Wet and dry epoch durations of spatially averaged rain rate,their probability distributions and scaling properties

This article is concerned with the notion of duration of wet and dry epochs in stochastic processes of spatially averaged (instantaneous) rain rate over a given region. Gamma, Lognormal, and Inverse Gaussian parametric families of probability distributions have been considered as candidate models for the distribution of such durations. Goodness of these model's fit to data of dry and wet epoch durations obtained from real time series of spatially averaged rain rate, has been tested with Pearson's -test. The parameters of each of these models have been estimated by maximum likelihood and method of moments, based on TOGA-COARE measurements of tropical rainfall. The hypotheses of independence and identical distribution (i.i.d.) among durations of dry or wet epochs have also been tested using a certain version of the Wald-Wolfowitz test. Finally, the effect of spatial scale on the moments of dry and wet epoch durations has also been investigated, pointing to self-similarity of the underlying random structures over space. The main result of this study is that among the three candidate models, Inverse Gaussian is the one conforming most adequately with all the classical testing criteria implemented here, and also with the newly established scaling behavior of both dry and wet epoch duration processes over space. This is a remarkable finding, considering that the Inverse Gaussian family has recently been also justified from a theoretical viewpoint as a reasonable model for the probability distributions of dry and wet epoch durations.     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

Rao-Blackwell versions of the Horvitz-Thompson and Hansen-Hurwitz in adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design and developed two unbiased estimators, the modified Horvitz-Thompson (HT) and Hansen-Hurwitz (HH) estimators, for this sampling design and noticed that these estimators are not a function of the minimal sufficient statistics. He applied the Rao-Blackwell theorem to improve them. Despite having smaller variances, these latter estimators have not received attention because a suitable method or algorithm for computing them was not available. In this paper we obtain closed forms of the Rao-Blackwell versions which can easily be computed. We also show that the variance reduction for the HH estimator is greater than that for the HT estimator using Rao-Blackwell versions. When the condition for extra samples is 0$$ " align="middle" border="0"> , one can expect some Rao-Blackwell improvement in the HH estimator but not in the HT estimator. Two examples are given.     

The use of composite sampling in contaminated sites—a case study

Simulated composite sampling was carried out using data from a contaminated site. The values obtained by composite sampling were compared with the results obtained using discrete (individual) samples. It is appropriate to use a modified investigation level (MIL) when using composite samples. The MIL is lower than the standard investigation level, (IL). Various MILs were considered in this study. Too low an MIL will indicate that some composite samples require further investigation, when none of the discrete samples comprising the composite would have exceeded the IL. Too high an MIL will result in some discrete samples that exceed the IL being missed. A suggested MIL is IL/ where n is the number of discrete samples in the composite sample. This MIL was found to give few false negatives but many fewer false positives than the IL/n rule. Although this MIL was effective on the test data it could be site specific. Some local areas of high concentration may be missed with composite samples if a lower investigation level is used. These however do not make a large contribution to the health risk because they will have a contaminant level only slightly higher than the IL, and the neighboring samples must have a low concentration of the contaminant. The increased risk due this cause may be more than offset by the higher sampling density made possible through the economies of composite sampling When composite sampling is used as the first phase of an adaptive cluster-sampling scheme, it must be augmented by additional samples to delineate the contaminated area to be cleaned up. Composite sampling can also be effectively used in a clean up unit technique, where a clean up unit is represented by one or more composite samples. Suggestions are given for when composite sampling can be used effectively.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Multimodal signals,imperfect information,and identification of sex in red-backed salamanders (<Emphasis Type="Italic">Plethodon cinereus</Emphasis>)

Theoretical treatments and empirical studies both suggest that signals that occur in multiple sensory modes have superior detectabilities, discriminabilities, and memorabilities. There is also an intuitive link between signal detectability, discriminability, and memorability and the quality of information that is transferred via the signaler. We investigated the role of information quality and sensory modality in the sexual identification of intruding conspecifics by territorial male red-backed salamanders (Plethodon cinereus). Our results imply that these salamanders are able to discriminate between intruding male and female conspecifics (based on the allocation of aggression) in bimodal scenarios (vision and olfaction) even under situations in which the information available about the intruders sexual identities is reduced in quality. In unimodal scenarios (olfaction only), male residents exhibited heightened levels of aggression toward male secretions and reduced levels of aggression toward female secretions. In unimodal scenarios where information pertaining to the sex of the stimulus was reduced in quality, male residents displayed intermediate levels of aggression relative to the responses that male and female stimuli received respectively. Although resident males touched bimodal stimuli significantly more than they touched unimodal stimuli, we were unable to find support for the notion that sensory modality greatly influences how male resident red-backed salamanders allocate aggression toward intruding male versus female stimuli.Communicated by H. Kokko     

Statistical inference on patch-specific survival and movement rates from marked animals

Empirical estimates of patch-specific survival and movement rates are needed to parametrize spatially explicit population models, and for inference on the effects of habitat quality and fragmentation on populations. Data from radio-marked animals, in which both the fates and habitat locations of animals are known over time, can be used in conjunction with continuous-time proportional hazards models to obtain inferences on survival rates. Discrete-time conditional logistic models may provide inference on both survival and movement rates. We use Monte Carlo simulation to investigate accuracy of estimates of survival from both approaches, and movement rates from conditional logistic regression, for two habitats. Bias was low (relative bias < 0.04) and interval coverage accurate (close to the nominal 0.95) for estimates of habitat effect on survival based on proportional hazards. Bias was high ( relative bias 0.60) and interval coverage poor ( = 0.26 vs. nominal 0.95) for estimates of habitat effect based on conditional logistic regression; bias was especially influenced by heterogeneity in survival and the shape of the hazard function, whereas both bias and coverage were affected by ‘memory’ effects in movement patterns. Bias estimates of movement rate was low ( relative bias < 0.05), but interval coverage was poor ( = 0.48–0.80), possibly as a result of poor performance of a Taylor series estimate of variance. An example is provided from a radio-telemetry study of 47 wintering American woodcock (Scolopax minor), illustrating practical difficulties in field studies to parametrize these models. We also discuss extensions of continuous-time models to explicitly include a movement process, and further examine tradeoffs between continuous and discrete models.     

Lack of social entrainment of free-running circadian activity rhythms in the Australian sugar glider (Petaurus breviceps: Marsupialia)

Summary Social influence on circadian activity rhythms was investigated in the nocturnal Australian marsupial Petaurus breviceps. The activity of two and two was recorded electroacoustically and observed by an IR television camera in LD 12:12 (10¹:10^-1lx) and in LL (10^-1lx) when housed isolated and in pairs (+). In LD-entrained animals the average duration of locomotion, orientation movements, grooming and total activity is influenced by social housing, and individually different activity patterns are harmonized. In constant illumination conditions, however, the members of a pair are not mutually synchronized and free-run with different circadian periodlengths. Therefore social influence on the LD-entrained activity rhythm in Petaurus should be interpreted as social masking rather than direct influence on the circadian system.     

Ranked set sample design for environmental investigations

Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions     

Genetic parentage in the indigo bunting: a study using DNA fingerprinting

Summary Parentage of nestlings in a North Carolina population of indigo buntings (Passerina cyanea) was analyzed using DNA fingerprinting. Three minisatellite DNA probes (wild type M13, Jeffreys' 33.15 and 33.6) were used to analyze nuclear DNA isolated from muscle biopsies of 63 nestlings, their parents, and other local adults. Each probe detected approximately 15 scorable fragments per individual, with 18%–39% overlap between probes. The proportion of bands shared (using all fragments over all three probes) between presumably unrelated adults averaged 0.23. Of the 63 offspring analyzed, 35 had at least one fragment not present in either putative parent. The distribution of offspring with novel fragments was distinctly bimodal. The lower mode (offspring with 0, 1, or 2 novel fragments, N=41) fit a Poisson distribution, a pattern expected if mutation (estimated rate per fragment= 0.01) were the source of the novel fragments. The remaining 22 offspring had more novel fragments than could be explained by mutation alone (minimum of four independent fragments across all three probes, =8.2). A low band-sharing proportion with the resident male ( =0.24) and high band-sharing with the resident female ( =0.60) implicated extra-pair fertilizations as the source of all 22. Thus in this sample, 35% of all nestlings came from extra-pair fertilizations and none from intra-specific brood parasitism. Of 25 broods sampled, 12 (48%) had at least one excluded offspring. In 3 broods all of the offspring excluded the resident male. Band-sharing proportions between excluded nestlings within a brood could not distinguish between single and multiple extra-pair paternity. Although young males tended to be excluded less often than older males, wing length and weight were not associated with the frequency of exclusion. Weight and wing length of females also were not associated with involvement in EPCs. Six of the 22 excluded offspring (in 3 broods) shared a large proportion of bands and had fewer than four novel fragments when compared to the fingerprints of a neighboring territorial male, implicating those males as actual fathers. The parentage of the remaining 16 offspring (in 9 broods) could not be clearly assigned because (1) one or more neighbors were not sampled or (2) difficulties in scoring across gels prevented confident alignment of fingerprint bands, and insufficient DNA was obtained from muscle samples to allow reanalysis of potential actual fathers on the same gel as excluded nestlings.     

Significance tables for the exact variance test for the Poisson distribution with alternative underdispersion

Fisher (1950) introduced the variance or dispersion index test statistic to test deviations of the Poisson distribution. For this test approximate critical values exist for large sample sizes. If the number of observations is small this approximation can lead to a wrong conclusion. For small samples, the exact critical values can only be derived by enumeration of all possibilities. Tables of critical values for overdispersion already exist (e.g., Rao and Chakravarti, 1956) However, in many biological situations underdispersion, a more-regular-than-Poisson distribution, is a common phenomenon. Therefore, we have tabulated in this paper the one-tailed critical values for a small number of observations under the null hypothesis (H₀) that the random variable is Poisson distributed against the alternative hypothesis of underdispersion. With the help of this table, the hypothesis that the observations in a data set are Poisson distributed, can be tested easily with the variance test. The tables are illustrated with examples from the literature and some observations from our own research. In general, the ² approximation gives a smaller significance level than the exact variance test.     

Effects of cadmium on Pontoporeia affinis (Crustacea: Amphipoda) in laboratory soft-bottom microcosms

Laboratory soft bottom microcosms, containing sediment with natural populations of meio-and microfauna and the amphipod Pontoporeia affinis Lindström, were used to investigate chronic effects of cadmium on a typical Baltic Sea benthic community. Temperature, salinity, organic content of the sediment and the life cycles of the amphipods in laboratory control microcosms were in good agreement with conditions in the Baltic Sea. In Experiment 1, P. affinis was exposed to four assayed cadmium concentrations, 0 (control), 6.3, 41 and 127 g Cd·1^-1, for 265 d. At the lowest cadmium concentration (6.3 g Cd·1^-1), the sediment contained about 700 times, and P. affinis about 1 700 times, the water concentration at the end of the experiments. In microcosms without P. affinis, the sediments accumulated less cadmium. Effects on P. affinis embryogenesis were detected after 105 d of exposure in all tested cadmium concentrations. Mortality of juveniles was significantly increased after 265 d of exposure in mean assayed concentrations of 41 and 127 g Cd·1^-1. In Experiment 2, P. affinis was exposed to cadmium in assayed concentrations, 0, 6.5 and 46 g Cd·1^-1 for 460 d. At the lowest water concentration (6.5 g Cd·1^-1), the prolonged exposure did not increase the sediment concentration, which indicates a steady state, while concentrations in P. affinis reached about 3 500 times the lowest water concentration after 460 d. Juvenile P. affinis matured sexually and reproduced normally in all microcosms, but their offspring died in all microcosms with added Cd. This occurred at water concentrations not uncommon in polluted marine areas. The effects are serious in comparison to those found in conventional short-term laboratory experiments with the same concentrations and demonstrate the importance of long-term experiments in ecotoxicology.     

Oxygen consumption inNeomysis americana (Crustacea: Mysidacea), and the effects of naphthalene exposure

Oxygen uptake ( ) of individual mysids was measured in a novel continuous flow respirometer for 24-h periods, and in a sealed chamber respirometer for several hours. Mysids were acclimated 30–100d under conditions which allowed complete life-cycle cultivation. was normalized for mysid size using an unconventional linear regression: log ( ) vs log (body water). Compared to the conventional regression, log ( ) vs log (body mass), the new approach showed two advantages: significantly greater coefficient of determination,r ², and removal of differences in between sexes. Minimum rates of oxygen uptake measured in the continuous flow respirometer were lower than sealed chamber measurements, and may more accurately reflect standard metabolic rate. Hourly data also showed a daily cycle when adjusted to represent a standard size mysid. Exposure to ca 1.1 mg l^-1 naphthalene increased and the range of spontaneous shown by the mysids; exposure to ca 0.1 mgl^-1 naphthalene depressed the range of . Both exposures caused aberrations in the daily cycle.     

Population genetic and phylogeographic structure of wahoo,<Emphasis Type="Italic"> Acanthocybium solandri</Emphasis>, from the western central Atlantic and central Pacific Oceans

The wahoo, Acanthocybium solandri (Cuvier, 1832), is a pelagic, highly migratory, scombroid fish, distributed worldwide throughout tropical and warm temperate seas. To evaluate population genetic and phylogeographic structure against a null hypothesis of panmixia, the entire mitochondrial DNA control-region (~890 base pairs) was sequenced for 231 wahoo. Samples were collected from 1997 to 2001 from seven sites: North Carolina (NC; n=23), east central Florida (CF; n=30), Bimini, Bahamas (BB; n=40), southern tip of Florida (SF; n=21), Cayman Islands (CI; n=23), northern Gulf of Mexico (NG; n=54), and Hawaii (HI; n=40). Inter-annual samples were obtained from four of these locations (NC, BB, SF, NG). Seventeen haplotypes were shared by individuals within and among samples; 187 singleton haplotypes were observed. Within-sample haplotype diversities ranged from 0.995 to 1.000 (overall h=0.999) and within-sample nucleotide diversities ranged from 0.049 to 0.055 (overall =0.053). A neighbor-joining tree based on inter-haplotypic distances revealed two monophyletic lineages differing by 13.6% nucleotide divergence. Nested within each major lineage were several, well-supported subclades. There was no evidence of temporal heterogeneity in haplotype distributions. Partitioning mtDNA variation, 99.75% of the variance was within samples and 0.25% (P=0.307) between samples; the fixation index (_ST=0.0025) was not significant. Likewise, pairwise _ST values were low or negative, and none were significant on a table-wide basis. Exact tests for sample differentiation in haplotypes were also non-significant. All population analyses were consistent with the null hypothesis of panmixia. However, analytical power was limited by sample size. Mismatch distributions were inconsistent with expected distributions based on sudden-expansion and static-growth models. Wahoo exhibit concurrently high haplotype and nucleotide diversities, presumably a consequence of secondary contact between historical subpopulations rather than a long, stable evolutionary history. Given the level of geographic and individual sampling, wahoo thus far represent the sole example of a scombroid or xiphioid fish exhibiting coarse-grain genetic homogeneity across a broad, inter-oceanic range despite a deeply coalescing genealogical structure. Accordingly, cooperative fishery management on a broad, inter-ocean scale may be warranted.Communicated by J.P. Grassle, New Brunswick     

Physiological responses of Mytilus edulis and Cardium edule to aerial exposure

Physiological responses of two bivalves (Mytilus edulis L. and Cardium edule L.) to intertidal conditions were studied. Specimens were collected from S. W. England in autumn/winter, 1980, and acclimatized to either intertidal or subtidal regimes before measurement of rates of heat dissipation and oxygen uptake during 5 h of air exposure, and rates of , particle clearance, ammonia excretion, and food-absorption efficiency during 7 h of reimmersion. Subtidal individuals were either intermittently or continuously fed in order to distinguish the effects of periodic food supply from the effects of air exposure. Specimens of M. edulis had low aerial rates of (14 to 20% of aquatic rate), and was greater than the energy equivalent of , indicating that they were largely anaerobic. In contrast, C. edule air-gaped and had higher aerial rates of and (50 to 75% of aquatic rate). There were behavioural and metabolic differences in the responses of intertidally and subtidally acclimatized mussels and cockles to air exposure. Intertidal individuals of both species were more quiescent, had lower aerial rates of and , and showed a conditioned response at the expected time of reimmersion. The reduction in aerial rate of was an energy-saving mechanism and the payment of the oxygen-debt within 2 h of reimmersion represented a significant cost. The heat increment associated with feeding and digestion was estimated as 15 to 17% of the oxygen uptake by M. edulis during all stages of recovery. M. edulis adapted to the intertidal regime by reducing its time-averaged aerial and aquatic rates of ammonia excretion. In contrast, C. edule maintained a high aerial and aquatic rate of ammonia excretion. The clearance rates of M. edulis recovered rapidly (0.5 to 1.5 h) following reimmersion, whereas those of C. edule recovered more slowly, particularly for the subtidal individuals following acute exposure (>4 h). There was no evidence of increased clearance rate or absorption efficiency by intertidal individuals to compensate for the loss of feeding time. Intertidally acclimatized individuals of M. edulis and C. edule had more energy available for growth (scope for growth) integrated over a 12 h period and higher growth efficiencies than subtidal individuals subjected to acute air exposure and intermittent feeding regimes. This was the result of reduced aerial and aquatic rates of energy expenditure, a relatively small cost in terms of the payment of oxygen-debt and a rapid recovery of clearance rate following reimmersion.     

Oxygen and carbon dioxide exchange in the polychaete Nereis virens: influence of ventilation activity and starvation

The influence of ventilation activity and starvation on O₂ uptake and CO₂ production in the polychaete Nereis virens Sars was investigated during September 1986 using worms collected on intertidal flats outside the Nærå Strand estuary, Denmark. The activity level, measured as ventilation rate, , was linearly related to active O₂ uptake, , for worms inhabiting artificial burrows (i.e. tubes) in the laboratory. at 16°C was two and four times the extrapolated standard O₂ uptake ( =0) when was 100 and 500 ml g^-1 h^-1, respectively. The use of tubes had no significant effect on N. viren's temporal ventilation pattern, D_v, compared to natural burrows in sediment. The ventilation rate, , however, was 2 to 3 times higher in tubes than in burrows. Starvation affected both ventilation and gas exchange. increased slightly during the first six days remaining constant thereafter. D_v, on the othe hand, decreased during the first six days followed by a gradual increase to Day 20. The observed decrease in D_v (%) from Day 0 to 1 was attributed to insufficient acclimation of the worms. The time integrated ventilation rate, × D_v, increased gradually throughout the 20 d starvation period. and declined rapidly during the first days of starvation. After 10 d the gas exchange reached steady levels at about 50% of the initial rate. The observed decrease in metabolic rate during starvation was explained by a rapid initial reduction in specific dynamic action (SDA) followed by a gradual exhaustion of readily available metabolic reserves, e.g. glycogen and lipids.     

Ecophysiology of the benthic amphipod Monoporeia affinis in an open-sea area of the northern Baltic Sea: seasonal variations in oxygen consumption and ammonia excretion

Seasonal variations in the oxygen uptake rate ( ) and ammonia excretion rate ( ) of the benthic deposit-feeding amphipod Monoporeia affinis vere studied in an open-sea population of the northern Baltic Sea during three consecutive years (1991 to 1993). In the early summer an increase in the weightspecific by 22% (standard 1-mg individual) was registered; an even more striking change was noted in the , which showed an increase in the early summer of ca. six times the extremely low winter/spring valnes. The metabolic changes observed could not be attributed to temperature, which remained at steadystate throughout the year, nor could seasonal variations in the biochemical composition of the amphipods explain the results. Therefor, it is evident that quality-food abundance following the sedimentation of the spring phytoplankton bloom induces the observed early-summer elevations in and . In turn, the marked decrease in the towards autumn reflects the gradual depletion of quality-food in the benthic environment. Atomic O: N ratios indicated that at the sampling location, M. affinis uses lipid almost exclusively for metabolic energy throughout the year, except in early summer when the use of lipid and protein was observed to be almost equal. Results also indicated a time-lag between sedimentation of the phytoplankton bloom and metabolic response in the amphipod population.     

Quantitative estimates of the meiofauna from the deep sea off North Carolina,USA

In 1974 the authors collected, sorted and enumerated meiofauna from 400, 800 and 4000 m off North Carolina, USA. Samples were replicated respectively with 4 boxcores and 21 subsamples, 2 boxcores and 7 subsamples and 2 boxcores and 8 subsamples. Total meiofaunal numbers were highest in fine silt sediment at 800 m ( =891.9 10 cm_–2) and lowest in very fine silt at 4000 m ( =73.5 10 cm_–2). Fine sand at 400 m yielded a mean of 442.4 10 cm^–2. At all depths, most fauna were located in the upper 3 cm of sediment ( depth distribution=2.2 cm), and typically only nematodes and foraminiferans were found below 4 cm. Total community abundances significantly differed with depth; however, there were no differences among replicate boxcores at particular depths. Since most (85.7%) of the variance was associated with subsamples from a boxcore, it appears that meiofauna densities are homomeneous within large areas at particular depths, and that patchiness is a smallscale phenomenon at the level of the 10 cm² subsampler. Comparisons of sorting efficiencies of live and preserved samples indicated that to accurately enumerate formainiferans, samples must first be fixed and stained, while turbellarians and oligochaetes must be sorted live.Contribution No. 151 from the Belle W. Baruch Institute for Marine Biology and Coastal Research. This research was supported by the Oceanography Section, National Science Foundation, NSF Grant GA-42792, and GC-00005 to Duke University for R.V. Eastward operations.     

Reproduction and growth of Holothuria atra (Echinodermata: Holothuroidea) at two contrasting sites in southern Taiwan

Reproductive periods and growth of two populations of Holothuria atra Jaeger distinctly different in body size at two sites of southern Taiwan were determined. Individuals examined in the present study were collected between march 1990 and February 1992. At Nanwan (21° 57N, 120° 45E), large individuals (351 to 1400 g wet wt) spawned from June to September. At Wanlitung (22°N, 120° 42E), a small proportion of frequently dividing individuals (<190 g wet wt) have mature gonads in May, June and September, but histological examination revealed no sign of spawning. Sexual recruits, defined as small individuals <5 g wet wt without sign of regeneration, were not found at either site during this 2-yr study. After the peak of fission at Wanlitung, 40% of the population showed signs of external regeneration. At Nanwan, small individuals transferred from Wanlitung grew from 6 g (n=6) to 166±8 g within 8 mo, and from 48±4 g (n=50) to 324±16 g within 1 yr, with a 6.8-fold biomass increase in 1 yr. At Wanlitung, the monthly average body weight of H. atra is between 33 and 62 g, apparently due to frequent fission, and the biomass increased only 2.9-fold in 1 yr. In southern Taiwan, sexual reproduction of H. atra occurs in large individuals. Asexual reproduction, occurring in small individuals, is the chief mechanism for population maintenance and increase, but it may decrease sexual reproductive potential.     

Markov Chain Monte Carlo on optimal adaptive sampling selections

Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO₂ emissions in Yellowstone National Park as a practical illustrative example.