On joint subtree distributions under two evolutionary models.
نویسندگان
چکیده
In population and evolutionary biology, hypotheses about micro-evolutionary and macro-evolutionary processes are commonly tested by comparing the shape indices of empirical evolutionary trees with those predicted by neutral models. A key ingredient in this approach is the ability to compute and quantify distributions of various tree shape indices under random models of interest. As a step to meet this challenge, in this paper we investigate the joint distribution of cherries and pitchforks (that is, subtrees with two and three leaves) under two widely used null models: the Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model. Based on two novel recursive formulae, we propose a dynamic approach to numerically compute the exact joint distribution (and hence the marginal distributions) for trees of any size. We also obtained insights into the statistical properties of trees generated under these two models, including a constant correlation between the cherry and the pitchfork distributions under the YHK model, and the log-concavity and unimodality of the cherry distributions under both models. In addition, we show that there exists a unique change point for the cherry distributions between these two models.
منابع مشابه
Maximum Agreement Subtree in a Set of Evolutionary Trees-Metrics and Efficient Algorithms
The maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species. An agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent (under a suitable definition) in all given evolutionary trees. Recently, dynamic programming ideas were used to provide polynomial time algorithms for finding a ma...
متن کاملReconstruction of Evolutionary Trees from Pairwise Distributions on Current Species
Suppose that the evolution of a character possessed by a number of current species is modelled as a Markov random eld on an evolutionary tree. Suppose that for each pair of current species we know the joint probability distribution of the pair of characters possessed by that pair of species. We give conditions under which the evolutionary tree can be reconstructed from knowledge of these pairwi...
متن کاملA JOINT DUTY CYCLE SCHEDULING AND ENERGY AWARE ROUTING APPROACH BASED ON EVOLUTIONARY GAME FOR WIRELESS SENSOR NETWORKS
Network throughput and energy conservation are two conflicting important performance metrics for wireless sensor networks. Since these two objectives are in conflict with each other, it is difficult to achieve them simultaneously. In this paper, a joint duty cycle scheduling and energy aware routing approach is proposed based on evolutionary game theory which is called DREG. Making a trade-off ...
متن کاملiteRates: An R Package for Implementing a Parametric Rate Comparison on Phylogenetic Trees
Patterns of diversification rate variation detected in phylogenetic hypotheses are frequently used to infer historical, ecological, and evolutionary processes. The parametric rate comparison (PRC) is a method for detecting rate variation in trees that models branch lengths as random variables drawn from familiar statistical distributions. iteRates is a library of functions for the R statistical...
متن کاملA Note on the Bivariate Maximum Entropy Modeling
Let X=(X1 ,X2 ) be a continuous random vector. Under the assumption that the marginal distributions of X1 and X2 are given, we develop models for vector X when there is partial information about the dependence structure between X1 and X2. The models which are obtained based on well-known Principle of Maximum Entropy are called the maximum entropy (ME) mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theoretical population biology
دوره 108 شماره
صفحات -
تاریخ انتشار 2016