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Conceived and designed the experiments: LBC IB. Performed the experiments: LBC IB SV EM FB. Analyzed the data: LBC. Wrote the paper: LBC.

The authors have declared that no competing interests exist.

Neutral models and differential responses of species to environmental heterogeneity offer complementary explanations of species abundance distribution and dynamics. Under what circumstances one model prevails over the other is still a matter of debate. We show that the decay of similarity over time in rocky seashore assemblages of algae and invertebrates sampled over a period of 16 years was consistent with the predictions of a stochastic model of ecological drift at time scales larger than 2 years, but not at time scales between 3 and 24 months when similarity was quantified with an index that reflected changes in abundance of rare species. A field experiment was performed to examine whether assemblages responded neutrally or non-neutrally to changes in temporal variance of disturbance. The experimental results did not reject neutrality, but identified a positive effect of intermediate levels of environmental heterogeneity on the abundance of rare species. This effect translated into a marked decrease in the characteristic time scale of species turnover, highlighting the role of rare species in driving assemblage dynamics in fluctuating environments.

Explaining the causes of variation in patterns of distribution and abundance of species within and between habitats has proved to be a formidable task for ecologists, due to the complexity of ecological systems

Neutrality implies that environmental heterogeneity does not translate into differential probabilities of success for individual species

Ecological drift is not the only mechanism that can explain gradual changes in composition and abundance of species in space and time. The differential response of species to environmental heterogeneity can also produce autocorrelated patterns of variation in assemblages

Correlative studies have a central role in tests of neutrality and novel analytical techniques are continuously developed to enable the fit of neutral and non-neutral models to observational data

Here we combine a study of temporal change in assemblages of algae and invertebrates of rocky seashores over a period of 16 years, with an experimental analysis of the influence of temporal variability of disturbance on these assemblages. We use the observational data to test the prediction that observed temporal patterns of decay in similarity would be undistinguishable from those generated by a neutral model based on ecological drift under realistic patterns of natural disturbance, if neutrality holds. With the experimental data we test the hypothesis that, under neutrality, assemblages would not be affected by changes in temporal variance of disturbance (the clustering of events in time), provided that overall intensity of disturbance (i.e. the total number of events and their magnitude over a given period of time) does not change with levels of variance. This hypothesis is based on the argument that neutral assemblage dynamics depend on death and colonization events that are a function of the number of individuals removed by disturbance, in addition to dispersal limitation. Thus, in a series of disturbances, it is the overall intensity of events that should matter, not the temporal variance of the series

To test whether the response of assemblages to changes in environmental variance is consistent with neutrality or deviates from it, we fit to the experimental data both the dispersal unlimited and dispersal limited versions of the neutral theory of biodiversity

Changes in temporal variance of disturbance may have long-term effects on assemblage dynamics if they affect the probability of occurrence of species. Theoretical studies and laboratory experiments have indicated that negative density-dependence in population growth may reduce the risk of extinction and increase population abundance of rare species during long periods of adverse environmental conditions, which are more likely to occur under high levels of environmental variance

A total of 68 species were identified over the course of the study. Analyses that focused on the most abundant species [using the Bray-Curtis index, see eq. (1) in

Data are for assemblages of rocky shores (continuous red line) and assemblages generated under ecological drift (grey lines and symbols) with seasonal variation in disturbance. A temporal lag corresponds to a period of three months. Mantel r's were based on the Bray-Curtis (BC, circles) and Squared Cord Distance (SCD, squares) indexes of similarity for modeled data. Only temporal patterns based on BC similarities are shown for observed data; those based on the SCD index were similar. Dashed red lines are 95% Confidence Intervals obtained by bootstrapping the empirical data 1000 times with replacement. Error bars for modeled data are 1 standard deviation over 100 replicated simulations. Mantel's coefficients for observed data were significantly different from zero (unadjusted probabilities) from lag 1 to lag 13 and from lag 20 to lag 30. Model parameters were estimated from a data set containing 29 species and were θ = 4.71 and

Temporal variance of disturbance had no effect on species rank-abundance distributions resulting from neutral drift, either under constant or variable rates of immigration (

Analysis of the experimental data proceeded with the comparison of the fit of the local Zero-Sum-Multinomial (lZSM) and meta Zero-Sum-Multinomial (mZSM) distributions to the Control, low-variance (LV), medium-variance (MV) and high-variance (HV) conditions, separately. These analyses were based on the likelihood-ratio statistic (LR), as it is commonly done to compare the fit of different models to a given data set. It is important to note, however, that the LR statistic is negatively related to species richness under a true null hypothesis of neutrality – i.e. the power of the test depends on species richness (Jabot and Chave, unpublished data). Thus, the canonical approach to assess the significance of the LR statistic using the ^{2} distribution is not appropriate when the goal is to compare the outcome of multiple tests performed across assemblages that differ in species richness, as in our case. To circumvent this problem, we assessed the significance of the LR statistic by comparing observed values to null distributions derived by simulating neutral drift under the same levels of richness as those observed in the Control, LV, MV and HV conditions and under realistic regimes of disturbance (see

Total abundance | Richness | mZSM | lZSM | LR | |||

Parameters | θ | θ | |||||

Control | 4597 | 32 | 4.9 | 7.7 | 0.039 | 2.1 | 0.25 |

LV | 3279 | 28 | 4.1 | 5.5 | 0.094 | 2.4 | 0.553 |

MV | 3398 | 28 | 4.1 | 5.2 | 0.069 | 6.1 | 0.135 |

HV | 3490 | 25 | 3.6 | 5.1 | 0.059 | 6.0 | 0.098 |

LR, Likelihood Ratio test with probabilities (

Inspection of the rank-abundance curves (

Data are for Control (blue line), Low Variance (green dashed line), Medium Variance (red line) and High Variance (pink line) experimental conditions. The Control and Low Variance curves differed from the Medium and High Variance curves for the presence of a tail of rare species. Full statistics are reported in

The inset shows an increase in abundance of rare species (mean abundances in the range 0.1–10) associated with enhanced temporal variance of disturbance; cc:

To examine the influence of disturbance on rare species in more detail, we calculated the probability of observing singleton species at every time step during the course of the experiment in the Control, LV, MV and HV conditions using eqn. 18 in

Parameters θ and

Fitting the relative species abundance and species turnover distributions to Control data provided an estimate of

The observational data generally supported neutral drift as the mechanism driving temporal changes in assemblages, when variation was quantified with dissimilarity measures that emphasized changes in abundant species. Possible exceptions were the overestimation by the neutral model of observed temporal autocorrelation at the shortest time scale (3 months) and a slight underestimation of observed correlation at time lags 4 and 5. Neutral drift was also supported at the shortest time scale of 3 months and at scales larger than 24 months when variation in rare species was considered. At intermediate time scales (between 3 and 24 months), neutral theory predicted too low values of correlation for dissimilarity measures that emphasized changes in abundance of rare species. The experimental results indicated that a change in temporal variance of disturbance alone – i.e. with no concomitant changes in overall intensity – had no statistically detectable effect on species rank-abundance distributions, so that neutrality was not rejected by these tests. Increasing temporal variance of disturbance, however, led to the disappearance from the MV and HV curves of the tail of rare species that characterized the rank-abundance curves of the Control and LV conditions. The analysis of temporal dynamics indicated that these effects involved density-dependent processes leading to a rare species advantage with increasing levels of environmental fluctuations.

Observed patterns of temporal decay of similarity were consistent with neutrality at most time scales. Ecological drift, however, generated too much short-term temporal variation in abundance of rare species compared to natural patterns, at time scales between 3 months and two years. Increasing intensity of disturbance (regimes of disturbance corresponding to two turnovers of assemblages in

One might argue that higher levels of autocorrelation in observed compared to simulated data reflected a sampling artefact due to the accumulation of many small samples over a long period

This situation is similar to what reported by McGill

Collectively, the data in the literature and our findings suggested that neutrality may be more common at intermediate spatial and temporal scales

The field experiment did not reject neutrality at the time scale of two years. The rank-abundance distributions obtained under the different perturbation regimes were all fitted by the most parsimonious neutral model (the mZSM distribution), consistently with the hypothesis of neutrality. Although these distributions did not differ among experimental conditions, species that were rare in the LV treatment were affected positively by an increase of temporal variance of disturbance (MV condition). Thus, rare species benefited from an initial increase in environmental variance above ambient levels, although some of these species could not persist under the most extreme regime of temporal variance of disturbance (HV condition).

We recognize that observing no response to an experimental manipulation is not necessarily evidence that the null hypothesis is correct. Hence, observing no significant variation in rank-abundance distributions to changes in environmental variability may not necessarily be evidence of neutrality. Theoretical studies, for example, have reported no effect of the temporal characteristics of the disturbance regime on long-term outcomes of non-neutral assemblages

As an attempt to mitigate these problems, we compared observed values of the LR statistic to null distributions originated by simulating neutral drift under the same levels of species richness and similar disturbance regimes as those obtained in Control and manipulated conditions. Despite difficulties in interpretation, our experimental results could explain why, in the correlative analysis, neutral dynamics deviated from observed patterns more when the similarity measure emphasized changes in abundance of rare species than when reflecting changes in common species. Abundant specie appeared insensible to changes in temporal variance of disturbance and their long-term dynamics were described well by neutral drift. Rare species, in contrast, were affected by changes in temporal variance of disturbance and although these effects did not elicit significant changes in the models used to fit the rank-abundance distributions, they may account for the deviations from neutral drift observed under natural settings. Rare species appeared to play a key role in driving temporal changes in assemblages because of their susceptibility to fluctuations in environmental conditions.

Insights into the mechanisms underlying these patterns were provided by the

It should be noted that the analytical expressions used to determine the probability of observing singleton species and to fit the dynamical model of

Our results have several important ecological implications. First, they offer a unified view of currently separated theories relating environmental variance, density-dependent processes and assemblage dynamics

Assemblages were sampled non-destructively with visual counts every three months between 1991 and 2006. Data were obtained from quadrats distributed on a rocky shore about 1 km long in the northwest Mediterranean (43°30′N, 10°20′E). On average, 96 plots were sampled in each occasion, actual numbers varying in relation to weather conditions and availability of resources. Quadrats ranged in size from 10×10 to 20×20 cm, to comply with the requirements of other research projects. These sizes were appropriate to sample the small species of algae and invertebrates that characterized the shore and did not result in different estimates of either mean abundances or spatial and temporal variances of species

Data from the first year of sampling were used to estimate the parameters of the neutral theory by fitting a local Zero-Sum-Multinomial distribution

The number of individuals killed at each time step was chosen to reflect seasonal events of disturbance. Simulating neutral drift under constant disturbance may not be realistic, particularly in temperate marine systems where the frequency and intensity of disturbance may vary seasonally. To assess whether there were seasonal patterns of disturbance on our shores, we calculated the number of strong storms (defined as those resulting in waves >3 m high) occurring in the different seasons over the period 2000–2007, for which we could find wave climate data (courtesy of the Istituto Idrografico e Mareografico di Pisa). Over this period, 31% of strong storms occurred in spring, 21% in summer and 24% in each of the two remaining seasons. To incorporate seasonal variation of disturbance in our analysis, we simulated neutral drift by distributing death events across seasons in the same proportion as the observed events of disturbance.

Temporal changes in assemblages were examined with Mantel correlograms and compared between observed and modeled data. This procedure enabled us to determine the temporal scale at which observed patterns of correlation diverged from those predicted by the neutral model. Similarity was quantified using various indexes that emphasized different aspects of assemblage dynamics. We applied the Bray-Curtis index to untransformed data to emphasize changes in the most abundant species, the Jaccard index to emphasize compositional changes and the Square Cord Distance to assess the influence of changes in abundance of rare species _{ij}_{ik}_{ij}_{ik}

Mantel correlograms were generated using package ecodist in R

Neutral drift was simulated using package untb in R

To test the sensitivity of assemblages to changes in environmental fluctuations, we manipulated the temporal variance of events of disturbance in 54 experimental plots distributed in the same study area where the long-term observations were collected, between November 2001 and October 2003. Disturbances consisted in the mechanical removal of organisms from experimental plots through a standardized procedure that reproduced the effects of wave shock during heavy storms ^{2}) was obtained by distributing the events of disturbance at approximately regular intervals. The medium (MV = 8.8 months^{2}) and high (HV = 26.8 months^{2}) levels of variance were obtained by distributing disturbances more heterogeneously over the course of the study. The experimental levels of intensity, spatial extent and temporal variance of disturbance were realistic for the system under study

Experimental and control plots were sampled seven times during the course of the experiment, with three replicate 12×10 cm quadrats placed randomly in each plot. Only the central 50×50 cm area of the largest plots was sampled, so that abundances were estimated at the same spatial scale in large and small plots. Sampling was done as described for the long-term observational study.

We used species rank-abundance distributions to test the hypothesis that assemblages would retain the same structure under different levels of temporal variability, as expected under neutrality. For these analyses, data for each level of temporal variance of disturbance were combined across levels of intensity and plot size. Given the experimental design, this procedure enabled us to examine the effects of temporal variance of disturbance while keeping intensity and spatial extent constant, so to maximize replication for the main test of interest (

The meta and local Zero-Sum-Multinomial distributions (mZSM and lZSM, respectively) were fitted to rank-abundance data using Etienne and Ewens sampling formulae, respectively ^{2} distribution. As an alternative, we assessed the significance of the LR statistic by comparing observed values to null distributions derived by simulating neutral drift under the same levels of richness observed for the Control, LV, MV and HV conditions and under realistic disturbance regimes.

To generate the null distribution for a particular condition, we simulated neutral drift in 10 plots each containing 400 individuals. Data were generated using Etienne's algorithm

To test the hypothesis that temporal variance of disturbance affects the long-term dynamics of the system, we fitted the relative species abundance and species turnover distributions to control and experimental data using eqn. 1 and eqn. 2 in Azaele

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Mantel correlograms for different regimes of disturbance and similarity indexes. Shown are patterns of temporal decay in similarity for observed (blue or open symbols) and neutral (grey symbols) data. Open symbols are used to indicate Mantel's coefficients for observed data that did not differ significantly from zero. Probabilities were not corrected for multiple testing. Lines around observed data are 95% bootstrapped Confidence Intervals. Bars for neutral data are ±1 s.d. obtained form 100 replicated simulations. The first panel complements the results presented in the main text for a regime of disturbance corresponding to one turnover of assemblages. The other panels compare the different indexes of similarity for patterns of mortality corresponding to 0.5 and 2 turnovers over 15 years. Differences between observed and modeled data based on the SCD (Squared Cord Distance) index were less pronounced under very low levels of mortality (disturbance = 0.5 turnover). In contrast, the degree to which the neutral model based on Jaccard and Bray-Curtis measures overestimated autocorrelation at the smallest time scales, was emphasized by low levels of mortality. Note the different scales on the vertical axes.

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Neutral drift under constant and variable regimes of disturbance and immigration. (A) Shown are mean species rank-abundance distributions over 100 replicated simulations (±1 s.d.) of neutral drift under constant (bleu symbol) and variable (pink symbol) regimes of disturbance. Neutral drift was simulated for a local assemblage of 5000 individuals connected to a metacommunity of 100000 individuals, with parameter θ = 7.7 and ^{2} = 2500. Changing values of parameters did not change the qualitative outcome of the simulation, with constant and variable regimes of disturbance yielding overlapping rank-abundance distributions. Other details are explained in

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Null distributions of the likelihood-ratio statistic (LR) originated by simulating neutral drift under the same levels of richness observed for the Control, LV, MV and HV conditions.

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The manuscript benefited from the comments of Sandro Azaele, Jarome Chave, Rampal Etienne, Frank Jabot and Amos Maritan. We are grateful to the numerous people that assisted with the field work over the years. This is contribution number 8038 of MARBEF.