Catch estimation in the presence of declining catch rate due to gear saturation

One strategy for estimating total catch is to employ two separate surveys that independently estimate total fishing effort and catch rate with the estimator for total catch formed by their product. Survey designs for estimating catch rate often involve interviewing the fishermen during their fishing episodes. Such roving designs result in incomplete episode data and characteristically have employed a model in which the catch rate is assumed to be constant over time. This article extends the problem to that of estimating total catch in the presence of a declining catch rate due, e.g., to gear saturation. Using a gill net fishery as an example, a mean-of-ratios type of estimator for the catch rate together with its variance estimator are developed. Their performance is examined using simulations, with special attention given to effects of restrictions on the roving survey window. Finally, data from a Fraser River gill net fishery are used to illustrate the use of the proposed estimator and to compare results with those from an estimator based on a constant catch rate.     

Catch Estimation with Restricted Randomization in the Effort Survey

One common method for estimating total catch is to multiply an estimate for CPUE, the catch per unit effort, by an estimate of total effort obtained from an independent second survey. In general, estimating total effort requires that sample times are chosen at random over the full fishing period; however, in practice, this may not always be possible and the usual estimator may be severely biased. Such a restriction in randomization is likely when aircraft are used to make instantaneous counts of fishing activity. This article proposes alternate estimators for use with both access and roving designs in conjunction with effort surveys for which sample times are not random. Ratio type estimators based on activity counts are developed under various scenarios and their performance examined under simulation. In addition, optimizing strategies for use with multiple activity counts are explored. Finally, data from an in-river gill net fishery on the Fraser River is used to illustrate these results.     

Relative Efficiency of Estimators of the Mean of a Normal Distribution when Coefficient of Variation is Known

A biased but simple and consistent estimator of the parameter ? has been obtained for the normal distribution N(?, a?₂), ?>0 where a is a known constant. It is shown that the estimator is more efficient than the sample mean or any suitably chosen constant multiple of the sample standard deviation. It is also proved to be more efficient than the mimumum variance unbiased estimator among a typical class of unbiased estimators derived by RASUL KHAN (1968).     

Estimation of the hazards ratio in two grouped samples

A simple estimator of the hazards ratio of two grouped samples is proposed. If the number of time grouping intervals is fixed, the following asymptotics hold: unbiasedness, and full efficiency when the true hazards ratio is 1 and the probability of failure in each interval is small. Under the latter condition, the estimator is equivalent to "MHP" estimator (Mantel-Haenszel estimator for a Poisson model). Simulations show that this estimator performs better than others when grouping is coarse. An asymptotically unbiased estimator of its variance is proposed.     

A Class of Almost Unbiased Estimators for Finite Populations Mean Using Two Auxiliary Variables

For estimating finite population mean -Y₀ of study character y₀, a class of almost unbiased estimators applying jackknife technique envisaged by Quenouille (1956) is derived. Optimum unbiased estimator (OUE) is also investigated with its variance formula. An empirical study is carried out to demonstrate the performance of the constructed estimator over the usual unbiased estimator, Srivastava (1965), Singh (1967), Singh and Biradar (1992), Tracy , Singh , and Singh (1996) and other almost unbiased estimators.     

Mapping Fishing Effort through AIS Data

Several research initiatives have been undertaken to map fishing effort at high spatial resolution using the Vessel Monitoring System (VMS). An alternative to the VMS is represented by the Automatic Identification System (AIS), which in the EU became compulsory in May 2014 for all fishing vessels of length above 15 meters. The aim of this paper is to assess the uptake of the AIS in the EU fishing fleet and the feasibility of producing a map of fishing effort with high spatial and temporal resolution at European scale. After analysing a large AIS dataset for the period January-August 2014 and covering most of the EU waters, we show that AIS was adopted by around 75% of EU fishing vessels above 15 meters of length. Using the Swedish fleet as a case study, we developed a method to identify fishing activity based on the analysis of individual vessels’ speed profiles and produce a high resolution map of fishing effort based on AIS data. The method was validated using detailed logbook data and proved to be sufficiently accurate and computationally efficient to identify fishing grounds and effort in the case of trawlers, which represent the largest portion of the EU fishing fleet above 15 meters of length. Issues still to be addressed before extending the exercise to the entire EU fleet are the assessment of coverage levels of the AIS data for all EU waters and the identification of fishing activity in the case of vessels other than trawlers.     

Estimation of a Secondary Parameter in a Group Sequential Clinical Trial

In this article, we investigate estimation of a secondary parameter in group sequential tests. We study the model in which the secondary parameter is the mean of the normal distribution in a subgroup of the subjects. The bias of the naive secondary parameter estimator is studied. It is shown that the sampling proportions of the subgroup have a crucial effect on the bias: As the sampling proportion of the subgroup at or just before the stopping time increases, the bias of the naive subgroup parameter estimator increases as well. An unbiased estimator for the subgroup parameter and an unbiased estimator for its variance are derived. Using simulations, we compare the mean squared error of the unbiased estimator to that of the naive estimator, and we show that the differences are negligible. As an example, the methods of estimation are applied to an actual group sequential clinical trial, The Beta-Blocker Heart Attack Trial.     

The state of exploitation of the commercial demersal fishery of Cameroon

The state of exploitation of the demersal fisheries resources of Cameroon has been assessed using the classic Schaefer's (1954) model and the Gulland'ss (1961) moving average. The euilibrium yield found with the Schaefer method is statistically different (95 % probability) and higher than the Gulland approach. Because equilibrium models consistently over-estimate MSY and its related optimum effort, management option should target the 95 % value of the estimated parameters. The resources are being over-fished; as an immediate alternative to the urgent concern, catch and/or effort quotas could be allocated to the various fishing companies, with the total allocated catch and/or effort (for all fishing companies) 5% less than the estimated parameters. Enforcement control of that policy would be simplified as fishing activities are localised in the two main estuaries of the “Cameroon River” and Riodel-Rey;results should be complemented by economic studies of the fishery, as these economic factors would explain or better predict the behaviour of the fishing industry.     

Mean and variance of ratio estimators used in fluorescence ratio imaging

BACKGROUND: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS: The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. RESULTS: We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. CONCLUSIONS: We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators.     

On Moors' Randomized Response Model

This paper considers a modification of famous unrelated question randomized response model due to Moors' (1971). The estimator based on the proposed strategy is shown to be unbiased and always more efficient than the estimator for Moor's model.     

Estimating risk difference in multicenter studies under baseline-risk heterogeneity

In this paper, we consider the case of efficient estimation of the risk difference in a multicenter study allowing for baseline heterogeneity. We consider the optimally weighted estimator for the common risk difference and show that this estimator has considerable bias when the true weights (which are inversely proportional to the variances of the center-specific risk difference estimates) are replaced by their sample estimates. In addition, we propose a new estimator for this situation of the Mantel-Haenszel type that is unbiased and, in addition, has a smaller variance for small sample sizes within the study centers. Simulations illustrate these findings.     

Marine protected areas in 'nonlinear' ecosystems

The very large changes observed within marine communities, owing to excessive harvesting, have been attributed to switches between alternative stable states. Correspondingly large reductions in overall fishing effort are usually difficult to implement. For such 'nonlinear' ecosystems, introducing large marine protected areas, with low to zero harvesting, but without reduction in overall fishing effort, can give a marked increase in total yield of the depleted stocks. These increases, however, are still less than can be achieved by reducing fishing effort.     

A spatially explicit capture–recapture estimator for single‐catch traps

Single‐catch traps are frequently used in live‐trapping studies of small mammals. Thus far, a likelihood for single‐catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture–recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous‐time model for SECR to derive a likelihood for single‐catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single‐catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single‐catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single‐catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single‐catch likelihood with unknown capture times remains intractable for now, researchers using single‐catch traps should aim to incorporate timing devices with their traps.     

Estimating the unbiased estimator theta for population genetic survey data

We consider a method of approximating Weir and Cockerham's theta, an unbiased estimator of genetic population structure, using values readily available from published studies using biased estimators (Wright's F(ST) or Nei's G(ST)). The estimation algorithm is shown to be useful for both model populations and real-world avian populations. However, the correlation between Wright's F(ST) and Weir and Cockerham's theta is strong when compared among 39 empirical avian datasets. Thus, the advantage of approximating an unbiased estimator is unclear considering the small actual effect of theta's bias-removing power on empirical datasets.     

On estimating the heterozygosity and polymorphism information content value

The polymorphism information content (PIC) value is commonly used in genetics as a measure of polymorphism for a marker locus used in linkage analysis. In this communication we have derived the uniformly minimum variance unbiased estimator of PIC along with its exact variance. We have also calculated the exact variance of the maximum likelihood estimator of PIC which is asymptotically an unbiased estimator. In order to find this variance we have derived a recursive formula to calculate the moments of any polynomial in a set of variables that are multinomially distributed.     

Uniformly minimum variance unbiased estimation of gene diversity

Gene diversity is an important measure of genetic variability in inbred populations. The survival of species in changing environments depends on, among other factors, the genetic variability of the population. In this communication, I have derived the uniformly minimum variance unbiased estimator of gene diversity. The proposed estimator of gene diversity does not assume that the inbreeding coefficient is known. I have also provided the approximate variance of this estimator according to Fisher's method. In addition, I have developed a numerical resampling-based method for obtaining variances and confidence intervals based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. Efficiency in estimation of the gene diversity based on these two estimators is discussed. In accordance with the simulation results, I found that the uniformly minimum variance estimator developed in this report is more accurate for estimation of gene diversity than the maximum likelihood estimator.     

Strong direct and inconsistent indirect effects of fishing found using stereo-video: Testing indicators from fisheries closures

Candidate indicators of the direct and indirect effects of fishing can be developed by investigating fisheries closures. We tested a suite of such indicators in areas open to fishing but with suspected differences in effort, using baited remote underwater stereo-video methods. In particular, we predicted that greater fishing would result in decreased biomass of high risk target species and indirectly increase the biomass of small-bodied non-target species. As predicted, the biomass of target species was found to be greater in areas of lower fishing effort and in deeper waters. However, no indirect effects of fishing were detected and any community-level effects were driven by differences in the biomass of target species. In particular, assemblage length class analysis of covariance (ANCOVA), size spectra analysis and the abundance-biomass comparison (ABC) method did not provide any evidence of indirect effects of fishing. The magnitude of the differences in fishing effort between the two areas sampled, may be sufficient to significantly affect target fisheries species, but insufficient to lead to indirect effects on non-target populations. It is also possible that the predicted indirect effects do not occur in this assemblage, due to weak trophic linkages between species. Differences observed using the ABC method were attributed to variation in the abundance of large herbivorous fishes, which are not fished. We also found assemblage length class ANCOVA and size spectra to be insensitive to the direct effects of fishing where large numbers of non-target individuals are sampled along with fished species. We suggest diet studies and comparisons across stronger gradients in fishing pressure to further investigate the indirect effects of fishing in this assemblage.     

Stabilization Coefficient of Random Variable

Coefficient of variation, standard deviation divided by mean, has some essential defects. Its density, expectation and variance are too complex to make the statistical inference for such a coefficient. The definition of stabilization coefficient is just the reciprocal of variation coefficient, mean divided by standard deviation. Such a coefficient has a simple expectation and a simple variance, and is an asymptotically unbiased estimator and a consistent estimator of its true value. Furthermore, coefficient of stabilization has an asymptotic normality. Due to its statistical advantages, coefficient of stabilization is easy to be tested statistically. In some applied fields, usually, there is an increasing standard deviation accompanying an increasing mean. Coefficient of stabilization can be practically used for some comparison studies in such fields. Illustrations about comparing microorganism strains are given in this paper. The robustness of stabilization coefficient is satisfactory.     

Some general points in estimating heterogeneity variance with the DerSimonian-Laird estimator

In this paper we consider estimating heterogeneity variance with the DerSimonian-Laird (DSL) estimator as typically used in meta-analysis. In its general form the DSL estimator requires inverse population-averaged study-specific variances as weights, in which case the estimator is unbiased. It has become common practice, however, to use estimates of the study-specific variances instead of their population-averaged versions. This can lead to considerable bias. Simulations illustrate these findings.     

The Social Aspects of Fishing Effort

While economic literature inspired by the “tragedy of the commons” has emphasised people’s tendency to increase fishing effort beyond desirable levels, sociologists and anthropologists who have studied the social aspects of fishing have often emphasised the capacity of these factors to restrict fishing effort. The article addresses the influence of social norms and communication on fishing effort in an empirical study of the Atlantic blue whiting fishery. The data were generated at a time when this fishery had yet to see efficient quota regulations, and had been subject to a rapid growth in fishing effort, making it the largest fishery in the Atlantic. The article argues that social norms and communication patterns in the fishing fleet create a synergic effect of co-operation and competition on fishing effort. The article questions the view that social norms and communication necessarily represent a solution to the tragedy of the commons.