Power laws, Discontinuities and Regional City Size Distributions

Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classics in the city size distributions are snapshots of stable states within urban systems in flux.

Model complexity affects transient population dynamics following a dispersal event: A case study with pea aphids

Stage-structured population models predict transient population dynamics if the population deviates from the stable stage distribution. Ecologists’ interest in transient dynamics is growing because populations regularly deviate from the stable stage distribution, which can lead to transient dynamics that differ significantly from the stable stage dynamics. Because the structure of a population matrix (i.e., the number of life-history stages) can influence the predicted scale of the deviation, we explored the effect of matrix size on predicted transient dynamics and the resulting amplification of population size. First, we experimentally measured the transition rates between the different life-history stages and the adult fecundity and survival of the aphid, Acythosiphon pisum. Second, we used these data to parameterize models with different numbers of stages. Third, we compared model predictions with empirically measured transient population growth following the introduction of a single adult aphid. We find that the models with the largest number of life-history stages predicted the largest transient population growth rates, but in all models there was a considerable discrepancy between predicted and empirically measured transient peaks and a dramatic underestimation of final population sizes. For instance, the mean population size after 20 days was 2394 aphids compared to the highest predicted population size of 531 aphids; the predicted asymptotic growth rate (λmax) was consistent with the experiments. Possible explanations for this discrepancy are discussed. Includes 4 supplemental files.

Phytoplankton Dynamics in Three Rocky Mountain Lakes, Colorado, U.S.A.

In 1984 and 1985 seasonal changes in phytoplankton were studied in a system of three lakes in Loch Vale, Rocky Mountain National Park, Colorado. Three periods were evident: (1) A spring bloom, during snowmelt, of the planktonic diatom Asterionella Formosa, (2) a mid- summer period of minimal algal abundance, and (3) a fall bloom of the blue-green alga Oscillatoria limnetica. Seasonal phytoplankton dynamics in these lakes are controlled partially by the rapid flushing rate during snowmelt and the transport of phytoplankton from the highest lake to the lower lakes by the stream, Icy Brook. During snowmelt, the A. formosa population in the most downstream lake has a net rate of increase of 0.34 d-1, which is calculated from the flushing rate and from the A. formosa abundance in the inflow from the upstream lake and in the downstream lake. Measurement of photosynthetic rates at different depths during the three periods confirmed the rapid growth of A. formosa during the spring. The decline in A. formosa after snowmelt may be related to grazing by developing zooplankton populations. The possible importance of the seasonal variations in nitrate concentrations were evaluated in situ enrichment experiments. For A. formosa and O. limnetica populations, growth stimulation resulted from 8- or 16-micromolar amendments of calcium nitrate and sulfuric acid, but the reason for this stimulation could not be determined from these experiments.

Deterministic Solutions for a Step-growth Polymerization

Chain topology, including branch node, chain link and cross-link dynamics that contribute to the number of elastically active strands and junctions, are calculated using purely deterministic derivations. Solutions are not coupled to population density distributions. An eigenzeit transformation assists in the conversion of expressions derived by chemical reaction principles from time to conversion space, yielding transport phenomena type expressions where the rate of change in the molar concentrations of branch nodes with respect to conversion is expressed as functions of the fraction of reactive sites on precursors and reactants. Analogies are hypothesized to exist in cross-linking space that effectively distribute branch nodes with i reacted moieties between cross-links having j bonds extending to the gel. To obtain solutions, reacted sites on nodes or links with finite chain extensions are examined in terms of stoichiometry associated with covalent bonding. Solutions replicate published results based on Miller and Macosko’s recursive procedure and results obtained from truncated weighted sums of population density distributions as suggested by Flory.