Stochastic Matrix Models Research Articles

Application of Stochastic Matrix Model with Improved GLR Algorithm in English Translation Studies

The rapid development of today’s society is accompanied by the explosive growth of information data; in the process of information transmission, language is a very important carrier. Among all kinds of communication languages, English always occupies an important position and is one of the most commonly used languages in social life. Therefore, the practical significance of English education is self-evident. With the popularization of the Internet, intelligent phrase recognition in machine translation is the key technology. With the help of natural language processing technology, an English translation corpus can be built to accurately mark the parts of speech of short words, and phrase recognition technology is used to correct grammatical ambiguity effectively. Structural ambiguity is a difficult problem in the field of English translation. Based on the random matrix model of the improved GLR algorithm, phrase structure labelling is constructed through the phrase corpus. Revised annotation can effectively improve the accuracy of academic translation, and intelligent English translation is realized through recognition technology. Simulation experiments verify the effectiveness of the model, and the results show that the English translation intelligent recognition model has a high proofreading accuracy. When the value of P is 0.95, the high accuracy can be retained to the maximum and the efficiency and feasibility of improving the GLR algorithm in machine translation can be improved.

Research on Financial Strategy and Financial Capability of Grassroots Power Supply Enterprises Based on Stochastic Matrix Model

On the basis of the generation, evolution, and development of the basic power supply enterprise’s financial core competence, this article determines the connotation and essence of the basic power supply enterprise’s financial core competence, so as to play a guiding role in fully and correctly grasping the basic power supply enterprise financial core competence. This article focuses on the formation mechanism and factors of the financial core competence of grassroots power supply enterprises and reviews the latest research hotspots and their theoretical significance in academia. By applying the random matrix model to evaluate the core financial capabilities of grassroots power supply enterprises, it proposes a path for cultivating and improving the core financial capabilities of grassroots power supply enterprises. Through a detailed and powerful discussion, it is possible to effectively improve the financial management efficiency of grassroots power supply enterprises and quickly adapt to the needs of market changes, so as to meet the interests of relevant stakeholders of grassroots power supply enterprises as much as possible. Considering the market competition environment, it is found that the positive relationship between corporate responsibility information disclosure and the degree of earnings management is only significant in low-competitive markets, which also shows that with the intensification of market competition, the degree of information asymmetry decreases. The ability of power supply is also increasing, which will weaken the mechanism of grassroots power supply enterprises to conceal earnings management behavior through corporate responsibility information disclosure. The results show that corporate responsibility information may become a tool to cover up the management of grassroots power supply enterprises to manipulate earnings and reduce the quality of earnings reports, and this behavior will be different in grassroots power supply enterprises with different characteristics and external environments. This will help to form an objective understanding of corporate responsibility information disclosure behaviors, identify the motives of grassroots power supply companies’ responsible behaviors for regulators, standardize corporate responsibility disclosure norms, and take differentiated measures for different situations.

A Nonlinear Stochastic Matrix Model for the Analysis of the Association between International Trade Growth and Environmental Change

This study uses a nonlinear stochastic matrix for an in-depth analysis of the association between international trade growth and environmental change. First, for a class of uncertain stochastic nonlinear time-lag systems, this study investigates its time-lag-related robust stochastic stabilization problem. A memory-free state feedback controller for the system is then obtained to ensure the effectiveness of the system performance. This makes the system more general and the corresponding theoretical results less conservative. Finally, numerical examples are given to further verify the validity and feasibility of the results. The “tariff measure” based on the magnitude of adverse changes in trade policy is not an accurate measure of trade policy uncertainty; the stochastic volatility method measures trade policy uncertainty by including tariff fluctuations that have been communicated in advance in the trade policy uncertainty indicator and fail to identify the different commodities that occur during the current trade friction. The trade policy uncertainty index constructed through textual analysis of newspapers can better reflect the trade policy uncertainty during this trade friction between China and the United States, and the rich time-varying nature can also reflect the alternating changes of tension and détente in economic and trade relations over some time. The analysis of the mechanism reveals that exporters have fewer emission reduction facilities than nonexporters but significantly lower energy consumption intensity for coal and water than nonexporters, reasoning that the mechanism by which exporters are more environmentally friendly than nonexporters lies in their cleaner energy use mix. Following the conclusions of this study, relevant policy recommendations are put forward, specifically the use of more efficient energy sources in the production process and more investment in energy efficiency and emission reduction to combat pollution.

Acute and lagged fitness consequences for a sagebrush obligate in a post mega-wildfire landscape.

Species responses to disturbance influence their extinction risks. Greater sage‐grouse (Centrocercus urophasianus) are bioindicators of sagebrush ecosystem health and the loss of sagebrush (Artemisia spp.) due to wildfire, can cause long‐term declines in sage‐grouse populations and other sagebrush obligate species. We examined the demographic response of a greater sage‐grouse population following a mega‐wildfire using stochastic age‐structured female‐based matrix models over 6 years (2013–2018). Notably, chick survival (range = 0.18–0.38) and female survival (yearling range: 0.20–0.68; adult range: 0.27–0.75) were low compared to values reported for greater sage‐grouse in other parts of their distribution. Greater sage‐grouse displayed variation in demographic tactics after the fire; however, adult female survival explained most of the variation in λ during each year, which reflected a declining population in 3 of 6 years with more uncertainty observed in 2015 when populations may have been increasing, and 2017 and 2018, when populations may have been declining. The continued annual population decline observed since 2016 suggested there were additional strong environmental impacts that may have been compounded by the fire effects, prolonging recovery of greater sage‐grouse. Our results support others that reported negative effects to greater sage‐grouse demographics from broad‐scale fire and provide a baseline for understanding how this species responds to loss of sagebrush cover based on their life history strategy.

Collision of Shaped Boulders With Sand Substrate Investigated by Experimental, Stochastic, and Discrete Approaches

This paper focuses on experimental and numerical studies aiming to better characterize the rebound kinematics between a natural soil and rock boulders using single‐block collision models. The variability of the dissipative parameters needed to reproduce the experimental results was studied considering two different approaches: stochastic transfer matrix and discrete element model (DEM). An experimental process taking into account all possible variables related to the collision was setup for small‐scale tests involving cylindrical and triangular boulders that introduces natural variability during impact. The objective of the experimental tests is to identify the relationship between incident and reflected velocities (before and after impact, respectively), in order to improve the predictability of the two numerical proposed approaches. The experimental results help to quantify the amount of energy losses during impacts and thus expands the knowledge to reproduce more realistic rockfall events. This work is divided in three main axes: (i) statistical analysis of experimental trajectories based on experimental tests; (ii) stochastic approach predicting in a simple way from initial velocities the kinematic of blocks after rebounds; and (iii) calibration of a discrete element model including probabilistic analysis based on Monte Carlo approach. This way, the two collision approaches presented in this work are able to predict rebounds in terms of averages, standard deviations, and distributions.

Living in a world of fire: the population dynamics of Mulinum spinosum in Northwestern Patagonia grasslands

How do fire frequency and fire size affect the long-term population dynamics of Mulinum spinosum? Which demographic parameters contribute most to the overall effect of fire on population growth? What is the relative importance of resprouting in sustaining population increase? Grass-shrub northwestern Patagonian steppe, Argentina. We monitored five permanent plots excluded from grazing for 6 years. We measured shrub abundance, dimensions, reproductive status, seedling emergence, and the size structure of M. spinosum, a resprouting native shrub inhabiting the northwest Patagonian steppe. Data were used to parametrize a stochastic matrix model developed to explore the influence of fire frequency and fire size on long-term population dynamics. We analyzed hypothetical scenarios that included fire frequencies ranging from one per year up to exclusion. Except for annual fires, projections show growing populations regardless of fire frequency. For fire return intervals greater than 50 years, the population becomes independent of fires, with an annual population growth rate of 5.6%. The results suggest two relevant aspects of the population dynamics of this species: M. spinosum is well adapted to the current fire frequency and its resprouting capability will allow M. spinosum to survive and persist in the community, even under frequent fires. Climate change models forecast an increase in summer temperature in NW Patagonia and, consequently, an enhanced fire frequency. Fire is a driver of M. spinosum encroachment that gets worse in overgrazed grasslands. Mulinum spinosum encroachment derivate in a relative replacement of palatable grasses by shrubs changes the ecosystem functionality and reduces productivity. Controlling this process is highly difficult and we suggest a change in the land use for the areas already deteriorated.

Interaction between habitat limitation and dispersal limitation is modulated by species life history and external conditions: a stochastic matrix model approach

Traditionally, species absence in a community is ascribed either to dispersal limitation (i.e., the inability of propagules of a species to reach a site) or to habitat limitation (abiotic or biotic conditions of a site prevent species from forming a viable population); sowing experiments can then distinguish between these two mechanisms. In our view, the situation is even more complicated. To demonstrate the complexity of the problem, we designed and applied simulations based on an extension of matrix models covering effects of propagule pressure and habitat limitation, and reflecting various characteristics of a species and of a habitat. These included life history, fecundity, seed bank viability of a species, habitat carrying capacity and disturbances. All the investigated factors affected proportion of occupied habitats. Whereas they can, to a large extent, compensate for each other, simultaneous decrease of habitat suitability and propagule input can be detrimental to the survival of a population. Our model demonstrated that in many cases, the absence of a species in a community is of stochastic nature, and result of interaction of species life history and various external conditions, and thus cannot be simply attributed to a single cause. The model results are supported with examples of case studies. The results also explain some well-known ecological phenomena, as decrease of niche breadth from the center to the margins of area of distribution. Finally, the model also suggests some caveats in interpretation of the results of sowing experiments.

The albatross of assessing and managing risk for long-lived pelagic seabirds

Pelagic predators such as albatross have long been of conservation concern, but assessing their status poses numerous challenges. A standard monitoring method for albatross is colony-based nest counts to track numbers of breeders. However, a variable proportion of the population skips breeding in any given year and cannot be quantified by nest counts, creating several complications to efforts in understanding population dynamics. We used stochastic demographic matrix models for black-footed (Phoebastria nigripes) and Laysan (P. immutabilis) albatross to investigate: i) the potential for the skipping behavior of breeders to create apparent density dependence in nest counts, ii) the limitations to assessing population trends from nest counts and implications for evaluating impacts from fisheries bycatch, including calculating Potential Biological Removal values, and iii) the relative importance of at-sea versus on-island threats to population viability. We found the increased likelihood of these albatrosses skipping breeding following a successful season – a feature common to many seabirds and other taxa – results in substantial negative temporal auto-correlation in the observable population that can be misinterpreted as negative density dependence, with important implications for inferences about population viability. Black-footed albatross appear limited by fisheries bycatch, while Laysan albatross, which have low estimated bycatch mortality, are currently at greater risk from island-based threats. Our results suggest a cautionary approach to managing black-footed and Laysan albatross should be adopted because detecting population declines from nest counts could take decades. Ultimately, we highlight the inherent difficulties in assessing population status and trends in long-lived species such as albatross.

The plight of a plover: Viability of an important snowy plover population with flexible brood care in Mexico

Shorebird populations often rely on wetland habitats, for which they are considered important indicators of ecosystem health. Populations residing at low latitudes remain vastly understudied in comparison with populations from high latitudes. Here we use detailed behavioural and demographic observations during all life stages in combination with stage specific modelling to predict the population trajectory of a snowy plover (Charadrius nivosus) population at Bahía de Ceuta, Sinaloa, Mexico. In North America this shorebird is threatened, with many monitored populations declining. Our stochastic matrix model for the Ceuta population, which closely matched our field observations, suggests that the population is a sink with a 99.8% probability of going extinct within 25years. Low apparent adult survival, which declined over time presumably because of poor reproductive success and/or permanent emigration in response to habitat degradation, had the largest impact on the population trajectory. We recommend urgent habitat management actions to address volatile water levels and hence increase reproductive success of this species at this important breeding site. Acknowledging the relative effects of flexible brood care on individual fitness and population dynamics presents an intriguing dilemma for conservation. We found that the flexible parental care system of snowy plovers affected chick survival: broods deserted by polyandrous females early after hatching had significantly lower survival than broods not deserted or those deserted late. Overall, deserting females raised fewer fledglings in this population than females that cared. Taken together, our study reveals unsustainable variation in local vital rate dynamics. To understand how this population contributes to regional source-sink dynamics, future research should evaluate the importance of immigration and emigration among neighbouring populations.

Variable vital rates and the risk of population declines in Adélie penguins from the Antarctic Peninsula region

AbstractPredicting population responses in changing environments is an important task for ecologists. In polar regions, climate warming, loss of sea ice, and more frequent anomalous events suggest that further reductions in ice‐dependent animal populations are likely. We assess the risk of near‐term (30‐year) depletion of an Adélie penguin (Pygoscelis adeliae) population with a stochastic matrix model parameterized with 30 yr (1982–2011) of data from the Copacabana colony on King George Island, Antarctica. The model was fitted to nest census data by estimating correction factors for survival rates estimated from a multi‐state mark–recapture model. We modeled future survival and fecundity scenarios during the projection period (2012–2041) based on a two‐state Markov chain that randomly assigned survival rates and reproductive success from their respective historical distributions to represent “good” and “poor” years. Monte Carlo simulation was used to estimate population trajectories across a range of progressively worse survival conditions. The results suggest that, given historical distributions of survival and reproductive success, a limited scope for recovery of the population is present, commensurate with recent stabilization in population size at the study site. However, our projections mainly suggest that the Adélie penguin population will decline if the frequency of years with poor survival remains at, or increases above, its 30‐year mean. The risk of local depletion within 30 yr, defined according to International Union for Conservation of Nature categories for endangered and critically endangered species, was 33% for >90% declines, but near 100% for 50% declines given status‐quo conditions. As survival conditions worsen, the risk of substantive depletions rose rapidly. Given expectations of further environmental and ecosystem changes in the northern Antarctic Peninsula region, continued declines in Adélie penguin population size at the northern extent of their range should be expected.

Unravelling the natural dynamics and resilience patterns of underwater Mediterranean forests: insights from the demography of the brown alga Cystoseira zosteroides

Summary Despite being among the most important habitat‐forming organisms in temperate seas almost nothing is known about the demography of many algal species. This limits our ability to understand the effects of global and local stressors and to predict future trends under ongoing environmental change, which in turn hinders conservation actions. Cystoseira species develop important forest‐like assemblages along the sublittoral zone in the Mediterranean Sea. In this study we investigated the natural population dynamics and resilience patterns of a deep‐water brown and canopy‐forming macroalga, Cystoseira zosteroides. We used density‐dependent and stochastic matrix models to estimate its basic life‐history and compare it with other relevant habitat‐forming marine (brown algae) and terrestrial (plants) species. We also evaluated the consequences of increasing the disturbances caused by storms and the impact of lost fishing gear, and their interaction, on C. zosteroides population dynamics. The population dynamics of C. zosteroides showed similar patterns to terrestrial long‐lived species such as shrubs and trees, with high survival due to their investment in structural biomass. Our data and models suggest that this species is able to buffer mortality pulses by increasing the number of recruits (and probably recruit survival) due to the new space liberated and, therefore, lower intraspecific competition. Nevertheless, when storm disturbances were more frequent than once every 50 years, their populations collapsed, and this effect worsened when several stressors acted simultaneously. Our results improve our understanding about the demography of algal forests, and highlight the fact that increases in local and global stressors may erode the resilience of macroalgae, resulting in a loss of structural complexity in the benthic communities of temperate seas. Synthesis. Our findings reveal that deep‐water C. zosteroides forests display slow population dynamics, similar to terrestrial perennials and trees. The increase in disturbance frequencies due to global and local stressors and their interaction will cause the decline of underwater macroalgal forests and may induce profound changes in their population and community dynamics.

The Use of Surrogate Data in Demographic Population Viability Analysis: A Case Study of California Sea Lions.

Reliable data necessary to parameterize population models are seldom available for imperiled species. As an alternative, data from populations of the same species or from ecologically similar species have been used to construct models. In this study, we evaluated the use of demographic data collected at one California sea lion colony (Los Islotes) to predict the population dynamics of the same species from two other colonies (San Jorge and Granito) in the Gulf of California, Mexico, for which demographic data are lacking. To do so, we developed a stochastic demographic age-structured matrix model and conducted a population viability analysis for each colony. For the Los Islotes colony we used site-specific pup, juvenile, and adult survival probabilities, as well as birth rates for older females. For the other colonies, we used site-specific pup and juvenile survival probabilities, but used surrogate data from Los Islotes for adult survival probabilities and birth rates. We assessed these models by comparing simulated retrospective population trajectories to observed population trends based on count data. The projected population trajectories approximated the observed trends when surrogate data were used for one colony but failed to match for a second colony. Our results indicate that species-specific and even region-specific surrogate data may lead to erroneous conservation decisions. These results highlight the importance of using population-specific demographic data in assessing extinction risk. When vital rates are not available and immediate management actions must be taken, in particular for imperiled species, we recommend the use of surrogate data only when the populations appear to have similar population trends.

Variation in the local population dynamics of the short-lived Opuntia macrorhiza (Cactaceae).

Spatiotemporal variation in demographic rates can have profound effects for population persistence, especially for dispersal-limited species living in fragmented landscapes. Long-term studies of plants in such habitats help with understanding the impacts of fragmentation on population persistence but such studies are rare. In this work, we reanalyzed demographic data from seven years of the short-lived cactus Opuntia macrorhiza var. macrorhiza at five plots in Boulder, Colorado. Previous work combining data from all years and all plots predicted a stable population (deterministic log lamda approximately 0). This approach assumed that all five plots were part of a single population. Since the plots were located in a suburban-agricultural interface separated by highways, grazing lands, and other barriers, and O. macrorhiza is likely dispersal limited, we analyzed the dynamics of each plot separately using stochastic matrix models assuming each plot represented a separate population. We found that the stochastic population growth rate log lamdaS varied widely between populations (log lamdaS = 0.1497, 0.0774, -0.0230, -0.2576, -0.4989). The three populations with the highest growth rates were located close together in space, while the two most isolated populations had the lowest growth rates suggesting that dispersal between populations is critical for the population viability of O. macrorhiza. With one exception, both our prospective (stochastic elasticity) and retrospective (stochastic life table response experiments) analysis suggested that means of stasis and growth, especially of smaller plants, were most important for population growth rate. This is surprising because recruitment is typically the most important vital rate in a short-lived species such as O. macrorhiza. We found that elasticity to the variance was mostly negligible, suggesting that O. macrorhiza populations are buffered against large temporal variation. Finally, single-year elasticities to means of transitions to the smallest stage (mostly due to reproduction) and growth differed considerably from their long-term elasticities. It is important to be aware of this difference when using models to predict the effect of manipulating plant vital rates within the time frame of typical plant demographic studies.

The Impact of the Second Seasonal Spawn on the Nantucket Population of the Northern Bay Scallop

AbstractNantucket, Massachusetts, has one of the last remaining commercial fisheries of the bay scallop Argopecten irradians, which is based largely on natural recruitment. Though previously thought to spawn only once in early summer at age 1, individuals of the northern subspecies often spawn again in late summer or fall, and recruits from this second spawning can survive to reproduce again in their second summer. We formulated an age‐based Leslie matrix model and estimated population growth rate with and without a second spawn based on data from 5 years of life history research. Elasticity analysis revealed that the population growth rate was most sensitive to juvenile survival, the major factor in recruitment rate, and year‐1 adult fertility was a close second. We varied those two rates randomly in a stochastic matrix model, which represented the effect of environmental fluctuations on population growth. A life history modeled with a second spawn had a negligible effect on the deterministic population growth rate under constant conditions, but under variable conditions the second spawn increased the mean of the stochastic growth rates up to 58.3% over that of a single early‐spawning life history. These results suggest that the second spawn is a successful bet‐hedging strategy. The northern bay scallop increases its chances for successful recruitment in a variable environment by spreading reproductive effort over more than one period in a season. This strategy appears to have sustained the Nantucket scallop population in spite of severe annual fluctuations and the eventual collapse seen in other locations.Received March 6, 2015; accepted June 19, 2015

Time-invariant and stochastic disperser-structured matrix models: Invasion rates of fleshy-fruited exotic shrubs

Interest in spatial population dynamics includes applications to the spread of disease and invasive species. Recently, models for structured populations have been extended to incorporate temporal variation in both demography and dispersal. Here we propose a novel version of the model that incorporates structured dispersal to evaluate how changes in the relative proportion of mammalian, and short- and long-distance avian dispersers affect the rate of spread of an invasive shrub, Ardisia elliptica in Everglades National Park. We implemented $45$ time-invariant models, including one in which a single dispersal kernel was estimated from field data by pooling all seedlings, and $44$ that were disperser-structured in which dispersal kernels were estimated separately for gravity-, catbird-, robin- and raccoon-dispersed seed. Robins, the longest distance dispersers, are infrequent. Finally we implemented a time-varying model that included variability among years in the proportion of seeds that were taken by robins. The models estimated invasion speeds that ranged from $3.9$ to $34.7$ m $ yr^{-1}$ . Infrequent long-distance dispersal by robins were important in determining invasion speed in the disperser-structured model. Comparing model projections with the (historically) known rate of spread, we show how a model that stratifies seeds by dispersal agents does better than one that ignores them, although all of our models underestimate it.

Habitat-specific demography and conservation of Geoffroy's cats in a human-dominated landscape

Abstract The understanding of the spatial structure and dynamics of populations can guide conservation decisions, but studies of this type focused on small (< 7-kg) carnivores are rare. We compared survival, reproduction, and dispersal of radiocollared Geoffroy's cats (Leopardus geoffroyi) in a protected area and adjacent cattle ranches in Argentina to assess the effects of livestock management and its associated disturbances (i.e., hunting by humans) on the demography of this felid. Thirteen cats in the park and 13 in the ranches were radiotracked for up to 556 days in 2007–2008. We evaluated the Geoffroy's cat population trajectory at the landscape level using a stage-structured, stochastic matrix model based on our estimated vital rates. The study occurred during a prolonged drought, likely affecting estimated vital rates. Survival in the ranches was 52% lower than in the park; mortalities were due to intraguild predation in the park and were human-related in the ranches. Dispersal from the ranches was...

Modeling black bear population dynamics in a human-dominated stochastic environment

Many large carnivore populations exist in human-influenced stochastic environments where availability of natural food sources vary annually and anthropogenic food sources can supplement energetic demands, but at a potential demographic cost due to human–wildlife conflict and subsequent conflict management. Understanding how these competing factors influence a population is complex and difficult to study, but here we demonstrate the utility of using a stochastic projection matrix model and perturbation analysis to gain insight into this problem. We modeled a black bear population subjected to stochastic failures of fruiting and masting species, but with access to garbage in urban environments. We parameratized our model with data from a 6-year study on black bears in Aspen, Colorado and data synthesized from other research studies. Using computer simulation, we investigated the effect that different levels of conflict-bear removal can have on a bear population by comparing a “reference” scenario where bears did not benefit from human food sources or experience conflict-bear removals with two urban scenarios where bears had varying access to human foods, but conflict bears were removed. We used perturbation analyses to evaluate consequences for changing population vital rates and to estimate the impact each vital rate change had on population growth. Simulations were used to identify how much variation in each vital rate influenced variation in the population growth rate. We identified the survival rate of breeding adult females during good natural food years as having the highest elasticity value. We found that the benefit of increased cub production from available human food sources during natural food failure years was quickly negated if management of conflict bears through removal reduced adult female survival. Increasing the frequency of years when natural food production fails resulted in disproportionate impacts from available urban food and conflict-bear removals, where population growth rates in a High Removal scenario declined 1.5 times faster than in the reference scenario. Our findings suggest that for regions where changing climates will increase the frequency of natural food failures, managers may need to utilize non-lethal practices in managing conflict bears and municipalities will need to secure human food sources to reduce the need for conflict-bear removals and potential population declines.

Analytical solution of a stochastic model of risk spreading with global coupling

We study a stochastic matrix model to understand the mechanics of risk spreading (or bet hedging) by dispersion. Up to now, this model has been mostly dealt with numerically, except for the well-mixed case. Here, we present an analytical result that shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to the geometric one, because the sample size is finite.

Risk-based group decision making regarding renewable energy schemes using a stochastic graphical matrix model

Improvements to sustainability are generally measurable based on their environmental, economic, and socio-cultural effects. This study applied this concept by developing and empirically testing a risk-based method for assessing renewable energy policy. An integrated theoretical framework is proposed for analyzing group decision-making regarding renewable energy (RE) policy selection. The proposed graphical matrix approach combined with Monte Carlo simulation compares alternative RE schemes by identifying and measuring critical performance indicators with acceptable reliability. The mathematical model reliably prioritizes alternatives using majority voting to address uncertainty in multi-criteria decision making process. A case study using historical data from previous RE development projects to confirm the feasibility of this approach. Compared to the conventional deterministic method, the stochastic graphical matrix approach provides more reliable estimation accuracy, decision quality, and efficiency in selection of sustainable renewable energy. The systematic approach provides policy makers information for use in evaluation by synthesizing the judgments of a panel of experts.

Stochastic density-dependent matrix model for extrapolating individual-level effects of chemicals to the population: Case study on effects of Cd on Folsomia candida

The extrapolation of individual-level effects observed in standard bioassays to the population level is one of the major challenges in ecotoxicology and ecological risk assessment of chemicals. Most of the information about ecotoxicity of chemicals is currently derived from laboratory ecotoxicological tests in which individual-level effects (e.g., the effects on individual life span, fertility, and body growth) of toxic chemicals are measured. However, the risk of chemicals at the population level may be strongly affected by stochastic events that can arise from population structure, density dependence, timing of exposure and environmental fluctuations which are not considered in laboratory experiments. In this study, we present a general matrix population model framework for assessing the ecological risks of chemicals on populations in the field by accounting for density dependence and environmental stochasticity arising from seasonal environmental fluctuations. As an illustration, we present a case study that predicts effects of cadmium (Cd) on Folsomia candida populations by considering environmental stochasticity arising from temporal and/or spatial temperature variation. The model results show that extrapolating individual-level effects of Cd to a higher level of biological organization without considering environmental variability underestimates effects of chemicals on population growth rate. Chemicals can also reduce the population size at its carrying capacity. The latter phenomenon arises from different effects of toxicants on different age/stage classes combined with natural demographic processes. One important and useful population-level endpoint that can combine all these effects (i.e. environmental variability, chemical-specific toxicity, and density dependence) is the mean time to extinction. Our model simulation results show that the mean time to extinction of the F. candida population exposed to 1000mg Cd/kg soil can be reduced by 40% compared to the control population. Nevertheless, this significant reduction will not lead to fast extinction of the population as the estimated mean time to extinction is over 3000 years. Based on these results, a population of F. candida exposed to this concentration of Cd may not be considered to be endangered. However, other stresses (like habitat fragmentation, food limitation, etc.) can additionally influence the mean time to extinction.