Short-Term Dynamical Interactions Among Extrasolar Planets

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. We apply our fitting methods to the GJ876 radial velocity data (Marcy et al. 2001), and argue that the mass factors for the two planets are likely in the 1.25-2.0 rangeComment: 13 pages, including 4 figures and 3 tables Accepted by Astrophyiscal Journal Letter

Stochastic Dominance, Entropy and Biodiversity Management

In this paper we develop a model of population dynamics using the Shannon entropy index, a measure of diversity that allows for global and specific population shocks. We model the effects of increasing the number of parcels on biodiversity, varying the number of spatially diverse parcels to capture risk diversification. We discuss the concepts of stochastic dominance as a means of project selection, in order to model biodiversity returns and risks. Using a Monte Carlo simulation we find that stochastic dominance may be a useful theoretical construct for project selections but it is unable to rank every case.

Economic Growth and Threatened and Endangered Species Listings: A VAR Analysis

We conduct several analyses to examine the link between threatened and endangered species listings and macroeconomic activity. Preliminary tests using ordinary least squares are run on both time series data on the national level and cross sectional data at the state level. The analysis is then extended using vector autoregressive (VAR) techniques. VAR results, impulse response functions and variance decompositions are reported to shed more light on the causal relationships between threatened and endangered species, GDP and population. Our results indicate that there is little or no empirical evidence that GDP growth rates lead to changes in the number of threatened and endangered species listings.

Stochastic Dominance, Entropy and Biodiversity Management

In this paper we develop a model of population dynamics using the Shannon entropy index, a measure of diversity that allows for global and specific population shocks. We model the effects of increasing the number of parcels on biodiversity, varying the number of spatially diverse parcels to capture risk diversification. We discuss the concepts of stochastic dominance as a means of project selection, in order to model biodiversity returns and risks. Using a Monte Carlo simulation we find that stochastic dominance may be a useful theoretical construct for project selections but it is unable to rank every case. Key Words: Stochastic Dominance, Entropy, Biodiversity Management

Economic Growth and Threatened and Endangered Species Listings: A VAR Analysis

We conduct several analyses to examine the link between threatened and endangered species listings and macroeconomic activity. Preliminary tests using ordinary least squares are run on both time series data on the national level and cross sectional data at the state level. The analysis is then extended using vector autoregressive (VAR) techniques. VAR results, impulse response functions and variance decompositions are reported to shed more light on the causal relationships between threatened and endangered species, GDP and population. Our results indicate that there is little or no empirical evidence that GDP growth rates lead to changes in the number of threatened and endangered species listings. Key Words: Economic growth, endangered and threatened species, vector autoregression

A Dynamical Analysis of the 47 UMa Planetary System

The mass and period ratios of the two planets orbiting 47 UMa suggest a possible kinship to the Jupiter-Saturn pair in our solar system. We explore the current dynamical state of the 47 UMa system with numerical integrations, and compare the results with analytic secular theory. We find that the planets in the system are likely participating in a secular resonance in which the difference in the longitudes of pericenter librates around zero. Alternately, it is possible that the system is participating in the 7:3 mean motion resonance. We show that stability considerations restrict the mutual inclination between the two planets to 40 degrees or less, and that this result is relatively insensitive to the total mass of the two planets. We present hydrodynamical simulations which measure the torques exerted on the planets by a hypothesized external protoplanetary disk. We show that planetary migration in response to torques from the disk may have led to capture of the system into a 7:3 mean-motion resonance, although it is unclear how the eccentricities of the planets would have been damped after capture occured. We show that Earth-mass planets can survive for long periods in some regions of the habitable zone of the nominal co-planar system. A set of planetary accretion calculations, however, shows that it is unlikely that large terrestrial planets can form in the 47 UMa habitable zone.Comment: Accepted by the Astrophysical Journal (Original submission November 2001