On the role of body size in a tri-trophic metapopulation model

 A particular tri-trophic (resource, prey, predator) metapopulation model with dispersal of preys and predators is considered in this paper. The analysis is carried out numerically, by finding the bifurcations of the equilibria and of the limit cycles with respect to prey and predator body sizes. Two routes to chaos are identified. One is characterized by an intriguing cascade of flip and tangent bifurcations of limit cycles, while the other corresponds to the crisis of a strange attractor. The results are summarized by partitioning the space of body sizes in eight subregions, each one of which is associated to a different asymptotic behavior of the system. Emphasis is put on the possibility of having different modes of coexistence (stationary, cyclic, and chaotic) and/or extinction of the predator population. Received 1 August 1995; received in revised form 8 January     

An Application of Renewal Theory to Contraceptive Follow-up Studies,Exemplified by an Intrauterine Device Study

Contraceptive practice consists of a series of recurrent events of use and nonuse. Application of the life table technique for analysis of multiple-segment contraceptive usage is not entirely satisfactory. In this paper the renewal process approach is applied to the results of contraceptive follow-up studies involving all segments of use. By means of this model, it is possible to estimate the proportion of current users, the average duration of actual use, and the average number of segments used by the acceptors. The practical importance of these parameters for the evaluation of family planning programs is considered.     

Geographic views of human development

Human development can be divided into three stages: human ancestors (Lower Palaeolithic), early human races (Middle Palaeolithic) and modern humans (Upper Palaeolithic). Regional differentiation has been detected in the Lower Palaeolithic and is strongly developed in the Middle Palaeolithic but continues into the Upper Palaeolithic less marked. Clearly mixture at all levels accounts for this. Early humans absorbed the pre-existing regionalizations even as they further differentiated. Modern humans resulted from Upper Palaeolithic people spreading across the world and again absorbing the previous differentiations.