Equal Probability Of Capture Research Articles

Abundance of freshwater Irrawaddy dolphins in the Mahakam River in East Kalimantan, Indonesia, based on mark-recapture analysis of photo-identified individuals

From February 1999 to August 2002 ca 9,000km (840 hours) of search effort and 549 hours of observation on Irrawaddy dolphins (Orcaella brevirostris) were conducted by boat in the Mahakam River in East Kalimantan, Indonesia. An abundance estimate based on mark-recapture analysis of individuals photographed during separate surveys is presented here. Petersen and Jolly-Seber analysis methods were employed and compared along with earlier estimates derived from strip-transect analysis and direct counts. These comparisons serve to evaluate the biases of each method and assess the reliability of the abundance estimates. The feasibility of video-identification is also assessed. Total population size calculated by Petersen and Jolly-Seber mark-recapture analyses, was estimated to be 55 (95% CL=44-76; CV=6%) and 48 individuals (95% CL=33-63; CV=15%) respectively. Estimates based on strip-transect and direct count analysis for one sampling period, which was also included in the mark-recapture analysis, were within the confidence limits of the Jolly-Seber estimate (Ncount = 35 and Nstrip = 43). Calculated potential maximum biases appeared to be small, i.e. 2% of N for Petersen and 10% of N for the Jolly-Seber method, which are lower than the associated CVs. In addition, a high re-sight probability was calculated for both methods varying between 65% and 67%. Video images were considered a valuable, supplementary tool to still photography in the identification of individual dolphins in this study. For future monitoring of trends in abundance using mark/recapture analyses, a time interval is recommended between the two sampling periods that is short enough to minimise the introduction of errors due to gains and losses. Also, survey area coverage during photoidentification should be similar to avoid violation of the assumption of equal capture probabilities. The alarmingly low abundance estimates presented underline the need for immediate and strong action to preserve Indonesia’s only known freshwater dolphin population.

Use of a capture-recapture statistical model to assess morbidity and mortality of road traffic accidents in Gaza Strip: a retrospective study

BackgroundIn low-income and middle-income countries, road traffic injuries (RTIs) are commonly under-reported. In this study I estimated the incidence of RTIs and RTI deaths in Gaza Strip using the capture-recapture method. MethodsAll data registered on RTIs and RTI deaths from Jan 1 to Dec 31, 2018, were obtained from police records and Palestinian Ministry of Health hospital records. Linked data from these two sources are available through a web-based registry. When possible, records in the two sets of records were linked by an identification number. I used the Chapman formula of capture-recapture to estimate the numbers of RTIs and RTI deaths: (R=[(R1 + 1)(R2 + 1)/(r+1)]–1). FindingsThe Ministry of Health hospital and the traffic police registries included 1722 and 1356 records, respectively. 970 records could be linked. Although the Ministry of Health hospital records reported more RTIs, fewer than the police records contained information about the injury type and vehicle involved (1053 [61%] vs 1302 [96%] and 849 [49%] vs 1139 [84%], respectively. Most individuals involved in RTIs were men (1313 [76%] in hospital records and 1039 [77%] in police records). 684 (40%) individuals in the hospital records and 516 (38%) in the police records were younger than 15 years and 712 (41%) and 541 (40%), respectively, were in the 15–35-year age group. Most (523 [94%]) of the linked RTIs involved four-wheeled vehicles. The number of RTIs estimated by the Chapman method was 2407 (95% CI 2354–2460), meaning that hospital records captured 72% and police records captured only 56%. The hospital and police records included 16 and 57 deaths, respectively, 14 of which had linked records. Of these deaths, 29 (51%) in the police records and 10 (62%) in the hospital records involved people younger than 15 years, and 45 (79%) and 16 (100%), respectively involved four-wheeled vehicles. The total number of fatalities estimated by the Chapman method was 65 (95% CI 55–74). Therefore, the hospital records captured only 25% whereas police records captured 88%. The population of Gaza Strip in 2018 was 1 932 843 in 2018. Thus, based on the estimated values, the incidence of RTIs would have been 125 per 100 000 population and that for RTI deaths fatalities would have been 3·4 per 100 000 population. InterpretationThe capture re-capture method has some methodological biases, such as it requires an equal probability of capture between data sources, perfect linkage of data from data sources, and closed populations. However, it might be a powerful tool to improve estimates of the incidence of RTIs and RTI deaths where reporting is incomplete. Neither the Ministry of Health hospital nor the police registry independently provided accurate numbers. Both registries should be strengthened to provide reliable information not only on numbers but also on crash circumstances, injury patterns, road users, vehicles involved, and behavioural risk factors. Reporting of injury cause, manifestation, location, severity, and type could be improved by use of a standardised systems, such as ICD-10 codes. FundingNone.

Sampling designs matching species biology produce accurate and affordable abundance indices

Wildlife biologists often use grid-based designs to sample animals and generate abundance estimates. Although sampling in grids is theoretically sound, in application, the method can be logistically difficult and expensive when sampling elusive species inhabiting extensive areas. These factors make it challenging to sample animals and meet the statistical assumption of all individuals having an equal probability of capture. Violating this assumption biases results. Does an alternative exist? Perhaps by sampling only where resources attract animals (i.e., targeted sampling), it would provide accurate abundance estimates more efficiently and affordably. However, biases from this approach would also arise if individuals have an unequal probability of capture, especially if some failed to visit the sampling area. Since most biological programs are resource limited, and acquiring abundance data drives many conservation and management applications, it becomes imperative to identify economical and informative sampling designs. Therefore, we evaluated abundance estimates generated from grid and targeted sampling designs using simulations based on geographic positioning system (GPS) data from 42 Alaskan brown bears (Ursus arctos). Migratory salmon drew brown bears from the wider landscape, concentrating them at anadromous streams. This provided a scenario for testing the targeted approach. Grid and targeted sampling varied by trap amount, location (traps placed randomly, systematically or by expert opinion), and traps stationary or moved between capture sessions. We began by identifying when to sample, and if bears had equal probability of capture. We compared abundance estimates against seven criteria: bias, precision, accuracy, effort, plus encounter rates, and probabilities of capture and recapture. One grid (49 km2 cells) and one targeted configuration provided the most accurate results. Both placed traps by expert opinion and moved traps between capture sessions, which raised capture probabilities. The grid design was least biased (−10.5%), but imprecise (CV 21.2%), and used most effort (16,100 trap-nights). The targeted configuration was more biased (−17.3%), but most precise (CV 12.3%), with least effort (7,000 trap-nights). Targeted sampling generated encounter rates four times higher, and capture and recapture probabilities 11% and 60% higher than grid sampling, in a sampling frame 88% smaller. Bears had unequal probability of capture with both sampling designs, partly because some bears never had traps available to sample them. Hence, grid and targeted sampling generated abundance indices, not estimates. Overall, targeted sampling provided the most accurate and affordable design to index abundance. Targeted sampling may offer an alternative method to index the abundance of other species inhabiting expansive and inaccessible landscapes elsewhere, provided their attraction to resource concentrations.

Appropriateness of the Darroch Estimator for Monitoring Adult Chum Salmon on the Middle Yukon River, Alaska

AbstractFrom 1996 to 1999, a Darroch two‐sample stratified capture–recapture experiment was conducted on adult chum salmon Oncorhynchus keta in the Yukon River, Alaska. Annual release of marked chum salmon ranged from 8,527 to 18,631 fish. At the recovery site, 15,581–45,232 fish were examined for marks annually. The percentage of tagged fish among those examined for marks ranged from 2.8% to 6.4%. Abundance estimates ranged from 189,742 (SE = 6,967) to 654,296 (SE = 21,921) fish during the four study years. Weekly estimates ranged from 6,796 to 126,268 fish. The assumption of a closed population was evaluated in light of life history and other data. One closure violation due to sample starting and ending dates was mitigated using migration times. We used statistical analysis and modeling to evaluate assumptions of (1) equal probability of capture, (2) equal probability of movement, and (3) random mixing of fish. Logistic regression suggested that the probability of recapture was not independent of length and gender in 8 of 32 weeks among years. Modeling changes in the probabilities of movement and capture indicated that differences in movement would cause little bias in population estimates relative to differences in capture. However, length‐ and gender‐stratified and unstratified population estimates showed little difference (e.g., in 1997: length‐stratified estimate = 351,138 fish, gender‐stratified estimate = 333,842 fish, unstratified estimate = 333,057 fish). Three explanations were offered for these results: violations were due to changes in the probability of movement, statistical tests were overly sensitive, or the estimator was robust to the assumption violations. Probability of recapture was related to bank orientation (i.e., nonrandom mixing) only in 1999. Annual estimates during the study documented a decline in the spawning population. Weekly estimates indicated that run timing was inconsistent among years. The estimates compared favorably with other assessments of the run. We concluded that the Darroch estimator was reasonably applied to data collected via fish wheels for this population.

MARK–RECAPTURE ESTIMATES OF POPULATION PARAMETERS FOR SELECTED SPECIES OF SMALL MAMMALS

We used program CAPTURE to analyze 1,535 capture–recapture data sets from 33 species of small mammals for sources of variation in capture probabilities and to characterize species-specific responses to mark–recapture trapping. Program CAPTURE contains 8 models to account for all possible combinations of heterogeneity (h), behavioral response (b), and time (t) effects on capture probabilities. Model Mo (equal capture probabilities) was selected most often by CAPTURE as the most appropriate model for small sample sizes, reflecting the difficulty of detecting unequal probabilities of capture in small data sets. Heterogeneity in capture probabilities among individuals was evident in larger data sets for all species of small mammals examined. Strong behavioral responses were detected in several species. Sylvilagus, Tamias amoenus, Glaucomys sabrinus, Perognathus longimembris, and Microtus ochrogaster were trap shy, whereas Tamias striatus, Tamias townsendii, Spermophilus richardsonii, Perognathus parvus, Reithrodontomys megalotis, Peromyscus maniculatus, Peromyscus truei, Sigmodon hispidus, Microtus californicus, and Microtus pennsylvanicus were trap prone. Time effects were not apparent for most species except where they were accompanied with heterogeneity. Murid species had the highest estimated probabilities of capture, followed by heteromyids, sciurids, and leporids in decreasing order. Estimates of abundance from model Mh were significantly greater than those from models Mb, Mo, and Mt, which likely reflects the negative bias of these latter estimators.

ESTIMATING DETECTION PROBABILITY PARAMETERS FOR PLETHODON SALAMANDERS USING THE ROBUST CAPTURE–RECAPTURE DESIGN

Recent concern over global amphibian population declines has highlighted a need for more extensive, rigorous monitoring programs. Two sources of variation, spatial variation and variation in detection probability, make the design and implementation of effective monitoring programs difficult. We used Pollock's robust design in a 3-year capture–recapture study to estimate detection probability and temporary emigration for Plethodon salamanders in Great Smoky Mountains National Park (Tennessee/North Carolina), USA. We used 12 competing models to determine the importance of temporary emigration, and we explored temporal and behavioral effects on conditional capture probabilities. The top 4 models all included random temporary emigration, and Akaike model weights indicated that this parameter was the most important. Models that contained behavioral effects in capture probabilities were selected more often than models with equal capture probabilities for marked and previously unmarked individuals. The “best” model contained random emigration and behavioral effects and was selected 4 times as often as any other model. When we included Markovian emigration, the probability of emigrating from the surface usually was less than the probability of remaining an emigrant (73% of site-years). Markovian emigration estimates often were similar and always had overlapping confidence intervals, thus the Markovian model rarely was chosen over the random emigration models (only 9.6% of site-years). Our study is the first to formally estimate temporary emigration in terrestrial salamander populations, and our results verify that significant proportions of terrestrial salamander populations are subterranean. We determined that the probability of capturing salamanders on the surface may also vary temporally within a sampling season. Therefore, we caution against using unadjusted count indices to compare salamander populations over time or space unless detection probabilities are estimated. Temporary emigration models will improve abundance estimates when a large proportion of the population is unavailable for capture during a given sampling period.

Stratified Capture-Recapture Estimation of the Size of a Closed Population

This paper considers the estimation of the size of a closed population in a stratified capturerecapture experiment using the stratified Petersen-Lincoln model introduced by Darroch (1961, Biometrika 48, 241-260). A generalization of Darroch's model where the tagging or the recovery probabilities depend on explanatory variables possibly related to the capture mechanism is proposed. A simple scoring algorithm for the estimation of the nuisance parameters (i.e., the vectors of tagging and of recovery probabilities and the matrix for the distribution of the units in the capturerecapture area) is derived. This algorithm is based on a new closed-form expression for the inverse of the Fisher information matrix of the conditional likelihood for the estimation of the nuisance parameters. Large sample tests for the tagging and the recovery probabilities are obtained. Pooling of adjacent recovery strata with equal capture probabilities is proposed as a method for getting accurate estimators of the size of the population. Conditional and unconditional estimators of the size of the population are proposed. Analyses of data on smolt migration illustrate the methodology presented in this paper.

Estimating Breeding Proportions and Testing Hypotheses about Costs of Reproduction with Capture-Recapture Data

The proportion of animals in a population that breeds is an important determinant of population growth rate. Usual estimates of this quantity from field sampling data assume that the probability of appearing in the capture or count statistic is the same for animals that do and do not breed. A similar assumption is required by most existing methods used to test ecologically interesting hypotheses about reproductive costs using field sampling data. However, in many field sampling situations breeding and nonbreeding animals are likely to exhibit different probabilities of being seen or caught. In this paper, we propose the use of multistate capture—recapture models for these estimation and testing problems. This methodology permits a formal test of the hypothesis of equal capture/sighting probabilities for breeding and nonbreeding individuals. Two estimators of breeding proportion (and associated standard errors) are presented, one for the case of equal capture probabilities and one for the case of unequal capture probabilities. The multistate modeling framework also yields formal tests of hypotheses about reproductive costs to future reproduction or survival or both fitness components. The general methodology is illustrated using capture—recapture data on female meadow voles, Microtus pennsylvanicus. Resulting estimates of the proportion of reproductively active females showed strong seasonal variation, as expected, with low breeding proportions in midwinter. We found no evidence of reproductive costs extracted in subsequent survival or reproduction. We believe that this methodological framework has wide application to problems in animal ecology concerning breeding proportions and phenotypic reproductive costs.

On the Use of Enumeration Estimators for Interspecific Comparisons, with Comments on a "Trappability" Estimator

Recently, Adler et al. (1984) studied the population dynamics of the meadow jumping mouse, Zapus hudsonius, in Massachusetts. As is typical of contemporary capture-recapture studies on small mammals, they used enumeration estimates of population size and survival despite the known biases of these estimators (Jolly and Dickson, 1983; Nichols and Pollock, 1983). Adler et al. (1984:390) noted that of density and survival rate during the active season for Zapus hudsonius in our study population were considerably lower than those obtained by Nichols and Conley (1982). They also compared estimates of 7 demographic for 3 species trapped on their grids: Z. hudsonius, Peromyscus leucopus, and Microtus pennsylvanicus. They found substantial differences between estimates for Z. hudsonius and the other 2 species. For example, the parameter they termed overall survival (14-day rate) was estimated at 0.13 and 0.09 for Zapus males and females, respectively, and 0.73 and 0.78 for Microtus males and females (Adler et al., 1984:389). On our Michigan study area, W. Conley and I found very similar point estimates of weekly survival probability for these 2 species (0.84 for Zapus, 0.89 for Microtus; Nichols and Conley, 1982), and these estimates did not differ significantly. In this note I do not argue that the apparent interspecific differences reported by Adler et al. (1984) are nonexistent. It may well be that such differences did exist on their study area. Instead, I point out that enumeration estimates are especially inappropriate for such interspecific comparisons and that they cannot be used to draw reasonable inferences about the underlying parameters of interest. This inappropriateness results largely from the fact that enumeration estimators estimate complicated functions of survival and capture probabilities (Nichols and Pollock, 1983) and that different species are often likely to have different capture probabilities. The relevance of capture probability to this argument leads to a second point, which involves the inappropriateness of an estimator for trappability that appears in Adler et al. (1984) and throughout the small mammal literature. The expected value of the enumeration survival rate estimator for capture period i, includes the survival and capture probabilities for every capture period subsequent to i in the entire experiment (see Nichols and Pollock, 1983: eq. 6). Because of this dependence on capture probability, 2 studied populations with identical survival probabilities but different capture probabilities would be expected to yield different enumeration survival estimates. Numerical examples of this problem appear in Figs. 1D and 1E of Nichols and Pollock (1983). These 2 examples show enumeration survival estimates for a single population with constant true survival over 12 capture periods. The difference between the survival estimates for periods with high (0.7) and low (0.3) capture probabilities exemplifies the problem that exists with interspecific comparisons in which the species do not have equal capture probabilities. Even if true survival probabilities are equal, the species with the lower capture probabilities will have lower enumeration survival estimates. W. Conley and I found substantial differences in the Jolly-Seber capture probability estimates for Z. hudsonius and M. pennsylvanicus trapped at the same times on the same grid (Table 1). Estimates for Zapus were consistently lower than those for Microtus until mid-September. We speculated that the crimped oats bait may have been especially attractive during the period of rapid weight gain preceding hibernation, resulting in the high Zapus capture probabilities in September. In any case, these differences in capture probability would have caused problems if we had used enumeration estimates to compare these 2 species. Enumeration estimates of population size and survival rate would have been biased low for both species, but the absolute value of the relative bias would have been greater for Zapus because of the lower capture probabilities. Thus, even if survival rate was similar for the 2 species, as was the case in our study, the enumeration estimate would have been lower for Zapus. Five of the 7 parameter estimates used in the interspecific comparisons of Adler et al. (1984) are functions of capture probability. Any differences between estimates for the different species may then reflect either true differences in the parameter of interest or differences in capture probability. For 3 of these estimators, average density, overall survival, and transiency rate, the effects of differences in capture probability 590 Vol. 67, No. 3

Trappability of coyotes relative to home range boundaries

Trappability of coyotes relative to location of the home range boundary was examined to determine whether animals were more susceptible to capture in an unfamiliar area. Susceptibility to trapping did not appear to increase on the edge or outside of home range boundaries, but equal probability of capture in areas receiving different intensities of use still needs to be assessed.

A simulation model for studying alternatives in mark-recapture experiments

The paper describes a simulation model which mimics mark-recapture experiments in a closed population. The model incorporates home-range movements, spatial patterns, and a ‘trap-happy’ or ‘trap-shy’ learning process, and yields typical mark-recapture data. Such a system allows biologists to study alternatives in mark-recapture experiments when the assumption of equal probability of capture is violated. Finally, several applications of the model are illustrated.

Simulation of Effects of Learned Trap Response on Three Estimators of Population Size

Evaluation of the Schnabel, geometric and nonparametric estimators of population size was performed on a model population of 100 individuals which possessed a bivariate normal home range model with ox = 1 and a, = 2, a random spatial pattern, an average initial probability of capture of p = 0.10 or p = 0.40 and either a trap happy or trap shy learning process. Data were generated from a model which simulated 10-sample mark-recapture experiments consisting of 25 traps. Evaluation of these estimators reveals the magnitude of bias and variability present in such circumstances. The results indicate that the nonparametric estimator was the most robust under these conditions. J. WILDL. MANAGE. 43(2):474-483 Estimating the size of an animal population presents complex problems to population ecologists. General reviews of some of the methods were presented by Overton (1969) and Seber (1973). Estimators which have been developed are based on various assumptions, some of which are not fully satisfied in practice. When assumptions are not satisfied, wide variation may result in the estimates. Since many different estimators are available, it is desirable to evaluate their performance under varying degrees of violation of the assumptions. This would provide the investigator a measure of the degree of robustness of the estimators and shed light into which one would be most suitable for a specific problem. Field evaluation of the estimators is possible if mark-recapture experiments are performed in areas where the true sizes of the populations are known. However, this information is rarely available. An alternate approach for determining the robustness of the estimators is to develop simulation models to mimic populations exposed to mark-recapture experiments. In such models the parameters that control the animals' response to trapping can be varied, resulting in differential magnitudes of assumption violation. Recently, simulation has been used in the study of estimators of population parameters. Gates (1969) used computer simulation to evaluate the bias of a variety of line transect density estimators. Burnham and Overton (1969) and Manly (1970) employed computer simulation in evaluating the behavior of various markrecapture estimators. In another paper, Manly (1971) used simulation to examine Jolly's (1965) variance formulas for estimators of population parameters. In the present study, computer simulation techniques were also used. The objective of this work was to evaluate the sample expectation, variance, bias, and mean square error of mark-recapture estimators of population size when the assumption of equal probability of capture of animals is violated in response to a learning process related to the previous capture history. Appreciation is extended to the Division of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, and to the Department of Fisheries and Wildlife, Michigan State University, East Lan' Present address: Department of Fisheries and Wildlife, Michigan State University, East Lansing, MI 48824. 474 J. Wildl. Manage. 43(2):1979 This content downloaded from 157.55.39.80 on Fri, 22 Apr 2016 05:57:59 UTC All use subject to http://about.jstor.org/terms SIMULATION OF LEARNED TRAP RESPONSE *Zarnoch 475 sing, Michigan, for computer time used in the development of the model and evaluation of the estimators of population size. ESTIMATORS OF POPULATION SIZE Letting N = number of individuals in the population and S = number of samples taken, the following estimators were evaluated. Schnabel.-The Schnabel estimator, modified by Chapman (1952), is defined

Striking Behavior of the Largemouth Bass and Use of the Binomial Distribution for its Analysis

Abstract Three hundred tagged largemouth bass (Micropterus salmoides) 14 to 29.5 cm long were divided into experimental groups of 100 fish which were designated as control, bait fishing, and artificial lure fishing. Since individuals were “known” by tag numbers, it was possible to test the hypotheses of (1) unequal vulnerability to angling among individuals and (2) hook avoidance learning. Results revealed that some conditioning or learning occurred among naive bass exposed to live bait angling for the first time. In the case of artificial lures and/or bass which were no longer naive, individuals appeared to have equal probability of capture and seemingly struck at random.

Population Cycles and Activity Patterns of the Dusky Salamander, Desmognathus fuscus fuscus

Population densities of the dusky salamander were determined in a Georgia Piedmont stream using a mark-recapture technique for density estimation. Highest densities were obtained from late spring to early summer when the salamanders are more active under optimal and stable environmental conditions. Lowest densities were recorded in winter, indicating the inactivity and torpidity of D. fuscus. Nocturnal estimates were greater than corresponding diurnal estimates throughout the study. Seasonal trends in population densities are chiefly attrilbuted to temperature, reproduction condition of adult females and relative abundance of the three age-size classes. Differences between diurmal and nocturnal density estimates are mainly attributed to the interaction of light, relative humidity and the differential mobility of the population components. Mark-recapture and population estimation techniques are discussed and evaluated. INTRODUCTION Desmo gnathus fuscus fuscus, a semiaquatic plethodontid, is a predator common in woodland streams of the Piedmont Region of the eastern United States. Its anatomy and life history (Wilder, 1913, 1917; Noble and Evans, 1932; Dunn, 1917, 1926), home range and activity (Barbour et al., 1969), dispersion patterns (Stewart and Bellis, 1970), homing ability (Barthalmus and Bellis, 1969, 1972), and position in the evolution of the desmognathines (Tilley, 1968) are well-documented. Most recent attention has been given to metabolic studies (Fitzpatrick et al., 1972) and the influence of urbanization on populations of this salamander (Orser and Shure, 1972). Mark-recapture as a technique for estimating certain population parameters has been applied to a variety of animal species. Despite its applicability, mark-recapture has seldom been used to estimate salamander densities (Spight, 1967; Burton and Likens, 1971; Orser and Shure, 1972). The Hayne (1949) method of density estimation is based on the increase in percentage of recaptured individuals as the number of marked individuals increases over time. Population density is estimated by the line of best fit to a plot of the percentage recaptured vs. the cumulative number previously marked. The Hayne method assumes a uniform population size with no recruitment or loss of animals during the population estimate. It further assumes equal probability of capture of marked and unmarked individuals. A previous study (Orser and Shure, 1972) indicated possible limitations in the application of mark-recapture and Hayne's method for density estimations of D. fuscus. This study also suggested that a comparison of diurnal and nocturnal population density estimations 1 Present address: Stone and Webster Engineering Corp., Division of Environmental Engineering, 225 Franklin St., Boston, Mass. 02107.

Aspects of the population dynamics of the western rock lobster, Panulirus cygnus George. I. Estimation of population density

Breakdowns in the assumptions made by the Jolly (1965) method of estimating population size were detected in mark-recapture experiments with the western rock lobster. Using information gathered from sampling by both baited traps and by diving it was shown that, in particular, the assumptions of (1) a single population and (2) equal probability of capture of marked and unmarked rock lobsters, were not valid at all times in the 'population' studied, and this resulted in underestimates of population density. However, it was found possible to make suitable corrections to the raw data to arrive at apparently unbiased estimates of population density. In the cases studied, the calculated unbiased estimates of population density agreed well with unbiased estimates calculated from information gathered by marking and recapturing by different methods. Single census and the De Lury (1958) methods also grossly underestimated population density.

General transport theory of noise in pn junction-like devices—I. Three-dimensional Green's function formulation

A general collective treatment of noise in three-dimensional junction devices of arbitrary geometry is presented, using Green's functions as in recent transport noise theories. The low-injection theory is extended to open-circuited devices. The density spectra are given in a form in which the volume part is linear in the Green's function and the covariance function, while the surface part is quadratic in the Green's function. The density covariance function for the short-circuited junction is Poissonian for low injection, except for a surface singularity. The noise input e.m.f and output current generator, as well as their cross correlation, are found directly for the hybrid transistor model and are expressed in the h′ parameters, without the usual network transformation. The exact results indicate distributed effects; in particular, the current gain in the noise expressions (α noise) is not equal to the small signal current gain α. The one-dimensional standard results are recovered in a lumped model approximation. For high injection, only the case of quasi band-band recombination (the Shockley-Read levels have equal capture probabilities for electrons and holes) is considered in this paper. The covariance function is then as for low injection but of half strength. The terminal noise depends, besides on the admittance or impedance and the current, on the emitter efficiency γ, the mobility ratio b, and the ratio of the junction admittance and the bulk admittance resulting from modulation effects. As a byproduct of this study, all pertinent network parameters are expressed in Green's functions.

Behavioral Responses of Unconfined Uinta Ground Squirrels to Trapping

Capture and recapture data are frequently used by wildlife scientists to estimate characteristics of animal populations. A common assumption is that each animal encountering a trap has the same chance of being captured and recaptured. To test this and related assumptions, this study was made of directly observed responses of unconfined Uinta ground squirrels (Citellus armatus) to various live-trapping experiences. Initially, the trap was the primary attractant. Bait increased this attraction but held some squirrels away from the trap entrance. The effect produced equal probability of capture on first encounter with baited and unbaited traps (n = 51). Squirrels captured on their first encounter (n =18) generally moved about the trap in one direction. Those not captured (n = 23) either did not chance upon the door, showed little interest in the trap, or became fixed at the rear near the bait. Experiments on 58 squirrels indicated capture was punishing and eating bait was rewarding. Simultaneous punishment and reward produced conflict between the tendencies to approach and to avoid the trap. The relative strengths of the tendencies determined whether or not squirrels were recaptured. Prebaiting reinforced entering the trap for bait but decreased the number of squirrels (n = 10) responding to the trap. Squirrels (n = 19) were more hesitant in approaching a trap at the site of capture than at a different location. Their response to the site was consistent with their experience at the site. Biologists often trap animals to obtain information on population parameters. Researchers generally assume that each animal encountering a trap has an equal and independent chance of being captured and recaptured. Some capture data suggest that the above assumption may be invalid owing to behavioral factors (Geis 1955, Tanaka 1956, Crowcroft and Jeffers 1961, and others). However, since researchers seldom observe animals responding to traps, information concerning the relationship between the behavior of animals and a trapping program is lacking. The present study is an attempt to supply such information. The study concerned the behavioral responses of adult Uinta ground squirrels to livetrapping. Results were drawn from direct observation of known individuals in an unconfined population. The objectives were to determine through a series of experiments how squirrels responded to a trap initially, to capture and recapture, to prebaiting, and to the site of capture. 1 Investigation supported in part by U. S. Public Health Service Fellowship MPM-18,460 and Division of University Research, Utah State University.

A Protective Device for Reducing Trap Disturbance

In recent years a great deal of attention has been given to the design of trapping procedures that conform to some of the assumptions of the statistical techniques often applied to small mammal populations (Stickel, 1946, 1948, 1954; Hayne, 1949; Morris, 1955). Basic to a number of the mathematical models used in the analysis of population data is the assumption of equal probability of capture. Tanaka (1951) and Edwards (1952) have demonstrated that this assumption is violated on both the individual and species level. An additional source of error, although obvious, has received little consideration in many population analyses. This is the practical problem of the disturbance of traps which reduces to zero the probability of a capture occurring for any disturbed trap. Admittedly, this probability is of a different nature from those referred to above, since it is independent of the individual or species, but it is of no less importance in studies concerned with the ascertainment of the number of effective traps available on any given trapping night. That disturbance of traps does occur (in addition to the evidence presented in this paper) and with sufficient frequency to prevent further trapping, has been reported by Brown …