An algorithm for computing Schubert varieties of best fit with applications.

We propose the geometric framework of the Schubert variety as a tool for representing a collection of subspaces of a fixed vector space. Specifically, given a collection of l-dimensional subspaces V1, …, Vr of ℝn, represented as the column spaces of matrices X1, …, Xr, we seek to determine a representative matrix K∈ℝn×k such that each subspace Vi intersects (or comes close to intersecting) the span of the columns of K in at least c dimensions. We formulate a non-convex optimization problem to determine such a K along with associated sets of vectors {ai} and {bi} used to express linear combinations of the columns of the Xi that are close to linear combinations of the columns of K. Further, we present a mechanism for integrating this representation into an artificial neural network architecture as a computational unit (which we refer to as an abstract node). The representative matrix K can be learned in situ, or sequentially, as part of a learning problem. Additionally, the matrix K can be employed as a change of coordinates in the learning problem. The set of all l-dimensional subspaces of ℝn that intersects the span of the columns of K in at least c dimensions is an example of a Schubert subvariety of the Grassmannian GR(l, n). When it is not possible to find a Schubert variety passing through a collection of points on GR(l, n), the goal of the non-convex optimization problem is to find the Schubert variety of best fit, i.e., the Schubert variety that comes as close as possible to the points. This may be viewed as an analog of finding a subspace of best fit to data in a vector space. The approach we take is well-suited to the modeling of collections of sets of data either as a stand-alone Schubert variety of best fit (SVBF), or in the processing workflow of a deep neural network. We present applications to some classification problems on sets of data to illustrate the behavior of the method.

Locally linear attributes of ReLU neural networks.

A ReLU neural network functions as a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a partitioning of the input space into convex polytopes, where each polytope is associated with a distinct affine mapping. The structure of this partitioning, together with the affine map attached to each polytope, can be analyzed to investigate the behavior of the associated neural network. We investigate simple problems to build intuition on how these regions act and both how they can potentially be reduced in number and how similar structures occur across different networks. To validate these intuitions, we apply them to networks trained on MNIST to demonstrate similarity between those networks and the potential for them to be reduced in complexity.

Hurricane wind regimes for forests of North America.

Despite the ubiquity of tropical cyclones and their impacts on forests, little is known about how tropical cyclone regimes shape the ecology and evolution of tree species. We used a simple meteorological model (HURRECON) to estimate wind fields from hurricanes in the Western North Atlantic and Eastern North Pacific tropical cyclone basins from storms occurring between 1851 and 2022. We characterize how the intensity and frequency of hurricanes differ among geographically distinct hurricane regimes and define four hurricane regimes for North America (Continental, Inland, Coastal, and Fringe). Along this coastal-to-inland gradient, we found major differences in the frequency and intensity of hurricane wind regimes. The Fringe regime experiences category 1 winds relatively frequently [return period (RP) 25 y], whereas the Inland regime experiences category 1 winds very infrequently (RP ~3,000 y). We discuss how species traits related to tree windfirmness, such as mechanical properties and crown traits, may vary along hurricane regime gradients. Quantitative characterization of forest hurricane regimes provides a critical step for understanding the evolutionary and ecological role of hurricane regimes in wind-prone forests.

Universal health care and political economy, neoliberalism and effects of COVID-19: A view of systems and complexity.

Sturmberg and Martin's application of systems and complexity theory to understanding Universal Health Care (UHC) and Primary Health Care (PHC) is evaluated in the light of the influence of political economy on health systems. Furthermore, the role that neoliberal approaches to governance have had in creating increased inequities is seen as a key challenge for UHC. COVID-19 has emphasized long standing discrepancies in health and these disadvantages require government will and cooperation together with adequate social services to redress these discrepancies in UHC.

Large tree mortality leads to major aboveground biomass decline in a tropical forest reserve.

Humans are transforming the ecology of the Earth through rapid changes in land use and climate. These changes can affect tropical forest structure, dynamics and diversity. While numerous studies have focused on diversity metrics, other aspects of forest function, such as long-term biomass dynamics, are often less considered. We evaluated plant community structure change (i.e., abundance, diversity, composition, and aboveground biomass) in a 2.25 ha forest dynamics plot located within a ~ 365 ha reserve in southern Costa Rica. We censused, mapped and identified to species all plants ≥ 5 cm diameter at breast height (DBH) in three surveys spanning 2010-2020. While there were no changes in late-successional species diversity, there were marked changes in overall species composition and biomass. Abundance of large (≥ 40 cm DBH) old-growth dense-wooded trees (e.g., Lauraceae, Rosaceae) decreased dramatically (27%), leading to major biomass decline over time, possibly driven by recent and recurrent drought events. Gaps created by large trees were colonized by early-successional species, but these recruits did not make up for the biomass lost. Finally, stem abundance increased by 20%, driven by increasing dominance of Hampea appendiculata. While results suggest this reserve may effectively conserve overall plant diversity, this may mask other key shifts such as large aboveground biomass loss. If this pattern is pervasive across tropical forest reserves, it could hamper efforts to preserve forest structure and ecosystem services (e.g., carbon storage). Monitoring programs could better assess carbon trends in reserves over time simply by tracking large tree dynamics.

Where Does Value Lie in Peer Support? An Exploratory Discussion of the Theories and Methods Underpinning Effective Research in Peer Support.

A literature review was undertaken in 2019 to review research into the effectiveness of peer support in chronic disease self-management. As with an earlier literature review, we found the results disappointing due to poor reporting and poor research design. Lack of information on training of peer supporters, unrealistically short timeframes to produce changes in health behaviors, and lack of any theoretical underpinning of the research design contributed to rating randomized controlled trials as poor to medium quality evidence. At the same time, systematic reviews consider peer support as effective, arguing that improved research design and evaluation would demonstrate this. This article discusses the need to examine more closely the contribution of peer support to chronic disease care as well as considering how research methods might more closely reflect that contribution and provide better evidence of the value of peer support to both participants and the health system.

Universal health coverage and primary health care: Their place in people's health.

Sturmberg and Martin in 2020 argue that universal health coverage (UHC) is mainly about financing, and primary health care (PHC) is about the right care at the right time to ensure health. They maintain that the World Health Organization has recently sent the wrong message about the "pillars" of PHC in their relationship to UHC. An understanding of political economy is required in order to come to terms with the bases of PHC and the fundamentals of UHC that dealing with inequities is not only an economic issue but fundamentally a political issue. Neoliberal decision-making can enhance inequities in society. Two chronic health conditions, diabetes and multiple sclerosis, are examples of conditions that lead to costly and debilitating consequences for patients but also lead to substantial economic costs in terms of lost workforce participation and lost productivity. These cases demonstrate the socio-political issues involved in the management of care for a number of illnesses. The upsurge of COVID-19 has placed an enormous strain on health and broader social and economic resources and challenged the pretext of UHC as health for all: substantial differences in equity and political commitment have emerged. Sturmberg and Martin argue that the joining of UHC and PHC needs leadership, which involves local communities and resourcing. PHC is a changing system based on power relationships involving funders and the health community. In Australia as in several countries, out-of-pocket costs have grown rapidly and have affected access for some groups to PHC and have challenged the pretext of equity in UHC. In the context of PHC and UHC, we support the position that health for all goes beyond health care for all, to embrace healthy lives promoting wellbeing.

Examining quality of life in an Australian cohort of people with epilepsy over six years - Understanding the role of stigma and mood.

AIM: Research examining quality of life (QoL) among people living with epilepsy (PWE) consistently highlights the detrimental impact of stigma, anxiety, and depression, as well as the dynamic and changing nature of QoL over time. This paper represents the first panel study of the Australian Epilepsy Longitudinal Survey (AELS), examining factors that influence the QoL of PWE over a six-year interval, particularly focusing on experiences of stigma, depression, and anxiety. METHODS: Ninety-two adults participated in both Wave 2 (T1; 2010) and Wave 4 (T2; 2016/17) of the AELS. Average age at T2 was 53.4 years [standard deviation (SD) = 15.3; range: 22-82; 55% female]. Over the study interval, there was a shift towards more younger participants moving out of high school and older participants moving into retirement. We explored the impact of (i) experiences of stigma, (ii) mood, and (iii) sociodemographic factors on QoL at both T1 and T2 via the use of correlation analyses. Hierarchical regression was used to determine the strongest predictors of QoL at T2. RESULTS: Occurrence of recent seizures, stigma, anxiety, and depression measured at T1 were all significantly correlated with total QoL at both T1 and T2. Sociodemographic factors including years of education, and weekly income before tax were not significantly correlated with QoL at either T1 or T2. QoL and depression at T1 were identified as the strongest predictors of QoL at T2 (six years later). DISCUSSION: The current study supports previous research highlighting the importance of psychological factors in understating QoL in PWE, particularly stigma, anxiety, and depression. In particular, it highlights the impact of depression on QoL over a 6-year interval, providing evident for the long-term nature of this relationship.

Needs for aids and equipment for the management of epilepsy in an Australian cohort.

AIM: This paper investigated the bases of needs for a range of epilepsy aids and equipment and expressed concerns about the use of such devices. METHOD: There was a 29.6% response rate (n = 393 of 1328) to Wave 4 of the Australian Epilepsy Longitudinal Study (AELS). The focus of Wave 4 was on the expressed needs and affordability of aids and equipment for people with epilepsy (PWE) and quality of life (QoL). Quantitative analysis was used to examine the association between self-reported need for aids and equipment, sociodemographic information, and QoL. Open-ended responses were subject to qualitative analysis. RESULTS: Approximately one-fifth of the sample felt that they needed specific aids, including emergency ID bracelets, seizure alarms, and seizure monitors. Those respondents who felt that they needed aids had more frequent seizures, had been recently injured by a seizure, and were less prosperous. The QoL of those in need of equipment was lower than that of those who felt that they did not need it. Qualitative analysis revealed a need for more information about the aids available, issues associated with affordability, and some concern about the utility of these aids for those who lived alone. DISCUSSION: Much research to date has focussed on the development and validation of devices for PWE and standards for testing. Fewer studies deal with the needs and experiences of PWE with regard to the use of such equipment. The development of these devices needs to ensure patient comfort and acceptability. In addition, there is a need to canvas the views of family, caregivers, and primary care providers on the usability of epilepsy aids and equipment. CONCLUSION: Further person-centered research is needed in assessing the need for and usability of aids and equipment for the management of epilepsy.

Reported service needs at diagnosis of epilepsy and implications for quality of life.

AIM: This paper reports on contributing factors to Quality of Life (QoL) in an Australian community sample of people with epilepsy (PWE). METHOD: Three hundred and ninety-three respondents or 29.6% of people on the Australian Epilepsy Research Register participated in Wave 4 of a longitudinal survey. A quantitative analysis was undertaken and a qualitative investigation examined open-ended responses by 44 PWE on the support services that they received following diagnosis of epilepsy. RESULTS: Total Quality of Life in Epilepsy-31 Items (QOLIE-31) score for the community-based sample was 55.99 (SD 19.85) [Range 6.34-96.20]. Age, paid employment, seizure frequency, number of antiepileptic drugs (AEDs), and perceived prosperity had significant impacts on QoL. In addition, use of support services showed that availability of a first seizure clinic, accurate information on support services and peer support were associated with the highest QoL. A qualitative investigation revealed that on first diagnosis, a lack of information was the main theme. Furthermore, PWE reported a lack of understanding of available supports by a range of health professionals, schools, and in the general community. DISCUSSION: Psychosocial factors were important in explaining QoL, and the positive effects of first seizure clinics, accurate information on support services, and of peer support have been confirmed in the literature. The lack of knowledge of support services on being diagnosed with epilepsy is a problem evident in the community and pathways are required to support people dealing with their epilepsy. CONCLUSION: More emphasis is needed in providing availability of supports to enhance the future wellbeing and QoL of people when epilepsy is diagnosed.

Health and Disease-Emergent States Resulting From Adaptive Social and Biological Network Interactions.

Health is an adaptive state unique to each person. This subjective state must be distinguished from the objective state of disease. The experience of health and illness (or poor health) can occur both in the absence and presence of objective disease. Given that the subjective experience of health, as well as the finding of objective disease in the community, follow a Pareto distribution, the following questions arise: What are the processes that allow the emergence of four observable states-(1) subjective health in the absence of objective disease, (2) subjective health in the presence of objective disease, (3) illness in the absence of objective disease, and (4) illness in the presence of objective disease? If we consider each individual as a unique biological system, these four health states must emerge from physiological network structures and personal behaviors. The underlying physiological mechanisms primarily arise from the dynamics of external environmental and internal patho/physiological stimuli, which activate regulatory systems including the hypothalamic-pituitary-adrenal axis and autonomic nervous system. Together with other systems, they enable feedback interactions between all of the person's system domains and impact on his system's entropy. These interactions affect individual behaviors, emotional, and cognitive responses, as well as molecular, cellular, and organ system level functions. This paper explores the hypothesis that health is an emergent state that arises from hierarchical network interactions between a person's external environment and internal physiology. As a result, the concept of health synthesizes available qualitative and quantitative evidence of interdependencies and constraints that indicate its top-down and bottom-up causative mechanisms. Thus, to provide effective care, we must use strategies that combine person-centeredness with the scientific approaches that address the molecular network physiology, which together underpin health and disease. Moreover, we propose that good health can also be promoted by strengthening resilience and self-efficacy at the personal and social level, and via cohesion at the population level. Understanding health as a state that is both individualized and that emerges from multi-scale interdependencies between microlevel physiological mechanisms of health and disease and macrolevel societal domains may provide the basis for a new public discourse for health service and health system redesign.

Motion Segmentation via Generalized Curvatures.

New depth sensors, like the Microsoft Kinect, produce streams of human pose data. These discrete pose streams can be viewed as noisy samples of an underlying continuous ideal curve that describes a trajectory through high-dimensional pose space. This paper introduces a technique for generalized curvature analysis (GCA) that determines features along the trajectory which can be used to characterize change and segment motion. Tools are developed for approximating generalized curvatures at mean points along a curve in terms of the singular values of local mean-centered data balls. The features of the GCA algorithm are illustrated on both synthetic and real examples, including data collected from a Kinect II sensor. We also applied GCA to the Carnegie Mellon University Motion Capture (MoCaP) database. Given that GCA scales linearly with the length of the time series we are able to analyze large data sets without down sampling. It is demonstrated that the generalized curvature approximations can be used to segment pose streams into motions and transitions between motions. The GCA algorithm can identify 94.2 percent of the transitions between motions without knowing the set of possible motions in advance, even though the subjects do not stop or pause between motions.

'I hate wasting the hospital's time': Experiences of emergency department admissions of Australian people with epilepsy.

AIM: This paper investigates the reasons and extent of hospital emergency department (ED) attendance by people with epilepsy in Wave 4 of The Australian Longitudinal Survey 2016-17. METHOD: Wave 4 had 393 respondents who completed the survey, which included questions relating to their use of hospital and healthcare services. Of these, 121 (31%; 82 females) reported one or more admissions to the ED within the previous 12 months. We conducted a mixed methods analysis - using quantitative measures to explore the type and number of admissions, factors relating to increased admissions, and a qualitative approach to explore respondent experiences of their admissions. RESULTS: Over half of the admissions reported were seizure-related, including injuries occurring as a result of seizures. More than 15% of respondents had more than four ED visits during the preceding 12 months of the survey. Those who had experienced seizures within the previous 12 months, irrespective of frequency, were more likely to have attended the ED compared with those who had not experienced a recent seizure. Self-reported income was another major factor in ED use. Experiences of hospitalization demonstrated frustration at being taken to the ED, loss of autonomy, and experiences of inappropriate care due to poor understanding of epilepsy. Some respondents did not want to waste the ED time as they felt that a rest was all they needed following a seizure. DISCUSSION: The rates of hospitalization for seizure-related reasons are in line with the findings of other epilepsy-related studies, as is the increased hospitalization rate of those from less well-off backgrounds. This study provided a valuable picture of the opinions and attitudes of people with epilepsy towards their healthcare services. CONCLUSION: While this is an analysis of a small cohort, the consistency of reported experiences suggests that ED is not always felt to be appropriate following a seizure, and misunderstanding around the appropriate treatment of epilepsy continues in healthcare services.

A sociological approach to resilience in health and illness.

Work on resilience in health and illness has been approached from a number of perspectives. These are the biological and psychosocial with a focus on the individual's responses to cope and adapt to changing circumstances wrought by changing physical health states. This we argue has a place but is far too narrow emphasizing the neoliberal view that the sick or imperfect individual is ultimately responsible for their own health outcomes. In this perspective, the individual's failure to cope or adapt may be seen as a personal failure to interact with the health system on offer. A broader sociological approach focuses on the overarching sociopolitical system within which health and illness occur and looks at the role of concepts such as growing social and economic inequity and the process by which neoliberalism establishes the framework of unequal opportunity and life chances. At this broader level, resilience relates to interplay between the sociopolitical and health systems and the individual. It is the role of the health system to provide opportunities, and supports and to reduce inequities to promote healthy lifestyle and beneficial coping approaches. We aim to understand and describe the mechanisms and opportunities afforded to individuals by their place in the social structure and to argue for health reform that makes a health system that assists all individuals be resilient. Longitudinal data from the Australian Epilepsy Longitudinal Survey are used to understand how income, inequity, and social isolation affect resilience over time.

A degradation debt? Large-scale shifts in community composition and loss of biomass in a tropical forest fragment after 40 years of isolation.

Habitat loss and fragmentation are among the biggest threats to tropical biodiversity and associated ecosystem services. We examined forest dynamics in a mid-elevation 365-ha fragment in southern Costa Rica. The fragment was isolated in the mid-1970s and belongs to the Las Cruces Biological Station. A 2.25-ha permanent plot was established in the center of the old-growth forest (>400 m to nearest edge boundary) and all plants >5 cm DBH were censused, mapped, and identified to species in two surveys taken ~5-6 years apart (>3,000 stems/survey). Although the reserve maintains high species richness (>200 spp.), with many rare species represented by only one individual, we document a strong shift in composition with a two-fold increase in the number of soft-wooded pioneer individuals. The dominant late-successional understory tree species, Chrysochlamys glauca (Clusiaceae), and most species in the Lauraceae, declined dramatically. Turnover was high: 22.9% of stems in the first survey were lost, and 27.8% of stems in the second survey represented new recruits. Mean tree diameter decreased significantly and there was a 10% decrease in overall biomass. Such alteration has been documented previously but only in smaller fragments or within ~100 m of an edge boundary. Further penetration into this fragment was perhaps driven by a progressive invasion of disturbance-adapted species into the fragment's core over time; the loss of once-dominant late successional species could be a contributing factor. The pattern found is of particular concern given that such fragments represent a substantial portion of today's remaining tropical habitat; further studies in similar-sized fragments that have been isolated for similar prolonged periods are called for.

Older people and knowledge of epilepsy: GPs can help.

BACKGROUND: Epilepsy is a common neurological disease with a high prevalence in people aged 65 years or older. Therefore, an understanding of the disease is important. The objective of this article was to determine older people's knowledge of epilepsy. METHODS: Electronic or paper-based surveys were completed by people aged 65 years and older. RESULTS: Five hundred and seventy-two surveys were completed, including 100 from people with epilepsy. Those with epilepsy had relatively poor knowledge of their condition, but they answered some questions significantly more correctly than participants without epilepsy. The main predictor of knowledge was clear information from a health professional. Two-thirds of those with epilepsy had their condition managed by a general practitioner. DISCUSSION: Older people with epilepsy need more information on their condition to facilitate better care management.

Multimorbidity: a sociological perspective of systems.

There has been a great tradition of looking at health and illness from a systems perspective. For clinicians and people with illnesses a lot can be gained by mapping the interface of different sectors to understand the nature of conditions. This paper aims to use Sturmberg et als. paper as a stepping off point to present a sociological approach to understanding multimorbidities and gain insights into the illness experience of these people in the greater social system of health and illness. Parsons' sick role provides a useful systems concept through which we can understand the role of doctors and the experience of illness as social, beyond the personal. We also use Bourdieu's concept of habitas and of structure and agency to make sense of multimorbidities being social, economic and a broader part of experiencing social systems. We posit that one option for people coping with multiple conditions is to change identity. We also examine the doctor and patient encounter for mutlimorbidities as being problematic as it forces attention on competence and responsibility in that continuing encounter.

Evaluating the ecological impacts of salvage logging: can natural and anthropogenic disturbances promote coexistence?

Salvage logging following windthrow is common throughout forests worldwide even though the practice is often considered inimical to forest recovery. Because salvaging removes trees, crushes seedlings, and compacts soils, many warn this practice may delay succession, suppress diversity, and alter composition. Here, over 8 yr following windthrow, we experimentally evaluate how salvaging affects tree succession across 11 gaps in Eastern deciduous forests of Pennsylvania, wherein each gap was divided into salvaged and control (unsalvaged) halves. Our gaps vary in size and windthrow severity, and we explicitly account for this variation as well as variation in soil disturbance (i.e., scarification) resulting from salvaging so that our results would be generalizable. Salvage logging had modest and ephemeral impacts on tree succession. Seedling richness and density declined similarly over time in both salvaged and unsalvaged areas as individuals grew into saplings. The primary impact of salvaging on succession occurred where salvaging scarified soils. Here, salvaging caused 41 to 82% declines in sapling abundance, richness, and diversity, but these differences largely disappeared within 5 yr. Additionally, we documented interactions between windthrow severity and scarification. Specifically, low-severity windthrow and scarification combined reinforced dominance by shade-tolerant and browse-tolerant species (Acer pensylvanicum, Fagus grandifolia). In contrast, high windthrow severity and scarification together reduced the density of a fast-growing pioneer tree (Prunus pensylvanica) and non-tree vegetation cover by 75% and 26%, respectively. This reduction enhanced the recruitment of two mid-successional tree species, Acer rubrum and Prunus serotina, by 2 and 3-fold, respectively. Thus, our findings demonstrate that salvaging creates novel microsites and mitigates competing vegetation, thereby enhancing establishment of important hardwoods and promoting tree species coexistence. Our results, coupled with an assessment of 27 published post-windthrow salvage studies, suggest short-term studies may overestimate the impact of salvaging on regeneration. We conclude that the ecological costs and benefits of salvaging depend upon the variation in canopy and soil disturbance severity as well as the timescale at which effects are evaluated. Thus, our findings are inconsistent with the view that salvaging inexorably undermines plant diversity; rather we suggest salvaging can promote tree species coexistence within various contexts.

Yttrium 90-ibritumomab tiuxetan plus rituximab maintenance as initial therapy for patients with high-tumor-burden follicular lymphoma: a Wisconsin Oncology Network study.

INTRODUCTION: Yttrium 90-ibritumomab tiuxetan (90Y-IT) radioimmunotherapy has proved to be effective in relapsed follicular lymphoma (FL). We conducted a clinical trial in which 90Y-IT followed by maintenance rituximab (MR) was evaluated as initial therapy for high-tumor-burden FL. METHODS: Eligible patients had histologically confirmed FL and met the GELF (Groupe d'Etude des Lymphomes Folliculaires) criteria for high tumor burden. All patients received a single dose of 90Y-IT. Patients with platelet counts of 150,000/mm³ or higher received 0.4 mCi/kg, and patients with platelet counts between 100,000/mm³ and 149,000/mm³ received 0.3 mCi/kg. At 6 months, patients without progressive disease (PD) received rituximab weekly for 4 weeks at a dose of 375 mg/m² (consolidation therapy), followed by MR consisting of the same dose every 3 months for a planned 5 years. RESULTS: From January 2005 through November 2007, a total of 16 patients were enrolled. The median age was 52 years (range, 37-75). The major toxicity from 90Y-IT was myelosuppression, with 88% and 31% of the patients experiencing grade 3 and grade 4 hematologic toxicity, respectively. The responses to 90Y-IT induction therapy were as follows: 7 patients with complete response/unconfirmed complete response (CR/Cru), 4 with partial response (PR), 3 with stable disease (SD), and 2 with progressive disease (PD). We identified 6 patients with early PD (range, 4-16 months) and 10 patients with prolonged remission (range, 37-101+ months). Compared with the patients who had prolonged remission, the patients who had early PD tended to have larger baseline nodal masses. The median progression-free survival (PFS) has not been reached after a median follow-up period of 48 months. The 3-year PFS and overall survival (OS) rates were 56% (95% CI, 37%-87%) and 93% (95% CI, 80%-100%), respectively. CONCLUSION: The overall response rate (ORR) to 90Y-IT was 69% in patients who had previously untreated, high-tumor-burden FL, which is lower than what is observed with contemporary rituximab/chemotherapy combinations. MR after 90Y-IT did convert all PRs to CRs. Alternative therapies should be considered for patients who have FL with large nodal masses (>9 cm), whereas very durable responses are possible in patients who have intermediate-size masses (>9 cm).

Pasture succession in the Neotropics: extending the nucleation hypothesis into a matrix discontinuity hypothesis.

The nucleation hypothesis appears to explain widespread patterns of succession in tropical pastures, specifically the tendency for isolated trees to promote woody species recruitment. Still, the nucleation hypothesis has usually been tested explicitly for only short durations and in some cases isolated trees fail to promote woody recruitment. Moreover, at times, nucleation occurs in other key habitat patches. Thus, we propose an extension, the matrix discontinuity hypothesis: woody colonization will occur in focal patches that function to mitigate the herbaceous vegetation effects, thus providing safe sites or regeneration niches. We tested predictions of the classical nucleation hypothesis, the matrix discontinuity hypothesis, and a distance from forest edge hypothesis, in five abandoned pastures in Costa Rica, across the first 11 years of succession. Our findings confirmed the matrix discontinuity hypothesis: specifically, rotting logs and steep slopes significantly enhanced woody colonization. Surprisingly, isolated trees did not consistently significantly enhance recruitment; only larger trees did so. Finally, woody recruitment consistently decreased with distance from forest. Our results as well as results from others suggest that the nucleation hypothesis needs to be broadened beyond its historical focus on isolated trees or patches; the matrix discontinuity hypothesis focuses attention on a suite of key patch types or microsites that promote woody species recruitment. We argue that any habitat discontinuities that ameliorate the inhibition by dense graminoid layers will be foci for recruitment. Such patches could easily be manipulated to speed the transition of pastures to closed canopy forests.