Using selection functions to describe changes in environmental variables

The selection function (which shows how the frequency of sampling units with the value X = x at one point in time must change in order to produce the distribution that occurs at a later point in time) is proposed for describing the changes over time in an environmentally important variable X. It is shown that the theory of selection functions as used in the study of natural selection and resource selection by animals requires some modifications in this new application and that a selection function is a useful tool in long-term monitoring studies because all changes in a distribution can be examined (rather than just changes in single parameters such as the mean), and because graphical presentations of the selection function are easy for non-statisticians to understand. Estimation of the selection function is discussed using a method appropriate for normal distributions and bootstrapping is suggested as a method for assessing the precision of estimates and for testing for significant differences between samples taken at different times. Methods are illustrated using data on water chemical variables from a study of the effects of acid precipitation in Norway.     

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Abstract

Three collectives of substances - plastics, plant nutrients, biotoxins - are candidates for monitoring programmes that could keep track of the quality of ocean waters for vital life processes. All three are not subject to systematic surveillance at present. They are each characterized by long residence times in the marine environment, by increasing influx, and by growing evidence of their deleterious impacts on living systems.     

Design-based ranked set sampling using auxiliary variables

A ranked set sampling protocol is proposed when an auxiliary variable is available in addition to the target variable in sample surveys. The protocol may be practically carried out without additional sampling effort or costs. Under the suggested sampling scheme, the estimators usually adopted in surveys with auxiliary information - such as the ratio estimator or the regression estimator - display surprising theoretical properties as well as high performance in practice.     

Desirable design characteristics for long-term monitoring of ecological variables

Long-term environmental monitoring places a set of demands on a sampling strategy not present in a survey designed for a single time period. The inevitability that a sample will become out of date must be a dominant consideration in planning a long-term monitoring programme. The sampling strategy must be able to accommodate periodic frame update and sample restructuring in order to address changes in the composition of the universe and changes in the perception of issues leading to new questions and concerns. The sampling strategy must be capable of adapting to such changes while maintaining its identification as a probability sample and its capacity to detect trends that span the update occasions. These issues are examined with respect to sub-population estimation, post-stratification via conditioning, and sample enlargement and reduction. Design features that involve complex sample structure create potentially serious difficulties, whereas an equal probability design permits greater adaptability and flexibility. Structure should be employed sparingly and in awareness of its undesirable effects.     

Mapping water chemical variables with spatially correlated errors

One of the most important considerations in many environmental studies is need to allow for correlations among the variables. Monitoring and analyzing relationships between chemical environmental parameters using spatial correlation based regression modelling is the main motivation of this applied study. For this purpose, some noticeable environmental parameters of data sets obtained from two lakes have been considered and the concentrations of chemical variables such as cadmium and nitrate have been appraised by a regression-based geostatistical methodology. The modelling procedure consists of two stages. In the first stage, spatial variables are analyzed via multi-linear regression and some relationships are provided. Next, by using the spatial auto-correlations of the residuals, a type of regression-based kriging procedure is applied. The capacity of the model for appraising the water chemical variables is also tested and performance comparisons with ordinary kriging are conducted. Finally, the applications showed that analyzing water chemical variables with spatially correlated errors is a convenient and applicable approach for assessing the environmental systems.     

Allometric constraints and variables of reproductive effort in brachyuran crabs

Allometric relationships of reproductive output were compared in 20 species from 7 families of brachyuran crabs from the east and west coasts of North America, using regression analysis of log reproductive parameters versus log body weight. Comparisons of crabs spanning 4 orders of magnitude in body weight indicated that female body size was the principal determinant of reproductive output: 95% of the variance in brood weight, 79% of the variance in the number of eggs per brood, 63% of the variance in annual brood weight, and 74% of the variance in annual fecundity were explained by body weight. Brood weight exhibited an isometric constraint to about 10% of body weight. Allometric limitations on space available for yolk accumulation in the body cavity appeared to be the main constraint on brood size. Ovum size increased significantly, but only slightly, with increasing body size. There was a significant trade-off between ovum size and the number of eggs per brood. There was no significant relationship between the number of broods per year and body size. The number of eggs per brood was significantly better than brood weight as a predictor of the number of broods produced per year by a species, indicating that demographic pressure on fecundity rather than energetic considerations is the primary selective mechanism influencing annual reproductive effort. Each of the 7 families of crabs exhibited trends toward distinct patterns for the suite of co-adapted reproductive traits. However, no interspecific reproductive patterns were apparent with respect to the variables of feeding type, salinity tolerance, habitat, and geographic range represented by the 20 species.     

Relevant variables to predict macrophyte communities in running waters

In both predictive theoretical and empirical models for aquatic plant communities in running waters, the development and competition are many times explained in terms of nutrients. Minerals necessary for growth are generally not assumed to be limiting, although they influence the important pH-value. At the same time it is known that factors such as oxygen-concentration, solar energy, salinity, dimension of the system and soil characteristics (including river sediments) influence the development of the community, and should be considered in modelling. Effects of water quantity and water quality on macrophytes are reviewed. These conditions are caused by processes in the landscape, characterised by a set of nested variables which explain the distribution of macrophyte species and communities. Relevant variables are described and grouped on three scales: regional, local and site conditions. Case studies with direct and indirect gradient analysis are presented. Statistical tests (stepwise regression with forward selection) reveal that each species distribution is explained by a characteristic set of relevant variables, ranging from soil type and dimension of the system, to nutrient and salinity concentration.     

Sexual selection and cuckoldry in a monogamous songbird: implications for sexual selection theory

Sexual selection is generally assumed to be weaker in monogamous than in polygynous animals. Recently, though, extra-pair fertilizations have been hailed as an important force in generating variance in reproductive success among males in socially monogamous species, thereby increasing the intensity of sexual selection. To see if extra-pair copulations contribute to variance in male reproductive success in the house finch (Carpodacus mexicanus), we used DNA fingerprinting to determine the paternity of chicks from 35 nests. This species is a socially monogamous passerine in which plumage brightness serves as a sexually selected indicator of male quality. Out of 119, nestlings 10 (8.3%) were fathered by a male other than the attending male, but cuckoldry occurred randomly with respect to the plumage colouration, size, or age of the attending male. Thus extra-pair fertilizations do not generate variance in male reproductive success with respect to plumage colour. On the other hand, a strongly male-biased sex ratio and asynchronous breeding by females may generate substantial variance in male reproductive success and could explain the evolution of ornamental colouration.     

Assessment of natural selection in a hybrid population of mussels: evaluation of exogenous vs endogenous selection models

We examined natural selection within a population of marine mussels, sampled in southwestern England in June 1991, containing a high frequency of hybrids between Mytilus edulis L. and M. galloprovincialis Lmk. This system is particularly tractable for the assessment of natural selection because hybridization is common and individual mussels can be aged, allowing changes in the frequency of hybrid genotypes among age classes to be determined. We show that strong viability selection occurs among hybrid genotypes which results in the virtual elimination of M. edulis–like genotypes from the population over a period of 3 years. Recombinant hybrid genotypes are intermediate in fitness, with M. edulis–like genotypes having a lower survival rate and M. galloprovincialis–like genotypes having a higher survival rate than genotypes of mixed ancestry. Since intermediate fitness for hybrid genotypes is inconsistent with endogenous selection models we conclude that the structure and position of this hybrid zone is probably generated by exogenous selection. This pattern of selection is a recurring feature of this hybrid population and likely occurs elsewhere in the hybrid zone. Selection against M. edulis–like genotypes appears to be offset by extensive immigration of larvae dispersed from pure populations of M. edulis. Received: 14 July 1997 / Accepted: 24 February 1998     

Using abiotic variables to predict importance of sites for species representation

In systematic conservation planning, species distribution data for all sites in a planning area are used to prioritize each site in terms of the site's importance toward meeting the goal of species representation. But comprehensive species data are not available in most planning areas and would be expensive to acquire. As a shortcut, ecologists use surrogates, such as occurrences of birds or another well‐surveyed taxon, or land types defined from remotely sensed data, in the hope that sites that represent the surrogates also represent biodiversity. Unfortunately, surrogates have not performed reliably. We propose a new type of surrogate, predicted importance, that can be developed from species data for a q% subset of sites. With species data from this subset of sites, importance can be modeled as a function of abiotic variables available at no charge for all terrestrial areas on Earth. Predicted importance can then be used as a surrogate to prioritize all sites. We tested this surrogate with 8 sets of species data. For each data set, we used a q% subset of sites to model importance as a function of abiotic variables, used the resulting function to predict importance for all sites, and evaluated the number of species in the sites with highest predicted importance. Sites with the highest predicted importance represented species efficiently for all data sets when q = 25% and for 7 of 8 data sets when q = 20%. Predicted importance requires less survey effort than direct selection for species representation and meets representation goals well compared with other surrogates currently in use. This less expensive surrogate may be useful in those areas of the world that need it most, namely tropical regions with the highest biodiversity, greatest biodiversity loss, most severe lack of inventory data, and poorly developed protected area networks.     

Abundance of estuarine crab larvae is associated with tidal hydrologic variables

Abundances of brachyuran megalopae and juveniles were measured throughout consecutive tidal cycles during six 2 to 3 d sampling periods in summer 1992, and associated with rates of change of tidal hydrologic variables in the Newport River Estuary. Current speeds and rates of pressure change fitted sinusoidal (tidal) models well; however, rates of salinity and temperature change did not. Analysis of plankton samples taken during spring and neap tides showed peak abundances during nighttime rising tides for all taxonomic groups: Callinectes sapidus, Uca spp., Xanthidae, and Pinnixa spp. megalopae, and Pinnotheres spp. juveniles. Megalopal and juvenile abundances from time-intensive sampling were related to rates of changes in the hydrologic variables using stepwise logistic regression. No hydrologic variable accounted well for the presence of Uca spp. megalopae. Megalopal presence was best predicted by current speed for Pinnixa spp. megalopae, and rates of changes in pressure for xanthid megalopae and Pinnotheres spp. juveniles, and salinity for C. sapidus megalopae. These variables might act as cues causing megalopae to ascend into the water column at a particular point in the flooding tide, and subsequently descend to or near the bottom prior to ebb flow. In this way, larvae which develop on the continental shelf or lower estuary undergo transport up the estuary by behaviorally altering their swimming activity and depth concurrent with tidal changes.     

A quantitative genetic model of altruistic selection

Summary A quantitative genetic model for evolution by altruistic selection based on family selection models used in agricultural genetics is presented. A quantitative genetic version of Hamilton's rule is derived which indicates that evolution will proceed in an altruistic direction whenever the ratic of between-to within-family (or group) heritability exceeds the absolute value of the within-to between-family selection differential ratio. This ratio of heritabilities is equal to a ratio which includes only the phenotypic and genetic intraclass correlation coefficients, thus no heritabilities actually need to be estimated in determining the possibility of altruistic evolution. The phenotypic intraclass correlation can be estimated with standard analysis of variance methods. The genetic intraclass correlation may be estimated by the average within-group coefficient of relationship using genealogical data, by Wright's F-statistics using allele frequency data, or by a theoretical model based on a knowledge of interaction and mating patterns. Selection differentials may be measured by the regression of relative fitness, or one of its major components, on the phenotype of interest. Selection can be considered altruistic only if within-and between-family selection differentials have opposite signs. Consideration of empirical data on genetic and phenotypic intraclass correlations indicates that evolution may proceed in an altruistic direction even if the within-family selection differential exceeds the one between families, especially in situations in which pertinent environmental factors are randomly distributed among families.     

Analysis of the influence of substrate variables on coral reef fish communities

A simple field technique to obtain a gross estimate of the surface area of a quadrat on a coral reef is described. This measure, termed the substrate rugosity index, was determined, in conjunction with two other substrate variables (vertical relief and coral species richness), in a series of 4 quadrats (10 to 40 m depth) along 4 transects. The mean substrate rugosity and vertical relief of a quadrat were highly correlated. A correlation analysis was made of the substrate variables and several reef fish community parameters (species richness, number of fishes and diversity). Species richness was highly correlated with substrate rugosity. This relationship was tested in two experimental quadrats and the results were generally in accord with those predicted. Stratification of the fish communities by body size revealed that the correlation with substrate rugosity was scale-dependent. The fish community parameters were poorly correlated with percentage substrate cover by corals (ramose and glomerate) and by sand. A significant area effect was determined for two species of sand-dwelling goby.     

Using structural equation modeling to investigate relationships among ecological variables

Structural equation modeling is an advanced multivariate statistical process with which a researcher can construct theoretical concepts, test their measurement reliability, hypothesize and test a theory about their relationships, take into account measurement errors, and consider both direct and indirect effects of variables on one another. Latent variables are theoretical concepts that unite phenomena under a single term, e.g., ecosystem health, environmental condition, and pollution (Bollen, 1989). Latent variables are not measured directly but can be expressed in terms of one or more directly measurable variables called indicators. For some researchers, defining, constructing, and examining the validity of latent variables may be the end task of itself. For others, testing hypothesized relationships of latent variables may be of interest. We analyzed the correlation matrix of eleven environmental variables from the U.S. Environmental Protection Agency's (USEPA) Environmental Monitoring and Assessment Program for Estuaries (EMAP-E) using methods of structural equation modeling. We hypothesized and tested a conceptual model to characterize the interdependencies between four latent variables-sediment contamination, natural variability, biodiversity, and growth potential. In particular, we were interested in measuring the direct, indirect, and total effects of sediment contamination and natural variability on biodiversity and growth potential. The model fit the data well and accounted for 81% of the variability in biodiversity and 69% of the variability in growth potential. It revealed a positive total effect of natural variability on growth potential that otherwise would have been judged negative had we not considered indirect effects. That is, natural variability had a negative direct effect on growth potential of magnitude –0.3251 and a positive indirect effect mediated through biodiversity of magnitude 0.4509, yielding a net positive total effect of 0.1258. Natural variability had a positive direct effect on biodiversity of magnitude 0.5347 and a negative indirect effect mediated through growth potential of magnitude –0.1105 yielding a positive total effects of magnitude 0.4242. Sediment contamination had a negative direct effect on biodiversity of magnitude –0.1956 and a negative indirect effect on growth potential via biodiversity of magnitude –0.067. Biodiversity had a positive effect on growth potential of magnitude 0.8432, and growth potential had a positive effect on biodiversity of magnitude 0.3398. The correlation between biodiversity and growth potential was estimated at 0.7658 and that between sediment contamination and natural variability at –0.3769.     

Age-dependent population dynamics with several interior variables and spatial spread

The problems of the asymptotic behavior of age-dependent population models with interior and spatial structures are considered. It is proved that the existence and uniqueness of the stable state and its exact form is founded for general linear models. Problems on the speed of convergence to stable state and transitional effects are investigated. Methods of solving two special classes of nonlinear models (separate models and models of the Gurtin-MacCami type) are suggested. A model of forest stand dynamics on the basis of conception of layer-mosaic characteristics of the spatial-temporal structure of stands is examined as an example of the application of given results.     

Solving the probabilistic reserve selection problem

The Reserve Selection Problem consists in selecting certain sites among a set of potential sites for biodiversity protection. In many models of the literature, the species present and able to survive in each site are supposed to be known. Here, for every potential site and for every species considered, only the probability that the species survives in the site is supposed to be known. The problem to select, under a budgetary constraint, a set of sites which maximizes the expected number of species is known in the literature under the name of probabilistic reserve selection problem. In this article, this problem is studied with species weighting to deal differently with common species and rare species. A spatial constraint is also considered preventing to obtain too fragmented reserve networks. As in Polasky et al. (2000), the problem is formulated by a nonlinear mathematical program in Boolean variables. Camm et al. (2002) developed a mixed-integer linear programming approximation that may be solved with standard integer programming software. The method gives tight approximate solutions but does not allow to tell how far these solutions are from the optimum. In this paper, a slightly different approach is proposed to approximate the problem. The interesting aspect of the approach, which also uses only standard mixed-integer programming software, is that it leads, not only to an approximate solution, but also to an upper limit on the true optimal value. In other words, the method gives an approximate solution with a guarantee on its accuracy. The linear reformulation is based on an upper approximation of the logarithmic function by a piecewise-linear function. The approach is very effective on artificial instances that include up to 400 sites and 300 species. Within an average CPU time of about 12 min, near-optimal solutions are obtained with an average relative error, in comparison to the optimum, of less than 0.2%.     

Mineralogical variables that control the antibacterial effectiveness of a natural clay deposit

As antibiotic-resistant bacterial strains emerge and pose increased global health risks, new antibacterial agents are needed as alternatives to conventional antimicrobials. Naturally occurring antibacterial clays have been identified which are effective in killing antibiotic-resistant bacteria. This study examines a hydrothermally formed antibacterial clay deposit near Crater Lake, OR (USA). Our hypothesis is that antibacterial clays buffer pH and Eh conditions to dissolve unstable mineral phases containing transition metals (primarily Fe²⁺), while smectite interlayers serve as reservoirs for time release of bactericidal components. Model pathogens (Escherichia coli ATCC 25922 and Staphylococcus epidermidis ATCC 14990) were incubated with clays from different alteration zones of the hydrothermal deposit. In vitro antibacterial susceptibility testing showed that reduced mineral zones were bactericidal, while more oxidized zones had variable antibacterial effect. TEM images showed no indication of cell lysis. Cytoplasmic condensation and cell wall accumulations of <100 nm particles were seen within both bacterial populations. Electron energy loss analysis indicates precipitation of intracellular Fe³⁺-oxide nanoparticles (<10 nm) in E. coli after 24 h. Clay minerals and pyrite buffer aqueous solutions to pH 2.5–3.1, Eh > 630 mV and contain elevated level (mM) of soluble Fe (Fe²⁺ and Fe³⁺) and Al³⁺. Our interpretation is that rapid uptake of Fe²⁺ impairs bacterial metabolism by flooding the cell with excess Fe²⁺ and overwhelming iron storage proteins. As the intracellular Fe²⁺ oxidizes, it produces reactive oxygen species that damage biomolecules and precipitates Fe-oxides. The ability of antibacterial clays to buffer pH and Eh in chronic non-healing wounds to conditions of healthy skin appears key to their healing potential and viability as an alternative to conventional antibiotics.     

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform, triangular, and exponential random variables.