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At least 19 records

Comparison of Likelihood Methods for Generalized Linear Mixed Models with Application to Quiet Supersonic Flights 2018 Data

Repeated measurement will be a feature of the survey data collected during the Quesst missionX-59 community response tests (CRT). Since each participant will report his or her categorical level of annoyance in response to multiple events, the responses from any single individual may be correlated with one another. Several models within the class of generalized linear mixed models (GLMM) are pertinent to the analysis of correlated categorical outcomes; the random intercept logistic regression model is one example. Both Bayesian and frequentist methods for fitting these models are available, with frequentist methods relying on some form of approximation (of either an integral or the integrand) that appears in the marginal likelihood function. Given several anticipated similarities of the X-59 CRT data to data collected during a past risk reduction, Quiet Supersonic Flights 2018 (QSF18), this short note is intended to create awareness. It documents an instance in which a reported population average dose-response relationship derived from QSF18 single event data was distorted by the integral approximation applied in likelihood-based methods. We review some of the available literature on the topic, compare the outputs of several different computational approaches implemented in available statistical software, and present simple corrective actions that may be useful during the Quesst mission.

dose-response model↗

Effects of hydrokinetic turbine sound on the behavior of four species of fish within an experimental mesocosm

The development of hydrokinetic energy technologies (e.g., tidal turbines) has raised concern over the potential impacts of underwater sound produced by hydrokinetic turbines on fish species likely to encounter these turbines. To assess the potential for behavioral impacts, we exposed four species of fish to varying intensities of recorded hydrokinetic turbine sound in a semi-natural environment. Although we tested freshwater species (redhorse suckers [Moxostoma spp], freshwater drum [Aplondinotus grunniens], largemouth bass [Micropterus salmoides], and rainbow trout [Oncorhynchus mykiss]), these species are also representative of the hearing physiology and sensitivity of estuarine species that would be affected at tidal energy sites. Here, we evaluated changes in fish position relative to different intensities of turbine sound as well as trends in location over time with linear mixed-effects and generalized additive mixed models. We also evaluated changes in the proportion of near-source detections relative to sound intensity and exposure time with generalized linear mixed models and generalized additive models. Models indicated that redhorse suckers may respond to sustained turbine sound by increasing distance from the sound source. Freshwater drum models suggested a mixed response to turbine sound, and largemouth bass and rainbow trout models did not indicate any likely responses to turbine sound. Lastly, findings highlight the importance for future research to utilize accurate localization systems, different species, validated sound transmission distances, and to consider different types of behavioral responses to different turbine designs and to the cumulative sound of arrays of multiple turbines.

16 TIDAL AND WAVE POWER↗

Extinction Dynamics of the Foot-and-Mouth Disease Virus Carrier State Under Natural Conditions

Foot-and-mouth disease (FMD) is one of the most economically important livestock diseases worldwide. Following the clinical phase of FMD, a large proportion of ruminants remain persistently infected for extended periods. Although extinction of this carrier state occurs continuously at the animal and population levels, studies vary widely in their estimates of the duration of persistent infection. There is a need for robust statistical models to capture the dynamics of persistent infection for the sake of guiding FMD control and trade policies. The goal of the current study was to develop and assess statistical models to describe the extinction of FMD virus (FMDV) persistent infection using data from primary longitudinal studies of naturally infected cattle and Asian buffalo in Vietnam and India. Specifically, accelerated failure time (AFT) models and generalized linear mixed models (GLMM) were developed to predict the probability of persistent infection in seropositive animals and identified carriers at the individual animal level at sequential time points after outbreaks. The primary studies were analyzed by country and combined using an individual-participant data meta-analysis approach. The models estimated similar trends in the duration of persistent infection for the study/species groups included in the analyses, however the significance of the trends differed between the models. The overall probabilities of persistent infection were similar as predicted by the AFT and GLMM models: 6 months: 99% (AFT) /80% (GLMM), 12 months: 51% (AFT) /32% (GLMM), 18 months: 6% (AFT) /5% (GLMM), 24 months: 0.8% (AFT) /0.6% (GLMM). These models utilizing diverse and robust data sets predict higher probabilities of persistence than previously published, suggesting greater endurance of carriers subsequent to an outbreak. This study demonstrates the utility of statistical models to investigate the dynamics of persistent infection and the importance of large datasets, which can be achieved by combining data from several smaller studies in meta-analyses. Results of this study enhance current knowledge of the FMDV carrier state and may inform policy decisions regarding FMDV persistent infection.

59 BASIC BIOLOGICAL SCIENCES↗

Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model

We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.

Conjuction Assessment↗

Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonly used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).

97 MATHEMATICS AND COMPUTING↗

Developing Rationale for Experimental Designs Employed During Forthcoming NASA Quesst Mission Community Noise Campaigns

Since the publication of R.A. Fisher’s “The Arrangement of Field Experiments” in 1926, the enumerated principles that contributed to the improvement of agricultural field experiments in the early 20th century (randomization, replication, blocking, and appropriate variation of factors) remain hallmarks of all well-designed clinical trials and scientific endeavors in the 21st century. Beginning in 2026, NASA will conduct community noise campaigns with the first-of-kind X-59 experimental aircraft to 1) demonstrate the possibility of quiet supersonic flight over land and 2) to collect live data about annoyance (a categorical response) in relation to estimated noise levels (an experimental factor) produced by the new noise phenomenon, a low-noise “sonic thump”. The resulting predicted relationship between perceptual response and estimated noise level, e.g., mixed logistic regression or related models in the class of generalized linear (mixed) models, is believed to be a useful policy tool that domestic and international regulators can use when deciding whether existing prohibitions of supersonic flight over land can be replaced with a noise-based limit. The X-59 is engineered with the expectation that annoyance in the tested ranges should be a rare outcome, and, consequently, NASA convened an interdisciplinary team to examine and refine the rationale underlying the experimental design for future community campaigns. In this presentation, we review relevant literature on experiments with rare binary outcomes, relate the deliberations of the NASA team to tenets of good experimental design, and highlight several challenges and operational realities of this ambitious campaign.

Design of Experiments; blocking; randomization; co↗

Interpretable Machine Learning for Characterizing Electric Vehicle Charging Behavior: Insights from Real-World Data

As electric vehicle (EV) adoption rises globally, concerns about the impact on aging electrical grids grow, particularly regarding the charging behavior of EV drivers. This study analyzes real-world driving and charging data from Ford battery electric vehicles (BEVs) collected between 2018 and 2019 to develop interpretable models that characterize charging behavior and quantify influencing factors. Prior research has relied on assumptions regarding driver behavior, often overlooking actual charging patterns. By employing generalized linear mixed models (GLMMs), this work offers insights into how various elements, such as next trip distance and state of charge (SOC), influence charging decisions. The dataset comprises over three million park-trip pairs from 1,997 vehicles, revealing that features related to driving behavior significantly dictate charging behavior, while infrastructure and regional factors have lesser impacts. The findings suggest that existing simulation models may oversimplify EV charging behavior assumptions. This work utilizes real-world EV driving and charging data to train interpretable models that describe charging behavior and quantify the factors most associated with how drivers use charging infrastructure. This research underscores the need for interpretable, data-driven methodologies to inform future EV infrastructure planning and grid management.

29 - ENERGY PLANNING, POLICY AND ECONOMY↗

Breeding latitude is associated with the timing of nesting and migration around the annual calendar among Purple Martin (Progne subis) populations

Timing is critical for species that migrate seasonally, as timing mismatches can lead to reduced reproductive success and population declines. We investigated the effect of breeding latitude on the migration timing of a long-distance migratory songbird (Purple Martin, Progne subis subis) by using light-level geolocators deployed across breeding sites between 26° and 53° latitude (n = 329). We used nesting data (1st egg dates; n=28,165) to explore latitudinal patterns in the timing of breeding. Using generalized linear mixed models (GLMMs) we found that breeding latitude was highly associated with timing around the calendar, explaining population-level timing across both spring and fall migration. Populations breeding at more northern latitudes migrated later in fall (mean days/degree latitude =2), in spring (mean days/degree latitude =3), and nested later (days/degree latitude = 3) than populations breeding at more southern latitudes. Generalized additive mixed models (GAMMs) revealed significant non-linearity between breeding latitude and spring and fall migration timing, and the timing of nesting. In spring, the most northern breeders (> 40 degrees N) were more synchronous in their timing, departing their nonbreeding sites and arriving earlier at their breeding sites relative to their breeding latitude. These most northern breeders also had similar nest timing and fall migration departure timing. Breeding latitude was also associated with seasonal partitioning of migratory and sedentary periods. The most northern breeders spent 10% more time on fall migration, 2% more at wintering grounds, 1% more on spring migration, and 13% less time at their breeding sites. Our results support the notion that selection for timing at breeding latitudes can have year-round effects on the timing of seasonal events in long-distance migratory songbirds. Future studies should examine whether these timing patterns associated with latitude limit phenotypic responses to climate change.

54 ENVIRONMENTAL SCIENCES↗

High-resolution (30-m) urban land cover projections for Los Angeles California Urban Area: 2010 to 2100 under SSP5

These data represent simulations of future land use and land cover (LULCC) for Los Angeles urban area (U.S. Census Bureau defined area) as raster tiff images at a 30-m pixel resolution and at decadal time steps from 2010 to 2100. LULCC classes in this product follow the National Land Cover Dataset (NLCD) classification. NLCD 21-24 correspond to open developed, low developed, medium developed, and high developed urban land classes, respectively. Only urban land cover classes (NLCD class 21, 22, 23, and 24) are dynamic over time; however, all NLCD classes are included in the final product. Therefore, NLCD classes that do not convert to an urban class will be similar to year 2000. The products were developed using a hybridized statistical and cellular automata approach. Linear mixed models (LMMs) were used to estimate future urban land budgets based on 1-km urban land fraction projections from Gao and Pesaresi (2021), whereas separate generalized linear mixed models (GLMMs) were used to estimate shifts in urban land intensities based on retrospective shifts in NLCD urban class intensities over a 20- year period. Based on urban land allocations from the statistical models, a cellular-automata and downscaling routine was used to simulate dynamic urban land expansion at a 30-m resolution based on suitability criteria. Scenarios of future urban landcover change projections include variant solutions for the Shared Socioeconomic Pathway 5 (SSP5) based on different population assumptions, different land use intensification assumptions, variable land zoning constraints, and iterative adjustments to correct for over allocation of urban expansion across decadal time periods from 2010 to 2100. This results in 320 raster products.

Land↗

High-resolution (30-m) urban land cover projections for Los Angeles California Urban Area: 2010 to 2100 under SSP3 and SSP5 [Updated simulations based on population-driven urban intensity transitions]

These data (v3) are updated from previous versions (1 and 2) in that they include consider the effects of population on transitions in urban land intensity. This leads to more reasonable differences in urban land projections under variant SSPs. For the present dataset, both SSP3 and SSP5 are provided. These data represent simulations of future land use and land cover (LULCC) for Los Angeles urban area (U.S. Census Bureau defined area) as raster tiff images at a 30-m pixel resolution and at decadal time steps from 2010 to 2100. LULCC classes in this product follow the National Land Cover Dataset (NLCD) classification. NLCD 21-24 correspond to open developed, low developed, medium developed, and high developed urban land classes, respectively. Only urban land cover classes (NLCD class 21, 22, 23, and 24) are dynamic over time; however, all NLCD classes are included in the final product. Therefore, NLCD classes that do not convert to an urban class will be similar to year 2000. The products were developed using a hybridized statistical and cellular automata approach. Linear mixed models (LMMs) were used to estimate future urban land budgets based on 1-km urban land fraction projections from Gao and Pesaresi (2021), whereas separate generalized linear mixed models (GLMMs) were used to estimate shifts in urban land intensities based on retrospective shifts in NLCD urban class intensities over a 20- year period. Based on urban land allocations from the statistical models, a cellular-automata and downscaling routine was used to simulate dynamic urban land expansion at a 30-m resolution based on suitability criteria. Scenarios of future urban landcover change projections include variant solutions for the Shared Socioeconomic Pathway 5 (SSP5) and SSP 3 based on different population assumptions, different land use intensification assumptions, variable land zoning constraints, and iterative adjustments to correct for over allocation of urban expansion across decadal time periods from 2010 to 2100. This results in 320 raster products.

Land↗

Environmental predictors of pulmonary nontuberculous mycobacteria (NTM) sputum positivity among persons with cystic fibrosis in the state of Florida

Nontuberculous mycobacteria (NTM) are opportunistic human pathogens that are commonly found in soil and water, and exposure to these organisms may cause pulmonary nontuberculous mycobacterial disease. Persons with cystic fibrosis (CF) are at high risk for developing pulmonary NTM infections, and studies have shown that prolonged exposure to certain environments can increase the risk of pulmonary NTM. It is therefore important to determine the risk associated with different geographic areas. Using annualized registry data obtained from the Cystic Fibrosis Foundation Patient Registry for 2010 through 2017, we conducted a geospatial analysis of NTM infections among persons with CF in Florida. A Bernoulli model in SaTScan was used to identify clustering of ZIP codes with higher than expected numbers of NTM culture positive individuals. Generalized linear mixed models with a binomial distribution were used to test the association of environmental variables and NTM culture positivity. We identified a significant cluster of M . abscessus and predictors of NTM sputum positivity, including annual precipitation and soil mineral levels.

59 BASIC BIOLOGICAL SCIENCES↗

Statistical Considerations for the Design and Execution of NASA's Community Noise Surveys

The World Health Organization defines community noise as noise emitted from all sources apart from noise at an industrial workplace. Example sources include neighborhood and construction noise, noise from road and rail, and air traffic noise. In particular, overland supersonic flights have been banned in the United States since the 1970s based on data accumulated during the 1960s; the degree of reported annoyance from the resulting sonic booms was a key factor leading to the prohibition. In subsequent years, scientific and engineering understanding has led to the potential to produce low amplitude sonic booms, or ‘sonic thumps’, during supersonic flight through aircraft design choices. Aircraft manufacturers have expressed renewed interest in producing supersonic commercial aircraft, but without appropriate changes to regulation, only overseas routes can be traveled supersonically. The National Aeronautics and Space Administration (NASA) will be flying the X-59 demonstrator aircraft in a series of community tests to begin in the 2024 fiscal year. In this presentation we provide some historical context for the current prohibitions on supersonic commercial flight. Using data collected during earlier NASA risk reduction tests, we demonstrate how generalized linear mixed models can be used to inform the functional dose-response response curve. Finally, we discuss some of the challenges in designing the future community studies and generalizing them to a nationally-representative dose-response curve. The study effort will be of national and international importance as the data and models prepared during the community tests will be provided to the International Civil Aviation Organization (ICAO) in order to help noise regulators determine if supersonic flight will be permitted over land once again and at what demonstrable noise levels.

Nathan B Cruze↗

Statistical Engineering Toward Commercial Supersonic Flight: NASA's Quesst Mission

NASA’s Quesst Mission has dual goals of demonstrating low-noise supersonic technology in flight and surveying public reactions to low-noise supersonic overflight. For half a century, commercial aircraft have been required to fly slower than the speed of sound over land to prevent “creating an unacceptable situation” on the ground due to sonic booms. However, aircraft shaping techniques honed through decades of research have dramatically changed the way shockwaves from supersonic flight merge together as they travel to the ground. What used to sound like a boom on the ground will be transformed into a thump. NASA is now building a full-scale, piloted demonstration aircraft called the X-59 to demonstrate low-noise supersonic flight. In 2024, the X-59 aircraft will commence a national series of community overflight surveys to collect data on how people perceive “sonic thumps.” The results will be provided to national and international noise regulators as they consider creating new standards that allow commercial supersonic flight over land at acceptably low noise levels. In this presentation we provide historical context for the current prohibitions on supersonic commercial flight. Using data collected during earlier NASA tests, we demonstrate how generalized linear mixed models can be used to inform the functional dose-response curve. We also illustrate simulation experiments of the variability of sonic thump exposure across the United States. Finally, we discuss some of the challenges in designing the future community studies and generalizing them to a nationally-representative dose-response curve.

Quesst↗

Mitigating the Impacts of Measurement Error in the Quesst Mission Community Noise Study

Beginning in 2025, the NASA Quesst mission will conduct a series of community response tests involving flyovers of the X-59 aircraft at select localities across the United States. Several waves of a longitudinal survey will be administered over approximately one month of testing in order to capture perceptual responses to low-amplitude sonic booms, or “sonic thumps”. Simultaneously, noise exposure levels will be estimated by fusing model-based predictions with measurements taken from a sparse network of monitors in the region. As one of the aims of the study is to produce a dose-response curve, a regression model relating perceptual response to noise exposure levels, it is important to acknowledge the potential attenuation bias that results from measurement error in the estimated noise exposure levels. In this presentation we review and compare several methods for dealing with measurement error in generalized linear mixed models. The methods are demonstrated on simulated data and real data collected during past NASA risk reduction studies.

measurement error↗

Ecological analysis of associations between groundwater quality and hypertension and cardiovascular disease in rural Saskatchewan, Canada using Bayesian hierarchical models and administrative health data

Highlights: • Hardness and magnesium were associated with decreased risk of cardiovascular disease. • Arsenic concentrations were not associated with the risk of cardiovascular disease. • Summarized water health standards were not associated with cardiovascular disease. Associations between groundwater quality and the prevalence of hypertension and ischemic heart disease were investigated in rural areas of the Canadian province of Saskatchewan. The partially ecological study was analyzed using Bayesian hierarchical models to account for spatial variability in risk. Exposure measures and health outcomes were estimated based on previously collected water quality surveillance data from public water supplies and private wells and administrative health data. Water quality exposures for each study region were estimated by applying geostatistical techniques to arsenic concentrations and principal component (PC) scores. The PC scores summarized groups of parameters measuring either health standards or aesthetic objectives described by the province. Generalized linear mixed models with a log link assessed associations between water quality and observed count of health outcomes relative to the expected value. The Bayesian models contained uncorrelated and spatially correlated random effects for each geographic region. Effect estimates were controlled for sex and age by stratification of case and expected case counts, for smoking by inclusion of sex- and age-specific prevalence of chronic obstructive pulmonary disease as a surrogate covariate, and for education and income by use of census data. There was no evidence for associations between groundwater arsenic concentrations in public or private water supplies and increased risk of hypertension or cardiovascular disease. An increase in the second aesthetic objectives PC score from public supplies was associated with a protective effect against ischemic heart disease. This PC value summarized hardness and magnesium Similarly, an increase in the second aesthetic objectives PC in private supplies was associated with decreased prevalence of hypertension. The results of this study are consistent with others demonstrating a relationship between elevated hardness and magnesium concentrations in drinking water and reduced risk of hypertension and cardiovascular disease. Further investigation is warranted with individual exposure history, particularly with respect to the potential beneficial effect of hard water on the prevalence of hypertension and cardiovascular disease.

54 ENVIRONMENTAL SCIENCES↗

Resident and transient coyotes exhibit differential patterns of movement behavior across heterogeneous landscapes in the southeastern United States

Coyotes (Canis latrans) are a highly adaptable canid species whose behavioral plasticity has allowed them to persist in a wide array of habitats throughout North America. As generalists, coyotes can alter movement patterns and change territorial strategies between residency (high site fidelity) and transiency (low site fidelity) to maximize fitness. Uncertainty remains about resident and transient coyote movement patterns and habitat use because research has reached conflicting conclusions regarding patterns of habitat use by both groups. We quantified effects of habitat on resident and transient coyote movement behavior using first passage time (FPT) analysis, which assesses recursive movement along an individual's movement path to delineate where they exhibit area-restricted search (ARS) behaviors relative to habitat attributes. We quantified monthly movement rates for 171 coyotes (76 residents and 53 transients) and then used estimated FPT values in generalized linear mixed models to quantify monthly habitat use for resident and transient coyotes. Transients had greater movement rates than residents across all months except January. Resident FPT values were positively correlated with agricultural land cover during fall and winter, but negatively correlated with agriculture during spring. Resident FPT values were also negatively correlated with developed habitats during May–August, deciduous land cover during June–August, and wetlands during September–January except November. FPT values of transient coyotes were positively correlated with developed areas throughout much of the year and near wetlands during July–September. Transient FPT values were negatively correlated with agriculture during all months except June and July. High FPT values (ARS behavior) of residents and transients were generally correlated with greater densities of edge habitat. Although we observed high individual variation in space use, our study found substantive differences in habitat use between residents and transients, providing further evidence that complexity and plasticity of coyote habitat use is influenced by territorial strategy.

54 ENVIRONMENTAL SCIENCES↗

Verification of Data-Driven Models of Physical Phenomena using Interpretable Approximation

Machine-learned models, specifically neural networks, are increasingly used as “closures” or “constitutive models” in engineering simulators to represent fine-scale physical phenomena that are too computationally expensive to resolve explicitly. However, these neural net models of unresolved physical phenomena tend to fail unpredictably and are therefore not used in mission-critical simulations. In this report, we describe new methods to authenticate them, i.e., to determine the (physical) information content of their training datasets, qualify the scenarios where they may be used and to verify that the neural net, as trained, adhere to physics theory. We demonstrate these methods with neural net closure of turbulent phenomena used in Reynolds Averaged Navier-Stokes equations. We show the types of turbulent physics extant in our training datasets, and, using a test flow of an impinging jet, identify the exact locations where the neural network would be extrapolating i.e., where it would be used outside the feature-space where it was trained. Using Generalized Linear Mixed Models, we also generate explanations of the neural net (à la Local Interpretable Model agnostic Explanations) at prototypes placed in the training data and compare them with approximate analytical models from turbulence theory. Finally, we verify our findings by reproducing them using two different methods.

42 ENGINEERING↗

The toughest animals of the Earth versus global warming: Effects of long‐term experimental warming on tardigrade community structure of a temperate deciduous forest

Abstract Understanding how different taxa respond to global warming is essential for predicting future changes and elaborating strategies to buffer them. Tardigrades are well known for their ability to survive environmental stressors, such as drying and freezing, by undergoing cryptobiosis and rapidly recovering their metabolic function after stressors cease. Determining the extent to which animals that undergo cryptobiosis are affected by environmental warming will help to understand the real magnitude climate change will have on these organisms. Here, we report on the responses of tardigrades within a five‐year‐long, field‐based artificial warming experiment, which consisted of 12 open‐top chambers heated to simulate the projected effects of global warming (ranging from 0 to 5.5°C above ambient temperature) in a temperate deciduous forest of North Carolina (USA). To elucidate the effects of warming on the tardigrade community inhabiting the soil litter, three community diversity indices (abundance, species richness, and Shannon diversity) and the abundance of the three most abundant species ( Diphascon pingue , Adropion scoticum , and Mesobiotus sp.) were determined. Their relationships with air temperature, soil moisture, and the interaction between air temperature and soil moisture were tested using Bayesian generalized linear mixed models. Despite observed negative effects of warming on other ground invertebrates in previous studies at this site, long‐term warming did not affect the abundance, richness, or diversity of tardigrades in this experiment. These results are in line with previous experimental studies, indicating that tardigrades may not be directly affected by ongoing global warming, possibly due to their thermotolerance and cryptobiotic abilities to avoid negative effects of stressful temperatures, and the buffering effect on temperature of the soil litter substrate.

54 ENVIRONMENTAL SCIENCES↗