Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Model Cortical Association Fields Account for the Time Course and Dependence on Target Complexity of Human Contour Perception

Can lateral connectivity in the primary visual cortex account for the time dependence and intrinsic task difficulty of human contour detection? To answer this question, we created a synthetic image set that prevents sole reliance on either low-level visual features or high-level context for the detection of target objects. Rendered images consist of smoothly varying, globally aligned contour fragments (amoebas) distributed among groups of randomly rotated fragments (clutter). The time course and accuracy of amoeba detection by humans was measured using a two-alternative forced choice protocol with self-reported confidence and variable image presentation time (20-200 ms), followed by an image mask optimized so as to interrupt visual processing. Measured psychometric functions were well fit by sigmoidal functions with exponential time constants of 30-91 ms, depending on amoeba complexity. Key aspects of the psychophysical experiments were accounted for by a computational network model, in which simulated responses across retinotopic arrays of orientation-selective elements were modulated by cortical association fields, represented as multiplicative kernels computed from the differences in pairwise edge statistics between target and distractor images. Comparing the experimental and the computational results suggests that each iteration of the lateral interactions takes at least ms of cortical processing time. Our results provide evidence that cortical association fields between orientation selective elements in early visual areas can account for important temporal and task-dependent aspects of the psychometric curves characterizing human contour perception, with the remaining discrepancies postulated to arise from the influence of higher cortical areas

Evenness mediates the global relationship between forest productivity and richness

1. Biodiversity is an important component of natural ecosystems, with higher species richness often correlating with an increase in ecosystem productivity. Yet, this relationship varies substantially across environments, typically becoming less pronounced at high levels of species richness. However, species richness alone cannot reflect all important properties of a community, including community evenness, which may mediate the relationship between biodiversity and productivity. If the evenness of a community correlates negatively with richness across forests globally, then a greater number of species may not always increase overall diversity and productivity of the system. Theoretical work and local empirical studies have shown that the effect of evenness on ecosystem functioning may be especially strong at high richness levels, yet the consistency of this remains untested at a global scale. 2. Here, we used a dataset of forests from across the globe, which includes composition, biomass accumulation and net primary productivity, to explore whether productivity correlates with community evenness and richness in a way that evenness appears to buffer the effect of richness. Specifically, we evaluated whether low levels of evenness in speciose communities correlate with the attenuation of the richness–productivity relationship. 3. We found that tree species richness and evenness are negatively correlated across forests globally, with highly speciose forests typically comprising a few dominant and many rare species. Furthermore, we found that the correlation between diversity and productivity changes with evenness: at low richness, uneven communities are more productive, while at high richness, even communities are more productive. 4. Synthesis. Collectively, these results demonstrate that evenness is an integral component of the relationship between biodiversity and productivity, and that the attenuating effect of richness on forest productivity might be partly explained by low evenness in speciose communities. Productivity generally increases with species richness, until reduced evenness limits the overall increases in community diversity. Our research suggests that evenness is a fundamental component of biodiversity–ecosystem function relationships, and is of critical importance for guiding conservation and sustainable ecosystem management decisions

Climatic controls of decomposition drive the global biogeography of forest-tree symbioses

The identity of the dominant root-associated microbial symbionts in a forest determines the ability of trees to access limiting nutrients from atmospheric or soil pools1,2, sequester carbon3,4 and withstand the effects of climate change5,6. Characterizing the global distribution of these symbioses and identifying the factors that control this distribution are thus integral to understanding the present and future functioning of forest ecosystems. Here we generate a spatially explicit global map of the symbiotic status of forests, using a database of over 1.1 million forest inventory plots that collectively contain over 28,000 tree species. Our analyses indicate that climate variables—in particular, climatically controlled variation in the rate of decomposition—are the primary drivers of the global distribution of major symbioses. We estimate that ectomycorrhizal trees, which represent only 2% of all plant species7, constitute approximately 60% of tree stems on Earth. Ectomycorrhizal symbiosis dominates forests in which seasonally cold and dry climates inhibit decomposition, and is the predominant form of symbiosis at high latitudes and elevation. By contrast, arbuscular mycorrhizal trees dominate in aseasonal, warm tropical forests, and occur with ectomycorrhizal trees in temperate biomes in which seasonally warm-and-wet climates enhance decomposition. Continental transitions between forests dominated by ectomycorrhizal or arbuscular mycorrhizal trees occur relatively abruptly along climate-driven decomposition gradients; these transitions are probably caused by positive feedback effects between plants and microorganisms. Symbiotic nitrogen fixers—which are insensitive to climatic controls on decomposition (compared with mycorrhizal fungi)—are most abundant in arid biomes with alkaline soils and high maximum temperatures. The climatically driven global symbiosis gradient that we document provides a spatially explicit quantitative understanding of microbial symbioses at the global scale, and demonstrates the critical role of microbial mutualisms in shaping the distribution of plant species

Evenness mediates the global relationship between forest productivity and richness

1. Biodiversity is an important component of natural ecosystems, with higher species richness often correlating with an increase in ecosystem productivity. Yet, this relationship varies substantially across environments, typically becoming less pronounced at high levels of species richness. However, species richness alone cannot reflect all important properties of a community, including community evenness, which may mediate the relationship between biodiversity and productivity. If the evenness of a community correlates negatively with richness across forests globally, then a greater number of species may not always increase overall diversity and productivity of the system. Theoretical work and local empirical studies have shown that the effect of evenness on ecosystem functioning may be especially strong at high richness levels, yet the consistency of this remains untested at a global scale. 2. Here, we used a dataset of forests from across the globe, which includes composition, biomass accumulation and net primary productivity, to explore whether productivity correlates with community evenness and richness in a way that evenness appears to buffer the effect of richness. Specifically, we evaluated whether low levels of evenness in speciose communities correlate with the attenuation of the richness–productivity relationship. 3. We found that tree species richness and evenness are negatively correlated across forests globally, with highly speciose forests typically comprising a few dominant and many rare species. Furthermore, we found that the correlation between diversity and productivity changes with evenness: at low richness, uneven communities are more productive, while at high richness, even communities are more productive. 4. Synthesis. Collectively, these results demonstrate that evenness is an integral component of the relationship between biodiversity and productivity, and that the attenuating effect of richness on forest productivity might be partly explained by low evenness in speciose communities. Productivity generally increases with species richness, until reduced evenness limits the overall increases in community diversity. Our research suggests that evenness is a fundamental component of biodiversity–ecosystem function relationships, and is of critical importance for guiding conservation and sustainable ecosystem management decisions

Evenness mediates the global relationship between forest productivity and richness

1. Biodiversity is an important component of natural ecosystems, with higher species richness often correlating with an increase in ecosystem productivity. Yet, this relationship varies substantially across environments, typically becoming less pronounced at high levels of species richness. However, species richness alone cannot reflect all important properties of a community, including community evenness, which may mediate the relationship between biodiversity and productivity. If the evenness of a community correlates negatively with richness across forests globally, then a greater number of species may not always increase overall diversity and productivity of the system. Theoretical work and local empirical studies have shown that the effect of evenness on ecosystem functioning may be especially strong at high richness levels, yet the consistency of this remains untested at a global scale. 2. Here, we used a dataset of forests from across the globe, which includes composition, biomass accumulation and net primary productivity, to explore whether productivity correlates with community evenness and richness in a way that evenness appears to buffer the effect of richness. Specifically, we evaluated whether low levels of evenness in speciose communities correlate with the attenuation of the richness–productivity relationship. 3. We found that tree species richness and evenness are negatively correlated across forests globally, with highly speciose forests typically comprising a few dominant and many rare species. Furthermore, we found that the correlation between diversity and productivity changes with evenness: at low richness, uneven communities are more productive, while at high richness, even communities are more productive. 4. Synthesis. Collectively, these results demonstrate that evenness is an integral component of the relationship between biodiversity and productivity, and that the attenuating effect of richness on forest productivity might be partly explained by low evenness in speciose communities. Productivity generally increases with species richness, until reduced evenness limits the overall increases in community diversity. Our research suggests that evenness is a fundamental component of biodiversity–ecosystem function relationships, and is of critical importance for guiding conservation and sustainable ecosystem management decisions

Native diversity buffers against severity of non-native tree invasions

Determining the drivers of non-native plant invasions is critical for managing native ecosystems and limiting the spread of invasive species$^{1,2}$. Tree invasions in particular have been relatively overlooked, even though they have the potential to transform ecosystems and economies$^{3,4}$. Here, leveraging global tree databases$^{5,6,7}$, we explore how the phylogenetic and functional diversity of native tree communities, human pressure and the environment influence the establishment of non-native tree species and the subsequent invasion severity. We find that anthropogenic factors are key to predicting whether a location is invaded, but that invasion severity is underpinned by native diversity, with higher diversity predicting lower invasion severity. Temperature and precipitation emerge as strong predictors of invasion strategy, with non-native species invading successfully when they are similar to the native community in cold or dry extremes. Yet, despite the influence of these ecological forces in determining invasion strategy, we find evidence that these patterns can be obscured by human activity, with lower ecological signal in areas with higher proximity to shipping ports. Our global perspective of non-native tree invasion highlights that human drivers influence non-native tree presence, and that native phylogenetic and functional diversity have a critical role in the establishment and spread of subsequent invasions

Native diversity buffers against severity of non-native tree invasions.

Determining the drivers of non-native plant invasions is critical for managing native ecosystems and limiting the spread of invasive species1,2. Tree invasions in particular have been relatively overlooked, even though they have the potential to transform ecosystems and economies3,4. Here, leveraging global tree databases5-7, we explore how the phylogenetic and functional diversity of native tree communities, human pressure and the environment influence the establishment of non-native tree species and the subsequent invasion severity. We find that anthropogenic factors are key to predicting whether a location is invaded, but that invasion severity is underpinned by native diversity, with higher diversity predicting lower invasion severity. Temperature and precipitation emerge as strong predictors of invasion strategy, with non-native species invading successfully when they are similar to the native community in cold or dry extremes. Yet, despite the influence of these ecological forces in determining invasion strategy, we find evidence that these patterns can be obscured by human activity, with lower ecological signal in areas with higher proximity to shipping ports. Our global perspective of non-native tree invasion highlights that human drivers influence non-native tree presence, and that native phylogenetic and functional diversity have a critical role in the establishment and spread of subsequent invasions