Rarefaction and extrapolation of species richness using an area-based Fisher's logseries

Exploring intrinsic distribution of phytoplankton relative abundance and biomass in combination with continental-scale field investigation and microcosm experiment

Phytoplankton are primary producers in aquatic ecosystems and their diversity directly affects the community stability and primary productivity. However, the commonly used diversity indices (such as Shannon and Pielou indices) were originally derived from other fields rather than ecology and did not have a direct biological explanatory function. There is still a need to incorporate biological explanatory functions into diversity evaluation methods and theories to bridge the gap between phytoplankton biodiversity and biological characteristics. This study aimed to explicate the intrinsic distribution patterns of phytoplankton relative abundance and biomass. Our study demonstrated an exponential distribution pattern of phytoplankton relative abundance and biomass ranking through field investigations of 367 phytoplankton samples in China and microcosm experiments, respectively. Microcosm experiments illustrated that the linear distribution of the specific growth rate ranking resulted in an exponential distribution of the relative phytoplankton biomass ranking due to exponential growth patterns. Through mathematical deduction, it was found that the three indices a, k and N in the exponential distribution could be considered as the critical relative abundance of extinction, competition coefficient and the environmental taxa capacity, respectively. We found that a was positively correlated with Shannon index and Pielou index, k was negatively correlated with Shannon index, Pielou index and Chao1 index. In addition, N and Chao1 index were almost exactly the same. Our study obtained these indices based on the distribution pattern of phytoplankton, enabling a comprehensive analysis of the phytoplankton community and providing novel insights for further evaluating the health of aquatic ecosystems.

Analysis of the bacterial and fungal populations in South African sorghum beer (umqombothi) using full-length 16S rRNA amplicon sequencing

There is a need to profile microorganisms which exist pre-and-post-production of umqombothi, to understand its microbial diversity and the interactions which subsequently influence the final product. Thus, this study sought to determine the relative microbial abundance in umqombothi and predict the functional pathways of bacterial and fungal microbiota present. Full-length bacterial 16S rRNA and internal transcribed spacer (ITS) gene sequencing using PacBio single-molecule, real-time (SMRT) technology was used to assess the microbial compositions. PICRUSt2 was adopted to infer microbial functional differences. A mixture of harmful and beneficial microorganisms was observed in all samples. The microbial diversity differed significantly between the mixed raw ingredients (MRI), customary beer brew (CB), and optimised beer brew (OPB). The highest bacterial species diversity was observed in the MRI, while the highest fungal species diversity was observed in the OPB. The dominant bacterial species in the MRI, CB, and OPB were Kosakonia cowanii, Apilactobacillus pseudoficulneus, and Vibrio alginolyticus, respectively, while the dominant fungal species was Apiotrichum laibachii. The predicted functional annotations revealed significant (p < 0.05) differences in the microbial pathways of the fermented and unfermented samples. The most abundant pathways in the MRI were the branched-chain amino acid biosynthesis super pathway and the pentose phosphate pathway. The CB sample was characterised by folate (vitamin B9) transformations III, and mixed acid fermentation. Biotin (vitamin B7) biosynthesis I and L-valine biosynthesis characterised the OPB sample. These findings can assist in identifying potential starter cultures for the commercial production of umqombothi. Specifically, A. pseudoficulneus can be used for controlled fermentation during the production of umqombothi. Likewise, the use of A. laibachii can allow for better control over the fermentation kinetics such as carbohydrate conversion and end-product characteristics, especially esters and aroma compounds.

An Overview of Modern Applications of Negative Binomial Modelling in Ecology and Biodiversity

Negative binomial modelling is one of the most commonly used statistical tools for analysing count data in ecology and biodiversity research. This is not surprising given the prevalence of overdispersion (i.e., evidence that the variance is greater than the mean) in many biological and ecological studies. Indeed, overdispersion is often indicative of some form of biological aggregation process (e.g., when species or communities cluster in groups). If overdispersion is ignored, the precision of model parameters can be severely overestimated and can result in misleading statistical inference. In this article, we offer some insight as to why the negative binomial distribution is becoming, and arguably should become, the default starting distribution (as opposed to assuming Poisson counts) for analysing count data in ecology and biodiversity research. We begin with an overview of traditional uses of negative binomial modelling, before examining several modern applications and opportunities in modern ecology/biodiversity where negative binomial modelling is playing a critical role, from generalisations based on exploiting its Poisson-gamma mixture formulation in species distribution models and occurrence data analysis, to estimating animal abundance in negative binomial N-mixture models, and biodiversity measures via rank abundance distributions. Comparisons to other common models for handling overdispersion on real data are provided. We also address the important issue of software, and conclude with a discussion of future directions for analysing ecological and biological data with negative binomial models. In summary, we hope this overview will stimulate the use of negative binomial modelling as a starting point for the analysis of count data in ecology and biodiversity studies.

Emergent Rarity Properties in Carabid Communities From Chinese Steppes With Different Climatic Conditions

Species abundance distributions (SADs) are increasingly used to investigate how species community structure changes in response to environmental variations. SAD models depict the relative abundance of species recorded in a community and express fundamental aspects of the community structure, namely patterns of commonness and rarity. However, the influence of differences in environmental conditions on SAD characteristics is still poorly understood. In this study we used SAD models of carabid beetles (Coleoptera: Carabidae) in three grassland ecosystems (desert, typical, and meadow steppes) in China. These ecosystems are characterized by different aridity conditions, thus offering an opportunity to investigate how SADs are influenced by differences in environmental conditions (mainly aridity and vegetation cover, and hence productivity). We used various SAD models, including the meta-community zero sum multinomial (mZSM), the lognormal (PLN) and Fisher’s logseries (LS), and uni- and multimodal gambin models. Analyses were done at the level of steppe type (coarse scale) and for different sectors within the same steppe (fine scale). We found that the mZSM model provided, in general, the best fit at both analysis scales. Model parameters were influenced by the scale of analysis. Moreover, the LS was the best fit in desert steppe SAD. If abundances are rarefied to the smallest sample, results are similar to those without rarefaction, but differences in models estimates become more evident. Gambin unimodal provided the best fit with the lowest α-value observed in desert steppe and higher values in typical and meadow steppes, with results which were strongly affected by the scale of analysis and the use of rarefaction. Our results indicate that all investigated communities are adequately modeled by two similar distributions, the mZSM and the LS, at both scales of analyses. This indicates (1) that all communities are characterized by a relatively small number of species, most of which are rare, and (2) that the meta-communities at the large scale maintain the basic SAD shape of the local communities. The gambin multimodal models produced exaggerated α-values, which indicates that they overfit simple communities. Overall, Fisher’s α, mZSM θ, and gambin α-values were substantially lower in the desert steppe and higher in the typical and meadow steppes, which implies a decreasing influence of environmental harshness (aridity) from the desert steppe to the typical and meadow steppes.

Extinction debt in local habitats: quantifying the roles of random drift, immigration and emigration

We developed a time-dependent stochastic neutral model for predicting diverse temporal trajectories of biodiversity change in response to ecological disturbance (i.e. habitat destruction) and dispersal dynamic (i.e. emigration and immigration). The model is general and predicts how transition behaviours of extinction may accumulate according to a different combination of random drift, immigration rate, emigration rate and the degree of habitat destruction. We show that immigration, emigration, the areal size of the destroyed habitat and initial species abundance distribution (SAD) can impact the total biodiversity loss in an intact local area. Among these, the SAD plays the most deterministic role, as it directly determines the initial species richness in the local target area. By contrast, immigration was found to slow down total biodiversity loss and can drive the emergence of species credits (i.e. a gain of species) over time. However, the emigration process would increase the extinction risk of species and accelerate biodiversity loss. Finally but notably, we found that a shift in the emigration rate after a habitat destruction event may be a new mechanism to generate species credits.

Evaluation of the estimate bias magnitude of the Rao's quadratic diversity index

Rao’s quadratic diversity index is one of the most widely applied diversity indices in functional and phylogenetic ecology. The standard way of computing Rao’s quadratic diversity index for an ecological assemblage with a group of species with varying abundances is to sum the functional or phylogenetic distances between a pair of species in the assemblage, weighted by their relative abundances. Here, using both theoretically derived and observed empirical datasets, we show that this standard calculation routine in practical applications will statistically underestimate the true value, and the bias magnitude is derived accordingly. The underestimation will become worse when the studied ecological community contains more species or the pairwise species distance is large. For species abundance data measured using the number of individuals, we suggest calculating the unbiased Rao’s quadratic diversity index.

Estimating species pools for a single ecological assemblage

BACKGROUND

The species pool concept was formulated over the past several decades and has since played an important role in explaining multi-scale ecological patterns. Previous statistical methods were developed to identify species pools based on broad-scale species range maps or community similarity computed from data collected from many areas. No statistical method is available for estimating species pools for a single local community (sampling area size may be very small as ≤ 1 km²). In this study, based on limited local abundance information, we developed a simple method to estimate the area size and richness of a species pool for a local ecological community. The method involves two steps. In the first step, parameters from a truncated negative trinomial model characterizing the distributional aggregation of all species (i.e., non-random species distribution) in the local community were estimated. In the second step, we assume that the unseen species in the local community are most likely the rare species, only found in the remaining part of the species pool, and vice versa, if the remaining portion of the pool was surveyed and was contrasted with the sampled area. Therefore, we can estimate the area size of the pool, as long as an abundance threshold for defining rare species is given. Since the size of the pool is dependent on the rarity threshold, to unanimously determine the pool size, we developed an optimal method to delineate the rarity threshold based on the balance of the changing rates of species absence probabilities in the sampled and unsampled areas of the pool.

RESULTS

For a 50 ha (0.5 km²) forest plot in the Barro Colorado Island of central Panama, our model predicted that the local, if not regional, species pool for the 0.5 km² forest plot was nearly the entire island. Accordingly, tree species richness in this pool was estimated as around 360. When the sampling size was smaller, the upper bound of the 95% confidence interval could reach 418, which was very close to the flora record of tree richness for the island. A numerical test further demonstrated the power and reliability of the proposed method, as the true values of area size and species richness for the hypothetical species pool have been well covered by the 95% confidence intervals of the true values.

CONCLUSIONS

Our method fills the knowledge gap on estimating species pools for a single local ecological assemblage with little information. The method is statistically robust and independent of sampling size, as proved by both empirical and numerical tests.

Rarefaction and extrapolation of species richness using an area-based Fisher's logseries

Fisher's logseries is widely used to characterize species abundance pattern, and some previous studies used it to predict species richness. However, this model, derived from the negative binomial model, degenerates at the zero‐abundance point (i.e., its probability mass fully concentrates at zero abundance, leading to an odd situation that no species can occur in the studied sample). Moreover, it is not directly related to the sampling area size. In this sense, the original Fisher's alpha (correspondingly, species richness) is incomparable among ecological communities with varying area sizes. To overcome these limitations, we developed a novel area‐based logseries model that can account for the compounding effect of the sampling area. The new model can be used to conduct area‐based rarefaction and extrapolation of species richness, with the advantage of accurately predicting species richness in a large region that has an area size being hundreds or thousands of times larger than that of a locally observed sample, provided that data follow the proposed model. The power of our proposed model has been validated by extensive numerical simulations and empirically tested through tree species richness extrapolation and interpolation in Brazilian Atlantic forests. Our parametric model is data parsimonious as it is still applicable when only the information on species number, community size, or the numbers of singleton and doubleton species in the local sample is available. Notably, in comparison with the original Fisher's method, our area‐based model can provide asymptotically unbiased variance estimation (therefore correct 95% confidence interval) for species richness. In conclusion, the proposed area‐based Fisher's logseries model can be of broad applications with clear and proper statistical background. Particularly, it is very suitable for being applied to hyperdiverse ecological assemblages in which nonparametric richness estimators were found to greatly underestimate species richness.