مقالے کی معلومات
جلد
شمارہ
مقالے کی قسم
زبان
تلخیص
The paper attempts to briefly review the methods of random number generation and such numbers from some commonly used probability distributions such as Normal, Binomial and Poisson distributions in biological and particularly in ecological work. Besides, Monte Carlo simulation theory is briefly introduced. The Monte Carlo simulation is applied to i) Genetic drift and ii) Random walk models of predator-prey interaction. Simulation of genetic drift is accomplished for haploid and diploid populations. In addition, genetic drift is also examined together with mutation. For a high mutation rate an example of peppered moth Bistson betularia is chosen in which mutation occurs from typical form c (typica) to C (carbonaria).Computer programs were developed for linear congruential and multiplicative congruential methods of random number generation and the two methods were tested and compared. Both linear congruential and multiplicative congruential methods of random number generation gave almost equally good results in terms of period length, uniformity of distribution and with regard to other tests of randomness. Monte Carlo simulations of genetic drift for both haploid and diploid populations showed that smaller population size showed marked fluctuations and greater number of fixation (as well as loss) of alleles either A or a. Genetic drift scenarios incorporating high mutation rate (0.041) gave upward trends of increasing frequency of carbonaria C gene with increasing number of generations suggesting predominance of carbonaria population with the passage of time. These results support the field studies. The random walk model of predator-prey interaction involves random movement of predator (random walk) on a square grid having a prey population (N ≥ 100 ) where they search, encounter and capture (or fail to capture) the prey. These stochastic events are simulated through a Monte Carlo technique suggested earlier with modifications. The method involves defining an r r grid that contains the uniformly distributed prey population. The predators (a few in number) walk over the grid randomly feeding on the prey when encountered and captured. It is assumed that the predator is unable to capture and eat all of them in a cell. Each prey has a certain probability of escape or hiding from the predator. The probability of capture PC is fixed at the beginning. Furthermore, the maximum consumption of the predator in one cell (Cx ) is also fixed prior to simulation. The predator is allowed to move on the grid in all four directions of movement with equal probability. When the maximum time units of the simulation are completed, average and standard deviation of both encounter and consumption are computed for each of the K predators. The simulations gave some interesting results with regard to encounter, consumption and escape of prey. The random walk stochastic model given here is certainly an improvement over the deterministic model since the former captures a number of stochastic events involved in the process beginning with the movement of predator to the encounter,capture (or escape) and consumption of the prey.
S. Shahid Shaukat, Asma Zafar, Noreen Noor, Moazzam Ali Khan. (2020) RANDOM NUMBERS AND MONTE CARLO SIMULATION: APPLICATIONS IN GENETIC DRIFT AND RANDOM WALK MODELS OF PREDATOR-PREY INTERACTION, , Volume 17, Issue 2.
-
Views
532 -
Downloads
49