1 Human Influence on Predator-Prey 2 Relationship: Red Panda and Snow 3 Leopard 1 4 Jagat Kafle 1 5 Pokhara, Nepal 6 Corresponding author: 1 7 Jagat Kafle 8 Email address: jagatkafl
[email protected] 9 ABSTRACT 10 This paper is a mathematical model based upon the human influence on the predator-prey relationship 11 between Red Panda and Snow Leopard, which are the major species in the mountain ecosystem. It 12 explores if these species get extinct in a certain area due to imbalance in their interaction. First, simple 13 model of the species is discussed with no interaction between the species. Interactive model is then 14 introduced to simulate their population when they interact with each other. The human influence is then 15 introduced to the interactive model to observe if the species get extinct. The data in this paper are 16 approximated for a certain area based upon the population density and habitat of the two species. All the 17 models are simulated in python programs using Euler’s method. 18 LIST OF VARIABLES 19 u(t) : Population of Red Panda at time t 20 v(t) : Population of Snow Leopard at time t 21 t : time, in months du 22 : Change in population of Red Panda with time dt dv 23 : Change in population of Snow Leopard with time dt 24 k : Carrying capacity of the land area for a given population 25 α : Population increase rate of Red Panda [per month] 26 δ : Population decrease rate of Snow Leopard [per month] 27 β : Interaction constant of Red Panda and Snow Leopard [per month] 28 γ : Interaction constant of Red Panda and Snow Leopard [per month] 29 σ : Decrease in Red Panda population per month due to Human Influence 30 θ : Decrease in Snow Leopard population per month due to Human Influence PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.27896v1 | CC BY 4.0 Open Access | rec: 13 Aug 2019, publ: 13 Aug 2019 31 INTRODUCTION 32 Red Panda (Ailurus fulgens) are native to the Himalayas and Southern China.