Precision estimates and suggested sample sizes for length-frequency data

For most fisheries applications, the shape of a length-frequency distribution is much more important than its mean length or variance. This makes it difficult to evaluate at which point a sample size is adequate. By estimating the coefficient of variation of the counts in each length class and taking a weighted mean of these, a measure of precision was obtained that takes the precision in all length classes into account. The precision estimates were closely associated with the ratio of the sample size to the number of size classes in each sample. As a rule-of-thumb, a minimum sample size of 10 times the number of length classes in the sample is suggested because the precision deteriorates rapidly for smaller sample sizes. In absence of such a rule-of-thumb, samplers have previously under-estimated the required sample size for samples with large fish, while over-sampling small fish of the same species.

Wadge Bank trawl fishery studies. Pt. 4. An analysis of the length frequency measurements of the sea bream (Lethrinus nebulosus) made in 1949 and 1953 to 1958

Length frequency distributions of the sea bream collected during the period 1953 to 1958 have been analysed. The increase in average sizes of the sea bream with depth suggests a movement to deeper waters with increase in size. By numbers, the sea bream is more abundant between 21 and 30 fathoms than in deeper areas. The recruitment was continuous and regular. There is no sign of entry or progression of a dominant brood throughout the period under study. Length frequency distribution shows three distinct modes. The first mode occurs regularly but does not progress beyond 40cm, recruitment being balanced by natural and fishing mortality. The other two which are not regular are probably the result of fishing outside regular areas. Short sections of “growth” lines which fit into one another when extrapolated, are evident. The larger lines obtained by extrapolation are parallel to one another. These tentative "growth lines" indicate that this species which enters the fishing grounds, when 15 cm or larger in length are exploited by the trawl fishery for a period of three to four years. This species appears to be six months old when it enters the fishing grounds and increases in length by about 37.5 cm in the next 30 months. Later growth slows down. The average size of the specimens sampled continued to get smaller from 1953 till 1957. It is shown that this reduction in size is due to increased fishing effort.

Size frequency distribution and carapace length-total length relationship of Acetes chinensis in the Kutubdia channel of Bangladesh coast

The seasonal mean size distribution of A. chinensis were estimated as 29.229mm ±4.77, 25.125mm ±2.55, 25.165mm ±2.29 and 32.44mm ±3.63 for annual, monsoon, postmonsoon and pre-monsoon period, respectively. Seasonal mean carapace length distribution were estimated as 9.37mm ±1.457, 8.063mm ±0.63,8.258mm ±0.59 and 10.37mm ±l.ll3 for annual, monsoon, post-monsoon and the pre-monsoon season. The carapace length and total length relationships was found to be TL= - 1.39±3.23 CL. Linear relation was found in arithmetic and as well as logarithmic scale.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Frequency distribution of graded turbidite cycles in DSDP sediments from the Coral Sea Basin and the Sea of Japan

At sites 390 and 392 (Deep Sea Drilling Project, Leg 44) on the Blake nose, thoroughly lithified Lower Cretaceous limestone more than 250 m thick is abruptly overlain by a condensed sequence of Barremian to Eocene pelagic carbonate ooze. The Lower Cretaceous sediments consist of three units: limestone with moldic porosity (base), oolitic limestone, and fenestral limestone. Subaerial diagenesis of the limestone section is recorded by (1) caverns with vertical dimensions of up to 10 m, (2) stalactitic intergranular cement, and (3) meniscus sediment (or cement). Compatible with these subaerial features are mud cracks, fenestral fabrics, intraclasts, and cryptalgal structures. Inasmuch as these shallow-water and tidal-flat deposits are now beneath 2,607 m of sea water (plus 99 m of younger sediments), they serve to dramatize the apparent degree of Barremian and later subsidence of this part of the Atlantic outer continental shelf. Porosity and permeability are high in vuggy samples, which are common in the skelmoldic limestone. Cementation has destroyed most of the extensive primary porosity of the two younger units.

Theory of radar imaging using time-frequency distribution

The concept of radar was developed for the estimation of the distance (range) and velocity of a target from a receiver. The distance measurement is obtained by measuring the time taken for the transmitted signal to propagate to the target and return to the receiver. The target's velocity is determined by measuring the Doppler induced frequency shift of the returned signal caused by the rate of change of the time- delay from the target. As researchers further developed conventional radar systems it become apparent that additional information was contained in the backscattered signal and that this information could in fact be used to describe the shape of the target itself. It is due to the fact that a target can be considered to be a collection of individual point scatterers, each of which has its own velocity and time- delay. DelayDoppler parameter estimation of each of these point scatterers thus corresponds to a mapping of the target's range and cross range, thus producing an image of the target. Much research has been done in this area since the early radar imaging work of the 1960s. At present there are two main categories into which radar imaging falls. The first of these is related to the case where the backscattered signal is considered to be deterministic. The second is related to the case where the backscattered signal is of a stochastic nature. In both cases the information which describes the target's scattering function is extracted by the use of the ambiguity function, a function which correlates the backscattered signal in time and frequency with the transmitted signal. In practical situations, it is often necessary to have the transmitter and the receiver of the radar system sited at different locations. The problem in these situations is 'that a reference signal must then be present in order to calculate the ambiguity function. This causes an additional problem in that detailed phase information about the transmitted signal is then required at the receiver. It is this latter problem which has led to the investigation of radar imaging using time- frequency distributions. As will be shown in this thesis, the phase information about the transmitted signal can be extracted from the backscattered signal using time- frequency distributions. The principle aim of this thesis was in the development, and subsequent discussion into the theory of radar imaging, using time- frequency distributions. Consideration is first given to the case where the target is diffuse, ie. where the backscattered signal has temporal stationarity and a spatially white power spectral density. The complementary situation is also investigated, ie. where the target is no longer diffuse, but some degree of correlation exists between the time- frequency points. Computer simulations are presented to demonstrate the concepts and theories developed in the thesis. For the proposed radar system to be practically realisable, both the time- frequency distributions and the associated algorithms developed must be able to be implemented in a timely manner. For this reason an optical architecture is proposed. This architecture is specifically designed to obtain the required time and frequency resolution when using laser radar imaging. The complex light amplitude distributions produced by this architecture have been computer simulated using an optical compiler.

A simple method for estimating growth parameters from multiple length-frequency data in presence of continuous recruitment

The extended recruitment season for short-lived species such as prawns biases the estimation of growth parameters from length-frequency data when conventional methods are used. We propose a simple method for overcoming this bias given a time series of length-frequency data. The difficulties arising from extended recruitment are eliminated by predicting the growth of the succeeding samples and the length increments of the recruits in previous samples. This method requires that some maximum size at recruitment can be specified. The advantages of this multiple length-frequency method are: it is simple to use; it requires only three parameters; no specific distributions need to be assumed; and the actual seasonal recruitment pattern does not have to be specified. We illustrate the new method with length-frequency data on the tiger prawn Penaeus esculentus from the north-western Gulf of Carpentaria, Australia.

Effect of individual variability on estimation of population parameters from length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock when there is individual variability in the von Bertalanffy growth parameter L-infinity and investigate the possible bias in the estimates when the individual variability is ignored. Three methods are examined: (i) the regression method based on the Beverton and Holt's (1956, Rapp. P.V. Reun. Cons. Int. Explor. Mer, 140: 67-83) equation; (ii) the moment method of Powell (1979, Rapp. PV. Reun. Int. Explor. Mer, 175: 167-169); and (iii) a generalization of Powell's method that estimates the individual variability to be incorporated into the estimation. It is found that the biases in the estimates from the existing methods are, in general, substantial, even when individual variability in growth is small and recruitment is uniform, and the generalized method performs better in terms of bias but is subject to a larger variation. There is a need to develop robust and flexible methods to deal with individual variability in the analysis of length-frequency data.

Length-weight relationships of the anchoveta, Cetengraulis mysticetus, in the Gulf of Panama

ENGLISH: Knowledge of the length-frequency distribution and the length-weight relationships of the anchoveta is essential for converting the catch statistics of that species from pounds to numbers of fish. Such conversions are necessary for various types of investigations, especially those involving estimation of the population size and mortality rates. The analysis of the results of a recent tagging program conducted with anchovetas in the Gulf of Panama (Bayliff, 1965) requires that such conversions be made. Length-frequency data for the anchoveta have already been collected and published (Howard and Landa, 1958; Bayliff, 1964). The present report deals with length-weight data from fish collected in various .areas of the Gulf of Panama in all months of the year and in several different years. Opportunity is thus afforded to compare the length-weight relationships of fish of different year classes in different areas, months, and years. SPANISH: El conocimiento de la distribución de la frecuencia de longitud y de las relaciones entre la longitud y el peso de la anchoveta es esencial en las estadísticas de captura de esta especie para la conversión de peso en libras a número de peces. Estas conversiones son necesarias para varios tipos de investigación, especialmente las que se refieren a la estimación del tamaño de la población y de las tasas de mortalidad. Estas conversiones se requieren para analizar los resultados de un programa reciente de marcación de anchovetas en el Golfo de Panamá (Bayliff, 1965). Los datos de la frecuencia de longitud de la anchoveta ya han sido recolectados y publicados (Howard y Landa, 1958; Bayliff, 1964). El presente informe trata de los datos de longitud y peso de los peces recolectados en varias áreas del Golfo de Panamá durante todos los meses del año y durante varios años. Esto ofrece la oportunidad de comparar las relaciones entre la longitud y el peso de peces pertenecientes a varias clases anuales en áreas, meses y años diferentes.

Length-frequency estimation for yellowfin tuna (Thunnus albacares) caught by commercial fishing gear in the Eastern Pacific Ocean

ENGLISH: Methods of collecting samples for the purpose of estimating the numbers and weights of fish caught, by length interval, are described. Several models for two-stage sampling are described, and the equations for the estimators and their variances are given. The results from a brief simulation study are used to show the differences between estimates made with the different models. Estimators for the average weights of fish in the catch and their variances are also described. These average weights are used to provide improved estimates of the total annual catches of yellowfin taken from the eastern Pacific Ocean, east of 150°W, between 1955 and 1990. SPANISH: Se describen los métodos de recoger de muestreo para estimar el número o peso de peces capturados, por intervalo de talla. Se describen varios modelos para el muestreo de dos etapas, y se presentan las ecuaciones para los estimadores y sus varianzas. Se usan los resultados de un breve estudio de simulación para indicar las diferencias entre estimaciones realizadas con los distintosmodelos. También se describe un estimador para el peso promedio de peces en la captura y su varianza. Se usan estos estimadores para calcular estimaciones mejoradas de las capturas anuales totales de aleta amarilla tomadas del Océano Pacífico oriental, al este de 150°W, entre 1955 y 1990. (PDF contains 41 pages.)