Accurate mapping of species distributions is a fundamental goal of modern biogeography, both for basic and applied purposes. This is commonly done by plotting known species occurrences, expert-drawn range maps or geographical estimations derived from species distribution models. However, all three kinds of maps are implicitly subject to uncertainty, due to the quality and bias of raw distributional data, the process of map building, and the dynamic nature of species distributions themselves. Here we review the main sources of uncertainty suggesting a code of good practices in order to minimize their effects. Specifically, we claim that uncertainty should be always explicitly taken into account and we propose the creation of maps of ignorance to provide information on where the mapped distributions are reliable and where they are uncertain

Various ecological mechanisms influence the forms of species richness relationships (SRRs). These mechanisms can be gathered under five general categories: more individuals, environmental heterogeneity, dispersal limitations, biotic interactions, and multiple species pools. Often only the first two categories are discussed. In contrast, we examine all five and explore how they can influence the form of SRRs. We discuss how various sampling schemes and methods of SRR construction can be used to gain insight about how various processes influence species richness patterns. The field is ripe for probing these effects through more complex simulation models or more sophisticated mathematical approaches. To facilitate deeper understanding, we need to embrace the full spectrum of SRRs and reconsider the assumed common knowledge about the functional form of SRRs. The relationship between species richness and the space or time over which it is sampled has received increasing attention over the past decade, resulting in extensive debates about terminology and methods of construction. These debates reflect deep conceptual issues; to resolve them we discuss the long history of species richness relationships (SRRs) and the connections among different methodological and terminological approaches. We reinforce recent calls to organize the variety of methods used to construct SRRs into a cohesive structure. SRRs are descriptors of various aspects of inventory (α‐ and γ‐) diversity and the various types of SRRs serve different purposes. Contrary to most claims, SRRs do not provide a direct measure of differentiation (β‐) diversity.

The efficiency of four nonparametric species richness estimators first-order Jackknife, second-order Jackknife, Chao2 and Bootstrap was tested using simulated quadrat sampling of two field data sets (a sandy 'Dune' and adjacent 'Swale') in high diversity shrublands (kwongan) in south-western Australia. The data sets each comprised > 100 perennial plant species and > 10 000 individuals, and the explicit (x-y co-ordinate) location of every individual. We applied two simulated sampling strategies to these data sets based on sampling quadrats of unit sizes 1/400th and 1/100th of total plot area. For each site and sampling strategy we obtained 250 independent sample curves, of 250 quadrats each, and compared the estimators' performances by using three indices of bias and precision: MRE (mean relative error), MSRE (mean squared relative error) and OVER (percentage overestimation). The analysis presented here is unique in providing sample estimates derived from a complete, field-based population census for a high diversity plant community. In general the true reference value was approached faster for a comparable area sampled for the smaller quadrat size and for the swale field data set, which was characterized by smaller plant size and higher plant density. Nevertheless, at least 15-30% of the total area needed to be sampled before reasonable estimates of St (total species richness) were obtained. In most field surveys, typically less than 1% of the total study domain is likely to be sampled, and at this sampling intensity underestimation is a problem. Results showed that the second-order Jackknife approached the actual value of St more quickly than the other estimators. All four estimators were better than Sobs (observed number of species). However, the behaviour of the tested estimators was not as good as expected, and even with large sample size (number of quadrats sampled) all of them failed to provide reliable estimates. First- and second-order Jackknives were positively biased whereas Chao2 and Bootstrap were negatively biased. The observed limitations in the estimators' performance suggests that there is still scope for new tools to be developed by statisticians to assist in the estimation of species richness from sample data, especially in communities with high species richness

We discuss the usefulness of the concept of Potential Natural Vegetation (PNV), which describes the expected state of mature vegetation in the absence of human intervention. We argue that it is impossible to model PNV because of (i) the methodological problems associated to its definition and (ii) the issues related to the ecosystems dynamics.We conclude that the approach to characterizing PNV is unrealistic and provides scenarios with limited predictive power. In places with a long-term human history, interpretations of PNV need to be very cautious, and explicit acknowledgement made of the limitations inherent in available data

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Although the maintenance of diversity of living systems is critical for ecosystem functioning, the accelerating pace of global change is threatening its preservation. Standardized methods for biodiversity assessment and monitoring are needed. Species diversity is one of the most widely adopted metrics for assessing patterns and processes of biodiversity, at both ecological and biogeographic scales. However, those perspectives differ because of the types of data that can be feasibly collected, resulting in differences in the questions that can be addressed. Despite a theoretical consensus on diversity metrics, standardized methods for its measurement are lacking, especially at the scales needed to monitor biodiversity for conservation and management purposes. We review the conceptual framework for species diversity, examine common metrics, and explore their use for biodiversity conservation and management. Key differences in diversity measures at ecological and biogeographic scales are the completeness of species lists and the ability to include information on species abundances. We analyse the major pitfalls and problems with quantitative measurement of species diversity, look at the use of weighting measures by phylogenetic distance, discuss potential solutions and propose a research agenda to solve the major existing problems.

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