37 8C. After 24 h of growth, 50 ml of the culture was transferred to a flask

with fresh media. These volumes guaranteed that the total number of bacterial cells in the

flask after a full day’s growth, and total number of cells transferred, matched the

corresponding numbers of cells from the plate runs.

In all three environments, the densities of each type were determined every 24 h, and all

treatments were replicated in triplicate. We terminated the experiments after one week

(approximately 66 generations), because by this time we detected a substantial number of

resistant mutants derived from the S population (for example, the dense clumps within the

C patches in Fig. 3a). Evolution of R from S violates an assumption of our model and can

lead to a change in the predicted dynamics, especially if the cost of resistance ismuch lower

in the de novo R mutants (see low values of DR in Fig. 1e).We are currently exploring such

evolutionary phenomena both theoretically and experimentally. It should be noted that

one week suffices for a single 15-ml droplet placed in the centre of a plate to nearly cover the

plate under the Static Plate regime.

Additional starting conditions

We manipulated the starting strain frequencies and initial spatial configuration on the

plates in two additional sets of runs (data not shown). First, we repeated the experiments

as outlined above with the same initial hexagonal lattice pattern, but using another

random assignment of the strains (taken from the probability distribution above).

Second, rather than initiating the plates with droplets in a hexagonal pattern, we mixed

the bacterial strains in soft agar at different starting frequencies (with S in excess and C

and R rare) and poured the agar over the plates, resulting in an initially ‘unclumped’

distribution.

|对生态的核心目标之一是确定机制保持生物多样性1，2。许多理论模型表明，物种共存竞争，如果生态过程如分散，移动和相互作用，发生在小空间的范围1 - 10。尤其是，这可能是不传递群落的例子，即那些没有严格的竞争力的等级3，6,8,11。经典的非传递系统涉及一个群落包括3种竞争物种，满足类似于儿童游戏石头纸剪刀的关系，在石头压碎剪刀，剪刀剪纸张和纸覆盖石头。这种关系在一些自然系统中已被论证12，4。有些模型预测，局部相互作用和分散足以确保所有3种物种共存于这样的群落，而多样性的丢失是生物进化发生在较大范围6，8的结果。在这里，我们使用非示范菌群,包含3种大肠杆菌，来测试的这些用于实证的预测。我们发现在我们实验的菌群中，当分散和相互作用，发生在较大的空间范围，多样性迅速消失，而当生物进化局部化，所有物种共存。

对于研究繁殖和生物多样性的保持15，17，微生物群落实验已被证明是有用的。特别是，群落内包含能产生毒素（大肠杆菌素）的大肠杆菌已经成为生态理论学家3 ,6,8,18和微生物学家21 - 27的关注中心。大肠埃希氏菌株拥有’大肠杆菌素 ’质粒，包含基因是用来编码大肠杆素（毒素）的，一种特异性免疫蛋白（即呈现细胞免疫的大肠杆菌素）和溶解蛋白质（这是当细胞力在压下，导致部分细胞裂解和随后释放的大肠杆菌素时表达的）26,27。一般来说，只有一小部分大肠杆菌细胞的裂解并释放大肠杆菌素。大肠杆菌素敏感型细菌被大肠杆菌素杀死，但偶尔的突变使其对大肠杆菌素产生抵抗力。最常见的基因突变是改变细胞膜的蛋白质，使其凝结或转移大肠杆菌素23，24,26,27。在某些情况下，抗性细胞（R）的增长速度在将超过大肠杆菌素细胞（C）的增速，但将小于敏感细胞(R)的增长速度。出现这种情况是因为R避免其携带所的质粒竞争型的损失21,22,26,27，但受到影响，因为大肠杆菌素受体和转移蛋白质还参与了关键的细胞功能，如吸收营养21,23,24,26,27。在这种情况下S可以取代R（增长速度优势），R可以代C（因为R有增长速度优势），c可以取代S（C杀死S）。也就是说，的C - S- R的群落满足了石头纸剪刀关系。

使用在一个在修改的格子基础上的达雷特和莱文仿真方法，我们从理论上探讨了在C-S-R菌群中，空间范围对生物进化的作用。分散和相互作用是局部时，我们看到’菌落的形成（1a类型）。这些菌落在格子上彼此追逐，C侵犯S，S取代R,R侵犯C（图1a，b）项。在这个流动镶嵌的菌落中，任何一种类型的局部获利迅速被另一种类型享有。这一平衡的结果是多样性的维护（图1C）。然而，当分散和相互不只单独的在局部（也就是说，在’充分混合的’系统见框1）,这种平衡会失去。在混合系统，不断再分配的C迅速使S灭绝，则R战胜C（图1d）。达雷特和莱文6描述在空间规模的类似的定性效果的大肠杆菌素模型，敏感，’骗子’株（其中一个骗子的定义以一个少的竞争成本生产少的大肠杆菌素类型）。

当在模拟中生物进化是局部的，共存发生在一个大范围的模型参数值内（图1e段），这表明结果对具体选择的参数值不是很敏感。在混合系统的情况下，共存从未发生在的参数空间显示区域在图1e。和达雷特，莱文一致，我们的模拟结果表明，上述三个不分等级的品种可以共存当分散和相互作用相互作用是局部的，而群落充分混合，一个种类会排斥其他种类。

为了验证这一结论，我们使用三种大肠杆菌：大肠杆菌素产生菌（C），敏感菌株（S）和抗性品系（R），可满足了石头纸剪刀竞争力关系（见模型）。放置我们的C - S - R的群落在以下三个环境：（1）’瓶’（良好的混合环境，使分散和相互作用不完全使局部的）;（2）’静态板’（一种环境，使分散和相互主要是局部）和（3）混合板’（环境这两个极端之间的中间）

在瓶的环境中，细菌生长在含有液体培养基的摇动的瓶中。我们每24小时向一个新鲜培养基中转移部分菌落。在静态板块环境，生长的细菌在液体培养基表面。每24小时，我们在一个无菌平绒布覆盖的平台上压每块板，然后在绒上放一个新的板。此方法转移小部分样品，并让转移的样本保持前一个板上的菌落相对位置。混合板环境和静态板环境相同，除了在每次转移完全生长的菌落板时在绒上按几次，每次旋转不同的角度（见方法）。

图2a显示在静态环境中的C，S和R种群在整个实验维持在较高密度。板的照片显示的空间相对位置在实验中变化（图3a）。粉红色和黄色是不同种群的分界（图 3B）,清楚地表明R追赶C，C追赶S。不可能看到S追赶R，因为这两个品种增长到相近的密度。但S密度并没有随着时间的推移不断减少（图2a）的，S确实追逐R.因此共存不是由于完全的空间隔离（图3），相互作用（例如，竞争和杀死）发生在菌落之间的分界，这些结果支持在一个空间结构的平衡追逐的情况下，非等级群落可能导致维持多样性的预言。

瓶环境的结果显示在图2B。相对于静态板环境，在研究完成之前，S和C均下降到他们可被检测的下限。瓶和板之间的动态不同并不仅仅体现液体和表面的生长条件差异。在每个转移时仅仅混合生长菌落表面（即，我们的混合板环境）让动态变化非常类似于烧瓶环境（图2C型）。因此，看来分离和相互作用必须是局部的，共存在这个种群发生。

为了检测我们结果的说服力，我们在开始时使用不同的空间相对位置和使用菌种比例来重复上述的实验工作（见方法）。在考虑到的情况中，我们发现变化和我们原本的实验十分一致。那就是，当生物进化局部化,它们的相互追逐中，这三个品种至少共存66代，。当进化分非局部化，S和C被R取代(资料未显示）。这个观察说明我们的结果的产生不是因为我们选择的特殊的起始条件。

这里介绍的工作是在两个最近趋势的生物多样性研究的的关键处。首先是空间范围在生物进化中的作用2，4，9，17。它在理论上已经证明，仅仅让相互作用性和分散的发生在局部可以促进在种群多样性2，4，5，6，7，8，9，11。我们的实验结果证实了这些预测。第二个趋势是关于非等级竞争关系3，6，11，28，29。最近的理论认为，在资源数量有限时，只要物种无等级关系，共存的物种数量惊人的高。我们的研究体系是一个非常简单的三者关系：石头纸剪刀。我们的实验结果预测，非等级的竞争关系可以促进多样性。但是，在我们的情况下，生态进化的局部化也是必要的。

在其他自然群落，局部化的过程可能对共存也很重要的。对于许多相对固定的生物，如植物，一些海洋无脊椎动物和由膜组成的微生物，分散和相互作用往往发生在小空间范围。这种生物群落也可能会出现非传递关系。举例来说，如果一个物种产生毒素（一种普遍现象，发生在许多种植物30，海洋微生物13，真菌 30，基本上每个主要细菌系27），将有可能出现无传递情况。如果毒素的生产成本高，敏感型和抗性品种存在，与耐药相关成本小于与生产相关的毒素，这种情况会发生。然而，这些成本的相对大小是至关重要的共存的前提。具体来说，如果反抗或相克作用的成本不是太大或太小，群落将可崩溃，即使种群保持非传递关系（例如，看到图的黑暗部分图1e段）。如果我们的实验群落的相对成本是自然群落的代表，那么我们可以预测生物进化的规模，以确定植被和与之相克植被植物之间，维护生物多样性的可能性。珊瑚礁无柄有毒无脊椎动物，以及生产抗生素的微生物群落。对于进一步研究局部分散和相互作用在物种共存方面，这些群落可能是理想的系统。



图1

在格子上模拟的预测（专栏1）a,b。在模拟中计算机网格在一个小范围的邻域3000（a）和3200（b）。时间的单位是一个’时段’，等于62,500格点的更新（一个时段，是任何一个给定的250×250网格的平均更新时间。该菌株的彩色编码如下：C是红色，S是蓝色的，R是绿色的，空的格点是白色的。在相同的模拟中进行完整的群落演变d。，一个模拟的群落演变包含一个整体的邻域。C和d是对数转换。当一个菌株数量趋向于零，我们在有关图的横坐标上用钻石标志代表变为0的时间。对于a,b,c,d，我们使用了以下主要技术参数比： C =1/3, S,0 = 1/4, R = 10/32, andτ= 3/4（见专栏1）。动态变化的敏感度由参数值变化而变化。对于（τ， R）的值的绘制，灰度显示局部模拟运行中（多于10个），共存发生了至少10000个时段。混合程度较轻地区，共存的概率较高。对于所有的模拟，我们要求， ，（至少在混合系统）这确保，S取代R,R取代,C（如C组有足够的密度）取代S

图2

实验群落动态处理：a，静态板,b瓶,c,混合板。虚线表明，有关种群的数量下降到低于能检测的下限。数据点表示三个物种在复制，线条描绘平均标准误差。数据点被24小时分隔，大约产生10代细菌。



图3在静态板环境中，照一系列具有代表性的随时间变化的照片。我们开始这个实验是将纯净环境中的小液滴沉入六边形格子中，其中每个点的菌中种随机分配。 a，实验菌群空间形状的改变显示在第一个板的照片。C细胞密度较小因此很不同于S和R。C内部出现了浓密的增长的’点’被确定为对S抗性细胞。空层存在于C和S分界，在此扩散的大肠杆菌素阻碍了S细胞生长，但其中C细胞未在此生长。C和R边界缺少空层。b，在第二块板，追逐的情况突出，给予初始菌株的空间分布，保存以供参考。C和S之间的边界会染成黄色,C和R的边界粉红色。

方法

试验系统

我们使用产大肠杆菌的大肠杆菌E2类系统：株BZB1011（S）和E2C - BZB1011（C）和E2R – BZ（R），C用抗T6噬菌体标记，R用抗T5噬菌体标记。除了不可转移的质粒和生产者，C和S基因相同。R的得到是从S中选抗大肠杆菌素突变体。所有的菌种用选择的板计数，S用差计数。一段时间，我们用核实抗T6噬菌体生产大肠杆菌素，抗T5噬菌体标记不生产来检验标记物。

确定应变关系

增大两个相互竞争菌群数量，确定它们相对合适的关系。，在10毫升Luria–Bertani (LB)培养液和有4毫升软琼脂的琼脂板表面。X和y菌种的合适关系是



x0和y0的是初始密度，xF和yF增长24小时后的密度。

我们发现在液体环境中 w(R,S) = 0.59 0.097 ，w(R,C) = 1.91 0.399 ，而在平板上w(R,S) = 0.73 0.142 and w(R,C) = 1.90 0.230.，但我们看到C产生大肠杆菌素的有效杀死S细胞（例如，在一个S的菌群中，大肠杆菌素会使之产生明显空斑）。因此，C杀死S，S比 R长的快，R比 C长的快。

群落动态跟踪

在静态板块的环境中，细菌生长的4毫升软琼脂表面，已被倒在硬LB琼脂底座上。初始化板，15升纯培养液滴被滴在31点六角形格子上（图3a）。液滴模式是随机分配在每个格点的菌种根据可能的概率：Pr{C} = 0.25, Pr{S} = 0.5, and Pr{R} = 0.25.经过24小时在37℃条件下的培养，我们将完全生长的菌群按在覆盖丝绒的一个平台上。然后，将三个新板压在丝绒，注意保持方向。第一个板被用于计算后第二天增长后的菌种密度。这是通过刮去有菌群的软琼脂层放入10毫升生理盐水与，离心几秒钟的混合物，然后按照标准的选择方式。第二个板被用于菌群繁殖（即，为了第二天的增长后在丝绒上按）。第三个板用于照相（见图3）。

除了以下不同,混合板块环境和静态板相同：在每次转移时，将菌落充分生长的板（1）轻轻地按下到丝绒上，（2）顺时针随机旋转角度和压第二次，（3）逆时针随机旋转角度和压第三次（4）顺时针随机旋转角度和压第四次。新鲜的板，再压在绒上来开展这项’混合’样本。

我们的瓶环境是125毫升的瓶,33.75毫升lb肉汤,使之旋转,转速为125转每分，在37℃环境中.经过24小时的增长，50微升培养液被转移到一个新瓶。这些转移的量确保了一整天的增长后，转移出的细菌，能代表原瓶中相应细菌。

在所有这三个环境中，每24小时测每种菌落的密度，所有的操作方法被重复三次。我们一个星期后（约66代）结束试验，因为这个时候，我们发现了S大量突变，(例如C密度变大，3a图）。R从S的进化违反了我们的模型假设，可能导致在预测动态的变化，特别抗性成本低于R突变成本.（图1中 R更小）。目前，我们正在从理论和实验研究方面研究这些进化现象。应当指出，一滴15微升滴在一个板的中心位置几乎覆盖下的静态板实验,一星期就足够了。

额外的起始条件

我们在两个额外装置控制开始菌落比例和空间相对位置（未显示数据）。首先，我们重申了上文所述的相同的初始六边形格子图案，但使用另一种随机分配（采取上述实验可能的分布）。二，而不是在一开始滴在六角形格子，我们在柔软的琼脂上用不同比例混合细菌（以S过多,C和R很少），倒在板块的琼脂，出现初始的不成菌落的分布。

方框1

我们将C - S - R的菌群培养在250 ×250的常规方格,定期分界。要启动模拟如图1，每个格点随机独立分配了以下几种状态：由C,S或R细胞占据或’空状态’。我们使用了不同步的更新方案，随机挑选中心格点和看其状态改变。这取决于它现在的状态和周边。附近的大小代表了生物进化的空间范围。为探索空间范围的作用，我们模拟两种不同大小的附近范围。当8个格点环绕一个中心点,相互作用（即，杀和空间竞争）和分散（即是’出生’）是局部化。当附近区域包括网格每一点，相互作用和分散不再局部化，而种群行为就像一充分混合的系统。这两种方式，如果一个空的格点选定被更新，它被杀死的概率 i。虽然 R, C是固定值， S是不是，它等于， S,0 +τ(fC), S,0,表示无C在S旁边时S死亡概率，τ表示C周围的毒性。