【正文】 alfree distribution as a partial differential equation, Theor. Pop. Biol. 67 (20xx) 101–108. [15] C. Cosner, Y. Lou, Does movement toward better environments always benefit a population?, J. Math. Anal. Appl. 277 (20xx) 489–503. [16] J. Dockery, V. Hutson, K. Mischaikow, M. Pernarowski, The evolution of slow dispersal rates: A reaction–diffusion model, J. Math. Biol. 37 (1998) 61–83. [17] . Fretwell, . Lucas, On territorial behavior and other factors influencing habitat distribution in birds. I. Theoretical development, Acta Biotheor. 19 (1970) 16–36. [18] D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equation of Second Order, second ed., SpringerVerlag, Berlin, 1983. [19] P. Grindrod, Models of individual aggregation or clustering in single and multispecies munities, J. Math. Biol. 26 (1988) 651–660. 具適應性的人口疏散模型的 整體解 24 [20],On the global txistence of solutions to an aggregation madol,(20xx)379398 [21] and ,Broundness in a quasitinear parabolicparabolic KellerSegel System with subticat sensitivity, Equations ,252 (20xx)692715 [22] . McPeek, . Holt, The evolution of dispersal in spatially and temporally varying environments, Am. Nat. 140 (1992) 1010– 1027. [23] M. Kshatriya, C. Cosner, A continuum formulation of the ideal free distribution and its applications for population dynamics, Theor. Pop. Biol. 61 (20xx) 277– 284. [24] S. Kirkland, . Li, . Schreiber, On the evolution of dispersal in patchy environments, SIAM J. Appl. Math. 66 (20xx) 1366– 1382. [25] V. Hutson, K. Mischaikow, P. Pol225。 Udxxu ??? ? ? ? ?? ??? ?????? 0)(: )(0)(: xux UdxxmFxux The first of these conditions simply requires the total population to be conserved. The second condition is obtained by integrating the previous formula for the density u(x). It can be used to determine F and the region where u(x) 0 by viewing it as a constraint an。作為一個本科生，由于經驗的匱乏，難免有許多考慮不周全的地方，如果沒有導師的督促指導，同學的支持鼓勵，想要獨自完成這個論文是相當困難的 . 在這里，我要感謝我的導師陶有山老師 .老師平日里工作繁 忙，但在我做畢業(yè)論文的每個階段，從論文開題到查閱資料，中期檢查，后期撰寫與修改等整個過程中都給予了我悉心的指導 .一絲不茍的工作作風，求真務實的態(tài)度，踏實的鉆研精神，不僅授我以文，而且教我做人，雖僅歷時數月，卻給我受益無窮 . 在此表達對陶老師的衷心感謝！ 最后感謝東華大學四年來對我的栽培，同時我也快樂地度過了本科四年的學習生活 . 具適應性的人口疏散模型的 整體解 26 原文及譯文 Random dispersal versus fitnessdependent dispersal Robert Stephen Cantrell Chris Cosner Yuan Lou Chao Xie This work extends previous work (Cantrell et al., 20xx [9]) on fitnessdependent dispersal for a single species to a twospecies petition model. Both species have the same population dynamics, but one species adopts a bination of random and fitnessdependent dispersal and the other adopts random dispersal. Global existence of smooth solutions to the timedependent quasilinear parabolic system is studied. When a single species has a strong tendency to move up its fitness gradient, it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution (Cantrell et al., 20xx [9]). For the twospecies petition model, if one species has strong tendency to move up its fitness gradient, such approximately ideal free dispersal is advantageous relative to random dispersal. Bifurcation analysis shows that two peting species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate. 1. Introduction This work extends our previous work [9] on fitnessdependent dispersal for a single species to a twospecies petition model, with one species adopting a bination of random and fitnessdependent dispersal and the other adopting random dispersal. 具適應性的人口疏散模型的 整體解 27 The model we considered in [9] has the form ? ?? ? ? ?? ?? ???? ???????????? 0, ,nuxfuu uxufuxfuuu t ?? ?? () Where ? ???? ,0R , and ? ? ? ? uxmuxf ??, () The function u(x, t) represents the density of a single species with random diffusion coefficient μ, and α measures the tendency of the species to move upward along the gradient of the fitness of the species, measured by f (x, u). We assume that μ is a positive constant and α is a nonnegative constant. Ω is a bounded region in RN with boundary ?Ω, and n denotes the outward unit normal vector on ?Ω. Throughout this paper we assume that m ∈ C2,γ (Ω) for some γ ∈ (0, 1) and m is positive somewhere in Ω, and u(x, 0) is continuous, nonnegative and not identically zero in Ω. We briefly summarize some of the main results in [9] as follows: ? (Global existence in time) Suppose that μ 0 and α _ 0. Then () has a unique solution u ∈ C2,1(Ω (0,∞)) ∩ C(Ω [0,∞)). ? (Existence of positive steady state) If u = 0 is linearly unstable, then () has at least one positive steady state. Note that if _Ω m 0, u = 0 is linearly unstable for any μ 0 and α _ 0. ? (Global attractor) If m 0 in Ω, then for large α/μ, () has a unique positive steady state which is also globally asymptotically stable. To study the evolution of dispersal, a mon approach, initiated by Hastings [24] for reaction– diffusion models, is to consider models of two populations that are ecologically identical but use different dispersal strategies. In general, using such a modeling approach would lead to a system of the form ? ?? ? ? ?? ?? ?? ? ? ?? ????????????????????????????????0,),(),(,nvuxguunvuxfuuvuxvfvuxgvvvvuxufvuxufuutt???????? () where f is as in (), and g represents part of an alternate dispersal strategy. For example, g = 0 具適應性的人口疏散模型的 整體解 28 would correspond to unconditional dispersal of anisms by simple diffusion, g = m would correspond to advection up resource gradient witho