Cobb-Douglas生产函数在养殖管理中的应用

本文通过对番鸭养殖场的调查，得到总收益与养鸭数量、饲料量、固定资产、劳动力、药品（含疫苗）。5个投入因素的数据。运用Cobb-Douglas生产函数建立投入产出数学模型，并对其进行弹性分析和边际产量分析。为达到合理、高收益的养殖生产提供科学依据。     

HABITAT PATCH OCCUPANCY DYNAMICS OF GLAUCOUS‐WINGED GULLS (LARUS GLAUCESCENS) II: A CONTINUOUS‐TIME MODEL

ABSTRACT. The diurnal distribution and abundance dynamics of loafing Glaucous‐winged Gulls (Larus glaucescens) were examined at Protection Island National Wildlife Refuge, Strait of Juan de Fuca, Washington. Asynchronous movement of gulls among three habitat patches dedicated to loafing was modeled as a function of environmental variables using differential equations. Multiple time scale analysis led to the derivation of algebraic models for habitat patch occupancy dynamics. The models were parameterized with hourly census data collected from each habitat patch, and the resulting model predictions were compared with observed census data. A four‐compartment model explained 41% of the variability in the data. Models that predict the dynamics of organism distribution and abundance enhance understanding of the temporal and spatial organization of ecological systems, as well as the decision‐making process in natural resource management.     

A STAGE‐STRUCTURED MODEL WITH TWO TIME‐STEPS FOR ANALYZING THE POPULATION DYNAMICS OF RHEA AMERICANA UNDER VARIABLE ENVIRONMENTAL CONDITIONS

ABSTRACT. The Ñandú or Rhea americana is an autochthonous species perfectly adapted to the pampas environment and only distributed in South America. The species exhibits an unusual breeding system combining polygyny, polyandry, communal nests and exclusive male parental care, which seems to contradict the idea of selfish genes. Our aim has been to construct a mathematical model based on the short term population dynamics of Rhea, living in the wild or in semi‐captivity, and taking into account environmental factors that vary from year to year. Due to the characteristics of its life cycle, it was necessary to develop a model that allows us to differentiate between the survival and fertility rates of each age group and the distinct behavior during breeding and non‐breeding seasons. Therefore, a quarterly differentiated stage‐structured discrete model was needed. Time steps of different lengths are used for modeling chicks or “charos' on the one hand, and juveniles and adults on the other. Environmental variables have been incorporated into the model because they affect the reproductive success of the species. Different scenarios are given as illustrations of the model use. Finally, the possibility of harvesting has been introduced in the model. The model is intended as a first step towards more refined models and systematic data gathering with the purpose of leading the way to a computational tool for risk assessment and decision‐making.     

A HABITAT BASED MODEL FOR THE DISTRIBUTION OF FOREST INTERIOR NESTING BIRDS IN A FRAGMENTED LANDSCAPE

ABSTRACT. Increased awareness of the plight of many forest dwelling species has made necessary the development of methods for projecting the spatial distribution of these populations. This is particularly important for populations that currently occupy forest fragments and that are likely to be exposed to further disruption of their natural habitat. In this paper we develop a model for predicting the distribution of a bird population that evolved as forest interior dwellers. This model uses as its basis knowledge of the relationship between demographic characteristics of the population and the qualities of the habitat where individuals reside. We make the assumption that individuals will be naturally drawn to areas where they might expect greater reproductive success and repelled from areas where there is a high degree of intraspecific competition (high density). We apply the model to the ovenbird population in a large region of the Midwest. We use the model to examine the relative extent to which the surplus production from two major source areas supports extensive sink populations. The basic diffusion model parameterized by county forest cover data projects a population distribution which compares favorably with the results from the breeding bird count.     

ANALYSIS OF SENSITIVITY AND UNCERTAINTY IN AN INDIVIDUAL‐BASED MODEL OF A THREATENED WILDLIFE SPECIES

Sensitivity analysis—determination of how prediction variables affect response variables—of individual‐based models (IBMs) are few but important to the interpretation of model output. We present sensitivity analysis of a spatially explicit IBM (HexSim) of a threatened species, the Northern Spotted Owl (NSO; Strix occidentalis caurina) in Washington, USA. We explored sensitivity to HexSim variables representing habitat quality, movement, dispersal, and model architecture; previous NSO studies have well established sensitivity of model output to vital rate variation. We developed “normative” (expected) model settings from field studies, and then varied the values of ≥ 1 input parameter at a time by ±10% and ±50% of their normative values to determine influence on response variables of population size and trend. We determined time to population equilibration and dynamics of populations above and below carrying capacity. Recovery time from small population size to carrying capacity greatly exceeded decay time from an overpopulated condition, suggesting lag time required to repopulate newly available habitat. Response variables were most sensitive to input parameters of habitat quality which are well‐studied for this species and controllable by management. HexSim thus seems useful for evaluating potential NSO population responses to landscape patterns for which good empirical information is available.     

A discrete two-stage population model: continuous versus seasonal reproduction

A discrete two-stage model which describes the dynamics of a population where juveniles and adults compete for different resources is developed. A motivating example is the green tree frog (Hyla cinerea) where tadpoles and adult frogs feed on separate resources. First, continuous breeding is assumed and the asymptotic behavior of the resulting autonomous model is fully analyzed. It is shown that the unique interior equilibrium is globally asymptotically stable when the inherent net reproductive number is greater than one. However, when the inherent net reproductive number is less than one, the population becomes extinct. Then a seasonal breeding described by a periodic birth rate with period 2 is assumed. It is proved that for this nonautonomous model a period two solution is globally asymptotically stable when the inherent net reproductive number is greater than one and when the inherent net reproductive number is less than one the population becomes extinct. Finally, the advantage (in terms of maximizing the number of juveniles and adults in the population over a fixed time period) of having a seasonal breeding is studied by comparing the average of the juvenile and adult numbers of the periodic solution for the nonautonomous model to the equilibrium solution of the autonomous model. Our results indicate that for high birth rates the equilibrium of the autonomous model is higher than the average of the two cycle solution. Therefore, all other factors being equal, seasonal breeding appears to be deleterious to populations with high birth rates. However, for low birth rates seasonal breeding can be beneficial. It is also shown that for a range of birth rates the nonautnomous model is persistent while the solution to the autonomous model goes to extinction.     

CONTROL OF A METAPOPULATION HARVESTING MODEL FOR BLACK BEARS

ABSTRACT. We develop a metapopulation harvesting model that includes density‐dependent immigration and emigration and apply Pontryagin's maximum principle to derive an optimal harvesting and reserve design strategy. The model is designed to mimic the black bear population of eastern Tennessee and western North Carolina. Model results suggest that a forest region's population can be maintained despite high harvest levels due to emigration from a connected, un‐harvested park region. The amount of shared border between the park and forest region is important in determining the optimal harvesting strategy. This technique offers new insight on the spatial control of protected populations.     

PREDICTING GULL/HUMAN CONFLICTS WITH MATHEMATICAL MODELS: A TOOL FOR MANAGEMENT

Abstract Gulls are highly adaptable animals that thrive in proximity to humans. Although gulls enjoy legal protection in North America, England, and Europe, they often conflict with human interests by spreading disease, transporting contaminants, fouling public areas with droppings, and colliding with aircraft. Of particular concern are aggregates of “loafing” gulls that gather on parking lots, rooftops, and airport runways. Loafing in birds is a general state of immobility that involves behaviors such as sleeping, sitting, standing, resting, preening, and defecating. The ability to predict the incidence of aggregated loafing provides a first step toward the amelioration of bird/human conflicts. We used mathematical models to predict the aggregate loafing behavior of gulls as a function of environmental conditions and tested model portability across years, phase of breeding cycle, loafing location, and species. Because groups of loafing birds quickly reassemble after disturbance, algebraic models for the steady‐state dynamics can be obtained from the differential equations using time‐scale analysis. The accessible management tool requires data collection on an appropriate time scale and information‐theoretic model selection from a suite of alternative algebraic models.     

MULTISPECIES MODELING FOR ADAPTIVE MANAGEMENT OF HORSESHOE CRABS AND RED KNOTS IN THE DELAWARE BAY

Abstract Adaptive management requires that predictive models be explicit and transparent to improve decisions by comparing management actions, directing further research and monitoring, and facilitating learning. The rufa subspecies of red knots (Calidris canutus rufa), which has recently exhibited steep population declines, relies on horseshoe crab (Limulus polyphemus) eggs as their primary food source during stopover in Delaware Bay during spring migration. We present a model with two different parameterizations for use in the adaptive management of horseshoe crab harvests in the Delaware Bay that links red knot mass gain, annual survival, and fecundity to horseshoe crab dynamics. The models reflect prevailing hypotheses regarding ecological links between these two species. When reported crab harvest from 1998 to 2008 was applied, projections corresponded to the observed red knot population abundances depending on strengths of the demographic relationship between these species. We compared different simulated horseshoe crab harvest strategies to evaluate whether, given this model, horseshoe crab harvest management can affect red knot conservation and found that restricting harvest can benefit red knot populations. Our model is the first to explicitly and quantitatively link these two species and will be used within an adaptive management framework to manage the Delaware Bay system and learn more about the specific nature of the linkage between the two species.     

Analysis of a game of graph solitaire

Let G be a simple undirected graph. To each vertex assign one of two colours say red or blue. A solitaire game is played on G as follows. A move consists of selecting a blue vertex, inverting the colours of its neighbours and then deleting the chosen vertex and all edges incident upon it. The goal is to delete all the vertices. The question of finding a winning strategy in the case when G is a simple cycle was proposed in the problems section of the American Mathematical Monthly. In this article some general results on winning colour configurations are derived and the game is analysed for certain other graph classes.     

Optimal stopping, free boundary, and American option in a jump-diffusion model

This paper considers the American put option valuation in a jump-diffusion model and relates this optimal-stopping problem to a parabolic integro-differential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its counterpart European price and the early exercise premium. Compared with the Black-Scholes (BS) [5] model, this premium has an additional term due to the presence of jumps. We prove the continuity of the free boundary and also give one estimate near maturity, generalizing a recent result of Barleset al. [3] for the BS model. Finally, we study the effect of the market price of jump risk and the intensity of jumps on the American put option price and its critical stock price.     

A greedy algorithm for partition of unity collocation method in pricing American options

A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF‐PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF‐PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF‐PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.     

Existence of allometry model parameters and their asymptotic formulae for a large population

A theory of population that fails to consider a major determinant of the characteristics of populations is not an adequate theory. Standard texts in population biology and ecology tend to ignore body size as a factor in population dynamics, although birth and death rates, survivorship and longevity, population density and home range size, cycle periods for population boom and crash, and the annual increment in mortality due to aging all show a strong correlation with body mass. Studies in the evolutionary biology of aging require good estimates of the age-dependent mortality rate coefficient. In this paper, we provide an interval of existence of mortality rate parameters M _r and b and their asymptotic expressions in Allometry survival model, in the absence of age-specific mortality data.     

Production Runs for Multiple Products: The Full-Capacity Heuristic

This paper presents the full-capacity heuristic, a procedure for determining run sizes for scheduling N products which must be produced on the same machine. First, the optimal solution for scheduling two products at full capacity is reviewed. Then a heuristic method is presented for solving the N product, full capacity problem. The method involves: (i) judgementally selecting the sequence of set-ups in the fundamental cycle; (ii) determining the relative durations of each run within the cycle by solving a system of linear equations; and (iii) computing the associated optimal cycle length and annual cost. Finally, there is discussion of how to apply the full capacity method in the more common situation when there is slack production capacity available.     

Iterative algorithms for the curfew planning problem

The curfew planning problem is to design an annual timetable for railway track maintenance teams. Each team is capable of handling certain types of repairs and replacement jobs. The jobs are combined into a set of projects according to their locations and types. The timetable shows which project should be worked on by each team on a weekly basis throughout an entire year. Our objective is to design a schedule with minimum network disruption due to ongoing maintenance projects that require absolute curfew. Absolute curfew projects are those that cause complete closure of the rail traffic. For tackling this problem, we develop four optimization-based iterative algorithms. We also present very promising computational results obtained within a few minutes using data provided by a major North American railroad.     

A TWO‐STAGE INFORMATION‐THEORETIC APPROACH TO MODELING LANDSCAPE‐LEVEL ATTRIBUTES AND MAXIMUM RECRUITMENT OF CHINOOK SALMON IN THE COLUMBIA RIVER BASIN

ABSTRACT. Many anadromous salmonid stocks in the Pacific Northwest are at their lowest recorded levels, which has raised questions regarding their long‐term persistence under current conditions. There are a number of factors, such as freshwater spawning and rearing habitat, that could potentially influence their numbers. Therefore, we used the latest advances in information‐theoretic methods in a two‐stage modeling process to investigate relationships between landscape‐level habitat attributes and maximum recruitment of 25 index stocks of chinook salmon (Onocorhynchus tshawy‐tscha) in the Columbia River basin. Our first‐stage model selection results indicated that the Ricker‐type, stock recruitment model with a constant Ricker a, i.e., recruits‐per‐spawner at low numbers of fish) across stocks was the only plausible one given these data, which contrasted with previous unpublished findings. Our second‐stage results revealed that maximum recruitment of chinook salmon had a strongly negative relationship with percentage of surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and private moderate‐high impact managed forest. That is, our model predicted that average maximum recruitment of chinook salmon would decrease by at least 247 fish for every increase of 33% in surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and privately managed forest. Conversely, mean annual air temperature had a positive relationship with salmon maximum recruitment, with an average increase of at least 179 fish for every increase in 2°C mean annual air temperature.     

Analysis for an environmental friendly seedling breeding system

Most seedlings of crops are produced in solar greenhouse or nursery, from which some problems about energy waste and environment pollution arise. This study aims at investigating the characteristics and effect of an environmental friendly type seedling breeding system. The results demonstrate that crops can grow with a short period and little pollution in the new seedling breeding system with total manpower controllable environment that is not influenced by geography, climate and other natural conditions. By multilayer, nonplanar seedling breeding and annual batches arrangement, utilization ratio of unit area land and seedlings yield can be improved for several times and even more than 10 times. Conclusions can be obtained from the tomato seedling breeding experiments: (1) each growth index of tomato seedlings that are under the conditions of 291 μmol/m² s artificial illumination intensity is remarkably better than those produced in greenhouse with natural lights. (2) The environment of the seedling breeding system can be accurately controlled. The segmented temperature changed management can be applied according to the photosynthetic characteristics of plants, and not affected by the outside environment, which makes each growth index of tomato seedling constant in different seasons. The seedlings thus grow strong and can achieve the level of commodity seedlings after 20–30 days. (3) The temperature and humidity environment of the seedling breeding system can be accurately controlled according to plants growth demands.     

Notes on contributors

Mathematics in the United States developed slowly over its first one hundred years. Before the appearance of successful mathematics journals, American mathematicians depended on science journals to publish their work. Three journals, the Transactions of the American Philosophical Society, the Memoirs of the American Academy of Arts and Sciences, and the American Journal of Science and Arts, played pivotal roles in the development of a mathematics publication community.     

On the American option‐pricing model with an uncertain volatility

In this paper, we study an American option‐pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets. Copyright © 2015 John Wiley & Sons, Ltd.     

HABITAT PATCH OCCUPANCY DYNAMICS OF GLAUCOUS‐WINGED GULLS (LARUS GLAUCESCENS) I: A DISCRETE‐TIME MODEL

ABSTRACT. Diurnal habitat occupancy dynamics of Glaucous‐winged Gulls were evaluated in a system of six habitats on and around Protection Island, Washington. Data were collected on the rates of gull movement between habitat patches, and from these data the probabilities of transitions between habitats were estimated as functions of tide height and time of day. A discrete‐time matrix model based on the transition probabilities was used to generate habitat occupancy predictions, which were then compared to hourly census data. All model parameters were estimated directly from data rather than through model fitting. The model made reasonable predictions for two of the six habitats and explained 45% of the variability in the data from 2003. The construction and testing of mathematical models that predict occupancies in multiple habitats may play increasingly important roles in the understanding and management of animal populations within complex environments.