disturbances (i.e. density-independent mortality) cause small-scale extinctions, a good colonizer/poor competitor and a poor colonizer/good competitor can stably coexist at larger spatial scales. Because there is a trade-off, neither strategy could replace the other in a moderately disturbed system and the relative occupancy of competitors depends upon disturbance frequency. However, in these models, local coexistence between these two strategies is imposs- ible because the dominant competitor always replaces the better colonizer within a patch. The presence of any trade- off is often cited as evidence against the role of neutral dynamics in structuring communities (Turnbull et al. 2005 Ellis et al. 2006). Yet several recent publications suggest that even though relatively few strategies along a niche gradient can coexist, within any single niche strategy, multiple functionally similar or equivalent species can coexist, mimicking neutral-type dynamics (Hubbell 2005 Gravel et al. 2006 Holt 2006 Scheffer & van Nes 2006). Recently, Fukami et al. (2007) showed that adaptive radiation in Pseudomonas bacteria resulted in both the filling of empty niches and the evolution of ecological equivalents coexisting within niches. Thus, the presence of trade-offs may not necessarily refute neutral dynamics (Hubbell 2005). If we view the stabilizing mechanism (colonization ability) as part of a strict trade- off, then two species that have similar colonization abilities will also have similar competitive abilities within local patches. In the absence of any other local niche partitioning, these two, similarly competing species, should have similar fitness responses to local environ- mental conditions (Chesson 2000), meaning that either competitive exclusion takes many generations to occur or weak stabilizing mechanisms promote coexistence. I use data from aquatic microcosm experiments to test whether the risk of competitive exclusion decreases and time to local extinction increases as species become more similar. 2. A SIMPLE MODEL With a competition���colonization trade-off, species can stably coexist at larger spatial scales despite competitive differences. However, within local patches, such coex- istence is not possible if we assume that there is not any spatial subsidy effect enhancing one species birth rates over another (Mouquet et al. 2006). Furthermore, many competition���colonization models assume instantaneous competitive exclusion, but in considering a gradient from niche to neutral dynamics, the relative time for competi- tive exclusion is fundamentally important. Incorporating succession requires the addition of local niche dynamics to trade-off models (Pacala & Rees 1998). Here I assume that there is a strict trade-off between colonization and competitive ability. I am explicitly considering the dynamics of unicellular micro-organisms of a single trophic level inhabiting homogeneous, spatially discrete patches (e.g. Cadotte 2006, 2007). Given this simple system, the competition���colonization trade-off can be defined by two parameters: the intrinsic rate of increase for species i, ri , and the strength of interspecific competition (bij, the effect of species j on i ). Here I assume that intraspecific effects, bii , are constant. The population size of species i at time t is given by Ni t Z ri CbiiNi tK1 CbijNj tK1 C3 ��2:1�� where Ni,tK1 is the population size at time tK1 and 3 is the normally distributed stochasticity with a mean of 0 and standard deviation of 1. If there is a trade-off, then as ri increases, its effect on the other species, bji , must decrease. As the difference increases, the disparity between competitive effects also increases. Thus, within patches, increasing D means that the inferior competitor goes extinct faster (figure 1). Species with identical r���s (and thus b���s) will persist indefinitely, but even species with small D may persist for many generations if the magnitude of the difference in b���s is less than demographic stochasticity (3 in equation (2.1)). 3. A TEST USING MICRO-ORGANISMS Here I use data from the competition���colonization experiment of Cadotte et al. (2006). Using an artificial system of aquatic micro-organisms (protozoans and rotifers see figure 2 for species list), Cadotte et al. (2006) revealed that species exhibited competition��� colonization trade-offs, where the best competitors were generally poor colonizers and the best colonizers were typically poor competitors (figure 2). Colonization was measured as the relative time for species to colonize every patch in a discrete five-patch system, whereas competition was measured as the extinction probability in pairwise combinations with every other species (see Cadotte et al. (2006) for detailed methods). The patches in the colonization experiment were 125 ml Nalgene bottles filled with 100 ml of bacterialized nutrient solution, and with 4.76 mm threaded holes having nylon tube fittings 35 30 25 20 15 10 5 2 4 6 8 10 difference in rank colonization ablity time to extinction 25 20 15 10 5 0 5 10 15 20 time population size Figure 1. The time to observe a local extinction for pairwise species combinations from equation (2.1). Here 12 species are modelled with a strict competition���colonization trade-off. The best colonizer had riZ1.325 and was ranked 1, and subsequent species r���s were decreased by 0.025, with the 12th ranked species having riZ1.05. The 12th ranked species was also the best competitor with bi12Z0.65 and lower ranked species had lower bij���s by 0.05, with the best colonizer having bi1Z0.1. The inset shows two example simulations: one simulation is between two species with similar abilities (solid lines) and the other is for two species with very different abilities (dashed lines). For the similar species: solid black line, species rank 5 solid grey line, species rank 4. For the different species: dashed black line, species rank 11 dashed grey line, species rank 3. 2740 M. W. Cadotte Concurrent niche���neutral processes Proc. R. Soc. B (2007) on December 13, 2009 rspb.royalsocietypublishing.org Downloaded from

(Cadotte et al. 2006). Patches were linked serially, connected with 12.5 cm of clear Nalgene 4.76 mm PVC tubing. For the competition experiment, the two species were added to 50 ml of bacterialized solution in 250 ml glass jars. For both experiments, the presence of species was assessed with weekly 5 ml samples (and replaced with 5 ml of sterile nutrient solution). All experiments were replicated three times. Here I assume that the outcomes of species competition in Cadotte et al. (2006) result from fitness inequalities. I also assume that species inhabit a stable environment, are limited by a single resource and have colonization abilities that reflect maximal population growth rates (Warren et al. 2006). Competitive interactions are estimated in an extremely conservative manner: whether one of the two populations goes extinct, ostensibly due to competitive exclusion. Colonization ability was ranked by time to colonize all patches. Rank was calculated as the mean rank from 10 000 random draws of the individual replicates (see Cadotte et al. 2006). Since I observed exclusions over an eight-week interval, with weekly samplings, the data are said to be right-censored. Right-censored data are common in ���time to��� experiments where observations end at some arbitrary time and therefore represent a biased sampling where parameter estimation does not conform to widely used parametric estimations (Hosmer & Lemeshow 1999). Which species went extinct is not important here because as long as there was extinction, then these two species are said to exhibit fitness inequalities. Therefore, to estimate the probability of coexistence, I used the Kaplan���Meier product-limit estimator (Hosmer & Lemeshow 1999), which calculates the probability that a given population will persist beyond time t. The maximum-likelihood estimate of this probability is given by ^ S ��t�� Z Y ti!t ni K di ni ��3:1�� where ni is the number of surviving populations and di is the number of deaths at time ti. I used a parametric regression fittingtheprobabilityofcoexistencetoaWeibulldistribution against the absolute difference in colonization rank, and evaluated the model using a likelihood ratio test (presented as c2-value) comparing this model with a model containing only an intercept. Survival analysis was performed using the SURVIVAL Package, v. 2.31 with R v. 2.4.1 maintained by Thomas Lumley (www.r-project.org). 4. RESULTS The regression analysis reveals that the probability of successful coexistence between any two species is negatively related to the difference in their colonization rank (c1Z7.56, 2 pZ0.006 coefficientGs.e.ZK0.07892G 0.0289). To best illustrate this relationship, I grouped the colonization differences into three classes: (i) difference in colonization rank!3.00, (ii) differenceR3.00 and %6.00, and (iii) differenceO6.00. The probability of coexistence as a function of time is shown in figure 3, and the relationship between the probability of coexistence and the colonization difference classes is very similar to that for the continuous model above (c1Z8.75, 2 pZ0.003 coeffi- cientGs.e.ZK0.2814G0.0976). 5. IMPLICATIONS: HOW NICHE AND NEUTRAL PROCESSES CAN COEXIST One of the earliest axioms of ecology was that two species occupying the same niche results in competitive exclusion of the inferior competitor (Grinnell 1904, 1917 Gause 1934). However, this ���competitive exclusion principle��� was quickly cast into doubt as examples of coexistence in ecologically similar species surfaced (Ross 1957 Udvardy 1959 den Boer 1986). Since then, the idea that species coexist due to their similarities rather than their differences has repeatedly surfaced, primarily by ecologists studying tropical forests (e.g. Webb 2000 Hubbell 2006) and freshwater algae (Hutchinson 1967 Lewis 1977 1.0 0.8 0.6 0.4 0.2 0 0 2 4 6 8 time (weeks) probability of coexistence Figure 3. The Kaplan���Meier product-limit estimator of the probability of coexistence over time. The three lines refer to species classified by differences in colonization rank (D). Small (solid line), D!3 medium (dashed line), 3%D%6 large (dotted line), DO6. For clarity, 95% CIs were removed. competitive rank colonization rank 5 15 10 5 0 TP CS Ch Co PC Ur Sp PA Eu Le PB BA Ph 15 10 Figure 2. The relationship between competitive and coloniza- tion abilities, showing a competition���colonization trade-off (adapted from Cadotte et al. (2006)). Dashed lines show species locations along regression line. Species with similar colonization abilities are assumed to have similar fitnesses given laboratory conditions and resource availability. BA, Blepharisma americanum Ch, Chilomonas sp. Co, Coleps sp. CS, Colpidium striatum Eu, Euplotes sp. Le, Lepadella sp. PA, Paramecium aurelia PB, P. bursaria PC, P. caudatum Ph, Philodina sp. Sp, Spirostomum sp. TP, Tetrahymena pyriformis Ur, Uronema sp. Concurrent niche���neutral processes M. W. Cadotte 2741 Proc. R. Soc. B (2007) on December 13, 2009 rspb.royalsocietypublishing.org Downloaded from