STATISTICAL ASPECTS OF SAMPLING POPULATIONS OF FOREST ELEPHANTS

ABSTRACT. Statistical issues relating to a number of sampling methods which can be used to obtain estimates of the number, or density, of forest elephants are discussed. The most widely used method, distance sampling, is briefly described. A recently proposed method, recce sampling, that reduces sampling effort is described and discussed. Adaptive sampling, often used when populations are sparse, patchy or clustered, is described and proposed as an alternative. Model‐based and design‐based inferences are compared and their use in sampling forest elephant populations is discussed. Further considerations that are required to estimate or monitor changes in elephant populations over time are outlined.     

TOPOLOGICAL FRAMEWORK FOR FINITE INJURY

We formulate an abstract version of the finite injury method in the form of the Baire category theorem. The theorem has the following corollaries: The Friedberg-Muchnik pair of recursively enumerable degrees, the Sacks splitting theorem, the existence of a minimal degree below 0′ and the Shoenfield jump theorem.     

A FULL ANNUAL CYCLE MODELING FRAMEWORK FOR AMERICAN BLACK DUCKS

American black ducks (Anas rubripes) are a harvested, international migratory waterfowl species in eastern North America. Despite an extended period of restrictive harvest regulations, the black duck population is still below the population goal identified in the North American Waterfowl Management Plan (NAWMP). It has been hypothesized that density‐dependent factors restrict population growth in the black duck population and that habitat management (increases, improvements, etc.) may be a key component of growing black duck populations and reaching the prescribed NAWMP population goal. Using banding data from 1951 to 2011 and breeding population survey data from 1990 to 2014, we developed a full annual cycle population model for the American black duck. This model uses the seven management units as set by the Black Duck Joint Venture, allows movement into and out of each unit during each season, and models survival and fecundity for each region separately. We compare model population trajectories with observed population data and abundance estimates from the breeding season counts to show the accuracy of this full annual cycle model. With this model, we then show how to simulate the effects of habitat management on the continental black duck population.     

A UNIFIED FRAMEWORK FOR SOME INEXACT PROXIMAL POINT ALGORITHMS*

We present a unified framework for the design and convergence analysis of a class of algorithms based on approximate solution of proximal point subproblems. Our development further enhances the constructive approximation approach of the recently proposed hybrid projection–proximal and extragradient–proximal methods. Specifically, we introduce an even more flexible error tolerance criterion, as well as provide a unified view of these two algorithms. Our general method possesses global convergence and local (super)linear rate of convergence under standard assumptions, while using a constructive approximation criterion suitable for a number of specific implementations. For example, we show that close to a regular solution of a monotone system of semismooth equations, two Newton iterations are sufficient to solve the proximal subproblem within the required error tolerance. Such systems of equations arise naturally when reformulating the nonlinear complementarity problem.

     

KAPPA FUNCTION AS A UNIFYING FRAMEWORK FOR DISCRETE POPULATION MODELING

This paper develops a unified way to describe the various generalized discrete‐time nonlinear dynamical models with density dependence, Allee effects, and parasitoids. We show how the kappa function can be used to describe the probabilities involved in intra‐ or interspecific encounters, namely, (i) the probability of surviving to the next generation in the absence of parasitoids or Allee effects, (ii) the encounter probability associated with Allee effects, and (iii) the probability of escaping parasitism in the presence of parasitoids. Having introduced a phenomenological framework of modeling via the kappa function, we then provide a realistic mechanism through stochastic encounters, responsible for generating the kappa function to any of the three involved probabilities. The unified modeling through the kappa function yields insights into how abundances influence species interactions. It is now straightforward to use this unified modeling to analyze and investigate its consequences in species dynamics.     

A FREE-BOUNDARY PROBLEM TO DYNAMIC SYSTEM FOR PURE FOREST

A free-boundary model of nonlinear dynamic system for pure forest is presented, in which the felling rate is unbounded nearby the free boundary. The effiect of unbounded function on a priori estimate and analysis of regularity is overcome, and the existence and uniqueness of the global classical solution to this system are proved.     

区域分解界面预条件子构造的一般框架

1．引言考虑模型问题：其中ΩR2是多边形区域,常数n≥0．将Ω作非重叠区域分解：Ω＝假定：（i）当i≠j时,（ii）当Ωi与Ωj相邻时,是Ωi和Ωj的一条公共边记称为界面）;（iii）每个闪的尺寸为d,即存在常数co和q,使出包含（包含在）一个直径为C（）（Cod）的圆（国内）．非重叠区域分解方法的实质是,引进两个变量：内部变量。h和界面变量～．先在几上并行未解子问题,将。。消去（即用～表示）,得到～的方程（称为界面方程）;再求解界面方程,得到～的值;最后将～回代,得到。人的值（即原问题的解）．这类区域分解方法是否比重…     

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING*

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.     

缺失数据下WEIBULL分布的统计推断

本文给出了定数截尾缺失数据下Weibull分布参数的点估计和区间估计以及可靠度、失效率的置信限。     

随机截尾情形下MOBVE分布的统计推断

本文讨论联合生存函数的二元指数分布（ＭＯＢＶＥ）的统计推断问题，随机截尾寿命试验下的元件和患联系统的寿命试验数据被联合作用，文中给出了参数的极大似然估计并讨论了它们的渐近性质，还得到了若干关于参数的假设的渐近检验程序。     

至多一个分布变点的非参数统计推断

本文研究了连续分布函数变点的非参数统计推断问题.利用秩统计量和次序统计量,获得了变点的一种估计,不仅论证了点估计的强相合性,而且讨论了假设检验和区间估计.     

分布变点模型的非参数检验和区间估计

设X(1/n+1),…,X(i/n+1),…,x(n/n+2)是定义在[0,1]上的随机过程X(t)的n个等距独立观察值,其中X(i/n+1),0＜i/n+1≤r,服从公共连续分布F;X(i/n+1),τ＜i/n+1＜1,服从公共连续分布F*,F与F*不同;其中τ是过程X(t)的变点.用CUSUM及BrownianSheet方法给出了检测变点r位置的一个程序,并证明了所得结果是强相合的;同时也讨论了r的假设检验和区间估计.     

分布变点模型的非参数检验和区间估计

提 要设　是定义在［０,１］上的随机过程Ｘ（ｔ）的ｎ个等距独立观察值,其中,　服从公共连续分布Ｆ;,服从公共连续分布 Ｆ＊,Ｆ与Ｆ＊不同;其中,是过程 Ｘ（ｔ）的变点．用ＣＵＳＵＭ及Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ方法给出了检测变点τ位置的一个程序,并证明了所得结果是强相合的;同时也讨论了τ的假设检验和区间估计．     

至多一个分布变点的非参数检验及其渐近性质

本文研究了连续分布函数变点的假设检验问题,通过秩统计量和次序统计量方法,得到了相应的检验统计量及其渐近性质.     

OPTIMUM GROWTH AND REPRODUCTION SCHEDULES FOR FOREST TREES

A control theory optimization of iteroparous life histories indicates that if growth and reproduction are nonlinear functions of energy allocations, graded allocations of energy to potential reproduction can be optimal.     

SUSTAINABLE FOREST MANAGEMENT FOR OPTIMIZING MULTISPECIES WILDLIFE HABITAT: A COASTAL DOUGLAS-FIR EXAMPLE

Wildlife species viability optimization models are developed to convert a given set of initial forest conditions, through a combination of natural growth and management treatments, to a forest system which addresses the joint habitat needs of multispecies populations over time. A linear model of forest cover and wildlife populations is used to form a system of forest management control variables for wildlife habitat modification. The paper examines two objective functions coupled to this system for optimizing sustainable joint species viability. The first maximizes the product of periodic joint viabilities over all time periods, focusing management resources on long-term equilibria, with less emphasis on conversion strategy. The second iteratively maximizes the minimum periodic joint viability over all time periods. This focuses management resources on the most limiting time periods, typically the conversion phase periods. Both objective functions resulted in either point or cyclic equilibria, with cycle lengths equal to minimum forest treatment ages. A third objective, based on maximizing the minimum individual species periodic viability is used to examine single species emphasis. Examples are developed through a case study of 92 vertebrate species found in coastal Douglas-fir stands of northwestern California.     

变应力寿命试验的统计分析

本文利用 S-N-P 曲线和累积损伤原理,给出了变应力下产品的寿命分布,此分布不仅与应力水平有关,而且与各应力水平的次序有直接关系.在此分布的基础上,给出了变应力寿命试验的统计分析方法.这种方法不仅适用于疲劳试验,而且还可用于单项可变动应力寿命试验和加速寿命试验,以及各种应力组合的可变应力的寿命试验和加速寿命试验.为利用可变动组合应力的加速寿命试验,估计正常可变应力下的寿命特征提供了一种解决的方法.     

FRIEZE PATTERNS FOR REGULAR STAR POLYTOPES AND STATISTICAL HONEYCOMBS

Much has been written about the discovery by physicists of quasicrystals and the almost simultaneous discovery by geometers of nonperiodic tessellations and honeycombs. A somewhat similar serendipity occurred when crystallographers saw what happens when identical balls of plastic clay or lead shot are shaken together and uniformly compressed, or when the bubbles (all of the same size) in a froth are measured; and almost simultaneously geometers investigated statistical honeycombs. Alternate doses of oil and water in a thin tube may be regarded as a one-dimensional "froth" {∞}, each "bubble" having just 2 neighbours. Analogously, soapsuds sandwiched between parallel glass plates (close together) may be regarded as a two-dimensional froth {6,3}, each bubble having just 6 neighbours. Three-dimensional froth presents a far more difficult problem because there is no regular honeycomb having 4 cells at each vertex. The best available substitute seems to be a "statistical" honeycomb {p, 3,3} where p, instead of being rational, is a real number such as π/ arctan , somewhere between 5 and 6. ({5,3,3} is the regular 120-cell and {6,3,3} is non-Euclidean.) In such a statistical honeycomb, the number of neighbours for each bubble is 13.4, in good agreement with experiments in which the actual number is 12 or 14 and sometimes 15, but most often 13. Hoping not to be too fanciful, we venture to look for a statistical honeycomb {q,3,3,3} in Euclidean 4-space, q being a real number such as π/ arctan , somewhere between 4 and 5. ({4,3,3,3} is the 5-cube while {5,3,3,3} is non-Euclidean.) In this case the number of neighbours for one bubble in the 4-dimensional froth is computed to be about 28. This revised version was published online in August 2006 with corrections to the Cover Date.