Mathematical Analysis of Plant-Herbivore Interaction: With Temporal and Spatial Variations in the Ethiopian Climate
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Date
2018-12-03
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Addis Ababa University
Abstract
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.
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Keywords
Mathematical Analysis, Plant-Herbivore Interaction, Temporal and Spatial Variations, Ethiopian Climate