Team:Tongji China/Demonstrate
Tongji iGEM
Tongji iGEM
Demonstrate
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Situation
Our project aims to control the population of Diptera insects such as mosquitos, which do harm to human health. Among all the Diptera insects, Drosophila melanogaster is the only model creature, which has good methods to culture and operate, so we choose it as chassis to test our design in our project.
It will be great for us to get accurate changes of the whole population in the natural environment to test our system. But in fact, it is almost impossible for us to observe a small group in a specific area due to the lack of equipment and skills. Although Drosophila melanogaster has been regarded as a model creature for a long history, we only find a little published data about population changes of it.
Therefore, building the population growth model can help determine the effect of our system applying to natural environment.
It will be great for us to get accurate changes of the whole population in the natural environment to test our system. But in fact, it is almost impossible for us to observe a small group in a specific area due to the lack of equipment and skills. Although Drosophila melanogaster has been regarded as a model creature for a long history, we only find a little published data about population changes of it.
Therefore, building the population growth model can help determine the effect of our system applying to natural environment.
Model theory
In 1945, Leslie P H. introduced a mathematical method to predict the age structure and number of population with time by using the age structure of an initial population. Here we use Leslie matrix to make our model better.
According to the physiological characteristics of each individual, the maximum life age is divided into M groups, and then the distribution of age at different time will be discussed. The time is also dispersed into t= 0, 1, 2,... The interval is the same as that of the age group. T= 0 corresponds to the initial time.
Suppose, at the beginning (t= 0), the number of individuals in the I age group was Ni (0), i= 1, 2,... M. so the vector is:
a formula should be here
The reproductive rate of the I age group is f i (0) ,i= 1, 2,... M; survival rate was S I (> 0), i= 1, 2,... m - 1. Between two periods, there is an iterative relationship between the number of individuals in each age group ni:
a formula should be here
Make the matrix:
a formula should be here
Here is a part of result shows the differences between the proportions of female flies that can produce normal offspring in two different conditions are shown in Figure 1.
According to the physiological characteristics of each individual, the maximum life age is divided into M groups, and then the distribution of age at different time will be discussed. The time is also dispersed into t= 0, 1, 2,... The interval is the same as that of the age group. T= 0 corresponds to the initial time.
Suppose, at the beginning (t= 0), the number of individuals in the I age group was Ni (0), i= 1, 2,... M. so the vector is:
a formula should be here
The reproductive rate of the I age group is f i (0) ,i= 1, 2,... M; survival rate was S I (> 0), i= 1, 2,... m - 1. Between two periods, there is an iterative relationship between the number of individuals in each age group ni:
a formula should be here
Make the matrix:
a formula should be here
Here is a part of result shows the differences between the proportions of female flies that can produce normal offspring in two different conditions are shown in Figure 1.
It can be seen that in the case of the small mating rate, the inhibition effect of releasing sterile male flies with male-male courtship is more obvious to reducing population quantity, which is consistent with the purpose of our modeling.
Here also shows the result (Figure 2) when the number of modified fruit flies was five times as large as the wild flies and the mating rate is 0.4, the effect on the final population in 15 days. (The yellow line represents the sterile male flies with male-male courtship, and the purple line represents the sterile male flies)
Here also shows the result (Figure 2) when the number of modified fruit flies was five times as large as the wild flies and the mating rate is 0.4, the effect on the final population in 15 days. (The yellow line represents the sterile male flies with male-male courtship, and the purple line represents the sterile male flies)
