Optimizing performance of nonparametric species richness estimators under constrained sampling

Understanding the functional relationship between the sample size and the performance of species richness estimators is necessary to optimize limited sampling resources against estimation error. Nonparametric estimators such as Chao and Jackknife demonstrate strong performances, but consensus is lacking as to which estimator performs better under constrained sampling. We explore a method to improve the estimators under such scenario. The method we propose involves randomly splitting species‐abundance data from a single sample into two equally sized samples, and using an appropriate incidence‐based estimator to estimate richness. To test this method, we assume a lognormal species‐abundance distribution (SAD) with varying coefficients of variation (CV), generate samples using MCMC simulations, and use the expected mean‐squared error as the performance criterion of the estimators. We test this method for Chao, Jackknife, ICE, and ACE estimators. Between abundance‐based estimators with the single sample, and incidence‐based estimators with the split‐in‐two samples, Chao2 performed the best when CV < 0.65, and incidence‐based Jackknife performed the best when CV > 0.65, given that the ratio of sample size to observed species richness is greater than a critical value given by a power function of CV with respect to abundance of the sampled population. The proposed method increases the performance of the estimators substantially and is more effective when more rare species are in an assemblage. We also show that the splitting method works qualitatively similarly well when the SADs are log series, geometric series, and negative binomial. We demonstrate an application of the proposed method by estimating richness of zooplankton communities in samples of ballast water. The proposed splitting method is an alternative to sampling a large number of individuals to increase the accuracy of richness estimations; therefore, it is appropriate for a wide range of resource‐limited sampling scenarios in ecology.     

Assessing the performance of nonparametric estimators of species richness in meadows

To accurately measure the number of species in a biological community, a complete inventory should be performed, which is generally unfeasible; hopefully, estimators of species richness can help. Our main objectives were (i) to assess the performance of nonparametric estimators of plant species richness with real data from a small set of meadows located in the Basque campiña (northern Spain), and (ii) to apply the best estimator to a larger dataset to test the effects on plant species richness caused by environmental conditions and human practices. Two non-asymptotic and seven asymptotic accumulation functions were fitted to a randomized sample-based rarefaction curve computed with data from three well sampled meadows, and information theoretic methods were used to select the best fitting model; this was the Morgan-Mercer-Flodin, and its asymptote was taken as our best guess of true richness. Then, five nonparametric estimators were computed: ICE, Chao 2, Jackknife 1 and 2, and Bootstrap; MMRuns and MMMeans were also assessed. According to the criteria set for our performance assessment (i.e., bias, precision, and accuracy), the best estimator was Jackknife 1. Finally, Jackknife 1 was applied to assess the effects of terrain slope and soil parent material, and also fertilization, grazing, and mowing, on plant species richness from a larger dataset (20 meadows). Results suggested that grass cutting was causing a loss of richness close to 30%, as compared to unmowed meadows. It is concluded that the use of nonparametric estimators of species richness can improve the evaluation of biodiversity responses to human management practices.     

Patterns of species richness in a limestone grassland under different treatments in relation to spatial scale

Abstract. In an experiment in a limestone grassland on the Baltic island of Öland, SE Sweden, nutrient and water supply, light intensity and grazing regime were altered in 10 combinations during four years in 10 plots of 0.25 m² with subplots of 0.01 m² and 0.0004 m². Only the combined application of fertilizer and shade led to a strong decrease in average species richness (S₁) at all scales. When comparing species numbers summed up over all 10 replicates of each treatment (S_n) at the three quadrat sizes, differences in effect of these treatments were much smaller, and were so already at the finest scale. α-diversity, measured as (S_n - S₁ was quite constant over different scales for most treatments, i.e. diversity did not increase with an increase in scale. The ‘richness ratio’S_n/S₁ decreased with increasing scale, indicating an increasing degree of homogeneity at larger scales. Treatments which only included fertilizer or shade, maintained high species richness; this high richness was also maintained in combination with grazing and could then be explained by the denser packing of vegetation. Patterns of species richness were correlated at the large scale, but not at the finer scales, indicating a high degree of spatial and temporal heterogeneity at the finer scales. With increasing quadrat size species persistence increased which explains the small effect of certain treatments. Clearly, a range of scales has to be sampled in this type of vegetation to be able to measure different patterns, which may occur under different experimental treatments. The finest scale in this study can become too small, when certain treatments result in a coarse-grained vegetation pattern. The quadrat size of 10 cm x 10 cm should be included in the range of scales. It combines accuracy in sampling with efficiency in time effort, a reasonably large number of species sampled, and a strong differentiation in the effects of the various treatments.     

Are Plant Censuses Carried Out on Small Quadrats More Reliable than on Larger Ones?

Plant censuses are known to be significantly affected by observers’ biases. In this study, we checked whether the magnitude of observer effects (defined as the % of total variance) varied with quadrat size: we expected the census repeatability (% of the total variance that is not due to measurement errors) to be higher for small quadrats than for larger ones. Variations according to quadrat size of the repeatability of species richness, Simpson equitability and reciprocal diversity indices, Ellenberg indicator values, plant cover and plant frequency were assessed using 359 censuses of vascular plants. These were carried out independently by four professional botanists during spring 2002 on the same 18 forest plots, each comprising one 400-m² quadrat, four 4-m² and four 2-m² quadrats. Time expenditure was controlled for. General Linear Models using random effects only were applied to the ecological indices to estimate variance components and magnitude of the following effects (if possible): plot, quadrat, observer, plant species and two-way interactions. High repeatability was obtained for species richness and Ellenberg indicator values. Species richness and Ellenberg indicator values were generally more accurate but also more biased in large quadrats. Simpson reciprocal diversity and equitability indices were poorly repeatable (especially equitability) probably because plant cover estimates varied widely among observers, irrespective of quadrat size. Grouping small quadrats usually increased the repeatability of the variable considered (e.g. species richness, Simpson diversity, plant cover) but the number of plant species found on those pooled 16 m² was much lower than if large plots were sampled. We therefore recommend to use large, single quadrats for forest vegetation monitoring.     

Patterns of bird species richness and composition on islands off Arnhem Land,Northern Territory,Australia

The bird faunas of the adjacent Wessel and English Company island chains were sampled at two scales (0.25 ha quadrats and entire islands). Ninety‐six species were recorded from 226 quadrats, with the most frequently recorded species being mistletoebird Dicaeum hirundinaceum, brown honeyeater Lichmera indistincta, silver‐crowned friarbird Philemon argenticeps, bar‐shouldered dove Geopelia humeralis, northern fantail Rhipidura rufiventris and yellow white‐eye Zosterops lutea. At the quadrat scale, vegetation type was a major determinant of the abundance of individual species (and hence species composition), species richness and total bird abundance. Bird species composition and richness at the quadrat scale was also significantly affected by island isolation (particularly the amount of land within 20 km of the island perimeter). Island size had no effect on quadrat‐scale richness or total abundance. However, the abundance of 10 of the 38 most frequently recorded individual species was significantly related to island size, in most cases even when the comparison was restricted to similar habitats. The most striking cases were rufous fantail Rhipidura rufifrons, mangrove golden whistler Pachycephala melanura, brown honeyeater and yellow white‐eye, which were all significantly more abundant on smaller islands. One hundred and seventy‐one species were recorded from the 62 islands sampled. There was a very tight relationship between island size and the number of terrestrial species (73% of deviance explained) and of all species (84% of deviance explained). This relationship was improved (marginally) when isolation was included in the model. Ordination of islands by their terrestrial bird species composition was related to island size and isolation, and suggested an erratic species composition on small islands.     

Estimating species richness: still a long way off!

Xu et al., in this issue of the Journal of Vegetation Science, compare several species richness estimators. All the non‐parametric estimators, such as Chao and jackknife estimators, underestimated the true number, whereas all the area‐based models, based on species–area curves, overestimated it. No reliable method yet exists to predict the number of species in an area that is appreciably larger than the one(s) sampled.     

The use of incidence-based species richness estimators,species accumulation curves and similarity measures to appraise ethnobotanical inventories from South Africa

The incorporation of suitable quantitative methods into ethnobotanical studies enhances the value of the research and the interpretation of the results. Prediction of sample species richness and the use of species accumulation functions have been addressed little in applied ethnobotany. In this paper, incidence-based species richness estimators, species accumulation curves and similarity measures are used to compare and predict species richness, evaluate sampling effort and compare the similarity of species inventories for ethnobotanical data sets derived from the trade in traditional medicine in Johannesburg and Mpumalanga, South Africa. EstimateS was used to compute estimators of species richness (e.g. Jackknife), rarefaction curves, species accumulation curves and complimentarity. Results showed that while the Michaelis–Menten Means estimator appeared to be the best estimator because the curve approached a horizontal asymptote, it was not able to accurately predict species richness for one of the data sets when two of its subsamples were individually tested. Instead, the first-order Jackknife estimator best approximated the known richness.     

Effects of sampling time,species richness and observer on the exhaustiveness of plant censuses

Question: How may sampling time affect exhaustiveness of vegetation censuses in interaction with observer effect and quadrat species richness? Location: French lowland forests. Methods: Two data sets comprised of 75 timed, one‐hour censuses of vascular plants carried out by five observers on 24 400‐m² forest quadrats were analysed using mixed‐effect models. Results: The level of exhaustiveness increased in a semi‐logarithmic way with sampling time and decreased with quadrat species richness. After one hour, 20 to 30% of the species remained undetected by single observers. This proportion varied among observers and the discrepancy increased with increasing sampling time. Fixing the sampling time may make richness estimates vary less between observers but the time limit should be at least 30 min to reduce the bias in exhaustiveness between rich and poor quadrats. Conclusions We advocate the use of sampling methods based on spatially or temporally‐replicated censuses and statistical analyses that correct for the lack of census exhaustiveness in vegetation studies.     

Could we obtain better estimates of plot species richness from multiple‐observer plant censuses?

Question: Could we better estimate plot species richness by asking several botanists to survey the same plots and using non‐parametric estimators of richness? Location: Two French deciduous forests. Methods: Using replicated, independent censuses made by 11 professional botanists on the same eight 100‐m² forest plots, the relative performance of different richness estimators (Lincoln‐Petersen, Jackknife 1&2, Chao 1&2, Bootstrap, Chao Mth, Darroch) and the variation in their performance with the number of botanists involved (teams with two to eight botanists) were investigated. The sensitivity of these estimators to the presence of misidentifications in the data was also assessed. Results: When misidentifications are removed, Chao Mth estimators converged fastest to true richness, but none of the tested estimators correctly accounted for differences in exhaustiveness between the teams. Finally, all estimators were highly sensitive to misidentifications. Conclusions: Richness estimators are of little help in the presence of misidentifications and are ineffective at removing between‐team discrepancies, thus strongly limiting their usefulness in practice. Methods are presented to show how surveys can be designed to remove misidentifications and limit between‐team discrepancies. A sensible sampling design for 100‐m² plots in temperate forests would involve triplets of botanists and correcting data with the Chao N1. Pairs of botanists would already significantly improve the richness estimates, but such estimates would still be biased low. However, further research is needed to design new richness estimators that are more robust to observer effects.     

Multi-scale comparisons of cliff vegetation in Colorado

We developed a nested vegetation sampling protocol to sample the plant diversity on south-facing cliffs and cliff bases in Jefferson County, Colorado. The multi-scale plots included three nested spatial scales, 1 m², 20 m², and 40 m². We compared plant species richness and species diversity among large cliffs, medium cliffs, small cliffs, and non-cliff sites using Hill's diversity numbers (N ₀, N ₁, and N ₂) for the 1-m² quadrats. Species richness (N ₀) was calculated for the 20-m² and 40-m² plots. Our results indicate that plant species diversity on the cliff faces did not increase with increasing cliff area. This pattern was consistent at all three sampling scales. A model selection was run to determine if plant species diversity values on the cliff faces were associated with cliff variables. None of the cliff variables measured were good predictors of diversity at the 1-m² scale. However, at the 20-m² scale, canyon differences and a positive relationship with increasing cliff surface roughness explained 70% of the variability in species richness. Although most plant species sampled on the cliff faces were also found in the base plots, 13 species were sampled only on the cliff faces. Additionally, dry south facing cliffs support a mix of xeric and mesic plants indicating that cliffs may provide unique microenvironments for plant establishment. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Impact of Seeding Method on Diversity and Plant Distribution in Two Restored Grasslands

Previous studies have compared grassland restoration techniques based on resulting species richness and composition. However, none have determined if different techniques generate different plant distributions in space, which may further impact restoration success. This study tests if there are quadrat‐scale (1 m²) differences between paired drilled and broadcast plantings in diversity, composition, and plant distributions. Higher competition intensity in and more contiguous spaces between rows in drill‐seeded restorations were hypothesized to result in larger patches of native grasses and exotic species. Two paired drill‐ and broadcast‐seeded plantings were sampled in June 2007 in Iowa, U.S.A. Within 10 quadrats in each planting, we measured species abundance with point intercept sampling and plant distributions by dividing the quadrat into 64 cells and recording the most abundant species in each cell. Drilled and broadcast plantings at both sites had similar Simpson’s diversity and evenness. However, the effect of planting type on species richness, composition, and plant distribution was site dependent. Native warm‐season grasses in one site, and exotic species in the second, occupied more space and were distributed in larger patches in drilled plantings. Furthermore, drilled canopies consistently captured more light than broadcast canopies. This suggests that initial differences in seed placement can affect resulting plant distributions, resource use, and potentially long‐term species turnover. Mechanisms structuring vegetation in these communities need to be further investigated to determine if this approach can provide more information on long‐term diversity maintenance in restorations than traditional measures.     

The net result: evaluating species richness extrapolation techniques for littoral pond invertebrates

1. Total species richness for an assemblage or site is a valuable measure in conservation monitoring and assessment, but protocols for sampling and species richness determination in wetland habitats such as ponds, bogs or mires remain largely unrefined. 2. Techniques for estimation of total richness of an assemblage based upon replicated sampling offer the opportunity to derive useful estimates of total richness based upon small numbers of samples, and limit sampling‐derived disturbance which can be particularly problematic in small aquatic habitats. 3. We quantified the performance of eight of the most commonly encountered estimators of species richness for a variety of littoral zone macrofauna from ponds, comparing estimated richness to maximum richness derived from sampling. 4. Estimates using non‐parametric techniques based on species incidence provided the most accurate and precise estimates. The estimators Chao 2 and incidence‐based coverage estimator (ICE) from this category were reliable and consistent slight over‐estimators; the abundance‐based estimator Chao1 also performed well. 5. Species inventory based on relatively small numbers of samples might be significantly improved by use of non‐parametric estimators for quantification of species richness. 6. Use of non‐parametric estimators of species richness can assist biodiversity inventory by preventing erroneous rankings of habitat richness based upon observed species numbers from limited sampling.     

Evaluating the performance of species richness estimators: sensitivity to sample grain size

1. Fifteen species richness estimators (three asymptotic based on species accumulation curves, 11 nonparametric, and one based in the species-area relationship) were compared by examining their performance in estimating the total species richness of epigean arthropods in the Azorean Laurisilva forests. Data obtained with standardized sampling of 78 transects in natural forest remnants of five islands were aggregated in seven different grains (i.e. ways of defining a single sample): islands, natural areas, transects, pairs of traps, traps, database records and individuals to assess the effect of using different sampling units on species richness estimations. 2. Estimated species richness scores depended both on the estimator considered and on the grain size used to aggregate data. However, several estimators (ACE, Chao 1, Jackknifel and 2 and Bootstrap) were precise in spite of grain variations. Weibull and several recent estimators [proposed by Rosenzweig et al. (Conservation Biology, 2003, 17, 864-874), and Ugland et al. (Journal of Animal Ecology, 2003, 72, 888-897)] performed poorly. 3. Estimations developed using the smaller grain sizes (pair of traps, traps, records and individuals) presented similar scores in a number of estimators (the above-mentioned plus ICE, Chao2, Michaelis-Menten, Negative Exponential and Clench). The estimations from those four sample sizes were also highly correlated. 4. Contrary to other studies, we conclude that most species richness estimators may be useful in biodiversity studies. Owing to their inherent formulas, several nonparametric and asymptotic estimators present insensitivity to differences in the way the samples are aggregated. Thus, they could be used to compare species richness scores obtained from different sampling strategies. Our results also point out that species richness estimations coming from small grain sizes can be directly compared and other estimators could give more precise results in those cases. We propose a decision framework based on our results and on the literature to assess which estimator should be used to compare species richness scores of different sites, depending on the grain size of the original data, and of the kind of data available (species occurrence or abundance data).     

Evaluating outcomes of restoration ecology projects on limited budgets: assessment of variation in sampling intensity and sampling frequency for four habitat types

While best practices for evaluating restoration ecology projects are emerging rapidly, budget constraints often limit postrestoration monitoring, which emphasizes the need for practical and efficient monitoring strategies. We examined the postrestoration outcome for an ENGO (Nature Conservancy of Canada) project, to assess retroactively how variation in intensity and frequency of sampling would have affected estimates of plant species composition, diversity, and richness over time. The project restored four habitat types (mesic forest, oak woodland, wet meadow, and sand barren) using sculptured seeding of tallgrass prairie and woody species. Species‐level plant cover was monitored annually for 10 years in 168 2 × 2–m quadrats. We performed randomization tests to examine estimates of species diversity and richness as a function of the number of quadrats sampled, and assessed the necessity of annual sampling for describing changes in species composition and successional trajectories. The randomization tests revealed that sampling 10–17 quadrats, depending on habitat type, was sufficient to obtain estimates of species diversity that were at least 95% of values obtained from the whole dataset. Species richness as a function of number of quadrats sampled did not plateau, which suggests that rather than increasing the number of sampling quadrats, richness could be estimated more efficiently using nonquadrat based sampling techniques. Nonmetric multidimensional scaling analysis revealed that plant species composition largely stabilized by 3–5 years postrestoration depending on habitat type. By that time, native, seeded species dominated the restoration, and the benefits of annual sampling for tracking changes in species composition diminished.     

Sampling termites in forest habitats: A reply to Roisin and Leponce

Abstract To characterize the structure and species density of termite assemblages in tropical forests, we developed a sampling protocol based on a single large quadrat (belt transect) that standardises sampling effort and area. Emphasizing the estimation of species richness, Roisin and Leponce (2004, Austral Ecology, 29 : 637–46) recommend sampling numerous small quadrats, and varying the number of quadrats depending on local species density. However, their method would result in the loss of standardisation and speed, taking up to four times longer to collect and process the samples. We show that even for a subtropical forest with low species density, our protocol produces robust results.     

Application of species richness estimators for the assessment of fungal diversity

Species richness and distribution patterns of wood-inhabiting fungi and mycetozoans (slime moulds) were investigated in the canopy of a Central European temperate mixed deciduous forest. Species richness was described with diversity indices and species-accumulation curves. Nonmetrical multidimensional scaling was used to assess fungal species composition on different tree species. Different species richness estimators were used to extrapolate species richness beyond our own data. The reliability of the abundance-based coverage estimator, Chao, Jackknife and other estimators of species richness was evaluated for mycological surveys. While the species-accumulation curve of mycetozoans came close to saturation, that of wood-inhabiting fungi was continuously rising. The Chao 2 richness estimator was considered most appropriate to predict the number of species at the investigation site if sampling were continued. Gray's predictor of species richness should be used if statements of the number of species in larger areas are required. Multivariate analysis revealed the importance of different tree species for the conservation and maintenance of fungal diversity within forests, because each tree species possessed a characteristic fungal community. The described mathematical approaches of estimating species richness possess great potential to address fungal diversity on a regional, national, and global scale.     

Six years of submerged plant community dynamics in a freshwater tidal wetland

1. The dynamics of a submerged plant community were studied for 6 years in a freshwater tidal wetland. The degree and nature of change at several spatial scales (quadrat, transect and overall community) was determined, and the implications for community stability were assessed. 2. A high degree of change was recorded in 1 m² quadrats, and this was reflected in 10 m² transects as well. In quadrats, mean species richness changed every year. Species richness changed in >60% of quadrats each year. Stem number changed by as many as several 100 stems per quadrat from one year to the next. 3. Richness varied more among quadrats than among transects and varied less at the community level than among either quadrats or transects. Greater stability at the spatial scale of the whole community was reflected in high scores on the Jaccard and Morasita–Horn indices and Kendall's coefficient of concordance. 4. Although most of the submerged species were perennials, persistence at the local scale was low, and 4‐year persistence exceeded 50% for only one species. Change in abundance was largely independent among the species. 5. In the face of great small‐scale changes, species remain in the community (and the community persists) because of high recruitment rates.     

The ‘standardized search’: An improved way to conduct bird surveys

Abstract Bird surveys are among the most widely used biodiversity inventories and serve as the basis for an increasing proportion of pure and applied ecological research. It is rarely possible to conduct exhaustive censuses of all individuals present at a particular site, so stopping rules are routinely used to determine when sampling should finish. Most bird survey methods use (implicit) effort‐based stopping rules, either fixed times, fixed sampling areas (quadrats) or both, to standardize samples of different sites. If between‐site variation is high, however, a fixed sampling effort will generate samples of variable completeness with samples from smaller, less complex sites being more representative and complete than samples from larger, more complex sites. More importantly, quadrat‐based methods shift the scope of the overall study from bird occurrence in sites to bird occurrence in quadrats within sites, diminishing the impact of the research given that results cannot be extrapolated to relevant biological and management scales. Here I advocate an alternative means of conducting bird surveys, whereby the entire site is sampled and a results‐based stopping rule is used to ensure sample completeness is uniform across all sites. For example, a researcher may decide to continue sampling each site until two or fewer previously unencountered species are recorded in a 40‐min period. Samples of different sites will vary in both area and duration but will all be equivalently accurate estimates of species richness. This approach allows the avifauna of entire sites (whether territories, woodland remnants or catchments) to be sampled and compared directly, generating results and implications at the appropriate scale. In addition to yielding reliable measures of species richness, data collected this way can be used to calculate estimates of sample completeness and species incidence, two valuable metrics for ecological studies. This paper includes detailed worked examples of how to conduct a ‘standardized search’ and calculate sample completeness and species incidence estimates. I encourage further research on bird survey methods, and suggest that most current methods are insufficient, inconsistent and unreliable.     

Nonparametric Lower Bounds for Species Richness and Shared Species Richness under Sampling without Replacement

Summary A number of species richness estimators have been developed under the model that individuals (or sampling units) are sampled with replacement. However, if sampling is done without replacement so that no sampled unit can be repeatedly observed, then the traditional estimators for sampling with replacement tend to overestimate richness for relatively high-sampling fractions (ratio of sample size to the total number of sampling units) and do not converge to the true species richness when the sampling fraction approaches one. Based on abundance data or replicated incidence data, we propose a nonparametric lower bound for species richness in a single community and also a lower bound for the number of species shared by multiple communities. Our proposed lower bounds are derived under very general sampling models. They are universally valid for all types of species abundance distributions and species detection probabilities. For abundance data, individuals' detectabilities are allowed to be heterogeneous among species. For replicated incidence data, the selected sampling units (e.g., quadrats) need not be fully censused and species can be spatially aggregated. All bounds converge correctly to the true parameters when the sampling fraction approaches one. Real data sets are used for illustration. We also test the proposed bounds by using subsamples generated from large real surveys or censuses, and their performance is compared with that of some previous estimators.     

Time and space in the community structure of a species-rich limestone grassland

Abstract. The community structure of a species-rich grassland was investigated at a small spatial scale (0.001 m²), to determine whether evidence suggesting assembly rules could be found in temporal or spatial variation in either species richness or guild proportions. The community was alvar limestone grassland on the island of Öland, Sweden. Three sites were sampled: two lightly grazed, the other recently ungrazed. Plots with and without fertilizer were compared. Evidence was sought for restriction on the ability of species to co-occur within a limited spatial area. Restriction due to a limited number of niches available,‘niche limitation’, could be manifest as lower variance in quadrat richness than expected under a null model (i.e. RV_r, the ratio of observed: expected variance in richness, would be < 1.0). In several cases, RV_r values were significantly < 1.0, even using a patch model to allow for possible spatial variation in the environment. Low RV_r values were found only at the smallest square quadrat size, 10 cm². On Fertilized plots in the years immediately after application of fertilizer, low RV_r could not be demonstrated. Explanations of low RV_r other than niche limitation are considered, such as environmental heterogeneity (present and/or historical) and limitations to the co-occurrence of individual plant modules. Assembly rules based on guild membership were sought by looking at the variance across quadrats in the proportions of species from morphological guilds. An assembly rule would be seen as relatively constant proportion, estimated via RV_gp, the ratio of observed: expected variances in guild proportions. Significant guild proportionality was found in some cases. There was no evidence of guild proportionality in the years after the application of fertilizer. The significant effects in RV_r were more numerous than expected on a random basis, though not observed in every site in every year. Similar trends were seen in RV_gp. At the space/time scales examined, the species in a plant community may be constrained by assembly rules only intermittently, e.g. when resources are more limiting (Wiens 1977). Under this concept, when competition is relaxed, such as following fertilizer application, there is a temporary microhabitat ‘waterhole’ in which more species can coexist, and the assembly rules break down, at least temporarily whilst the species composition adjusts. There was some indication of a return to more deterministic community structure four years after fertilization commenced. Variants of van der Maarel's Carousel model were tested. A Niche-limited Carousel Model (i.e. a model in which there is some limitation in the number of species that can occupy a microsite) would imply restricted variation in richness through time for a single quadrat (temporal RV_r). Overall differences between years in species richness were demonstrated, and their effect removed; after this adjustment there was support for the Niche-limited Carousel Model. The extent of this limitation varied between sites. There were also consistent differences between quadrats in species richness. There was little evidence for constancy of guild proportions through time. The site that showed the strongest community structure in time and space, least year-to-year variation in mean species richness, and least response to fertilizer perturbation, is that on the shallowest soil. Possibly the thin soil results in greater resource limitation, supporting suggestions that assembly rules are stronger when resources are more limited.