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1、1,Principle of Maximum Entropy and One of its Applications in Ecology,2,main structure,1. Principle of Maximum Entropy 2. One of its Applications in Ecology,3,1. Principle of Maximum Entropy,What is Entropy ？ It was Rudolf Clausius who first proposed entropy, and applied it in thermodynamics. Later
2、on, Claude Elwood Shannon introduced the concept of entropy into information theory. Entropy refers to the degree of randomness or disorder in a thermodynamic system, and it has important application in cybernetics、 probability theory、number theory、astrophysics、 life science and other fields, differ
3、ent disciplines has lead to more specific definition, and it is a very important parameter in each fields. Shannon entropy If a random experiment have N possible results or a random message have N possible values, theprobabilityoftheoccurrence respectively expressedas then the entropy is defined as,
4、Usually we chose 2，e，10 as bs value .,4,Principle of Maximum Entropy The Principle of Maximum Entropy was first proposed by Jaynes in 1957. It indicates that : In know constraint conditions, the most possible distribution of an unknown events is the one which maximize its entropy .,5,2.One of its Ap
5、plications in Ecology,Shipley, Vile and Garnier developed a quantitative method, using The Principle of Maximum Entropy, to predict how biodiversity will vary across environments, which plant species from a species pool will be found in which relative abundances in a given environment, and which pla
6、nt traits determine community assembly. Thy conducted their study in 12 vineyards that had been abandoned between 2 and 42 years previously, within a 4 by 4 km area of southern France. The aboveground dry biomass of all species in each of four plots measuring 0.25 by 0.25 m was used to estimate rela
7、tive abundances for each site. They measured eight functional traits on 30 species.,6,(1),Once plants are at a site, the biomass(abundance) of each will be proportional to the total amount of resource units that each species is able to capture at that point in time. The total number of such captured
8、 resources at site k at time x, and the number that are captured by each species , defines the abundance structure of the community: . Defining relative abundance as Assume first a strict equivalence of species such that each species is equally likely to disperse and capture resources. There would b
9、e no species sorting and community assembly would be purely random. The number of different ways (W) that the N resource units, comprising the living biomass at a site, could be partitioned into a particular community structure is,7,They adopted the view of community assembly as a process of species
10、 sorting, And species sorting by the environment resulting in changes in species composition over an environmental gradient . Use breeders equation of quantitative genetics we can get,(2),(community-aggregated trait)is the mean value of a quantitative trait j of species i, occurring with proportion
11、at site k in a population of S Species at time x. represent heritability （the slope of a regression of offspring trait values on midparent trait values) and represent the force of selection for that trait at time x:,8,9,using the method of Lagrangian multipliers(拉格朗日乘子变分法), by defining a new system of equations:,partial derivates are set to zero,10,11,Thank you !,
