Random Placement Model Research Articles

Sars: an R package for fitting, evaluating and comparing species–area relationship models

The species–area relationship (SAR) constitutes one of the most general ecological patterns globally. A number of different SAR models have been proposed. Recent work has shown that no single model universally provides the best fit to empirical SAR datasets: multiple models may be of practical and theoretical interest. However, there are no software packages available that a) allow users to fit the full range of published SAR models, or b) provide functions to undertake a range of additional SAR‐related analyses. To address these needs, we have developed the R package ‘sars’ that provides a wide variety of SAR‐related functionality. The package provides functions to: a) fit 20 SAR models using non‐linear and linear regression, b) calculate multi‐model averaged curves using various information criteria, and c) generate confidence intervals using bootstrapping. Plotting functions allow users to depict and scrutinize the fits of individual models and multi‐model averaged curves. The package also provides additional SAR functionality, including functions to fit, plot and evaluate the random placement model using a species–sites abundance matrix, and to fit the general dynamic model of oceanic island biogeography. The ‘sars’ R package will aid future SAR research by providing a comprehensive set of simple to use tools that enable in‐depth exploration of SARs and SAR‐related patterns. The package has been designed to allow other researchers to add new functions and models in the future and thus the package represents a resource for future SAR work that can be built on and expanded by workers in the field.

English

English

Total volume of 3D small patch reefs reflected in aerial photographs can predict total species richness of coral reef damselfish assemblages on a shallow back reef

AbstractBecause fish have a high dispersal ability, an understanding coral reef fish metacommunity structure is vital for effective conservation. Coral reefs provide patchy habitat of various sizes and scales. We examined the species–area relationship (SAR) of damselfish (Pomacentridae) assemblages over 81 environmentally homogenous patch reefs ranging 0.07–45.4 m2 with low coral cover. Patch reefs were located in the shallow back reef (<2.5 m deep) off Ishigaki Island, Japan. Reef area was measured by performing image analysis of enlarged sections of a high‐resolution (>1/2500) color aerial photograph used as a fine‐scale seascape map. To assess the effects of three‐dimensional meso‐scale rugosity on species richness, we assumed that all reefs had a cylindrical shape and examined species by volume (area × height) relationships (SVR). Patch reef volume was a better determinant of species richness than area, and the regression functions of SVR provided better estimates of patch reef species richness. Neither the observed SVRs nor SARs, however, could be explained by a random placement model alone. Our results suggest that several small reefs are likely to have higher species richness than a single large reef of equivalent area in the shallow back reef where large patch reefs are flat. Thus, total patch reef volume (area × height) better reflects meso‐scale rugosity and is a useful indicator of total species richness relative to the total amount of essential habitat in shallow back reefs.

Exploring the spatially explicit predictions of the Maximum Entropy Theory of Ecology

AbstractAimThe maximum entropy theory of ecology (METE) is a unified theory of biodiversity that attempts to simultaneously predict patterns of species abundance, size and spatial structure. The spatial predictions of this theory have repeatedly performed well at predicting diversity patterns across scales. However, the theoretical development and evaluation of METE has focused on predicting patterns that ignore intersite spatial correlations. As a result the theory has not been evaluated using one of the core components of spatial structure. We develop and test a semi‐recursive version of the spatially explicit predictions of METE for the distance–decay relationship of community similarity and compare its performance with the classic random placement model of completely random species distributions. This provides a better understanding and stronger test of the spatial community predictions of METE.LocationNew World tropical and temperate plant communities.MethodsWe analytically derived and simulated the spatially explicit expectations of METE for the Sørensen index of community similarity. We then compared the distance–decay of community similarity of 16 mapped plant communities with METE and the random placement model.ResultsThe version of METE we examined was successful at capturing the general functional form of the observed distance–decay relationships, a negative power function relationship between community similarity and distance. However, the semi‐recursive approach consistently predicted lower intercepts and higher slopes than observed in the empirical distance–decay relationships and yielded worse predictions than the random placement model.Main conclusionsOur results suggest that while the current spatial models of METE accurately predict the spatial scaling of species occupancy, and therefore core ecological patterns like the species–area relationship, its semi‐recursive form does not accurately characterize spatially explicit patterns of correlation. More generally, this suggests that tests of spatial theories based only on the species–area relationship may appear to support the underlying theory despite significant deviations in important aspects of spatial structure.

Testing the influence of environmental heterogeneity on fish species richness in two biogeographic provinces.

Environmental homogenization in coastal ecosystems impacted by human activities may be an important factor explaining the observed decline in fish species richness. We used fish community data (>200 species) from extensive surveys conducted in two biogeographic provinces (extent >1,000 km) in North America to quantify the relationship between fish species richness and local (grain <10 km2) environmental heterogeneity. Our analyses are based on samples collected at nearly 800 stations over a period of five years. We demonstrate that fish species richness in coastal ecosystems is associated locally with the spatial heterogeneity of environmental variables but not with their magnitude. The observed effect of heterogeneity on species richness was substantially greater than that generated by simulations from a random placement model of community assembly, indicating that the observed relationship is unlikely to arise from veil or sampling effects. Our results suggest that restoring or actively protecting areas of high habitat heterogeneity may be of great importance for slowing current trends of decreasing biodiversity in coastal ecosystems.

A simple method for estimating species abundance from occurrence maps

Summary The issue of how to estimate species abundance from presence/absence maps has attracted much attention. Several methods have been developed to address this problem. However, those methods either overlook the structure of spatial autocorrelation of species distribution, thus leading to underestimation, or they demand extra information besides presence/absence maps. This study first developed a new method that takes account of spatial autocorrelation and only requires occurrence maps, without any extra information. This method was further improved by incorporating a correction factor to it. We used an index defined by joint counts of occupied and unoccupied cells to measure spatial autocorrelation and to correct the underestimation of the random placement model. The performance of our method was compared against four other major methods (random placement model, negative binomial model, Conlisk et al.'s method and Solow &amp; Smith's method) using both simulated and empirical data. The results showed that the performance of our method is comparable with other methods but requires less and readily obtained input data, a property important for real applications. We suggest this simple, data‐parsimonious method be a useful alternative to the currently available methods for estimating abundance from occurrence.

A novel photographic approach for monitoring the structural heterogeneity and diversity of grassland ecosystems

Aims Studies that investigate the space-filling heterogeneity of biological structures in plant communities remain scarce. The main objective of this study was to evaluate the relationship between newly developed photographic measures of structural heterogeneity in digital images and plant species composition in the context of a long-term grassland experiment. Methods We tested a close-range photographic protocol using measures of structural heterogeneity in gray-tone images, namely mean infor mation gain (MIG) and spatial anisotropy, to assess differences in the compositional (species richness) and functional characteristics (plant height and flowering) of 78 managed grassland communities. We also implemented a random placement model of community assembly to explore the links between our measures of structural complexity and the geometric pattern of plant communities. Important Findings MIG and spatial anisotropy correlated with the growth and species richness of grassland communities. Simulations showed that structural heterogeneity in gray-tone digital images is a function of the size distribution and orientation pattern of plant modules. This easy, fast and non-destructive methodological approach could eventually serve to monitor the diversity and integrity of various ecosystems at different resolutions across space and time.

Habitat use and coexistence of three territorial herbivorous damselfish on different-size patch reefs

In local reef fish communities, species richness increases with increasing reef area. At Ishigaki Island, Japan, species richness is much lower on large reefs in the shallow back reef than that expected from random placement model simulations (RPMS). As three aggressive territorial herbivorous damselfish, Stegastes nigricans, Stegastes lividus and Hemiglyphidodon plagiometopon, coexist only on such large reefs, we focused on these species and examined patterns of their distribution and abundance on 84 patch reefs of various sizes (area and height). We also examined their aggressive intra- and interspecific behavioural interactions and habitat use on the two large reefs (the largest complex patch reef and the large flat patch reef) among the 84 patch reefs. While the abundance of both S. lividus and H. plagiometopon was highly correlated with patch reef area, that of S. nigricans was closely correlated with patch reef height. For S. nigricans and S. lividus, interspecific interactions occurred significantly more frequently than intraspecific interactions on the large flat patch reef. However, there was no significant difference in frequencies of the two interaction types on the largest complex patch reef, where they three-dimensionally segregated conspecific territories. This study suggested that reef height as well as reef area influence the distribution and abundance of these territorial herbivorous damselfish in the shallow back reef. As large patch reefs cannot be tall allometrically in shallow back reefs, relatively flat patch reefs may not have the high species richness expected from RPMS based on reef area.

Vegetation Productivity/Stability and Other Possible Ecological Invariant Relationships Demonstrated in a Microplot Multispecies Pasture Sward

The relationship between vegetation functional characteristics of production, stability and descriptive characteristic of species diversity or dominance, and other possible compositional invariants were investigated in 2400 micro-plot sward of 20 species at randomly assigned positions and using different matrix sizes of adjacent plots and four harvest to derive a combination of “vegetations” of differing species configurations.Within the highest frequency section of the data there was little relationship between productivity and stability (deviance) and either species diversity or dominance (% contribution of 1st ranked species). However, considering all data, productivity increased with increasing dominance and was unrelated to species diversity, while stability increased with diversity. Of single parameters combining diversity and dominance, the gradient of the log abundance/rank relationship was superior to Shannon H, with both showing productivity increasing with dominance rather than diversity. The fate of individual micro-plots from a mixed species stand through successive harvests was consistent with the −3/2 thinning rule, though with species cumulative yields. The abundance/rank relationship was compared with many models. Where there was simultaneous fitting to both density and biomass relationships, self-thinning random particle packing models were best and offered an explanation of the process. The positive correlation between regional and local frequency was related to sample area in a random placement model. Observed species composition and mortality was simulated by consideration of plant size related growth and mortality, initial establishment, growth potential and variation in plant size.

Predicting species abundance distributions by simultaneously using number and biomass as units of measurement

AbstractThe universal observation that some species in an ecological community are common, but many more are rare, is neatly encapsulated in a species abundance distribution (SAD)1. However, the shape of the distribution can depend on the currency used to measure abundance 2. Here we show how the SADs for numerical abundance and biomass are related and how this relationship can be used to predict the form of the SAD. When plotted in log numerical abundance, log biomass space, species points lie within an approximately triangular area the limits of which are set by body size range, and the upper limit of abundance in both metrics. Under the simplifying, but reasonable, assumption that the observed scatter of species within this region is random, the shape of the SAD is immediately derived from simple geometrical considerations. For the SAD of numerical abundance this is a power curve. The biomass SAD can be either a power curve or, more frequently, a unimodal curve, which can approximate a log normal. This log triangular random placement model serves as a null hypothesis against which actual communities can be compared. Data from two intensively surveyed local communities indicate that it can give a good approximation, with species scattered within a triangle. Further, we can predict the consequences, for the SAD, of size-selective sampling protocols. We argue that mechanistic models of SADs must be able to account for the relative abundance of species in alternative currencies. Moreover, this approach will shed light on niche packing and may have application in environmental monitoring.

Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.

Optimal Methods for Proxy Placement in Coordinated En-Route Web Caching

The performance of en-route web caching mainly depends on where the caches are located and how the cache contents are managed. In this paper, we address the problem of proxy placement in en-route web caching for tree networks, i.e., computing the optimal locations for placing k web proxies in a network such that some specified objectives are achieved. Based on our proposed model, we formulate this problem as an optimization problem and compute the optimal locations using a computationally efficient dynamic programming-based algorithm. We also extend our solution for tree networks to solve the same problem for autonomous systems. Finally, we implement our algorithms and evaluate our model on several performance metrics through extensive simulation experiments. We also compare the performance of our model with the best available heuristic KMPC model, as well as the random proxy placement model. The implementation results show that our model outperforms all the other models with respect to all performance metrics considered. The average improvements of our model over the KMPC model and the random proxy placement model are about 31.9 percent and 58.6 percent in terms of all the performance metrics considered.

Differential responses of small mammals to fragmentation in a Thailand tropical forest

Fragmentation of tropical forests has wide-ranging effects on wildlife communities, but the actual mechanisms of species impoverishment remain poorly understood. Small mammal assemblages on recent land-bridge islands at Chiew Larn, Thailand, were compared with nearby continuous forest from the fifth to seventh years following island creation. Assemblages on islands rapidly developed a nested structure, converging in composition and representing a depauperate subset of those in continuous forest. Among species that persisted on islands, many had altered abundances, with some increasing and others declining. A “random placement model” accounted for the observed distributions of species on mainland sites but not on islands, suggesting that nested island assemblages were generated both by changes in species distributions and abundances after fragmentation. Six species were prone to extinction on islands, whereas three increased in abundance, apparently because they were good over-water colonizers or favored disturbed habitats on islands. We conclude that the development of nested mammal assemblages in the Chiew Larn archipelago was caused both by differential vulnerabilities of species to local extinction and by varying abilities of species to colonize islands and to thrive in disturbed island habitats.

Nested subset structure of larval mycophagous fly assemblages: nestedness in a non-island system.

Nested subset structure has been studied in archipelagoes and fragmented habitats, and has been attributed to differential colonization and extinction rates among species and nested environmental tolerances. In this experiment, we tested for nestedness in assemblages of mycophagous fly larvae. Twenty mushrooms in each of three size classes (4.8-6.0 g, 10-15 g, 21-32 g) were placed on moist potting soil in experimental cups. The cups were placed in oak and pine forests in Greenville, S.C., USA for 5 days, where they were available to ovipositing flies. Upon collection, the mushrooms were incubated in the laboratory for 3 weeks and all emerging flies were sorted by species, counted, and weighed. A random placement analysis was conducted to determine whether the species richness pattern was a sampling artifact of the species abundance distributions. The actual species richness pattern did not conform to the random placement model; most mushrooms contained significantly fewer species than predicted by random sampling. The communities were strongly nested as measured by two different indices, and the nestedness pattern was related to mushroom size. Small mushrooms usually produced no flies or a single species, Dohrniphora sp. (Phoridae). Medium and large mushrooms typically produced more species-rich communities that usually contained the phorid and Drosophila putrida, D. tripunctata, and Leucophenga varia. This core guild was nested within a more diverse assemblage that included D. falleni, Mycodrosophila dimidiata, a muscid, and two Leptocera sp. (sphaeroceridae). These patterns are tentatively explained in the context of nested desiccation tolerances, mediated by differences in mushroom size.

Database access path selection: A two step approach

In this paper, we develop an efficient two-step approach to database access path selection. In the first step, we use index threshold values to identify those queries for which index lookup is clearly the less expensive access path. For these queries, there is no need to estimate block selectivity, resulting in saving in processing cost. In the second step, we present a measure of clustering effect and empirically relate this measure to block selectivity. This method of estimating block selectivity can be performed much more quickly than the O( km) or O( m) flops required by some of the other approaches and relaxes a previous assumption that clusters are linearly ordered. In addition, its use does not hinge on particular assumptions of data distributions. We test this approach with a corporate file obtained from the COMPUSTAT database. The results of the test indicate that the approach leads to sound access path selections and is superior to the random placement model in estimating block selectivity.