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.

An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the eastern tropical Pacific Ocean

English: We describe an age-structured statistical catch-at-length analysis (A-SCALA) based on the MULTIFAN-CL model of Fournier et al. (1998). The analysis is applied independently to both the yellowfin and the bigeye tuna populations of the eastern Pacific Ocean (EPO). We model the populations from 1975 to 1999, based on quarterly time steps. Only a single stock for each species is assumed for each analysis, but multiple fisheries that are spatially separate are modeled to allow for spatial differences in catchability and selectivity. The analysis allows for error in the effort-fishing mortality relationship, temporal trends in catchability, temporal variation in recruitment, relationships between the environment and recruitment and between the environment and catchability, and differences in selectivity and catchability among fisheries. The model is fit to total catch data and proportional catch-at-length data conditioned on effort. The A-SCALA method is a statistical approach, and therefore recognizes that the data collected from the fishery do not perfectly represent the population. Also, there is uncertainty in our knowledge about the dynamics of the system and uncertainty about how the observed data relate to the real population. The use of likelihood functions allow us to model the uncertainty in the data collected from the population, and the inclusion of estimable process error allows us to model the uncertainties in the dynamics of the system. The statistical approach allows for the calculation of confidence intervals and the testing of hypotheses. We use a Bayesian version of the maximum likelihood framework that includes distributional constraints on temporal variation in recruitment, the effort-fishing mortality relationship, and catchability. Curvature penalties for selectivity parameters and penalties on extreme fishing mortality rates are also included in the objective function. The mode of the joint posterior distribution is used as an estimate of the model parameters. Confidence intervals are calculated using the normal approximation method. It should be noted that the estimation method includes constraints and priors and therefore the confidence intervals are different from traditionally calculated confidence intervals. Management reference points are calculated, and forward projections are carried out to provide advice for making management decisions for the yellowfin and bigeye populations. Spanish: Describimos un análisis estadístico de captura a talla estructurado por edad, A-SCALA (del inglés age-structured statistical catch-at-length analysis), basado en el modelo MULTIFAN- CL de Fournier et al. (1998). Se aplica el análisis independientemente a las poblaciones de atunes aleta amarilla y patudo del Océano Pacífico oriental (OPO). Modelamos las poblaciones de 1975 a 1999, en pasos trimestrales. Se supone solamente una sola población para cada especie para cada análisis, pero se modelan pesquerías múltiples espacialmente separadas para tomar en cuenta diferencias espaciales en la capturabilidad y selectividad. El análisis toma en cuenta error en la relación esfuerzo-mortalidad por pesca, tendencias temporales en la capturabilidad, variación temporal en el reclutamiento, relaciones entre el medio ambiente y el reclutamiento y entre el medio ambiente y la capturabilidad, y diferencias en selectividad y capturabilidad entre pesquerías. Se ajusta el modelo a datos de captura total y a datos de captura a talla proporcional condicionados sobre esfuerzo. El método A-SCALA es un enfoque estadístico, y reconoce por lo tanto que los datos obtenidos de la pesca no representan la población perfectamente. Además, hay incertidumbre en nuestros conocimientos de la dinámica del sistema e incertidumbre sobre la relación entre los datos observados y la población real. El uso de funciones de verosimilitud nos permite modelar la incertidumbre en los datos obtenidos de la población, y la inclusión de un error de proceso estimable nos permite modelar las incertidumbres en la dinámica del sistema. El enfoque estadístico permite calcular intervalos de confianza y comprobar hipótesis. Usamos una versión bayesiana del marco de verosimilitud máxima que incluye constreñimientos distribucionales sobre la variación temporal en el reclutamiento, la relación esfuerzo-mortalidad por pesca, y la capturabilidad. Se incluyen también en la función objetivo penalidades por curvatura para los parámetros de selectividad y penalidades por tasas extremas de mortalidad por pesca. Se usa la moda de la distribución posterior conjunta como estimación de los parámetros del modelo. Se calculan los intervalos de confianza usando el método de aproximación normal. Cabe destacar que el método de estimación incluye constreñimientos y distribuciones previas y por lo tanto los intervalos de confianza son diferentes de los intervalos de confianza calculados de forma tradicional. Se calculan puntos de referencia para el ordenamiento, y se realizan proyecciones a futuro para asesorar la toma de decisiones para el ordenamiento de las poblaciones de aleta amarilla y patudo.

Defining plausible migration rates based on historical tagging data: a Bayesian mark-recapture model applied to English sole (Parophrys vetulus)

A generalized Bayesian population dynamics model was developed for analysis of historical mark-recapture studies. The Bayesian approach builds upon existing maximum likelihood methods and is useful when substantial uncertainties exist in the data or little information is available about auxiliary parameters such as tag loss and reporting rates. Movement rates are obtained through Markov-chain Monte-Carlo (MCMC) simulation, which are suitable for use as input in subsequent stock assessment analysis. The mark-recapture model was applied to English sole (Parophrys vetulus) off the west coast of the United States and Canada and migration rates were estimated to be 2% per month to the north and 4% per month to the south. These posterior parameter distributions and the Bayesian framework for comparing hypotheses can guide fishery scientists in structuring the spatial and temporal complexity of future analyses of this kind. This approach could be easily generalized for application to other species and more data-rich fishery analyses.

Perspectives from agriculture: advances in livestock breeding - implications for aquaculture genetics

In this paper we present livestock breeding developments that could be taken into consideration in the genetic improvement of farmed aquaculture species, especially in freshwater fish. Firstly, the current breeding objective in aquatic species has focused almost exclusively on the improvement of body weight at harvest or on growth related traits. This is unlikely to be sufficient to meet the future needs of the aquaculture industry. To meet future demands breeding programs will most likely have to include additional traits, such as fitness related ones (survival, disease resistance), feed efficiency, or flesh quality, rather than only growth performance. In order to select for a multi-trait breeding objective, genetic variation in traits of interest and the genetic relationships among them need to be estimated. In addition, economic values for these traits will be required. Generally, there is a paucity of data on variable and fixed production costs in aquaculture, and this could be a major constraint in the further expansion of the breeding objectives. Secondly, genetic evaluation systems using the restricted maximum likelihood method (REML) and best linear unbiased prediction (BLUP) in a framework of mixed model methodology could be widely adopted to replace the more commonly used method of mass selection based on phenotypic performance. The BLUP method increases the accuracy of selection and also allows the management of inbreeding and estimation of genetic trends. BLUP is an improvement over the classic selection index approach, which was used in the success story of the genetically improved farmed tilapia (GIFT) in the Philippines, with genetic gains from 10 to 20 per cent per generation of selection. In parallel with BLUP, optimal genetic contribution theory can be applied to maximize genetic gain while constraining inbreeding in the long run in selection programs. Thirdly, by using advanced statistical methods, genetic selection can be carried out not only at the nucleus level but also in lower tiers of the pyramid breeding structure. Large scale across population genetic evaluation through genetic connectedness using cryopreserved sperm enables the comparison and ranking of genetic merit of all animals across populations, countries or years, and thus the genetically superior brood stock can be identified and widely used and exchanged to increase the rate of genetic progress in the population as a whole. It is concluded that sound genetic programs need to be established for aquaculture species. In addition to being very effective, fully pedigreed breeding programs would also enable the exploration of possibilities of integrating molecular markers (e.g., genetic tagging using DNA fingerprinting, marker (gene) assisted selection) and reproductive technologies such as in-vitro fertilization using cryopreserved spermatozoa.

Automated, objective texture segmentation of multibeam echosounder data - Seafloor survey and substrate maps from James Island to Ozette Lake, Washington Outer Coast

Without knowledge of basic seafloor characteristics, the ability to address any number of critical marine and/or coastal management issues is diminished. For example, management and conservation of essential fish habitat (EFH), a requirement mandated by federally guided fishery management plans (FMPs), requires among other things a description of habitats for federally managed species. Although the list of attributes important to habitat are numerous, the ability to efficiently and effectively describe many, and especially at the scales required, does not exist with the tools currently available. However, several characteristics of seafloor morphology are readily obtainable at multiple scales and can serve as useful descriptors of habitat. Recent advancements in acoustic technology, such as multibeam echosounding (MBES), can provide remote indication of surficial sediment properties such as texture, hardness, or roughness, and further permit highly detailed renderings of seafloor morphology. With acoustic-based surveys providing a relatively efficient method for data acquisition, there exists a need for efficient and reproducible automated segmentation routines to process the data. Using MBES data collected by the Olympic Coast National Marine Sanctuary (OCNMS), and through a contracted seafloor survey, we expanded on the techniques of Cutter et al. (2003) to describe an objective repeatable process that uses parameterized local Fourier histogram (LFH) texture features to automate segmentation of surficial sediments from acoustic imagery using a maximum likelihood decision rule. Sonar signatures and classification performance were evaluated using video imagery obtained from a towed camera sled. Segmented raster images were converted to polygon features and attributed using a hierarchical deep-water marine benthic classification scheme (Greene et al. 1999) for use in a geographical information system (GIS). (PDF contains 41 pages.)

Predicting the effects of climate change on sea turtle nesting habitat in Florida

Rising global temperatures threaten the survival of many plant and animal species. Having already risen at an unprecedented rate in the past century, temperatures are predicted to rise between 0.3 and 7.5C in North America over the next 100 years (Hawkes et al. 2007). Studies have documented the effects of climate warming on phenology (timing of seasonal activities), with observations of early arrival at breeding grounds, earlier ends to the reproductive season, and delayed autumnal migrations (Pike et al. 2006). In addition, for species not suited to the physiological demands of cold winter temperatures, increasing temperatures could shift tolerable habitats to higher latitudes (Hawkes et al. 2007). More directly, climate warming will impact thermally sensitive species like sea turtles, who exhibit temperature-dependent sexual determination. Temperatures in the middle third of the incubation period determine the sex of sea turtle offspring, with higher temperatures resulting in a greater abundance of female offspring. Consequently, increasing temperatures from climate warming would drastically change the offspring sex ratio (Hawkes et al. 2007). Of the seven extant species of sea turtles, three (leatherback, Kemp’s ridley, and hawksbill) are critically endangered, two (olive ridley and green) are endangered, and one (loggerhead) is threatened. Considering the predicted scenarios of climate warming and the already tenuous status of sea turtle populations, it is essential that efforts are made to understand how increasing temperatures may affect sea turtle populations and how these species might adapt in the face of such changes. In this analysis, I seek to identify the impact of changing climate conditions over the next 50 years on the availability of sea turtle nesting habitat in Florida given predicted changes in temperature and precipitation. I predict that future conditions in Florida will be less suitable for sea turtle nesting during the historic nesting season. This may imply that sea turtles will nest at a different time of year, in more northern latitudes, to a lesser extent, or possibly not at all. It seems likely that changes in temperature and precipitation patterns will alter the distribution of sea turtle nesting locations worldwide, provided that beaches where the conditions are suitable for nesting still exist. Hijmans and Graham (2006) evaluate a range of climate envelope models in terms of their ability to predict species distributions under climate change scenarios. Their results suggested that the choice of species distribution model is dependent on the specifics of each individual study. Fuller et al. (2008) used a maximum entropy approach to model the potential distribution of 11 species in the Arctic Coastal Plain of Alaska under a series of projected climate scenarios. Recently, Pike (in press) developed Maxent models to investigate the impacts of climate change on green sea turtle nest distribution and timing. In each of these studies, a set of environmental predictor variables (including climate variables), for which ‘current’ conditions are available and ‘future’ conditions have been projected, is used in conjunction with species occurrence data to map potential species distribution under the projected conditions. In this study, I will take a similar approach in mapping the potential sea turtle nesting habitat in Florida by developing a Maxent model based on environmental and climate data and projecting the model for future climate data. (PDF contains 5 pages)

Spatial and temporal variability in the relative contribution of king mackerel (Scomberomorus cavalla) stocks to winter mixed fisheries off South Florida

King mackerel (Scomberomorus cavalla) are ecologically and economically important scombrids that inhabit U.S. waters of the Gulf of Mexico (GOM) and Atlantic Ocean (Atlantic). Separate migratory groups, or stocks, migrate from eastern GOM and southeastern U.S. Atlantic to south Florida waters where the stocks mix during winter. Currently, all winter landings from a management-defined south Florida mixing zone are attributed to the GOM stock. In this study, the stock composition of winter landings across three south Florida sampling zones was estimated by using stock-specific otolith morphological variables and Fourier harmonics. The mean accuracies of the jackknifed classifications from stepwise linear discriminant function analysis of otolith shape variables ranged from 66−76% for sex-specific models. Estimates of the contribution of the Atlantic stock to winter landings, derived from maximum likelihood stock mixing models, indicated the contribution was highest off southeastern Florida (as high as 82.8% for females in winter 2001−02) and lowest off southwestern Florida (as low as 14.5% for females in winter 2002−03). Overall, results provided evidence that the Atlantic stock contributes a certain, and perhaps a significant (i.e., ≥50%), percentage of landings taken in the management-defined winter mixing zone off south Florida, and the practice of assigning all winter mixing zone landings to the GOM stock should

Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut

Population structure and variance effective size of red snapper (Lutjanus campechanus) in the northern Gulf of Mexico*

We assayed allelic variation at 19 nuclear-encoded microsatellites among 1622 Gulf red snapper (Lutjanus campechanus) sampled from the 1995 and 1997 cohorts at each of three offshore localities in the northern Gulf of Mexico (Gulf). Localities represented western, central, and eastern subregions within the northern Gulf. Number of alleles per microsatellite per sample ranged from four to 23, and gene diversity ranged from 0.170 to 0.917. Tests of conformity to Hardy-Weinberg equilibrium expectations and of genotypic equilibrium between pairs of micro-satellites were generally nonsignificant following Bonferroni correction. Significant genic or genotypic heterogeneity (or both) among samples was detected at four microsatellites and over all microsatellites. Levels of divergence among samples were low (FST ≤0.001). Pairwise exact tests revealed that six of seven “significant” comparisons involved temporal rather than spatial heterogeneity. Contemporaneous or variance effective size (NeV) was estimated from the temporal variance in allele frequencies by using a maximum-likelihood method. Estimates of NeV ranged between 1098 and >75,000 and differed significantly among localities; the NeV estimate for the sample from the northcentral Gulf was >60 times as large as the estimates for the other two localities. The differences in variance effective size could ref lect differences in number of individuals successfully reproducing, differences in patterns and intensity of immigration, or both, and are consistent with the hypothesis, supported by life-history data, that different “demographic stocks” of red snapper are found in the northern Gulf. Estimates of NeV for red snapper in the northern Gulf were at least three orders of magnitude lower than current estimates of census size (N). The ratio of effective to census size (Ne/N) is far below that expected in an ideal population and may reflect high variance in individual reproductive success, high temporal and spatial variance in productivity among subregions or a combination of the two.

Changes in consumer tastes in the demand for fish and meat in Malaysia

In this article the demand for fish and its substitute was estimated using a very flexible demand function, the Almost Ideal Demand System (AIDS) developed by Deaton and Muelllbaeur (1980), incorporating the habit formation variable to measure the impact of the changes in tastes in comsumer demand for fish and meat products from 1960 to 1990 in Malaysia. Information on price and income elasticities for these meat groups was also obtained. To incorporate consumption habit variables, the dynamic translating procedure proposed by Pollak (1970) and Pollak and Wales (1981) has been adopted. The overall results of the maximum likelihood estimates of the dynamic AIDS model are quite good where 19 of 30 coefficients are significantly different from zero and the minimum budget shares, the constant, are between zero and one for each meat type. Consumers tend to purchase and consume fish, chicken, and pork almost daily. Beef and mutton are only consumed occassionally since they are relatively more expensive. This finding is consistent with the trend observed in the per capita consumption and budget share where fish, chicken, and pork tended to dominate over beef and mutton from 1960 to 1990.

Technical efficiency in artisanal fisheries (AF) in Badagry local government area of Lagos State, Nigeria

This study examined the technical efficiency in artisanal fisheries in Lagos State of Nigeria. The study employed a two stage random sampling procedure for the selection of 120 respondents. The analytical techniques involved descriptive statistics and estimation of technical efficiency following maximum likelihood estimation (MLE) procedure available in FRONTIER 4.1. The MLE result of the stochastic frontier production function showed that hired labour, cost of repair and capital items are critical factors that influences productivity of artisanal fishermen with the coefficient of hired labour being highly elastic. This implies that employing more labour will significantly increase the catch in the study area. The predicted farm efficiency with an average value of 0.92 showed that there is a marginal potential of about 8 percent to increase the catch, hence the income of the fishermen. The study further examined the factors that influence productivity of fishermen in the study area. Year of education, mode of operation and frequency of fishing have important implication on the technical efficiency of fishermen in the study area.

Estimating long-term growth-rate changes of southern bluefin tuna (Thunnus maccoyii) from two periods of tag-return data

Southern bluefin tuna (SBT) (Thunnus maccoyii) growth rates are estimated from tag-return data associated with two time periods, the 1960s and 1980s. The traditional von Bertalanffy growth model (VBG) and a two-phase VBG model were fitted to the data by maximum likelihood. The traditional VBG model did not provide an adequate representation of growth in SBT, and the two-phase VBG yielded a significantly better fit. The results indicated that significant change occurs in the pattern of growth in relation to a VBG curve during the juvenile stages of the SBT life cycle, which may be related to the transition from a tightly schooling fish that spends substantial time in near and surface shore waters to one that is found primarily in more offshore and deeper waters. The results suggest that more complex growth models should be considered for other tunas and for other species that show a marked change in habitat use with age. The likelihood surface for the two-phase VBG model was found to be bimodal and some implications of this are investigated. Significant and substantial differences were found in the growth for fish spawned in the 1960s and in the 1980s, such that after age four there is a difference of about one year in the expected age of a fish of similar length which persists over the size range for which meaningful recapture data are available. This difference may be a density-dependent response as a consequence of the marked reduction in the SBT population. Given the key role that estimates of growth have in most stock assessments, the results indicate that there is a need both for the regular monitoring of growth rates and for provisions for changes in growth over time (possibly related to changes in abundance) in the stock assessment models used for SBT and other species.