Effect of Climate on Wildfire Size: A Cross-Scale Analysis

Theory predicts that wildfires will encounter spatial thresholds where different drivers may become the dominant influence on continued fire spread. Studying these thresholds, however, is limited by a lack of sufficiently detailed data sets. To address this problem, we searched for scale thresholds in data describing wildfire size at the Avon Park Air Force Range, south-central Florida. We used power-law statistics to describe the “heavy-tail” of the fire size distribution, and quantile regression to determine how the edges of data distributions of fire size were related to climate. Power-law statistics revealed a heavy-tail, a pattern consistent with scale threshold theory, which predicts that large fires will be rare because only fires that cross all thresholds will become large. Results from quantile regression suggested that different climate conditions served as critical thresholds, influencing wildfire size at different spatial scales. Modeling at higher quantiles (≥75th) implicated drought as driving the spread of larger fires, whereas modeling at lower quantiles (≤25th) implicated that wind governed the spread of smaller fires. Fires of intermediate size were negatively associated with relative humidity. Our results are consistent with the idea that fire spread involves scale thresholds, with the small-scale drivers allowing fires to spread after ignition, but with further spread only being possible when large-scale drivers are favorable. These results suggest that other data sets that have heavy-tailed distributions may contain patterns generated by scale thresholds, and that these patterns may be revealed using quantile regression.     

The role of genetic diversity in nest cooling in a wild honey bee, Apis florea

Simulation studies of the task threshold model for task allocation in social insect colonies suggest that nest temperature homeostasis is enhanced if workers have slightly different thresholds for engaging in tasks related to nest thermoregulation. Genetic variance in task thresholds is one way a distribution of task thresholds can be generated. Apis mellifera colonies with large genetic diversity are able to maintain more stable brood nest temperatures than colonies that are genetically uniform. If this phenomenon is generalizable to other species, we would predict that patrilines should vary in the threshold in which they engage in thermoregulatory tasks. We exposed A. florea colonies to different temperatures experimentally, and retrieved fanning workers at these different temperatures. In many cases we found statistically significant differences in the proportion of fanning workers of different patrilines at different experimental temperatures. This suggests that genetically different workers have different thresholds for performing the thermoregulatory task of fanning. We suggest, therefore, that genetically based variance in task threshold is a widespread phenomenon in the genus Apis.     

Ecological thresholds at the savanna-forest boundary: how plant traits, resources and fire govern the distribution of tropical biomes

Fire shapes the distribution of savanna and forest through complex interactions involving climate, resources and species traits. Based on data from central Brazil, we propose that these interactions are governed by two critical thresholds. The fire-resistance threshold is reached when individual trees have accumulated sufficient bark to avoid stem death, whereas the fire-suppression threshold is reached when an ecosystem has sufficient canopy cover to suppress fire by excluding grasses. Surpassing either threshold is dependent upon long fire-free intervals, which are rare in mesic savanna. On high-resource sites, the thresholds are reached quickly, increasing the probability that savanna switches to forest, whereas low-resource sites are likely to remain as savanna even if fire is infrequent. Species traits influence both thresholds; saplings of savanna trees accumulate bark thickness more quickly than forest trees, and are more likely to become fire resistant during fire-free intervals. Forest trees accumulate leaf area more rapidly than savanna trees, thereby accelerating the transition to forest. Thus, multiple factors interact with fire to determine the distribution of savanna and forest by influencing the time needed to reach these thresholds. Future work should decipher multiple environmental controls over the rates of tree growth and canopy closure in savanna.     

The temperature-size rule in ectotherms: may a general explanation exist after all?

The majority of ectotherms mature at a larger size at lower rearing temperatures. Although this temperature-size rule is well established, a general explanation for this phenomenon has remained elusive. In this article, we address the problem by exploring the proximate and ultimate reasons for why a temperate grasshopper, Chorthippus brunneus, is an exception to the temperature-size rule. Using a complete set of life-history data to parameterize an established life-history model, we show that it is optimal for this species to mature at a larger size at higher temperatures. We also show that plasticity in adult size is determined by the relative difference between the minimum temperature thresholds for growth and development rates. The mechanism relates to aspects of the biophysical model of van der Have and de Jong. Ectotherms that obey the temperature-size rule are identified as having a higher temperature threshold for development rate than for growth rate; exceptions are identified as having a lower temperature threshold for development rate than for growth rate. The latter scenario may arise broadly in two ways. These are discussed in reference to the thermal biology of temperate grasshoppers and ectotherms in general.     

Identifying the Threshold of Dominant Controls on Fire Spread in a Boreal Forest Landscape of Northeast China

The relative importance of fuel, topography, and weather on fire spread varies at different spatial scales, but how the relative importance of these controls respond to changing spatial scales is poorly understood. We designed a “moving window” resampling technique that allowed us to quantify the relative importance of controls on fire spread at continuous spatial scales using boosted regression trees methods. This quantification allowed us to identify the threshold value for fire size at which the dominant control switches from fuel at small sizes to weather at large sizes. Topography had a fluctuating effect on fire spread across the spatial scales, explaining 20–30% of relative importance. With increasing fire size, the dominant control switched from bottom-up controls (fuel and topography) to top-down controls (weather). Our analysis suggested that there is a threshold for fire size, above which fires are driven primarily by weather and more likely lead to larger fire size. We suggest that this threshold, which may be ecosystem-specific, can be identified using our “moving window” resampling technique. Although the threshold derived from this analytical method may rely heavily on the sampling technique, our study introduced an easily implemented approach to identify scale thresholds in wildfire regimes.     

Haptic discrimination of size and texture in squirrel monkeys ( Saimiri sciureus )

The present study analyzed haptic abilities of four squirrel monkeys. Using a two-alternative forced-choice procedure, stimuli were presented in a visually opaque box, allowing unrestrained test subjects to grab through a small opening and touch the discriminanda. Difference thresholds were determined by a modified method of limits. In the first experiment we determined size difference thresholds for the discrimination of circular cylinders using standard stimuli differing in diameter from 10 mm to 35 mm. In the second experiment a texture difference threshold was obtained for the discrimination of grooved surfaces (groove width 2-7 mm).The squirrel monkeys achieved a mean size difference threshold of 8% stimulus difference. The linear increase of absolute thresholds as a function of the starting stimulus size showed that haptic size discriminations in squirrel monkeys correspond to Weber's law. Three of the animals achieved a texture difference of 10% stimulus difference, while one monkey showed a distinctively lower haptic acuity. An analysis of the exploratory behavior points to a subject-related difference in the significance of cutaneous and kinesthetic information during size discriminations. Whereas differences in the animals' exploratory behavior did not correlate with the size difference threshold a subject achieved, different thresholds for texture discrimination can be explained by the different exploratory procedures the monkeys used to touch grooved surfaces. The low difference thresholds determined for the squirrel monkeys in the present study point to the significance of unrestrained test conditions for the assessment of the haptic capacity of a species.     

Haptic discrimination of size and texture in squirrel monkeys (Saimiri sciureus)

The present study analyzed haptic abilities of four squirrel monkeys. Using a two-alternative forced-choice procedure, stimuli were presented in a visually opaque box, allowing unrestrained test subjects to grab through a small opening and touch the discriminanda. Difference thresholds were determined by a modified method of limits. In the first experiment we determined size difference thresholds for the discrimination of circular cylinders using standard stimuli differing in diameter from 10 mm to 35 mm. In the second experiment a texture difference threshold was obtained for the discrimination of grooved surfaces (groove width 2-7 mm). The squirrel monkeys achieved a mean size difference threshold of 8% stimulus difference. The linear increase of absolute thresholds as a function of the starting stimulus size showed that haptic size discriminations in squirrel monkeys correspond to Weber's law. Three of the animals achieved a texture difference of 10% stimulus difference, while one monkey showed a distinctively lower haptic acuity. An analysis of the exploratory behavior points to a subject-related difference in the significance of cutaneous and kinesthetic information during size discriminations. Whereas differences in the animals' exploratory behavior did not correlate with the size difference threshold a subject achieved, different thresholds for texture discrimination can be explained by the different exploratory procedures the monkeys used to touch grooved surfaces. The low difference thresholds determined for the squirrel monkeys in the present study point to the significance of unrestrained test conditions for the assessment of the haptic capacity of a species.     

Ants in a labyrinth: a statistical mechanics approach to the division of labour

Division of labour (DoL) is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic) interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.     

The utility of behavioral models and modules in molecular analyses of social behavior

It is extremely difficult to trace the causal pathway relating gene products or molecular pathways to the expression of behavior. This is especially true for social behavior, which being dependent on interactions and communication between individuals is even further removed from molecular-level events. In this review, we discuss how behavioral models can aid molecular analyses of social behavior. Various models of behavior exist, each of which suggest strategies to dissect complex behavior into simpler behavioral 'modules.' The resulting modules are easier to relate to neural processes and thus suggest hypotheses for neural and molecular function. Here we discuss how three different models of behavior have facilitated understanding the molecular bases of aspects of social behavior. We discuss the response threshold model and two different approaches to modeling motivation, the state space model and models of reinforcement and reward processing. The examples we have chosen illustrate how models can generate testable hypotheses for neural and molecular function and also how molecular analyses probe the validity of a model of behavior. We do not champion one model over another; rather, our examples illustrate how modeling and molecular analyses can be synergistic in exploring the molecular bases of social behavior.     

Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genomewide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F(2) intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses.     

Effect of retentive markers on the dynamics of settlement: The case of arthropod silk

During a settlement decision, the presence of conspecifics is crucial to species subject to Allee effects, for which the number of founders affects the subsequent growth of the colony. Marking the area (physically or chemically) conveys information about the number of conspecifics present in a new patch. Here, we study how an individual affinity for the marker affects the dynamics of a foundation process. A generic population model is presented, in which marking and affinity for the marker are at stake. Our results show that population size thresholds can appear, below which settlement is not possible. This model is then used to study the dynamics of migration and aggregation in a set of interconnected populations. We show that affinity for the marker can induce asymmetries in the population distribution. Anelosimus eximius is a social spider subject to Allee effects, for which silk potentially acts as a marker. We test our predictions with field experiments involving two populations of A. eximius in a Y-shaped setup. The agreement between our experimental and theoretical results strongly supports the validity of the model. This allows us to use the model to estimate a realistic set of parameters of biological significance to this social spider.     

Interacting Epidemics and Coinfection on Contact Networks

The spread of certain diseases can be promoted, in some cases substantially, by prior infection with another disease. One example is that of HIV, whose immunosuppressant effects significantly increase the chances of infection with other pathogens. Such coinfection processes, when combined with nontrivial structure in the contact networks over which diseases spread, can lead to complex patterns of epidemiological behavior. Here we consider a mathematical model of two diseases spreading through a single population, where infection with one disease is dependent on prior infection with the other. We solve exactly for the sizes of the outbreaks of both diseases in the limit of large population size, along with the complete phase diagram of the system. Among other things, we use our model to demonstrate how diseases can be controlled not only by reducing the rate of their spread, but also by reducing the spread of other infections upon which they depend.     

Optimizing size thresholds in a plant–pollinator interaction web: towards a mechanistic understanding of ecological networks

Using functional traits together with abundance effects strengthens the prediction of interactions between pairs of species in ecological networks. Insights into the way species interact as well as prediction accuracy can be gained when thresholds for trait value combinations that make interactions possible are optimized through model selection. I present novel data of two subalpine plant–pollinator communities and build several stochastic models integrating flower abundance and morphological threshold rules that allow or restrict interactions between species. The number of correctly predicted interactions was highest when thresholds were set so that the insect’s proboscis was not shorter than the nectar-holder depth minus 1–1.6 mm, and not wider than the nectar-holder width minus 0.5 mm. In comparison with models based solely on plant abundance effects, the model incorporating optimized size thresholds better predicted the distribution of the trait differences between plants and insects. This indicates that a mechanistic approach of interaction webs based on optimized size thresholds provides valuable information on community structure. The possible implications for community functioning are discussed.     

Minor allele frequency thresholds strongly affect population structure inference with genomic data sets

A common method of minimizing errors in large DNA sequence data sets is to drop variable sites with a minor allele frequency (MAF) below some specified threshold. Although widespread, this procedure has the potential to alter downstream population genetic inferences and has received relatively little rigorous analysis. Here we use simulations and an empirical single nucleotide polymorphism data set to demonstrate the impacts of MAF thresholds on inference of population structure—often the first step in analysis of population genomic data. We find that model‐based inference of population structure is confounded when singletons are included in the alignment, and that both model‐based and multivariate analyses infer less distinct clusters when more stringent MAF cutoffs are applied. We propose that this behaviour is caused by the combination of a drop in the total size of the data matrix and by correlations between allele frequencies and mutational age. We recommend a set of best practices for applying MAF filters in studies seeking to describe population structure with genomic data.     

Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model

Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.     

Interval estimates for epidemic thresholds in two-sex network models

Epidemic thresholds in network models of heterogeneous populations characterized by highly right-skewed contact distributions can be very small. When the population is above the threshold, an epidemic is inevitable and conventional control measures to reduce the transmissibility of a pathogen will fail to eradicate it. We consider a two-sex network model for a sexually transmitted disease which assumes random mixing conditional on the degree distribution. We derive expressions for the basic reproductive number (R(0)) for one and heterogeneous two-population in terms of characteristics of the degree distributions and transmissibility. We calculate interval estimates for the epidemic thresholds for stochastic process models in three human populations based on representative surveys of sexual behavior (Uganda, Sweden, USA). For Uganda and Sweden, the epidemic threshold is greater than zero with high confidence. For the USA, the interval includes zero. We discuss the implications of these findings along with the limitations of epidemic models which assume random mixing.     

Excitability with multiple thresholds. A new mode of dynamic behavior analyzed in a regulated biochemical system

We analyze in a biochemical model the phenomenon of excitability in which suprathreshold perturbations of a stable steady state are amplified in a pulsatory manner. The two-variable model is that of an autocatalytic enzyme reaction with recycling of product into the substrate. This model was previously studied for the coexistence between two stable periodic regimes (birhythmicity). We show that the multiplicity of dynamic behavioral modes extends to the phenomenon of excitability. Whereas excitable behavior is generally characterized by a single threshold for excitation, two distinct thresholds may coexist in this model. Moreover, in these conditions, two different plateaux are obtained for the response amplitude when the stimulus is gradually increased. By means of phase plane analysis we explain the origin of multiple thresholds for excitability and predict the conditions for their occurrence. Implications of the phenomenon for excitable cells, in particular for neurons, are discussed.     

Residence time and potential range: crucial considerations in modelling plant invasions

A prime aim of invasion biology is to predict which species will become invasive, but retrospective analyses have so far failed to develop robust generalizations. This is because many biological, environmental, and anthropogenic factors interact to determine the distribution of invasive species. However, in this paper we also argue that many analyses of invasiveness have been flawed by not considering several fundamental issues: (1) the range size of an invasive species depends on how much time it has had to spread (its residence time); (2) the range size and spread rate are mediated by the total extent of suitable (i.e. potentially invasible) habitat; and (3) the range size and spread rate depend on the frequency and intensity of introductions (propagule pressure), the position of founder populations in relation to the potential range, and the spatial distribution of the potential range. We explored these considerations using a large set of invasive alien plant species in South Africa for which accurate distribution data and other relevant information were available. Species introduced earlier and those with larger potential ranges had larger current range sizes, but we found no significant effect of the spatial distribution of potential ranges on current range sizes, and data on propagule pressure were largely unavailable. However, crucially, we showed that: (1) including residence time and potential range always significantly increases the explanatory power of the models; and (2) residence time and potential range can affect which factors emerge as significant determinants of invasiveness. Therefore, analyses not including potential range and residence time can come to misleading conclusions. When these factors were taken into account, we found that nitrogen‐fixing plants and plants invading arid regions have spread faster than other species, but these results were phylogenetically constrained. We also show that, when analysed in the context of residence time and potential range, variation in range size among invasive species is implicitly due to variation in spread rates, and, that by explicitly assuming a particular model of spread, it is possible to estimate changes in the rates of plant invasions through time. We believe that invasion biology can develop generalizations that are useful for management, but only in the context of a suitable null model.     

Self-Organization on Social Media: Endo-Exo Bursts and Baseline Fluctuations

A salient dynamic property of social media is bursting behavior. In this paper, we study bursting behavior in terms of the temporal relation between a preceding baseline fluctuation and the successive burst response using a frequency time series of 3,000 keywords on Twitter. We found that there is a fluctuation threshold up to which the burst size increases as the fluctuation increases and that above the threshold, there appears a variety of burst sizes. We call this threshold the critical threshold. Investigating this threshold in relation to endogenous bursts and exogenous bursts based on peak ratio and burst size reveals that the bursts below this threshold are endogenously caused and above this threshold, exogenous bursts emerge. Analysis of the 3,000 keywords shows that all the nouns have both endogenous and exogenous origins of bursts and that each keyword has a critical threshold in the baseline fluctuation value to distinguish between the two. Having a threshold for an input value for activating the system implies that Twitter is an excitable medium. These findings are useful for characterizing how excitable a keyword is on Twitter and could be used, for example, to predict the response to particular information on social media.     

How citation boosts promote scientific paradigm shifts and nobel prizes

Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only through citation cascades. A quantitative analysis reveals how and why they happen. Science appears to behave like a self-organized critical system, in which citation cascades of all sizes occur, from continuous scientific progress all the way up to scientific revolutions, which change the way we see our world. Measuring the "boosting effect" of landmark papers, our analysis reveals how new ideas and new players can make their way and finally triumph in a world dominated by established paradigms. The underlying "boost factor" is also useful to discover scientific breakthroughs and talents much earlier than through classical citation analysis, which by now has become a widespread method to measure scientific excellence, influencing scientific careers and the distribution of research funds. Our findings reveal patterns of collective social behavior, which are also interesting from an attention economics perspective. Understanding the origin of scientific authority may therefore ultimately help to explain how social influence comes about and why the value of goods depends so strongly on the attention they attract.