An information-theoretical measure of taxonomic diversity

Traditional diversity indices are computed from the abundances of species present and are insensitive to taxonomic differences between species. However, a community in which most species belong to the same genus is intuitively less diverse than another community with a similar number of species distributed more evenly between genera. In this paper, we propose an information-theoretical measure of taxonomic diversity that reflects both the abundances and taxonomic distinctness of the species. Unlike previous measures of taxonomic diversity, such as Rao's quadratic entropy, in this new measure the analyzed taxonomic properties are associated with the single species instead of species pairs.     

Severe limitations of the FEve metric of functional evenness and some alternative metrics

The metric of functional evenness FEve is an example of how approaches to conceptualizing and measuring functional variability may go astray. This index has several critical conceptual and practical drawbacks:

1. Different values of the FEve index for the same community can be obtained if the species have unequal species abundances; this result is highly likely if most of the traits are categorical.
2. Very minor differences in even one pairwise distance can result in very different values of FEve.
3. FEve uses only a fraction of the information contained in the matrix of species distances. Counterintuitively, this can cause very similar FEve scores for communities with substantially different patterns of species dispersal in trait space.
4. FEve is a valid metric only if all species have exactly the same abundances. However, the meaning of FEve in such an instance is unclear as the purpose of the metric is to measure the variability of abundances in trait space.

We recommend not using the FEve metric in studies of functional variability. Given the wide usage of FEve index over the last decade, the validity of the conclusions based on those estimates is in question. Instead, we suggest three alternative metrics that combine variability in species distances in trait space with abundance in various ways. More broadly, we recommend that researchers think about which community properties (e.g., trait distances of a focus species to the nearest neighbor or all other species, variability of pairwise interactions between species) they want to measure and pick from among the appropriate metrics.     

On the relationship between Pielou’s evenness and landscape dominance within the context of Hill’s diversity profiles

Entropy-related biodiversity indices deriving their conceptual basis from Shannon’s information theory have a long history of use in ecology for quantifying community structure and diversity. In addition, in the last two decades, numerous information–theoretical indices, such as the landscape dominance index, have been extensively applied to characterize landscape diversity in space and time. In this contribution, we offer a simple analytical relation between Pielou’s evenness J and landscape dominance D within the broader context of Hill’s parametric diversity family. Within this context, we recommend the use of Hill’s diversity number evenness E_1,0 to overcome the shortcomings both of Pielou’s evenness J and the landscape dominance index D.     

Taking into account phylogenetic and divergence‐time uncertainty in a parametric biogeographical analysis of the Northern Hemisphere plant clade Caprifolieae

Aim To examine the biogeographical history of the angiosperm clade Caprifolieae (Caprifoliaceae) using parametric biogeographical reconstruction methods. The existing parametric method was extended to evaluate biogeographical reconstructions over the distribution of dated phylogenies. This method provides a framework for reconstructing large‐scale biogeography with parametric methods, while accounting for uncertainty in the phylogenetic relationships and divergence time. Location Asia, Europe and North America. Methods The biogeographical history of the major lineages of Caprifolieae was reconstructed over the posterior distribution of dated trees generated from Bayesian divergence‐time analyses. Results from a model with no geological constraints were compared with those from one where movement is disallowed across the North Atlantic after the Eocene. The most plausible scenarios were segregated at each node to test whether particular scenarios were reconstructed for particular divergence times. The parametric biogeographical method was also extended to estimate connectivity between areas so that the probability of dispersal between the major areas of the Northern Hemisphere could be explored. Results Phylogenetic results for Caprifolieae agreed with previous estimates using smaller sampling, but uncertainty remained despite efforts to resolve the relationships of the four genera within this clade using multiple markers. In addition to topological uncertainty, there were few fossils available for calibrations, resulting in large confidence intervals for divergence times. Divergence‐time analyses put the diversification of Caprifolieae at between 36 and 51 Ma and showed that Caprifolieae probably originated in Asia, with multiple movements into Europe and western and eastern North America. Main conclusions Newly developed parametric methods for biogeographical reconstruction incorporate more data and better models. Here, the parametric biogeographical reconstruction method has been extended to allow for topological and divergence‐time uncertainty. The analyses of Caprifolieae demonstrated that biogeographical hypotheses can be explored even where there are large confidence intervals on divergence times and uncertainty in topology. These results add to the growing evidence that Asia was an important source of Northern Hemisphere diversity throughout the Cenozoic.     

高寒草甸种间性状差异和物种均匀度对物种多样性与功能多样性关系的影响

物种多样性(SD)与功能多样性(FD)之间存在多种关系,但由于生态系统功能主要由物种的功能属性决定,因而功能多样性对生态系统功能的影响大于物种多样性的影响。但在种间性状差异和物种均匀度这两个构成功能多样性的基本成分中,何者对功能多样性影响更大,并进而决定SD-FD关系尚不明确。通过在高寒矮嵩草(Kobresia humilis)草甸为期6a的刈割(留茬1 cm、3 cm及不刈割)和施肥(尿素7.5 g m~(-2)a~(-1)+磷酸二胺1.8 g m~(-2)a~(-1)、不施肥)控制实验,研究了种间性状差异(33个物种13个性状)和物种均匀度(所有物种)对物种多样性(所有物种)与功能多样性(33个物种13个性状)之间关系的影响。研究结果显示:(1)物种多样性与功能多样性正相关,它们与多性状种间差异负相关,而与物种均匀度正相关。物种均匀度是导致功能多样性变化的主要因素,也是导致SD-FD正相关的原因,这是因为随着物种多样性增加,物种均匀度的增加程度大于多性状种间差异的减少程度,因而功能多样性增加,SD-FD正相关;(2)功能多样性指数(FD_(Rao)和FDis)随物种多样性指数(H')减速递增,表明群落存在一定的功能冗余,且功能冗余随物种多样性的增大而增大,但尚未达到产生SD-FD无相关性的极限H'值;(3)功能多样性对高寒草甸生态系统地上净初级生产力(ANPP)的影响大于物种多样性的影响,二元线性回归显示在同时考虑二者对ANPP的影响时,可排除物种多样性的作用。但由于物种多样性下降或物种丧失引起的物种功能性状丢失或性状空间维度减小将导致功能多样性降低,表明它们之间存在一定互补性,在研究生物多样性与生态系统功能关系时,同时考虑物种多样性和功能多样性的影响仍十分必要。     

On the fundamental nature of perception

The process of recognition or isolation of one or several entities from among many possible entities is termed intellego perception. It is shown that not only are many of our everyday percepts of this type, but perception of microscopic events using the methods of quantum mechanics are also intellego in nature. Information theory seems to be a natural language in which to express perceptual activity of this type. It is argued that the biological organism quantifies its sensations using an information theoretical measure. This, in turn, sets the stage for a mathematical theory of sensory perception.     

Additive partition of parametric information and its associated beta-diversity measure

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type . In this way, a parametric measure of -diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's -diversity for data on species relative abundances.     

On the interrelationship of permeability and structural parameters of vertebral trabecular bone: a parametric computational study

To characterise the flow of a fluid through a uniform porous medium, the medium may be completely described by its permeability, a measure of flow resistance. Fluid flow in the intertrabecular spaces of cancellous bone has been recognised as an important factor in a number of physical phenomena. In order to investigate the interdependence of permeability, porosity and the structural parameters, we adapted a morphological model and systematically varied its structural parameters. By simulating a viscous Stokes flow regime, we were able to estimate the anisotropic permeability tensor and performed an extensive, stepwise multivariate regression analysis to establish empirical relationships between the morphological parameters and the permeability for the anatomical directions individually. The regression analysis indicated high values of determination coefficients [0.88 < R² < 0.89 (transversal directions) and R² = 0.60 (longitudinal direction), porosity-based prediction and R² = 0.98 for all directions and information presented to the regression model]. We conclude that a pooled set of structural parameters may explain up to 98% of the permeability variability, the regression model predicts permeability values that match experimental data, and a good prediction performance could be achieved by only incorporating the porosity and either the degree of anisotropy (0.89 < R² < 0.91) or the trabecular spacing predictor (0.96 < R² < 0.97). These conclusions imply that trabecular thickness and shape parameters only play a minor role in the determination of vertebral trabecular bone permeability. However, a major limitation of the model is that it reflects an idealisation of the real, regionally varying structure of trabecular bone. Therefore, the goodness-of-fit estimates we are presenting should be considered as an upper bound limitation regarding the prediction performance.     

Changes in the diversity structure of avian assemblages in North America

Aim To determine the major patterns of change in avian diversity structure over space and time at a local resolution and continental extent in non‐urban areas in North America. Location The contiguous United States and southern Canada. Methods We used 1673 North American Breeding Bird Survey (BBS) routes containing 547 terrestrial and aquatic species to estimate four diversity components: species richness, individual abundance, taxonomic distinctness and species evenness. We implemented three levels of analysis to examine changes in diversity structure on a yearly basis from 1968 to 2003: (1) a canonical analysis of discriminance, (2) a univariate analysis across BBS routes, and (3) a univariate analysis at individual BBS routes. We estimated changes in similarity in species composition over time between 470,730 BBS route pairs. We also estimated the level of human activity at BBS routes using three spatial anthropogenic databases. Results BBS routes were located in non‐urban areas in association with low nighttime light activity and moderately low human population densities. The analysis of diversity structure indicated the presence of two independent patterns: (1) a temporally consistent pattern defined by increasing species richness (12% increase from 1968 to 2003) associated with limited gains in taxonomic distinctness, and (2) an association between species abundance and evenness related to variability in abundance associated with the most abundant species. The similarity analysis indicated that BBS routes located closer to the Atlantic and the Pacific coasts of the United States experienced the strongest patterns of homogenization of species composition. Main conclusions Our results suggest that avian diversity structure has changed at the local scale in non‐urban areas in North America. However, there was no evidence for a consistent continent‐wide pattern. Instead, the evidence pointed to the presence of regional factors influencing diversity patterns. This study provides a foundation for more detailed investigations of the spatiotemporal and taxonomic details of these general patterns.     

Geographic isolation and climate govern the functional diversity of native fish communities in European drainage basins

Aim In times of biodiversity crisis, it is extremely important to understand diversity gradients. In particular, the study of the diversity of ecological functions is a key issue for the management of ecosystem integrity. Here we identify areas of low functional diversity of the native fish fauna in European drainage basins and we determine the relative importance of three underlying mechanisms: environmental filtering, geographic isolation and climatic history. Location The European continent. Methods Based on 14 morphological traits that are closely related to fish function (habitat and dietary niches), three independent functional diversity indices [functional richness (FR), functional evenness (FE), functional divergence (FD)] were calculated for 128 European drainage basins with a total of 230 fish species. The indices were standardized for species richness using null models. The patterns of the standardized indices are described and three potentially underlying mechanisms are tested using variance partitioning and multi‐linear regression models. Results FR and FD were highest in eastern European drainage basins and in Great Britain and lowest in the Mediterranean. FE patterns were less pronounced. All observed patterns were mainly governed by geographic isolation and present environmental conditions. Within the environmental conditions, average annual temperature and precipitation were good predictors for functional diversity. The role of habitat diversity and size was negligible. Main conclusions Geographic isolation coupled with harsh environmental conditions such as extreme temperatures and low precipitation, as in Mediterranean regions, can lead to low FR and FD. This can be explained by extinction that could not be compensated by re‐colonization and high speciation. Due to their high functional redundancy, communities in these areas might better withstand further species extinctions on a small scale. Over the short term, however, their often extremely low FR suggests a less flexible functioning that can hinder their ability to withstand today's rapid environmental and anthropogenic threats.     

An evaluation of new parsimony‐based versus parametric inference methods in biogeography: a case study using the globally distributed plant family Sapindaceae

Aim Recently developed parametric methods in historical biogeography allow researchers to integrate temporal and palaeogeographical information into the reconstruction of biogeographical scenarios, thus overcoming a known bias of parsimony‐based approaches. Here, we compare a parametric method, dispersal–extinction–cladogenesis (DEC), against a parsimony‐based method, dispersal–vicariance analysis (DIVA), which does not incorporate branch lengths but accounts for phylogenetic uncertainty through a Bayesian empirical approach (Bayes‐DIVA). We analyse the benefits and limitations of each method using the cosmopolitan plant family Sapindaceae as a case study. Location World‐wide. Methods Phylogenetic relationships were estimated by Bayesian inference on a large dataset representing generic diversity within Sapindaceae. Lineage divergence times were estimated by penalized likelihood over a sample of trees from the posterior distribution of the phylogeny to account for dating uncertainty in biogeographical reconstructions. We compared biogeographical scenarios between Bayes‐DIVA and two different DEC models: one with no geological constraints and another that employed a stratified palaeogeographical model in which dispersal rates were scaled according to area connectivity across four time slices, reflecting the changing continental configuration over the last 110 million years. Results Despite differences in the underlying biogeographical model, Bayes‐DIVA and DEC inferred similar biogeographical scenarios. The main differences were: (1) in the timing of dispersal events – which in Bayes‐DIVA sometimes conflicts with palaeogeographical information, and (2) in the lower frequency of terminal dispersal events inferred by DEC. Uncertainty in divergence time estimations influenced both the inference of ancestral ranges and the decisiveness with which an area can be assigned to a node. Main conclusions By considering lineage divergence times, the DEC method gives more accurate reconstructions that are in agreement with palaeogeographical evidence. In contrast, Bayes‐DIVA showed the highest decisiveness in unequivocally reconstructing ancestral ranges, probably reflecting its ability to integrate phylogenetic uncertainty. Care should be taken in defining the palaeogeographical model in DEC because of the possibility of overestimating the frequency of extinction events, or of inferring ancestral ranges that are outside the extant species ranges, owing to dispersal constraints enforced by the model. The wide‐spanning spatial and temporal model proposed here could prove useful for testing large‐scale biogeographical patterns in plants.     

When cooperation begets cooperation: the role of key individuals in galvanizing support

Life abounds with examples of conspecifics actively cooperating to a common end, despite conflicts of interest being expected concerning how much each individual should contribute. Mathematical models typically find that such conflict can be resolved by partial-response strategies, leading investors to contribute relatively equitably. Using a case study approach, we show that such model expectations can be contradicted in at least four disparate contexts: (i) bi-parental care; (ii) cooperative breeding; (iii) cooperative hunting; and (iv) human cooperation. We highlight that: (a) marked variation in contributions is commonplace; and (b) individuals can often respond positively rather than negatively to the contributions of others. Existing models have surprisingly limited power in explaining these phenomena. Here, we propose that, although among-individual variation in cooperative contributions will be influenced by differential costs and benefits, there is likely to be a strong genetic or epigenetic component. We then suggest that selection can maintain high investors (key individuals) when their contributions promote support by increasing the benefits and/or reducing the costs for others. Our intentions are to raise awareness in—and provide testable hypotheses of—two of the most poorly understood, yet integral, questions regarding cooperative ventures: why do individuals vary in their contributions and when does cooperation beget cooperation?     

On the Equivalence of the Information-Theoretic Transmission-Measure to the Common χ2 Statistic

The results of a simulation study are presented in which the χ²-and the information theoretic approach to association measurement were compared to one another. It could be shown that neither the maximal values nor the minimal values obtainable for a given sample size coincide in all cases. The underlying association concepts are defined; implications are discussed.     

On the evolution of delayed recruitment to food bonanzas

Whereas food sharing by immediate recruitment to food bonanzasis relatively common, especially among birds, delayed recruitmentfrom overnight roosts is comparatively rare, although it hasbeen studied extensively in the common raven (Corvus corax).Two hypotheses have been advanced to explain the evolution ofdelayed recruitment. Under the status-enhancement hypothesis,delayed recruiting is favored because the recruiter's social statusincreases with the number of followers it leads to a food source.The posse hypothesis also focuses on the number of individualsrecruited to a site, but in this case aggregation is favoredbecause larger groups are more likely to usurp a carcass defendedby a pair of territorial adult ravens. We used a game-theoreticmodel to explore the logic of immediate versus delayed recruitmentin the light of these hypotheses. In particular, we identified threecritical values of the probability of immediate recruitment:that below which delayed recruitment is a cooperative strategy,that below which delayed recruitment is an evolutionarily stablestrategy, and that below which a mutant strategy of delayedrecruitment will invade a population of immediate recruitersto reach fixation. The model demonstrates that either status enhancementor the posse effect may alone suffice for the evolution of delayed recruitmentto food bonanzas via mutualistic information sharing at communal roosts.