Asymptotic Population Growth Rate Research Articles

Population Dynamics of the Dioecious Amazonian Palm Mauritia flexuosa: Simulation Analysis of Sustainable Harvesting

ABSTRACTThe dioecious, tropical palm Mauritia flexuosa has high ecological and economic value, but currently some wild populations are harvested excessively, which is likely to increase. In this study, we investigated the population dynamics of this important palm, the effects of harvesting, and suggested sustainable harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were assumed to be stable. We used a matrix population model to calculate the density‐independent asymptotic population growth rate (λ= 1.046) and to evaluate harvesting scenarios. Elasticity analysis showed that survival (particularly in the second and fifth size class) contributes more to the population growth rate, than growth and fecundity. To simulate a stable population at carrying capacity, density dependence was incorporated and applied to the seedling survival and growth parameters in the transition matrix. Harvesting scenarios were simulated with the density‐dependent population models to predict sustainable harvesting regimes for the dioecious palm. We simulated the removal of only female palms and showed how both sexes are affected with harvest intensities between 15 and 75 percent and harvest intervals of 1–15 yr. By assuming a minimum female threshold, we demonstrated a continuum of sustainable harvesting schedules for various intensities and frequencies for 100 yr of harvest. Furthermore, by setting the population model's λ= 1.00, we found that a harvest of 22.5 percent on a 20 yr frequency for the M. flexuosa population in Ecuador is consistent with a sustainable, viable population over time.

Modelling Cell Generation Times by Using the Tempered Stable Distribution

Summary We show that the family of tempered stable distributions has considerable potential for modelling cell generation time data. Several real examples illustrate how these distributions can improve on currently assumed models, including the gamma and inverse Gaussian distributions which arise as special cases. Our applications concentrate on the generation times of oligodendrocyte progenitor cells and the yeast Saccharomyces cerevisiae. Numerical inversion of the Laplace transform of the probability density function provides fast and accurate approximations to the tempered stable density, for which no closed form generally exists. We also show how the asymptotic population growth rate is easily calculated under a tempered stable model.

A NONINVASIVE DEMOGRAPHIC ASSESSMENT OF SEA LIONS BASED ON STAGE‐SPECIFIC ABUNDANCES

A pressing need exists to develop new approaches for obtaining information on demographic rates without causing further threats to imperiled animal populations. In this paper, we illustrate and apply a data-fitting technique based on quadratic programming that uses stage-specific abundance data to estimate demographic rates and asymptotic population growth rates (lambda). We used data from seven breeding colonies of California sea lions (Zalophus californianus) in the Gulf of California, Mexico. Estimates of lambda were similar to those from previous studies relying on a diffusion approximation using trends in total abundance. On average, predicted abundances were within 24% of the observed value for the inverse estimation method and within 29% of the observed value for the diffusion approximation. Our results suggest that three of the seven populations are declining (lambda < 1), but as many as six may be at risk. Elasticity and sensitivity analyses suggest that population management in most sites should focus on the protection of adults, whose survival generally contributes the most to lambda. The quadratic programming approach is a promising noninvasive technique for estimating demographic rates and assessing the viability of populations of imperiled species.

Using rainout shelters to evaluate climate change effects on the demography of Cryptantha flava

Summary Precipitation in arid regions is temporally variable with much of it arriving in discrete, unpredictable pulses. Climate change models predict an increase in the variation of precipitation, with longer droughts and larger rainfall events, in addition to increased temperatures. A life table response experiment (LTRE) was conducted with the herbaceous arid‐land perennial Cryptantha flava (Boraginaceae) from 1997 to 2000, in order to determine how variation in precipitation affects asymptotic population growth (l) and vital rates. Variation in precipitation took two forms, through rainout shelters erected just before and during the 1999 spring growing season, and through naturally occurring variation over the 4 years. An unexpected effect of rainout shelters on l was observed that could not be attributed to drought. The l value decreased greatly in control census plots in the 1998–99 transition but did not decrease in sheltered of plots. The 1999 spring, when shelters were in place, was unusually cold, resulting in frost damage to unsheltered plants. Plants under shelters experienced elevated nighttime temperatures and escaped frost damage. The greater value of l in the sheltered plots is attributable almost entirely to greater contributions of survival, growth and stasis. There were residual effects of the 1999 drought treatment in the 1999–2000 transition as l decreased in the sheltered populations while l increased in control populations. Compared to controls, there were large negative effects of survival, growth, and stasis and a large positive effect of retrogression in the droughted plots. Natural variation in fecundity contributed considerably to inter‐annual variation in l in control plots. Annual variation in fecundity strongly paralleled annual variation in seedling establishment. The relative contributions of other vital rates varied greatly among the annual transitions. Synthesis. The study illustrates the sensitivity of this arid‐land species to early season frost events and to variation in precipitation. It suggests the importance of considering the seasonal timing of precipitation events when projecting the population‐level consequences of global climate change, with particular attention given to precipitation that triggers germination and seedling establishment. Researchers using shelters to create drought treatments should consider their nighttime warming effects.

Management recommendations based on matrix projection models: The importance of considering biological limits

Matrix population models are a common tool for evaluating different management strategies. In general, under deterministic analyses, management strategies are recommended that improve those matrix transitions that are most sensitive or elastic with respect to the asymptotic population growth rate, λ. These recommendations usually ignore the biological limit for these transitions. In this paper we use the endangered Serengeti cheetah ( Acinonyx jubatus) as a case study to illustrate that ignoring biological limits leads to a recommendation that will not always achieve the desired goal of an asymptotic population growth rate, λ ⩾ 1. We estimate the survivorships of adult cheetahs in captivity using cheetah studbook data, which is a conservative estimate of the biological limit for the adult survivorship of wild cheetahs. Our analysis suggests that adult survival sharply decreases after 8.5 years. In addition, captive cheetahs older than 18 years do not reproduce. We modify a previously published population projection matrix to include the effect of senescence on survival and fecundity. Our model suggests that increasing adult survivorship alone is not sufficient to reverse population decline. However, an additional small increase in newborn survival is likely to result in a viable cheetah population. We show these conclusions hold even in the presence of relatively large parameter perturbations.

Monte Carlo analysis of parameter uncertainty in matrix models for the weed Cirsium vulgare

Summary Parameter uncertainty challenges the use of matrix models because it violates key assumptions underlying elasticity analyses. We have developed a matrix model to compare Monte Carlo methods with elasticity analyses for estimation of the relative importance of factors in the asymptotic population growth rate, λ, of Cirsium vulgare (spear thistle) in Nebraska, USA. We calculated λ for a base model using 11 parameter estimates available for Nebraska populations plus eight extracted from the literature, causing parameter uncertainty. We then calculated λ for 10 000 alternative models using Monte Carlo parameter estimation; parameters were drawn from the full range of each parameter in the literature and partial rank correlation analysis (PRCC) was used to order the parameters by the magnitude of their effect on λ. Monte Carlo analysis found that insect floral herbivory, affecting the regeneration transition, was the most important parameter affecting λ, whereas elasticity analyses suggested that the transition from small to medium size was the most significant. Statistical comparison, using PRCC vs. lower level elasticity (LLE), showed that the Monte Carlo analysis provided a more accurate assessment. As λ &gt; 1 in 99% of the model runs even with significant floral herbivory, we added two parameters influenced by weed management (probability of large thistles dying without producing seed and proportion of seeds that failed to germinate). Simulations that included reductions in these parameters, along with floral herbivory, led to λ &lt; 1 in 17% of the runs, suggesting these three factors interact to produce the low densities observed for this invasive thistle in our study area. Synthesis and applications. This study demonstrates the utility of the Monte Carlo approach for modelling weed dynamics with parameter uncertainty and multiple, potentially interacting, parameters. Invasive population growth by C. vulgare could be limited by a combination of weed management practices and the biotic resistance imposed by native floral herbivores.

Variation in northern bobwhite demography along two temporal scales

AbstractQuantification and understanding of demographic variation across intra‐ and inter‐annual temporal scales can benefit from the development of theoretical models of evolution and applied conservation of species. We used long‐term survey data for northern bobwhites (Colinus virginianus) collected at the northern and southern extent of its geographic range to develop matrix population models which would allow investigation of intra‐ and inter‐annual patterns in bobwhite population dynamics. We first evaluated intra‐annual patterns in the importance of a seasonal demographic rate to asymptotic population growth rate with prospective perturbation analysis (elasticity analysis). We then conducted retrospective analysis (life table response experiments) of inter‐annual patterns in the contribution of observed changes in demography to the observed change in population growth rate. Survival in the earliest age class during the nonbreeding season had the greatest potential influence in both the northern and southern populations. Examination of inter‐annual variation in demography indicated that variation in nonbreeding season survival in the earliest age class contributed the most to observed changes in population growth rate in the northern population. In contrast, changes in fertility in the earliest age class in the southern population had the greatest influence on changes in population growth rate. Prospective elasticity analyses highlight the similarities in bobwhite demography throughout different parts of its geographic range, while retrospective life table response experiments revealed important patterns in the temporal differences of bobwhite life history at the northern and southern extent of its geographic range.

TRANSIENT POPULATION DYNAMICS IN PERIODIC MATRIX MODELS: METHODOLOGY AND EFFECTS OF CYCLIC PERMUTATIONS

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.

DEMOGRAPHY OF CENTRAL AND MARGINAL POPULATIONS OF MONKEYFLOWERS (MIMULUS CARDINALISANDM. LEWISII)

Every species occupies a limited geographic area, but how spatiotemporal environmental variation affects individual and population fitness to create range limits is not well understood. Because range boundaries arise where, on average, populations are more likely to go extinct than to persist, range limits are an inherently population-level problem for which a demographic framework is useful. In this study, I compare demographic parameters and population dynamics between central and marginal populations of monkeyflowers, Mimulus cardinalis and M. lewisii, along an elevation gradient spanning both species' ranges. Central and marginal populations of both species differed in survival and fecundity. For M. lewisii, these components of fitness were higher in central than in marginal populations, but for M. cardinalis the converse was true. To assess spatiotemporal variation in population dynamics, I used transition matrix models to estimate asymptotic population growth rates (lambda) and found that population growth rates of M. lewisii were highest at the range center and reduced at the range margin. Population growth rates of M. cardinalis were highest at the range margin and greatly reduced at the range center. Life table response analysis decomposed spatiotemporal variation in lambda into contributions from each transition between life stages, finding that transitions from large nonreproductive and reproductive plants to the seed class and stasis in the reproductive class made the largest contributions to spatial differences in lambda. These transitions had only low to moderate sensitivities, indicating that differences in projected population growth rates resulted mainly from observed differences in transition matrix parameters and their underlying vital rates.

Evaluating effects of low quality habitats on regional population growth in Peromyscus leucopus: Insights from field-parameterized spatial matrix models

Due to complex population dynamics and source–sink metapopulation processes, animal fitness sometimes varies across landscapes in ways that cannot be deduced from simple density patterns. In this study, we examine spatial patterns in fitness using a combination of intensive field-based analyses of demography and migration and spatial matrix models of white-footed mouse (Peromyscus leucopus) population dynamics. We interpret asymptotic population growth rates from these spatial models as fitness-based measures of habitat-quality and use elasticity analysis to further explore model behavior and the roles of migration. In addition, we compare population growth rates at the spatial scale of single habitats and the landscape-level scale at which these habitats are assembled. To this end, we employ emerging techniques in multi-scale estimation of demography and movement and recently described vec-permutation methods for spatial matrix notation and analysis. Our findings indicate that the loss of low quality habitats or reductions in movement from these habitats into higher quality areas could negatively affect landscape-level population fitness.

Population Dynamics and Potential for Biological Control of an Exotic Invasive Shrub in Hawaiian Rainforests

Introduction of biological control agents to reduce the abundance of exotic invasive plant species is often considered necessary but risky. I used matrix projection models to investigate the current population dynamics of Clidemia hirta (Melastomataceae), an invasive shrub, in two rainforest stands on the island of Hawaii and to predict the efficacy of hypothetical biological control agents in reducing population growth rates. Stage-structured matrix models were parameterized with field data collected over 3 years from 2906 C. hirta plants in a recently invaded forest with an open overstory (Laupahoehoe) and 600 plants in a less recently invaded forest with a closed canopy (Waiakea). Asymptotic population growth rates (λ) for both populations in all years were greater than one, demonstrating that both populations were growing. Composite elasticities were high for the seedling life-history stage and fecundity, and near-term demographic elasticities suggested that changes in seedling survival would have the largest effect on population size in the short term. However, simulations showed that almost 100% of seedlings or new recruits produced per reproductive adult would have to be destroyed to cause populations to go locally extinct under current environmental conditions. Herbivores or pathogens that decrease survival across all vegetative stages by 12% at Waiakea and 64% at Laupahoehoe were projected to cause the populations to decline. Thus, biocontrol agents that reduce survival of multiple life-history stages rather than seed production should be pursued to control C. hirta in Hawaiian rainforests.

Bioenergetics‐based matrix population modeling enhances life‐cycle toxicity assessment of tilapia Oreochromis mossambicus exposed to arsenic

The objective of this study was to integrate a bioenergetics-based modeling approach into a population stage structure to enhance life-cycle toxicity assessments of the effects of waterborne arsenic (As) on the population dynamics of the tilapia Oreochromis mossambicus. The proposed mathematical model links a Leslie matrix population model and a universal ontogenetic growth model embedding the population-level growth rate and stage-specific modes of toxic action. We present data analyses of key parameters and distributions and discuss the processes of data capture and analysis and the impact of acute/chronic As toxicity responses on population-level effects. We employed a three-parameter Hill equation model to describe the relationship between tilapia whole-body burden and mortality in order to estimate the probability of stage-specific vital rate of survival. Using the DEBtox theory, we distinguished three modes of toxic action (MOA): direct effects on growth and indirect effects via maintenance and food consumption on inhibition by arsenic of the growth of a tilapia population. The asymptotic population growth rate decreased from lambda = 1.0027 for the control group to lambda = 0.9935 for tilapia population exposed to 4 microg mL(-1) As, indicating a potential risk of population intrinsic growth rates for tilapia exposed to higher levels of waterborne As. Our results estimated that an As concentration of 1.02 microg mL(-1) would cause a 50% reduction in the tilapia population. We found that the interplay between external stressors of waterborne As concentration and internally generated modes of action decreasing feeding in the juvenile stage and increasing the maintenance cost in the adult stage had a pronounced influence on the population stage structure of tilapia.

Population Momentum: Implications for Wildlife Management

Maintenance of sustainable wildlife populations is one of the primary purposes of wildlife management. Thus, it is important to monitor and manage population growth over time. Sensitivity analysis of the long-term (i.e., asymptotic) population growth rate to changes in the vital rates is commonly used in management to identify the vital rates that contribute most to population growth. Yet, dynamics associated with the long-term population growth rate only pertain to the special case when there is a stable age (or stage) distribution of individuals in the population. Frequently, this assumption is necessary because age structure is rarely estimated. However, management actions can greatly affect the age distribution of a population. For initially growing and declining populations, we instituted hypothetical management targeted at halting the growth or decline of the population, and measured the effects of a changing age structure on the population dynamics. When we changed vital rates, the age structure became unstable and population momentum caused populations to grow differently than that predicted by the long-term population growth rate. Interestingly, changes in fertility actually reversed the direction of short-term population growth, leading to long-term population sizes that were actually smaller or larger than that when fertility was changed. Population momentum can significantly affect population dynamics and will be an important factor in the use of population models for management.

Assessing the effect of habitat fragmentation on population dynamics: An implicit modelling approach

To better understand the impact of habitat fragmentation on population dynamics at the landscape scale, we develop a model combining a spatially implicit landscape model, a multisite Leslie-type model and an implicit model of habitat fragmentation. The studied species (Abax parallelepipedus, Coleoptera: Carabidae) is a corridor forest insect sensitive to wood fragmentation. The population of A. parallelepipedus was divided into three stages and move in the landscape between four classes of elements: wood, lane bordered by two hedgerows, hedgerow and agricultural matrix. The landscape representation was supposed to be implicit and the four classes of elements were randomly distributed in space. The originality of this approach is that we fit the movement frequency between elements according to woodland forest fragmentation. When wood fragmentation increases, the movement process can be very frequent and the method of aggregation of variables allows us to simplify the analysis of the model. Outputs of the model include the asymptotic population growth rate, stable stage structure and asymptotic spatial distribution that allow comparison of the influence of different spatial scenarios of wood fragmentation on population dynamics. Our results indicate that a single large patch of wood is better than several small patches of wood for population viability, that hedgerows have negative effects on population viability but lanes border by two hedgerows have positive effects even if they are randomly distributed at the landscape scale. When wood fragmentation is important, hedgerows create a population drain in woods and individuals pass and die more frequently in agricultural matrix.

Ramet dynamics in a centrifugally expanding clonal sedge: a matrix analysis

Carex humilis is a clonal sedge that can form distinct rings of densely aggregated ramets. We hypothesize that rings form because both production of new ramets and ramet dispersal are positively correlated to ramet size. This would lead to an overrepresentation of fast-moving and large ramets with high ramet production at the periphery, whereas slow-moving and small ramets with low ramet production would mainly be found in the interior of rings. We use matrix models to analyse how ramet populations both at the periphery and in the interior develop in the absence of ramet dispersal. We found that the stable size class distributions of ramets predicted by the models were not different from the distributions found in the field. Also, the asymptotic ramet population growth rates (λ1) were the same. Hence, we conclude that rings would form even in the absence of a link between ramet dispersal and ramet production. Further analysis of the matrix models showed that the ramet population increases at the periphery but decreases in the interior of rings because medium and large ramets produce fewer large ramets in the interior than at the periphery. We also found that the temporal variance in λ1 and transitions rates during the four study years was much higher at the periphery than in the interior. Our results suggest that rings may form because C. humilis ramets use below-ground resources from a much larger area than the one covered by the shoots. As the clone grows larger, the soil volume available to the ramets in the interior decreases because their access to soil outside the ring is cut-off by the ramets at the periphery. Ramet density in the interior is therefore decreasing.

Analysis of interspecific competition in perennial plants using Life Table Response Experiments

The impact of interspecific competition is usually measured by its effect upon plant growth, neglecting impacts upon other stages of the life cycle such as fecundity which have a direct influence upon individual fitness and the asymptotic population growth rate of a population (λ). We used parameterized matrix models for three perennial plant species grown with and without interspecific competition to illustrate how the methodology of Life Table Response Experiments (LTRE) can be used to link any change in population dynamics to changes in any part of the life cycle. Plants were herbaceous grassland species grown for two years in a field experiment at Rothamsted Experimental Station, England. Interspecific competition reduced λ by over 90% in all species. Survival and growth were slightly affected by competition whereas plant fecundity was greatly reduced. Nearly all of the observed difference in λ between the competition treatments was explained by the fecundity terms, and more precisely by a large difference in the number of seeds, and a high sensitivity of λ to the germination rate. Whereas most competition studies focus on the measurement of change in individual fitness, our study illustrates how informative it is to take account not only of the effect of competition upon vital rates but also of how different vital rates affect population growth rate.

Population dynamics of benthic shallow-water foraminifera: effects of a simulated marine snow event

In this microcosm experiment, we determined the population dynamics of benthic foraminifera from the northern Adriatic Sea (from 32 m water depth) and how they were affected by an artificial marine snow event (AMS). The study focussed on the performance of individuals in 2 dif- ferent size fractions: one commonly used in micropaleontological studies (with foraminifera >63 µm) and 1 with smaller individuals (38-63 µm). Microcosms were incubated for 2 or 4 wk, and under AMS or control conditions. For each, the numbers of live (Rose Bengal-stained) individuals of different spe- cies in both size fractions were counted. From this, demographic parameters (fecundity, survival, growth) of specimens in different size classes were assessed. With these data, population projection matrices were constructed for the 4 most abundant taxa (Bolivina spp., Stainforthia fusiformis, Non- ionella turgida and Hopkinsina pacifica) and all foraminifera together. From the limit properties of these matrices, asymptotic population growth rates (λ) were derived. The results indicate that num- bers of larger benthic foraminifera decline more strongly because of AMS than those of the smaller individuals, and that growth is seriously inhibited. AMS, however, enhanced fecundity. Under AMS conditions (i.e. temporary anoxia and, concomitantly, extra food), the foraminifera seem to shift to an alternative life-history pathway of rapid reproduction and limited growth. After the first 2 wk, values of demographic parameters increase under AMS conditions, resulting in quickly recovering popula- tions. In our view, these demographic characteristics are beneficial for the observed species in peri- odically stressful and disturbed ecosystems, and could explain the increasing success of these species in the progressively eutrophicated northern Adriatic Sea.

LONG-TERM ANALYSIS OF SURVIVAL, FERTILITY, AND POPULATION GROWTH RATE OF BLACK BEARS IN NORTH CAROLINA

We estimated survival, fertility, and realized and asymptotic population growth rates from 1981 to 2002 for a protected population of black bears (Ursus americanus) in the southern Appalachian Mountains. We used Akaike’s information criterion to assess the time interval for averaging observations that was best for estimating vital rates for our study, given our yearly sample sizes. The temporal symmetry approach allowed us to directly assess population growth and to address all losses and gains to the population by using only capture data, offering an alternative to the logistically intensive collection of reproductive data. Models that averaged survival and fertility across 5- and 7-year time intervals were best supported by our data. Studies of black bear populations with annual sample sizes similar to ours should be of at least 5 years in duration to estimate vital rates reliably, and at least 10 years in duration to evaluate changes in population growth rate (k). We also hypothesized that survival would not track changes in k because k is influenced by both survival and fertility. The 5-year model supported our hypothesis, but the 7-year model did not. Where long-term dynamics of large, relatively stable bear populations are of interest, monitoring survival is likely to be sufficient for evaluating trends in k. For rapidly changing, small populations, however, failure to incorporate fertility into assessments of k could be misleading.

Population models of farmed abalone Haliotis diversicolor supertexta exposed to waterborne zinc

A stage-classified demographic method was performed to investigate the effects of increased waterborne zinc (Zn) concentrations on the population dynamics of abalone Haliotis diversicolor supertexta. We reanalyzed the results of a 7-day acute and a 28-day chronic toxicity bioassays to examine the survival and growth performances when exposing abalone to different levels of zinc stresses. An energy-based biological approach was adopted to model the effects of zinc on fecundity. These data provided stage-specific schedules of vital rates that were used to parameterize a projection matrix model for abalone. Simulations were carried out to produce temporal population abundance changes under seven exposure scenarios including a control group and six treated cohorts ranged from 0.03 to 1 mg l −1 Zn. Model manipulations indicated that a reduction of individual growth rate was observed at an exposed Zn concentration greater than 0.12 mg l −1, whereas the significant influence of survivorship was occurred until the Zn concentration reached 0.25 mg l −1. For all treatments, Zn induced a slight decrease in fecundity. The asymptotic population growth rate decreased from λ=1.00 for the control group to λ=0.9968 for abalone population exposed to 1 mg l −1 Zn, indicating a potential risk of population intrinsic growth rates for abalone exposed to higher levels of waterborne Zn. These findings provide a pivotal effort for setting of the ambient water quality criterion for protecting the aquacultural species.

Do migratory or demographic disruptions rule the population impact of pollution in spatial networks?

Ecotoxicology supplies environmental quality criteria mainly based on the potential effects of contaminants on demographic rates of natural populations. Possible impacts through pollutant-induced disruptions of spatial behaviors are totally neglected. Should it be significant to take into account this “second way”? We developed the example of a hypothetical brown trout population living in a river network. We analyzed how behaviors of toxic avoidance or attraction during the spawning migration alter the impact of pollution. Attraction behaviors basically enhanced the bad effect of pollution. More interesting, avoidance behaviors can weakly lift the asymptotic population growth rate, while if there is density-dependent effects on recruitment, pollutant avoidance can actually lead to a substantial drop in equilibrium size. Our model allowed comparing the relative significance of migratory and demographic disruptions for explaining the population impacts of pollution; we thus stress on the need of increasing efforts to develop knowledge relative to toxicant-induced spatial behaviors and to integrate such effects in the definition of environmental quality criteria.