Yoshiharu Matsumiya

Estimation of population parameters by optimizing catch effort allocation

1) In this study, we have developed a new method to estimate population parameters and applied it to a concrete example on the situation that there are two fisheries resources which are depleted only by catch, and that these two resources are not caught equally because of the difference of prices. 2) Switching function, which is originally used to describe the effort allocation that one predator eats two preys, has been introduced. We have constructed a model of fishery in which each fisherman pursues economical optimum. 3) The population size of two species at the beginning of the fishing season, catchability coefficient and parameters of switching function are estimated by the criterion of minimum error sum of squares between CPUE (catch per unit effort) of data and that by model. 4) We have applied it to the diver fishery of abalone in Ojika Island, Nagasaki Prefecture. The model describes well the situation during the season that CPUE of the less expensive species increases gradually as the population of the other species is depleted. In this study, we have developed a new method to estimate population parameters and applied it to a concrete example on the situation that there are two fisheries resources which are depleted only by catch, and that these two resources are not caught equally because of the difference of prices. Switching function, which is originally used to describe the effort allocation that one predator eats two preys, has been introduced. We have constructed a model of fishery in which each fisherman pursues economical optimum. The population size of two species at the beginning of the fishing season, catchability coefficient and parameters of switching function are estimated by the criterion of minimum error sum of squares between CPUE (catch per unit effort) of data and that by model. We have applied it to the diver fishery of abalone in Ojika Island, Nagasaki Prefecture. The model describes well the situation during the season that CPUE of the less expensive species increases gradually as the population of the other species is depleted.

Reproductive value, harvest value, and impact multiplier as indicators for maximum sustainable fisheries

We studied the optimal age- and season-specific sustainable harvesting policy for a fish population. We assumed that body weight, reproduction rate, and natural mortality of a fish vary with age. By assuming completely age- and season-specific harvesting, we can obtain a new, simple criterion for fishing policy. Fishers should catch a fish of a particular age if, and only if, the current value at that age is larger than the harvest value plus the impact multiplier times the reproductive value. Here the harvest value is the expected yield per individual in the future, the impact multiplier is a shadow price for a laid egg and is constant irrespective of the age of the mother fish, and the reproductive value is the expected number of eggs spawned by a fish after that age.

Optimal age-dependent sustainable harvesting of natural resource populations : Sustainability value

We studied the optimal age-dependent harvesting of a natural resource population that achieves a maximum income under the constraint of sustainability, i.e. the reproductive adults numbers must exceed a given minimum. The resource species is assumed to be semelparous (a single reproduction over a life). The economic value and natural mortality coefficient can vary with age. The optimal age-dependent harvesting under the sustainability constraint is obtained using Pontryagin’s maximum principle. The constraint of resource sustainability can be treated as an additional term measured in the same units as economic income. Specifically, three terms: (1) current harvesting value, (2) future harvesting value, and (3) sustainability value, are calculated for each age, and the resources should be harvested at the maximum rate when their current harvesting value is greater than the sum of future harvesting value and sustainability value, and should not be harvested otherwise. Numerical analyses of several cases demonstrated that the optimal harvesting schedule depends critically on the natural mortality coefficient and the functional form of the economic value of the resource.

A study on the community analysis using three-factorial data (time x site x species)

1) This study is to demonstrate that the analysis of biological communities using scaling unstandardized squared Euclidean distance is extremely effective to deal with data which are quite generally collected by 3 factors (time x site x species). 2) The main part of this study has been explained in detail byWilliams andStephenson (1973). We have conducted some discussion introducing mathematic complementary explanation as well as expansive interpretation. 3) The dissimilarity measure based on squared Euclidean distance is used to classify clusters from a dendrogram obtained by cluster analysis. The outline of the community structure can be known by comparing the values of mean variance per comparison and interaction. 4) The table of mutual comparison among clusters introduces dynamic pattern expression for community. Contributions by species to time and site are capable of expressing a concrete role of the species. 5) We apply the technique above to the demersal fish community in Shijiki Bay, Hirado Island, Nagasaki Pref. Number of individuals caught with Gochi trawls at 11 fixed stations in 1975–1984 are used as material for analysis. 84 species is accounted. This study is to demonstrate that the analysis of biological communities using scaling unstandardized squared Euclidean distance is extremely effective to deal with data which are quite generally collected by 3 factors (time x site x species). The main part of this study has been explained in detail byWilliams andStephenson (1973). We have conducted some discussion introducing mathematic complementary explanation as well as expansive interpretation. The dissimilarity measure based on squared Euclidean distance is used to classify clusters from a dendrogram obtained by cluster analysis. The outline of the community structure can be known by comparing the values of mean variance per comparison and interaction. The table of mutual comparison among clusters introduces dynamic pattern expression for community. Contributions by species to time and site are capable of expressing a concrete role of the species. We apply the technique above to the demersal fish community in Shijiki Bay, Hirado Island, Nagasaki Pref. Number of individuals caught with Gochi trawls at 11 fixed stations in 1975–1984 are used as material for analysis. 84 species is accounted.