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The glomerular filtration rate (GFR) is the outcome of glomerular hemodynamics, influenced by a series of parameters: renal plasma flow, resistances of afferent arterioles and efferent arterioles (EAs), hydrostatic pressures in the glomerular capillary and Bowman's capsule, and plasma colloid osmotic pressure in the glomerular capillary. Although mathematical models have been proposed to predict the GFR at both the single-nephron level and the two-kidney system level using these parameters, mathematical equations governing glomerular filtration have not been well-established because of two major problems. First, the two-kidney system-level models are simply extended from the equations at the single-nephron level, which is inappropriate in epistemology and methodology. Second, the role of EAs in maintaining the normal GFR is underappreciated. In this article, these two problems are concretely elaborated, which collectively shows the need for a shift in epistemology toward a more holistic and evolving way of thinking, as reflected in the concept of the complex adaptive system (CAS). Then, we illustrate eight fundamental mathematical equations and four hypotheses governing glomerular hemodynamics at both the single-nephron and two-kidney levels as the theoretical foundation of glomerular hemodynamics. This illustration takes two steps. The first step is to modify the existing equations in the literature and establish a new equation within the conventional paradigm of epistemology. The second step is to formulate four hypotheses through logical reasoning from the perspective of the CAS (beyond the conventional paradigm). Finally, we apply the new equation and hypotheses to comprehensively analyze glomerular hemodynamics under different conditions and predict the GFR. By doing so, some concrete issues are eliminated. Unresolved issues are discussed from the perspective of the CAS and a desinger's view. In summary, this article advances the theoretical study of glomerular dynamics by 1) clarifying the necessity of shifting to the CAS paradigm; 2) adding new knowledge/insights into the significant role of EAs in maintaining the normal GFR; 3) bridging the significant gap between research findings and physiology education; and 4) establishing a new and advanced foundation for physiology education.

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Resilience is an organizational capacity in day-to-day practice and crisis situation performance. A one of a kind crisis for hospitals is the COVID-19 pandemic. The long duration and magnitude of this crisis offers the opportunity to gain insight into the complexity of crisis management and organizational resilience of hospitals. This interview study therefore explored the organizational resilience of Dutch hospitals during the first 14 months of the COVID-19 pandemic. Nine board members of nine Dutch hospitals were interviewed by means of a semi-structured interview that was built on thirteen indicators of organizational resilience. The results showed that board members considered their hospitals as resilient on almost all indicators. Their judgments varied about how prepared and ready for future crises they considered their hospital. According to board members, hospitals are mainly prepared for "acute" short-term crises, thanks to good crisis leadership, open communication and strong networks. A crisis as long as the COVID-19 pandemic was unprecedented and therefore more difficult to deal with. In between the infection waves, work processes were reflected upon to learn, anticipate and respond more smoothly to successive waves. However, the enduring nature of the COVD-19 crisis presented complex organizational challenges. Crisis operations were eventually scaled down and hospitals had to manage the crisis and regular care as two companies side by side. Each crisis manifests differently. Fostering trust in healthcare staff and allowing them to act autonomously during crises, while diligently monitoring external influences and potential future crises, are therefore paramount in developing organizational adaptive capacities.

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BACKGROUND: As a key determinant of ill-health, family violence is inadequately responded to within Aotearoa New Zealand health policy and practice. Without adequate system support, health professionals can often be unsure of what to do, or how to help. Developed in response to this system gap, 'Atawhai' aims to make it easier for primary care professionals to respond to family violence. METHODS: Underpinned by indigenous Maori customs, Atawhai combines complexity theory and participatory research methodologies to be responsive to the complexity involved in family violence. We worked with 14 primary care professionals across ten whakawhitiwhiti korero wananga (meetings for deliberate dialogue) to identify and develop primary care system pathways and tools for responding to family violence. This paper focuses on the development of Atawhai through wananga and observation methods. Methods used to capture change will be reported separately. FINDINGS: Atawhai is a relational response to family violence, focused on developing a network of trusted relationships between health and social care professionals to support safe responses to those accessing care. This study identified four key health system pathways to responsiveness and developed associated tools to support health care responsiveness to family violence. We found the quality of relationships, both among professionals and with those accessing care, coupled with critical reflection on the systems and structures that shape policy and practice are essential in generating change within primary care settings. CONCLUSIONS: Atawhai is a unique health care response to family violence evidenced on empirical knowledge of primary care professionals. Our theoretical lens calls attention to parts of the system often obscured by current health care responses to family violence. Atawhai presents an opportunity to develop a grassroots-informed, long-term response to family violence that evolves in response to needs.

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Solid waste is increasing rapidly worldwide. In this study, the solid waste (household waste, construction and demolition waste and industrial waste) management systems are treated as reverse supply chain to analyze the critical operational issues based on complex adaptive system theory. At the single-layer, the complexity of the various nodes at a layer arises from rational decision-making and behavioral heterogeneity. The solid waste generation layer is employed as an example to investigate the complexity of node behavioral decisions. Regression analysis results reveal that both endogenous (Attitude, Subjective norm, and Perceived behavioral control) and exogenous factors (Economic incentive, Government supervision, Technical support) positively influence sorting behavior. The effect of Economic incentive (ß=0.327P<0.001) and Attitude (ß=0.249P<0.001) on sorting behavior are the largest. In the multi-layer system, different layers communicate with each other through the material and financial flows and have cross-layer impacts. An agent-based model is developed to investigate the multi-layer feedforward influence mechanism of changes in key layers (e.g., sorting rate, disposal rate) and the material and financial flows adaptive adjustment direction of the solid waste reverse supply chain. High rate of participation and accuracy of source sorting can shorten material flow paths and reduce storage and transportation costs. The increase in disposal rate encourages the transition of solid waste from backfill to resource utilization. This study provides a practice reference for solid waste reverse supply chain and related enterprises managers.

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In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.

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BACKGROUND: Despite three decades of policy initiatives to improve integration of health care, delivery of health care in New Zealand remains fragmented, and health inequities persist for Maori and other high priority populations. An evidence base is needed to increase the chances of success with implementation of large-system transformation (LST) initiatives in a complex adaptive system. METHODS: This research aimed to identify key elements that support implementation of LST initiatives, and to investigate contextual factors that influence these initiatives. The realist logic of enquiry, nested within the macro framing of complex adaptive systems, formed the overall methodology for this research and involved five phases: theory gleaning from a local LST initiative, literature review, interviews, workshop, and online survey. NVivo software programme was used for thematic analysis of the interview, workshop, and the survey data. We identified key elements and explained variations in success (outcomes) by identifying mechanisms triggered by various contexts in which LST initiatives are implemented. RESULTS: The research found that a set of 10 key elements need to be present in the New Zealand health system to increase chances of success with implementation of LST initiatives. These are: (i) an alliancing way of working; (ii) a commitment to te Tiriti o Waitangi; (iii) an understanding of equity; (iv) clinical leadership and involvement; (v) involved people, whanau, and community; (vi) intelligent commissioning; (vii) continuous improvement; (viii) integrated health information; (ix) analytic capability; and (x) dedicated resources and time. The research identified five contextual factors that influenced implementation of LST initiatives: a history of working together, distributed leadership from funders, the maturity of Alliances, capacity and capability for improvement, and a continuous improvement culture. The research found that the key mechanism of trust is built and nurtured over time through sharing of power by senior health leaders by practising distributed leadership, which then creates a positive history of working together and increases the maturity of Alliances. DISCUSSION: Two authors (KMS and PBJ) led the development and implementation of the local LST initiative. This prior knowledge and experience provided a unique perspective to the research but also created a conflict of interest and introduced potential bias, these were managed through a wide range of data collection methods and informed consent from participants. The evidence-base for successful implementation of LST initiatives produced in this research contains knowledge and experience of senior system leaders who are often in charge of leading these initiatives. This evidence base enables decision makers to make sense of complex processes involved in the successful implementation of LST initiatives. CONCLUSIONS: Use of informal trust-based networks provided a critical platform for successful implementation of LST initiatives in the New Zealand health system. Maturity of these networks relies on building and sustaining high-trust relationships among the network members. The role of local and central agencies and the government is to provide the policy settings and conditions in which trust-based networks can flourish. OTHER: This study was approved by the Victoria University of Wellington Human Ethics Committee (Ethics Approval Number 27,356). The research was supported by the Victoria University of Wellington research grant (222,809) and from the University of Auckland Department of Medicine research fund (H10779).

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The COVID-19 pandemic has severely affected the hospitality industry. Many have treated the crisis as a temporary shock. However, there are those who see it as a turning point. Treating the hospitality industry as a complex adaptive system, this research uses the organizational resilience framework to investigate how hospitality organizations responded to the crisis. A mixed methods approach was employed, and two studies were conducted. A sample of managers from Omani hotels were interviewed and a content analysis was performed on the websites and annual reports of a sample of international hotel brands. The results revealed that the Omani industry's response was mostly limited to coping, whereas the international industry was active in anticipating, coping, and adapting to the pandemic. Strong support is provided for the notion of the pandemic as a turning point. An action framework has been developed to support firms in keeping pace with the industry's evolution.

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South Korea demonstrated its ability to respond effectively with rapid policy measures and implementation in the early stages of the pandemic. However, at the end of second year of the pandemic, South Korea reached a peak in its number of daily new cases. Why didn't South Korea maintain the initial successful performance? To answer the question, this study examined South Korea's pandemic response process through Complex Adaptive Systems (CAS), focusing on actors' behavior according to the phase transition. We found that the South Korean government failed to interact with the rapidly evolving public due to the different evolving pace. Dissonance between the government and the public resulted in distrust, fatigue, and resistance to the government's policy among people. From the case study of South Korea, this study emphasizes that not only individual governments, but also the international community, should anticipate and interact with the rapidly evolving public to prepare for the pandemic and post-pandemic era.

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This study aims to identify the driving forces behind interorganizational networks in China following disasters. Using the theory of complex adaptive systems, we identified the self-organization process of disaster response as the network formation process. We identified interorganizational networks that emerged in response to two natural hazards and two technical disasters by collecting data from multiple sources. The exponential random model analysis is performed to analyze the effects of structures and organizational attributes on network formation. In structuring networks for disaster response, findings demonstrate that bonding structures take precedence over bridging structures for organizations. Meanwhile, the sector and jurisdiction-based homophily effects facilitate network formation in disaster response. On the basis of research findings, five propositions describing the network formation process in China's disaster response are proposed. Such a theoretical model is essential for advancing research and practice in complex disaster network management.

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The extant theories on the quality and stability of marital relationships have some difficulties in explaining some of the complexities of marital behaviors. The present article is an initial attempt to explain the complexities of marital behaviors based on the science of complexity and neuroscience. This article proposes a new theoretical framework relying on this simple argument that marital behaviors, as one of the most complex human behaviors, are the product of one's brain's complex adaptive system (CAS). Hence, to understand the complexities of marital behaviors, a movement toward familiarity with the brain's CAS involved in marital behaviors needs to be started. The article presents the theory of brain complexity and marital behaviors (BCM) and outlines its assumptions, concepts, and propositions. Then, BCM is compared with the extant theories on happy and stable marriage, and finally, it was concluded by discussing the testability and the potential application of the theory. This article might inspire interdisciplinary studies of marital relationships, complex systems, and neuroscience and may have considerable practical implications.

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BACKGROUND: The tremendous physical and mental burden that comes with caregiving puts the intimate partners of patients diagnosed with advanced cancer at risk for mental disorders. However, most partners seem to be protected by resilience. Such a resilience process is promoted by certain individual characteristics (e.g., flexibility, positive attitude, internal strength, capacity to balance incoming and outgoing information, and ability to ask for and accept support and advice) and by the availability of a support network, consisting of family, friends, and healthcare professionals. Such a heterogeneous group striving towards the same goals can be considered a complex adaptive system (CAS), a concept stemming from complexity science. AIMS: To study the behavior of the support network through the lens of complexity science and to provide insights to the means by which an available network may promote resilience. METHODS: Nineteen interviews with members from the support networks of eight intimate partners were analyzed deductively using the CAS principles as a coding framework. Subsequently, the quotes under each principle were coded inductively to concretize patterns in the behavior of the support networks. Eventually, the codes were charted into a matrix to identify intra- and inter-CAS similarities, differences, and patterns. FINDINGS: The network's behavior adapts dynamically to the changing circumstances as the patient's prognosis worsens. Furthermore, the behavior is based on internalized basic rules (such as reassuring availability and maintaining communication without being intrusive), attractors (e.g., feeling meaningful, appreciated, or connected), and the history of the support network. However, the interactions are non-linear and often unpredictable due to the context member's own concerns, needs, or emotions. CONCLUSIONS: Applying the lens of complexity science to the behavior of an intimate partner's support network gives us insight into the network's behavioral patterns. Indeed, a support network is a dynamic system that behaves according to the principles of a CAS and adapts resiliently to the changing circumstances as the patient's prognosis worsens. Moreover, the behavior of the support network appears to promote the intimate partner's resilience process throughout the patient's care period.

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RATIONALE: Question Storming offers a method that enables one to hold the condition of uncertainty in reflection without the need for resolution. Global interdependencies and unprecedented access to information, social media and multiple forms of communications challenge our ability to see, understand and influence change effectively and efficiently. The tension and need to cope effectively with massive uncertainties cannot be resolved with current methods leading to a necessity for people to seek new ways to transform their understanding and explore new options for action. Problem-solving and facilitation of the past are not flexible or rapid enough to meet the current demands of decision making and action taking in the face of massive uncertainties. As a result, people face 'wicked unsolvable' issues in their personal and professional lives. AIMS AND OBJECTIVES: An international group of scholar-practitioners has adapted and tested an enquiry process. Question Storming-The Power of Questions is based on principles of complex adaptive systems, human systems dynamics, and self-organization. METHOD: A three-step method of inquiry and reflection opens new possibilities. RESULTS AND CONCLUSIONS: Question Storming has helped people see their wicked issues from new perspectives, understand them in useful ways and generate new options for action. This paper introduces Question Storming-the Power of Questions as a practical method for group inquiry in the presence of individual and group uncertainties/wicked issues. The Container, Difference, Exchange (CDE) model and Pattern Logic are presented to explain the paradigm-shifting dynamics experienced by participants, both individuals and members of the group. It concludes with emerging questions for future consideration. Question Storming generates a divergent problem space that decreases constraint and increases degrees of freedom to allow practical exploration of new and often surprising options for action.

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A burgeoning literature has investigated the relationship between tourism and regional CO2 emissions. However, the results are equivocal. Some scholars find that tourism induces more emissions, while others find that tourism benefits emission mitigation. Previous research suffers three deficiencies: (1) the CO2 emissions induced by tourism beyond the tourism sectors are neglected; (2) the role of tourism agglomerations in sustainable destination development is underrated; (3) the tripartite mechanism of tourism agglomerations, household income, and urban direct residential CO2 emissions (DRCEs) remains to be determined. Based on the theories of complex adaptive system and an empirical study of 30 provinces in China, we examine the relationship between the tripartite roles via multiple spatial econometric models. The results disclose that tourism agglomerations have dual effects on urban DRCEs and an inverted U-shaped effect on household income. The growth of tourism agglomerations has generally promoted urban DRCEs in many provinces of mainland China during the last fourteen years because its indirect effect (positive) outweighs the direct effect (negative). However, tourism agglomerations are feasible for low-carbon destinations once the emission-income decoupling happens. This study contributes to low-carbon destination management by presenting a more holistic image of the social-economic-environmental impacts of tourism agglomerations.

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In the context of global environmental change and continuous urbanization, enhancing urban resilience is an important way to improve urban emergency management capacity and achieve sustainable development of urban systems. It is of great significance to clarify the mechanisms and effects of urban resilience and carry out resilience measurement to improve the level of urban system resilience and alleviate the pressure of environmental disturbances on the stable operation of urban systems. As an important part of the "Belt and Road" Initiative and one of the few leading economic regions in western China, promoting the high-quality development of the Lanzhou-Xining urban agglomeration is of profound significance for strengthening ethnic unity and stabilizing the northwest and southwest regions. Based on the complex adaptive system (CAS) theory and the adaptive cycle model, this study understands urban resilience as the comprehensive result of urban system stability, self-organization, learning adaptability and transformability, constructs a multi-level open index evaluation system, and analyzes the spatio-temporal evolution characteristics of urban resilience of the Lanzhou-Xining urban agglomeration from the proposed design to the formal planning in 2010-2017. The findings are as follows: (1) Research on the urban resilience of the Lanzhou-Xining urban agglomeration verifies the applicability of the evolutionary urban resilience analysis framework and makes preliminary findings on urban resilience based on CAS theory, which provide a certain theoretical reference for the research on the spatio-temporal evolution of urban resilience. (2) From 2010 to 2017, significant differences are observed between various urban attributes. Resilience exhibits an overall upward trend, and spatial evolution changes from a double core (Lanzhou and Xining) to three cores (Lanzhou, Xining and Haidong) and polycentric modes. (3) Based on urban resilience characteristics and an urban system adaptability cycle model, this paper divides the Lanzhou-Xining urban agglomeration cities into four types (exploitation-reorganization, conservation-release, conservation-exploitation and exploitation), and proposes corresponding adaptive management countermeasures. These could be adopted as a reference to promote the high-quality development of the Lanzhou-Xining urban agglomeration.

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The 1987 United Nations Brundtland Report established the vision of sustainable development as "development that meets the needs of the present without compromising the ability of future generations to meet their own needs." How might we anticipate the requirements of future custodians of vast, continuously morphing socio-technical-ecological systems while addressing current pressing needs? An abstract, principled approach (such as axiomatic design) might help address such ambiguity. Such systems are composed of large numbers of information-processing agents/agencies that collectively form a complex adaptive system (CAS). The focus here is on financial sustainability: (1) what is a principled approach toward sustainable design? (2) What design insights might we obtain by studying financial crises forensically against sustainability successes in nature? (3) How to design for financial sustainability? This paper adopts the CAS framework alongside axiomatic design to help elicit design patterns and anti-patterns of sustainability. Inspired by nature, a promising inside-out design pattern emerges.

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This study examined the association between pressure injuries and complexity of abdominal temperature measured in residents of a nursing facility. The temperature served as a proxy measure for skin thermoregulation. Refined multiscale sample entropy and bubble entropy were used to measure the irregularity of the temperature time series measured over two days at 1-min intervals. Robust summary measures were derived for the multiscale entropies and used in predictive models for pressure injuries that were built with adaptive lasso regression and neural networks. Both types of entropies were lower in the group of participants with pressure injuries (n=11) relative to the group of non-injured participants (n=15). This was generally true at the longer temporal scales, with the effect peaking at scale τ=22 min for sample entropy and τ=23 min for bubble entropy. Predictive models for pressure injury on the basis of refined multiscale sample entropy and bubble entropy yielded 96% accuracy, outperforming predictions based on any single measure of entropy. Combining entropy measures with a widely used risk assessment score led to the best prediction accuracy. Complexity of the abdominal temperature series could therefore serve as an indicator of risk of pressure injury.

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Supply chain viability concerns the entire supply system rather than one company or one single chain to survive COVID-19 disruptions. Mobility restriction and overall demand decline lead to systematically cascading disruptions that are more severe and longer lasting than those caused by natural disasters and political conflicts. In the present study, the authors find that large companies and manufacturers with traditional advantages suffer greater losses than small ones, which is conceptualized as the "Hub Paradox" by empirically investigating one Warp Knitting Industrial Zone of China. An underload cascading failure model is employed to simulate supply chain viability under disruptions. Numerical simulations demonstrate that when the load decreases beyond a threshold, the viability will drop down critically. Besides, supply chain viability depends on two aspects: the adaptive capability of the manufacturers themselves and the adaptive capability of the connections of the supply network. The comparison study demonstrates that enhancing cooperative relations between hub and non-hub manufacturers will facilitate the entire supply network viability. The present study sheds light on viable supply chain management. Compared with conventionally linear or resilient supply chains, intertwined supply networks can leverage viability with higher adaptation of redistributing production capacities among manufacturers to re-establish overall scale advantages. Finally, the present study also suggests solving the "Hub Paradox" from the perspective of complex adaptive system. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-022-07741-8.

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We raise the new possibility that people diagnosed with developmental dyslexia (DD) are specialized in explorative cognitive search, and rather than having a neurocognitive disorder, play an essential role in human adaptation. Most DD research has studied educational difficulties, with theories framing differences in neurocognitive processes as deficits. However, people with DD are also often proposed to have certain strengths - particularly in realms like discovery, invention, and creativity - that deficit-centered theories cannot explain. We investigate whether these strengths reflect an underlying explorative specialization. We re-examine experimental studies in psychology and neuroscience using the framework of cognitive search, whereby many psychological processes involve a trade-off between exploration and exploitation. We report evidence of an explorative bias in DD-associated cognitive strategies. High DD prevalence and an attendant explorative bias across multiple areas of cognition suggest the existence of explorative specialization. An evolutionary perspective explains the combination of findings and challenges the view that individuals with DD have a disorder. In cooperating groups, individual specialization is favored when features that confer fitness benefits are functionally incompatible. Evidence for search specialization suggests that, as with some other social organisms, humans mediate the exploration-exploitation trade-off by specializing in complementary strategies. The existence of a system of collective cognitive search that emerges through collaboration would help to explain our species' exceptional adaptiveness. It also aligns with evidence for substantial variability during our evolutionary history and the notion that humans are adapted not to a particular habitat but to variability itself. Specialization creates interdependence and necessitates balancing complementary strategies. Reframing DD therefore underscores the urgency of changing certain cultural practices to ensure we do not inhibit adaptation. Key improvements would remove cultural barriers to exploration and nurture explorative learning in education, academia, and the workplace, as well as emphasize collaboration over competition. Specialization in complementary search abilities represents a meta-adaptation; through collaboration, this likely enables human groups (as a species and as cultural systems) to successfully adapt. Cultural change to support this system of collaborative search may therefore be essential in confronting the challenges humanity now faces.

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BACKGROUND: General practitioners (GPs) are often faced with complex problems, including patients with socio-economic and medical problems. However, the methods they use to approach these complexities are still not understood. We speculated that elucidating these methods using complex adaptive systems (CAS) methodology to comprehensively assess GPs' daily activities would contribute to improving the professional development of GPs. This study aimed to clarify how expert GPs handle complex problems and adapt to their community context through the ethnography of GPs and other healthcare professionals in terms of CAS. METHODS: We adopted the interdisciplinary team-ethnographic research approach. Five hospitals and four clinics in Japan which were considered to employ expert GPs were selected by purposive sampling. 62 individuals of various backgrounds working in these nine facilities were interviewed. Using field notes and interview data, the researchers iteratively discussed the adequacy of our interpretations. The first author (JH) prepared a draft report, which was reviewed by the GPs at the participating facilities. Through critical and iterative consideration of the different insights obtained, the final findings emerged together with representative data. RESULTS: We identified four approaches used by GPs to deal with complexities. First, GPs treat patients with complex problems as a whole being and address their problems multi-directionally. Second, GPs build horizontal, trusting relationships with other healthcare professionals and stakeholders, and thereby reduce the degree of complexity of problems. Third, GPs change the learning climate while committing to their own growth based on societal needs and by acting as role models for other professionals through daily interpersonal facilitation. Fourth, GPs share community vision with multi-professionals and thereby act as a driving force for organizational change. These various interactions among GPs, healthcare professionals, organizations and communities resulted in systematization of the healthcare and welfare network in their community. CONCLUSIONS: Expert GPs developed interconnected multidimensional systems in their community health and welfare networks to adapt to fluctuating social realities using four approaches. GPs' work environment may be considered as a complex adaptive system (CAS) and the approach of GPs to complexities is CAS-based. Our findings are expected to have practical applications for GPs.

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Speech sounds are an essential vehicle of information exchange and meaning expression in approximately 7,000 spoken languages in the world. What functional constraints and evolutionary mechanisms lie behind linguistic diversity of sound systems is under ongoing debate; in particular, it remains conflicting whether there exists any universal relationship between these constraints despite of diverse sounds systems cross-linguistically. Here, we conducted cross-linguistic typological and phylogenetic analyses to address the characteristics of constraints on linguistic diversity of vowel systems. First, the typological analysis revealed a power-law based dependence between the global structural dispersion and the local focalization of vowel systems and validated that such dependence was independent of geographic region, language family, and linguistic affiliation. Second, the phylogenetic analysis further illustrated that the observed dependence resulted from correlated evolutions of these two structural properties, which proceeded in an adaptive process. These results provide empirical evidence that self-organization mechanisms helped shape vowel systems and common functional constraints took effect on the evolution of vowel systems in the world's languages.