|Ph.D Student||Shamir Shiri|
|Subject||Setting Biodiversity Conservation Priorities: An Ecological-|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Mordechai Shechter|
|Full Thesis text - in Hebrew|
In recent years economists and ecologists have become increasingly interested in optimal conservation policies to protect natural areas and the biodiversity embodied in them. A famous metaphor that describes this conservation policy is the Noah's Ark problem: Noah had to decide which species he should take aboard the ark to survive, and which were to become extinct. Weitzman used diversity theory (1993) to provide quantitative indicators of which species to preserve. Furthermore, in his seminal work on the Noah's Ark problem (1998) he assumes that the survival probabilities are independent and the costs function is linear. One of Weitzman's conclusions is that the optimal policy is an extreme policy. So in the Noah's Ark model almost all species go on board either in full or not at all, except one species, which it's optimal survival probability might be interior because it is determined by the budget equality.
In the symbiotic Noah's Ark problem a central planner allocates a given budget to maximize the expected biodiversity. One of the species is the keystone species (Noah's family - the human species), and the others are keystone-species-dependant; these may be beneficiaries and/or predators, and they have a symbiotic relationship with the keystone species and vanishing biodiversity whenever Noah's family becomes extinct.
We divide our research into two parts. The first sets out the case of two species: one is a keystone species and the other is keystone-species-dependant. The second part presents the case of K species: one keystone species (i.e. Noah) with K>1 others, which are keystone-species-dependant. The optimal policy is examined under different cost functions. We assume first that the marginal cost of Noah's family tends to infinity when the family's survival probability increases up to its upper bound.
We obtain that under several assumptions on the costs function there is an optimal policy and budget equality.
In addition, when the costs function is convex on P0 (Noah's survival probability) and strictly convex in (P1,?,PK) (the survival probability conditioned on the event that Noah survives) the optimal policy is unique and P0 is also interior. We extend this symbiotic Noah's ark problem to the case with identical dependant species. When we assume that the costs functions are equal, and the biodiversity values of the dependant species are also equal, we obtain that the symmetric optimal policy is unique and equivalent to the two-species symbiotic model.