Hsin-I Wu

A model comparison for daylength as a function of latitude and day of year

A model that calculates the length of the day for a flat surface for a given latitude and day of the year is described. Calculated daylengths are within 1 minute of values published in Smithsonian Meteorological Tables and the Astronomical Almanac for latitudes between 40 ° North and South with a maximum error of 7 minutes occurring at 60 ° latitude. The model allows the use of different definitions of sunrise/sunset and the incorporation of twilight. Comparisons with other daylength models indicate that this model is more accurate and that variation in accumulated hours of daylight of up to one week over the course of the growing season can be accounted for by how sunrise/sunset are defined.

Self-thinning rule : a causal interpretation from ecological field theory

The self-thinning rule relates plant mass to plant density in crowded, even-aged stands by a power-law equation with an exponent 3:2. The rule is widely accepted as an empirical generalization and quantitative rule that applies across the plant kingdom. It has been called the only law in plant ecology. But the evidence supporting it has recently come under critical scrutiny. The theoretical and empirical bases for the density‐mass boundary have been questioned. Here we use ecological field theory and statistical mechanics to show how the stochastic nature of ecological interactions among individuals, due to spatial field effects such as the availability of neighborhood resources at the microscopic level, leads to self-thinning at the macroscopic level. The self-thinning rule emerges as a natural result of our theoretical approach. Puzzling experimental data that contradict the rule are also explained.

A physiologically based continuous-time Markov approach to plant growth modelling in semi-arid woodlands

Abstract A model for simulating the combined effects of water, light and nutrients on tree, shrub and grass growth in a semi-arid woodland is described. Continuous-time Markov (CTM) assumptions are used to derive a plant growth model based on general resource availability. Physiological interpretation of states and transitions facilitates the use of the abstract continuous-time Markov approaches. The model treats resources as an interacting group, and provides an approach by which a single equation can be used across all growth forms. Simulation results for a range of leaf areas and diameters for trees, shrubs and grasses agree with field observations. The poor relationship between leaf area and diameter of plants observed in intact semi-arid woodlands is interpreted as a consequence of competitive interactions for resources.

Whole-plant modelling: A continuous-time Markov (CTM) approach

Abstract Continuous-time Markov (CTM) mathematics can provide a standardized method to describe plant metabolism responses to multiple resource inputs. The utility of CTM techniques is demonstrated by a simple plant growth model with three resources (light, water and nutrients). Simple model response curves are presented that describe instantaneous growth rate in relation to light intensity, water, nutrients and biomass. The effects of varying resource use and tolerance on optimum growth are investigated using a Fermi-Dirac distribution function. The CTM approach to plant metabolism and growth is compared and contrasted to compartmental analysis and to King-Altman enzyme-kinetic techniques.

A semi-arid grazing ecosystem simulation model with probabilistic and fuzzy parameters

Many of todays grazing ecosystem management problems require a predictive understanding of the interactions between ecological processes acting across different spatiotemporal scales with complex soil, vegetation, climate, topographic and geologic characteristics. Due to complexity of ecosystems and the incomplete nature of empirical data for specific relationships involved in ecosystem dynamics, resource managers usually select management strategies without complete information or knowledge. Such vagueness in real world situations is also an obstacle to understanding and modeling ecosystem dynamics by means of conventional mathematical and computer simulation techniques. Modeling, simulating, and analyzing actual ecosystems can be significantly improved if modeling is extended to deal with imprecise and vague variables, relationships, and events. In this paper, a simulation model combining fuzzy imprecision with probabilistic uncertainty is formulated to study climate-plant-herbivore interactions in grassland ecosystems. This approach provides a unifying simulation framework to integrate numerical data, linguistic statements, and expert experience. The model includes treatment of imprecise and vague input variables as fuzzy variables, use of fuzzy arithmetic in equations when fuzzy and probability numbers are involved, and replacement of some of the relationships in the dynamic systems either with fuzzy conditional statements, or with fuzzy algorithms. The temporal patterns of herbivore population and primary production for a laissez-faire, extensive system in both Australia and China are modeled. The consistency of results obtained from the two simulations suggests the underlying mechanisms for semi-arid grassland ecosystems are those included in the model. Models combining fuzzy sets to quantify subjective parameters and traditional mechanistic techniques can be used to form a basis of long-term managerial policies for a sustainable grassland ecosystem.

Transition rule complexity in grid-based automata models

Grid-based automata models have been widely applied in simulating ecological process and spatial patterns at all spatial scales. In this paper, we present methods for calculating the effects of number of states, size of the neighborhood, means of tallying neighborhood states, and choice of deterministic or stochastic rules on the complexity and tractability of spatial automata models. We use as examples Conways Game of Life and models for successional dynamics in a mesquite savanna landscape in south Texas. The number of possible neighborhood state configurations largely determines the complexity of automata models. The number of different configurations in Life, a two-state, deterministic, voting-rule model with an eight-cell Moore neighborhood is 18. A similar model for the seven-state savanna system would have 21,021 different neighborhood configurations. For stochastic models, the number of possible state transitions is the number of neighborhood configurations times the number of possible cell states. A stochastic, unique neighbor model for the savanna system with a Moore neighborhood and seven possible states would have 282,475,249 possible neighborhood-based state transitions. Stochastic models with an eight-cell Moore neighborhood are probably most appropriate for ecological applications. The best options for minimizing the complexity of ecological models are using voting rather than unique neighbor transition rules, reducing the number of possible states, and implementing ecologically-based heuristics to simplify the transition rule table.

A modified Lotka-Volterra simulation model to study the interaction between arrow bamboo (Sinarundinaria fangiana) and giant panda (Ailuropoda melanoleuca)

Abstract A binary ecosystem of bamboo and panda with human intervention is studied by means of a modified Lotka-Volterra model. Through simulation runs, intrinsic properties, such as the resilient nature of the system and the vital role of supplementary food on the stability of this dynamic system, are examined. Estimation of parameters used in the model is explained. The analysis procedure used in this study can be extended to investigate other binary systems with human intervention.

Modeling of the dynamics of accelerated growth following feed restriction in chicks

Abstract A model for normal growth and accelerated growth resulting from an early-age feed restriction in chickens, has been constructed. The model describes normal growth by a Gompertz equation, whereas compensatory growth is the product of three terms: a time derivative of the Gompertz equation; a compensation factor which is a function of the severity of feed restriction and a time-dependent exponential term. The model was fitted to experimental results obtained in male and female broiler chicks, with the aid of an iterative algorithm, based on numerical integration of the time-function, in two steps.

A statistical physics approach to nearest neighbor distibution for individuals of finite size

Abstract Analysis of spatial patterns using the classical nearest neighbor distribution is based on geometric points which have no size. For real ecological objects, size constraints the placement of neighbors. Therefore, the implied assumption of the classical approach that the total nearest neighbor area equals the sample area is no longer valid. In this study, the most probable nearest neighbor distribution for circles of any fixed diameter is derived. The results are compared with previous data and models describing the spatial pattern of ant-lion pits.

Use of power index and two-phase density approach to study fine root dynamics

Abstract Dynamics of fine roots are analyzed in terms of variation in functional soil volume, i.e., the volume of soil occupied by active fine roots. Functional soil volume decreases with drier climatic conditions while the substantiated rooting density, i.e., rooting density within the functional soil volume, remains constant. Substantiated rooting density differs from mean root density, which is defined as root biomass averaged over the entire rooting volume. This approach reflects the biological reality that, as a fraction of fine roots cease to function, the soil volume they inhabit can be considered to be non-functional. Thus functional soil volume becomes increasingly porous, and this porosity can be represented in terms of a volumetric power index. Hydrological equilibrium theory (Grier and Running, 1977; Eagleson, 1982; Nemani and Running, 1989; Pierce et al., 1993) implies that climate, functional soil volume, and total leaf area for a community of plants are in equilibrium. By expressing the dynamic characteristic of functional soil volume in terms of changing leaf area measurements, i.e., that soil rooting volume expressed as a function of leaf area by a scaling exponent, the relationship between transpiration and leaf area based on hydrologic equilibrium theory is established (Hatton and Wu, 1995). Using measurements of plant transpiration rate, parameter values relating these variables can be obtained from nonlinear fitting procedures. Four data sets from Wycanna, Qld are use to illustrate the procedure of describing fine root dynamics