Aim Area thresholds, at which the form of the species–area relationship (SAR) changes abruptly, have played an important role in the theoretical framework of conservation biogeography and biodiversity research. The application of piecewise regressions has been advocated as a rigorous statistical technique to identify such thresholds within SARs, but a large variety of piecewise models remains untested. We explore the prevalence and number of thresholds in SARs and examine whether the currently widely used method for detecting the small island effect (SIE) is robust. Location Global. Taxon We consider all multicellular taxa based on the criteria of datasets selection. Methods We apply 15 regression models, including linear regression and piecewise regressions with two and three segments to 68 global island datasets that are sourced from the literature. Results The number of area thresholds in SARs varied among groups and correlated positively with area range of a studied system. Under the AIC or AIC c criterion, three‐segment piecewise models were more prevalent, whereas under the BIC criterion, two‐segment piecewise models were more prevalent. From the results of Aegean Sea isopods, West Indies herpetofauna, and Australian Islands mammals, we found evidence that the traditional criteria for detection of SIEs are not robust. Main conclusions Our study demonstrates that (a) to detect an SIE, the comparison should use as many models as possible, including not only variants with and without a left‐horizontal part, but also those with two and more segments; (b) naive use of the traditional two‐segment piecewise regressions may cause poor estimations of both slope and breakpoint values; (c) the number of thresholds increases with the area range of a studied system; (d) conservation biologists and applied ecologists should determine the number of area thresholds when estimating the precise species–area patterns and making management strategies in fragmented landscapes.

In current practice, a verification strategy is defined at the beginning of an acquisition program and is agreed upon by customer and contractor at contract signature. Hence, the resources necessary to execute verification activities at various stages of the system development are allocated and committed at the beginning, when a small amount of knowledge about the system is available. However, contractually committing to a fixed verification strategy at the beginning of an acquisition program fundamentally leads to suboptimal acquisition performance. Essentially, the uncertain nature of system development will make verification activities that were not previously planned necessary, and will make some of the planned ones unnecessary. In order to cope with these challenges, this paper presents an approach to apply set‐based design to the design of verification activities to enable the execution of dynamic contracts for verification strategies, ultimately resulting in more valuable verification strategies than current practice.

Verification activities increase an engineering team’s confidence in its system design meeting system requirements, which in turn are derived from stakeholder needs. Conventional wisdom suggests that the system design should be verified frequently to minimize the cost of rework as the system design matures. However, this strategy is based more on experience of engineers than on a theoretical foundation. In this paper, we develop a belief-based model of verification of system design, using a single system requirement as an abstraction, to determine the conditions under which it is cost effective for an organization to verify frequently. We study the model for a broad set of growth rates in verification setup and rework costs. Our results show that verifying a system design frequently is not always an optimal verification strategy. Instead, it is only an optimal strategy when the costs of reworking a faulty design increase at a certain rate as the design matures.

Verification activities, such as inspection, testing, analysis, and demonstration, improve one's confidence in the system meeting the system requirements during the development process. Frequent verification is often advocated as a strategy that minimizes costs of rework over the entire design process, where frequent verification involves verifying after any change in the design. However, this strategy is yet to be validated. In this paper, we develop a belief‐based model of verification in systems design to determine the conditions under which frequent verification is an optimal strategy for a vertically integrated organization. Our model uses belief distributions to capture the organization's dynamic confidence in the system design meeting a requirement of interest during the development process. It also captures the organization's dynamic confidence in the correctness of its development activities (or design process) as a function of past verification activities and current system maturity. The analysis of our model shows that frequent verification is a cost‐minimizing strategy for any level of belief in satisfying the requirement only when the organization has high confidence in the correctness of its design activities and the expected cost to rework a faulty design is greater than the costs to set up the verification activities throughout the development process. Otherwise, strategies with infrequent verification are superior. Our work contributes to the growing body of literature on the theoretical foundations of systems engineering and engineering design and seeks to provide practitioners with a means to determine optimal verification strategies.

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Correction activities (CAs), which can take the form of redesign, rework, or repair, are essential to system development. Whereas verification activities (VAs) provide information about the state of the system, CAs modify the state of the system to facilitate its correct operation. However, existing approaches to modeling and optimizing verification strategies take a simplistic approach to CAs. Specifically, CAs are modeled as an expected cost to achieve a desired confidence level after a VA has failed and are inherent to such VAs. In this paper, we present a modeling paradigm based on Bayesian networks (BNs) that captures the effects of different types of CAs. This modeling paradigm allows for the integration of verification and correction decisions (CDs) under a common framework. The modeling paradigm is illustrated in the notional case of a communication system.

Understanding biogeographic variation in species diversity patterns is important for conservation of biological diversity (Socolar et al., 2016;Vetaas & Grytnes, 2002). Elevational patterns of species richness, in recent decades, have received much attention in ecological and biogeographic studies (Brown,

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