Browsing by Author "Debalike, Manalebish"

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    Mathematical Analysis of Plant-Herbivore Interaction: With Temporal and Spatial Variations in the Ethiopian Climate
    (Addis Ababa University, 2018-12-03) Debalike, Manalebish; Mitiku, Semu (PhD); Lungu, Edward (Professor); Bewket, Woldeamlak (Professor)
    In ecology, the food chain pyramid suggests that there must be less consumers than their food source. In our case the balance in the population of plants and herbivores should be maintained in the ecosystem. Otherwise, the extinction of one or both population may occur. In the interaction between plants and herbivores that live in the same ecosystem, understanding the conditions in which coexistence equilibrium occurs answers a major question in ecology. In this interaction, plants serve as food for herbivores. Then the livelihood of herbivores highly depend on the availability of plants. Moreover, the abundance of the plant density alone does not guarantee the non-extinction of the herbivore population as they are assumed to reproduce sexually. Plant-herbivore relationship depends also on environmental factors like rainfall, temperature and altitude. Due to global climate change the increase/decrease in temperature and also in rainfall will have an effect on their interaction. Environmental noises both positive (such as putting extra water source for the herbivores, or fencing the land to recover by keeping herbivores away) and negative (such as animal/plant disease) often affect population dynamics. In this study, threshold conditions are obtained for the non extinction of the herbivore population and a trapping region is obtained to ensure coexistence of the population. Moreover, it has been shown that the dynamics of the population is significantly sensitive to the feeding rate and the harvest rate of the herbivore population. It was also found that the environmental noises added to the herbivore population resulted more change in the dynamics than those added to the plant population (food source). Ignoring the environmental noise could make the land management and wild life conservation difficult to maintain their goals. Furthermore, considering periodically changing rainfall and temperature, it has been shown that we can find a trapping region for the coexistence of populations. To validate the results of the mathematical model, real data from the Genale-Dawa river basin in the southern part of Ethiopia, is collected and used. The river basin represents the three major climatic zones of the country, the cool zone, temperate zone and hot lowlands. It is also found that if the temperature and rainfall varies with in 10% there is a possibility of extinction of population. This needs the attention of an environmental conservation people and/or those people who are animal farmers.