E. David Ford

STATISTICAL INFERENCE USING THE G OR K POINT PATTERN SPATIAL STATISTICS

Spatial point pattern analysis provides a statistical method to compare an observed spatial pattern against a hypothesized spatial process model. The G statistic, which considers the distribution of nearest neighbor distances, and the K statistic, which evaluates the distribution of all neighbor distances, are commonly used in such analyses. One method of employing these statistics involves building a simulation envelope from the result of many simulated patterns of the hypothesized model. Specifically, a simulation envelope is created by calculating, at every distance, the minimum and maximum results computed across the simulated patterns. A statistical test is performed by evaluating where the results from an observed pattern fall with respect to the simulation envelope. However, this method, which differs from P. Diggles suggested approach, is invalid for inference because it violates the assumptions of Monte Carlo methods and results in incorrect type I error rate performance. Similarly, using the simulation envelope to estimate the range of distances over which an observed pattern deviates from the hypothesized model is also suspect. The technical details of why the simulation envelope provides incorrect type I error rate performance are described. A valid test is then proposed, and details about how the number of simulated patterns impacts the statistical significance are explained. Finally, an example of using the proposed test within an exploratory data analysis framework is provided.

A MODEL OF COMPETITION INCORPORATING PLASTICITY THROUGH MODULAR FOLIAGE AND CROWN DEVELOPMENT

The model of competition for light presented here uses modular autonomy to incorporate plasticity in plant growth under competition. Once plants are characterized as composed of modules, then model structure for competition changes in a fundamental way. Interactions between the plant module and its local resource environment must be modeled rather than the traditionally viewed interactions between whole plants and their neighbors. We assume that a plant module interacts with its local resource environment regardless of whether this environment was altered by a neighbor or by the same plant. Two spatial processes are considered: resource acquisition and growth. The spatial pattern of resource acquisition by a module determines a growth and allocation pattern, e.g., the elongation of branches into a gap. The spatial structure of a module and its connection to the whole tree then determines the pattern of resource distribution and resource acquisition of the next time step.Plasticity of plant growth is incorporated by variation in both the efficiency of resource capture of modules and patterns of resource allocation for individuals of different canopy positions and results in individuals in the community having different spatial structures. The model simulates the three—dimensional development of tree crown structure over time. It is applied to the 30—yr development of a dense, spatially aggregated stand of Abies amabilis beginning with an initial pattern of seedlings. The importance of incorporation of plasticity is apparent when the model output is compared to observed height distribution and crown structure data. Simulations indicate that asymmetrical crown development, one form of plasticity, is advantageous to stand productivity and becomes more advantageous as the degree of spatial aggregation in the initial spacing of trees increases.

MULTI-CRITERIA ASSESSMENT OF ECOLOGICAL PROCESS MODELS

The Pareto Optimal Model Assessment Cycle (POMAC), a multiple-criteria model assessment methodology, is described for exploring uncertainty in the relationships between ecological theory, model structure, and assessment data. Model performance is optimized to satisfy, simultaneously, each component of a vector of assessment criteria (model outputs), rather than the usual procedure of optimizing performance with respect to a single criterion. Pareto Optimality is used to define the vector optimization. The Pareto Optimal Set reveals which combinations of assessment criteria the model can satisfy si- multaneously. Binary interval error measures, which classify whether a parameterization result is within an acceptable range of values, are defined for each criterion. Their use masks small differences in the performance of different parameterizations, allowing the Pareto Optimal Set to reveal conflicts in ability to achieve simultaneously different col- lections of criteria. POMAC improves the researchers ability to detect deficiencies and locate their sources. It is more stringent and informative than traditional model assessment procedures because it uses multiple criteria without weighting and aggregating them. The Pareto Optimal Set reveals the presence of deficiencies through the models inability to satisfy all the criteria simultaneously. POMAC then guides the researcher in locating deficiencies in: inadequate selection of component ecological hypotheses underlying the model, inadequate mathe- matical representations of these hypotheses, inadequate parameterization, poor selection and formulation of the assessment criteria, or combinations of these. In an example, POMAC is applied to the spatially explicit canopy competition model WHORL using ten assessment criteria. Each criterion was selected to provide information on different aspects of WHORLs functioning: three stand height distribution criteria, three crown morphology criteria, and four criteria focusing on stand competitions characteristic differentiation of growth rates. The Pareto Optimal Set was generated using simulated evolution optimization. POMAC revealed deficiencies in both the model structure and its assessment criteria, leading to an improved model and better understanding of its effective domain.

Simulation of branch growth in the Pinaceae: Interactions of morphology, phenology, foliage productivity, and the requirement for structural support, on the export of carbon†

Five interacting processes that determine the life cycle and productivity of a branch are simulated. Morphological development describes branch segment (branchlet) replication. Foliage development is controlled by production rate and longevity on each branchlet. Production of photosynthate, calculated as net biomass increment , may vary with branchlet age. Phenology defines the yearly brnachlet growth period and so influences foliage amount produced. Branchwood thickening is incremented to maintain a specified deflection profile. The export of potential biomass increment from the branch is estimated. These five processes together define branch growth as a balance between positive and negative feedbacks. In the early years of branch growth the more rapid the foliage development, the more available biomass increment there is to produce more foliage. However, as the branch elongates and foliage is held further from the tree, greater foliage amounts comes to require greater amounts of branchwood for support. The potential biomass increment exported from the branch to the trunk first increases, as foliage increases, and then decreases as the demand for supporting branchwood increases. Simulations show how the set point between the two feedback systems can be specified by phenology and morphology . For export an optimum length of time can be defined for branchlet growth when there is a balance between the amount of production invested in new foliage and the additional export to the trunk obtained from it. The necessity to simulate branchlet production as non-stationary over the branch lifetime is demonstrated. Two morphological systems for this are investigated; APICAL which specifies branchlet proliferation only according to length and order of parent branchlets and SEARCH which simulates plasticity in development through the inhibition of branchlet production according to local crowding. For the SEARCH algorithm there is an interaction with branchlet phenology that has a substantial influence on both the timing and amount of export to the trunk.

Light interacts with auxin during leaf elongation and leaf angle development in young corn seedlings

Abstract. Modern corn (Zea mays L.) varieties have been selected for their ability to maintain productivity in dense plantings. We have tested the possibility that the physiological consequence of the selection of the modern hybrid, 3394, for increased crop yield includes changes in responsiveness to auxin and light. Etiolated seedlings in the modern line are shorter than in an older hybrid, 307, since they produce shorter coleoptile, mesocotyl, and leaves (blade as well as sheath). Etiolated 3394 seedlings, as well as isolated mesocotyl and sheath segments, were less responsive to auxin and an inhibitor of polar auxin transport, N-1-naphthylphthalamic acid (NPA). Reduced response of 3394 to auxin was associated with less reduction of elongation growth by light (white, red, far-red, blue) than in 307, whereas the activity of polar auxin transport (PAT) and its reduction by red or far-red light was similar in both genotypes. NPA reduced PAT in etiolated 3394 seedlings much less than in 307. A characteristic feature of 3394 plants is more erect leaves. In both hybrids, light (white, red, blue) increases leaf declination from the vertical, whereas NPA reduces leaf declination in 307, but not in 3394. Our results support findings that auxin and PAT are involved in elongation growth of corn seedlings, and we show that light interacts with auxin or PAT in regulation of leaf declination. We hypothesize that, relative to 307, more erect leaves in the modern hybrid may be primarily a consequence of a reduced amount of auxin receptor(s) and reduced responsiveness to light in etiolated 3394 plants. The more erect leaves in 3394 may contribute to the tolerance of the modern corn hybrid to dense planting.

EFFECTS OF DATA QUALITY ON ANALYSIS OF ECOLOGICAL PATTERN USING THE K̂(d) STATISTICAL FUNCTION

The K(d) function is a summary statistic of all plant–plant distances in a mapped area. It offers the potential for detecting both different types and scales of patterns in a single map. Two types of errors occur in maps of individual plants. Data management errors, caused by transcription errors or other mishandling, are large errors and apply to small numbers of plants. Measurement errors, caused by the mapping techniques and equipment, are small errors that apply to all plants. Simulation of known spatial patterns combined with increasing levels of both types of error showed that: (1) data management errors cause the spatial patterns identified by the statistical function K(d) to become less significant but do not cause a shift in scale of the identified patterns; and (2) measurement errors caused the spatial patterns identified by K(d) to become less significant and to shift to larger scales. The effects of measurement errors are inversely proportional to the scale of interaction between plants on the map. Detection of inhibition between points is more sensitive to measurement error than detection of clustering; detection of small clusters is more sensitive than detection of large clusters; and measurement error tends to cause an overestimation of clumping size. For patterns with inhibition, estimating minimum establishment distance is more sensitive to error than the maximum distance at which inhibition affects survival probability. Two examples of tree spatial distributions from the Wind River Canopy Crane Research Facility stem map data set were analyzed using the K(d) function. Clusters of Thuja plicata were detected and were much larger than levels of mapping error identified in the data. Significant inhibition occurs between large (dbh ≥20 cm) trees of all species at a scale much greater than the level of mapping error. However, the minimum distance of significant inhibition (i.e., the distance within which neighbors are never found) was on the order of the mapping error. Accurate identification of inhibition may not be possible using K(d).

Structure and basic equations of a simulator for branch growth in the Pinaceae

The structure of a simulator for branch growth and morphological development in the Pinaceae is described. Growth is defined as the net production of foliage, the increment of branch thickening and the export of photosynthate to the trunk. Branch morphology is described by the spatial distribution of the branch segments, or branchlets, and a curvilinear profile of the whole branch as it bends under its own weight. Growth is the result of five interacting processes. Foliage development is the result of foliage production on the annual production of new branchlets and foliage death from older branchlets. Biomass production , (g biomass produced). (g foliage)-1, depends upon both the rate of production, which can vary with age of foliage, and the total amount of foliage of different ages. The distribution of biomass between the growth of the branch and export to the trunk of the tree is controlled by the phenology of shoot (branchlet) growth. During the period of branchlet growth biomass increment is distributed between branchlet elongation and the associated foliage growth and branchwood thickening . This is done so that branch posture in the vertical plane follows a particular deflection profile. The production of new branchlets is from the terminals of previous years branchlets and is made according to morphological rules . Two types of rules are described; simple numerical sequences where branchlet number depends upon the order and length of the parent branch and a process of lateral inhibition between branchlets combined with dependence upon branchlet order.

Persistence ofPseudotsuga menziesii (Douglas-fir) in temperate coniferous forests of the Pacific Northwest Coast, USA

Old-growthPseudotsuga-Tsuga forests of the Pacific Northwest Coast of North America are characterized by the presence of large, old trees ofPseudotsuga menziesii var.menziesii (Douglas-fir). Colonizing soon after a stand-replacing disturbance,P. menziesii persists in these forests, coexisting for centuries with the late-successional species.P. menziesii survives by maintaining emergent status in the uppermost part of the forest canopy, above the crowns of competing late-successional species. After reaching maximum tree height and crown size,P. menziesii maintains shoots and foliage of the established crown by epicormic shoot production. In this review, we propose that attaining emergent status in the upper canopy combined with the process of crown maintenance contributes to the persistence ofP. menziesii into later stages of succession, making this species a long-lived pioneer that between infrequent disturbances can coexist with late-successional species for centuries.

Using Multicriteria Analysis of Simulation Models to Understand Complex Biological Systems

Scientists frequently use computer-simulation models to help solve complex biological problems. Typically, such models are highly integrated, they produce multiple outputs, and standard methods of model analysis are ill suited for evaluating them. We show how multicriteria optimization with Pareto optimality allows for model outputs to be compared to multiple system components simultaneously and improves three areas in which models are used for biological problems. In the study of optimal biological structures, Pareto optimality allows for the identification of multiple solutions possible for organism survival and reproduction, which thereby explains variability in optimal behavior. For model assessment, multicriteria optimization helps to illuminate and describe model deficiencies and uncertainties in model structure. In environmental management and decisionmaking, Pareto optimality enables a description of the trade-offs among multiple conflicting criteria considered in environmental management, which facilitates better-informed decisionmaking.

Nutrients, moisture and productivity of established forests

Abstract The response of a forest to nutrient and moisture stresses is reflected in nutritional, physiological, and structural changes that include efficiency of nutrient use, translocation and cycling of nutrients, transpiration, retention of foliage, below-ground and above-ground allocation of carbon, as well as the structural development of the forest stand and its growth characteristics. This article reviews the relationship of forest ecosystems to nutrient and moisture stresses and addresses the means by which productivity can be enhanced by altering nutrient and moisture regimes. Considerable research has focused on optimizing productivity by minimizing nutrient and moisture stresses. Research involved in nutrient additions has led to the use of commercial fertilizers to improve forest productivity. The results suggest that many forests are deficient in N and P and, to a lesser extent, S, K, Mg and trace elements. The duration of response for most nutrient additions is, however, relatively brief and the efficiency of the tree in using fertilizer is relatively poor. Long-term correction of nutrient deficiencies is seldom achieved with chemical fertilizers. However, N added through symbiotic fixation or, on a more limited scale, through addition of municipal and industrial waste by-products, can provide an excellent long-term growth response. It is seldom feasible to change the moisture regime of a forest ecosystem through irrigation. However, field trials involving irrigation have demonstrated that moisture stress can limit productivity. There are various ways of minimizing moisture stress without irrigation, including mulching, removing ground-cover vegetation, and changing the spatial characteristics of the forest cover. Research trials show that forest ecosystems will respond to moisture and nutrient additions; however, these responses and interactions between nutrients and moisture are typically poorly understood, and many questions remain unanswered: Does fertilization increase moisture-use efficiency of a forest or simply improve the nutrition of the site? Does improving the moisture regime of a site improve productivity primarily by decreasing moisture stress or by increasing nutrient availability and the rate of nutrient uptake? Is there a synergism in growth response with the addition of both nutrients and moisture? The linkages between nutrients and moisture appear inseparable and confound experimentation in this field. Answers to these questions and issues need to be found for the future development of plantation forestry.