Ecologists often use models as a way of exploring natural systems. Some commonly

Question

Ecologists often use models as a way of exploring natural systems. Some commonly used models form the framework of much of this investigation. For example:

a. What are the common features of all of these models, and how do they relate to our understanding of the population growth process?

b. Inter and intra-specific interactions are fundamental components of ecological systems. How are such interactions expressed in the models?

c. Identify the terms in the EXPANDED RIGHT HAND SIDES (column 3 of table) of each of the model equations that represent DENSITY DEPENDENT INTERACTIONS (inter-specific or intra-specific) and explain them

For example, explain in the competition model has three terms on the expanded right hand side: rN, rNN/K1, and raNM/K1 . For each of these terms, identify whether it represents

1) interspecific interactions,

2) intraspecific interactions, or

3) something else, and why you think so.

Do this for each of the items on the expanded right hand side of each model

Differential Equation Expanded right hand side of Model equation Exponential growth diNld rN EdNld rNO-NIKO N-rNNIK Logistic growth Predator-Prey TrNO-ao/r) FrN aNO Competition

Explanation / Answer

a) All the different models give biologists an idea about the population and growth of a particular species of plants or animal. These mathematical models generate testable predictions and help biologists distinguish the pattern they see in nature and different mechanisms that may cause these patterns. They also provide a way to design and evaluate protocols to manage and control animal populations, natural resources (e.g., forests), wildlife resources (e.g., fisheries, deer population), and infectious diseases.

b) Interspecific interactions is the relationship between different species that results in better growth,reproduction or survival for atleast one species involved in the interacion without negatively affecting the other species. This type of interactions can be shown by commensalism,mutualism and a little by predator prey relations. Competition model shows both intraspecific and interspecific interactions. Intraspecific interactions is the rlationship between members of same species who compete for limited resources. This leads to a reduction fitness for both individuals.

c)Exponential growth - rN represents rate of increase in population size , intraspecific interaction as it happens within the species.

Logistic growth - rNN/K represents the total incease in population to the total carrying capacity of population.

Intraspecific interaction

Predator prey - N represents number of prey, O represents number of predators, a and b represents parameters describing interactions of two species.

Competitive - N represents population 1, M represents population 2, a represents effect of species 1 on 2, b represents effect of species 2 on 1,K 1 represents maximum carrying capacity of species1 , K2 represents maximum carrying capacity of species 2. Show interspecific and intraspecific interactions.

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