Redshank and Shellfish

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1 INTRODUCTION In viewing the world around us, population growth is a rich area in scientific interest it is apparent that single species is not usually separate with other population, since there are other population will effect this growth population. Population interaction may occur in variety ways, for example: they may compete with each other for needed resource (competition model), one species may prey upon other for its food source (predator-prey model) or they may cooperate with each other improving their ability to survive (cooperating model). Therefore, the Lotka-Volterra model is used for analysis the population growth. Between the populations interaction that stated before, the one that we would like to analysis is predator-prey model. In the context of predator-prey interaction, the population can be extended by considering harvesting, stocking, diffusion and time delay but we focus on harvesting in predator-prey. Now, the subject of harvesting in predator-prey systems has been interest to ecologist, economists and natural resource managers. In our, predator-prey model it is motivated by a specific conflict between shellfish and redshank species. The more important about harvesting in shellfish and redshank is shellfish harvested while redshank is protected. Although the redshank species are protected and not harvested but it is indirectly affected by harvesting its own food. In this case, we assume redshank depends entirely on shellfish for food other than another food. The amount of food eaten by redshank has an upper limit, even if shellfish are abundant. The redshank is a medium-sized wading bird, species a kind of aquatic bird. It has longish red legs and a long, straight bill. It is grey-brown above and whitish below. In flight, it shows very obvious white rear edges to the wings and a white 'V-shape' ups its back. The greatest
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