Math  /  Calculus

QuestionProblem 1: Multi-species Flocks Ph.D. candidate Jenny Muñez studies multi-species bird flocks in the Colombian Andes. She surveys birds from two species (species 1 and species 2) counting the number of birds every 50 m of elevation gain of along an elevational gradient starting at an altitude of 100 m and ending at 400 m . Her data is given in the following table and plot: \begin{tabular}{c|c|c} \begin{tabular}{c} Elevation \\ ee \end{tabular} & \begin{tabular}{c} \#Species 1 \\ N1(e)N_{1}(e) \end{tabular} & \begin{tabular}{c} \# Species 2 \\ N2(e)N_{2}(e) \end{tabular} \\ \hline 100 & 2.32 & 0.64 \\ 150 & 30.84 & 7.37 \\ 200 & 15.88 & 13.95 \\ 250 & 7.21 & 14.61 \\ 300 & 3.88 & 18.53 \\ 350 & 1.02 & 17.22 \\ 400 & 1.94 & 18.14 \\ \multicolumn{3}{c}{Δe=4001002=50\Delta e=\frac{400-100}{2}=50} \end{tabular} A. Use Riemann Sums to approximate the Niche size of species 1 (Blue) and species 2 (Orange) by approximating the following two definite integrals (show your calculations):
Niche Size Species 1: 100400N1(e)debN1(ei)Δe\quad \int_{100}^{400} N_{1}(e) d e \approx \sum^{b} N_{1}\left(e_{i}\right) \Delta e Δe=50\Delta e=50

Studdy Solution
The approximate niche size of Species 1 is 3154.5\mathbf{3154.5}, and the approximate niche size of Species 2 is 4523.5\mathbf{4523.5}.

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