(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 22854, 511] NotebookOptionsPosition[ 20694, 442] NotebookOutlinePosition[ 22076, 484] CellTagsIndexPosition[ 22033, 481] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Exercises lesson 1", "Title", CellChangeTimes->{{3.4323368555625*^9, 3.4323368600625*^9}}], Cell[CellGroupData[{ Cell["\<\ 1. Lack (1954) showed that in Common Swifts 11%, 61% and 96% of the females \ lay 1, 2 or 3 eggs. The proportion of young that fledge p as a function of \ clutch size C was approximately given as p(C) = 0.84 - (8.0*10^-6)*C^9.45. \ Evaluate graphically and analytically whether the observed clutch size \ conforms to the optimal Lack clutch size that would maximise the number of \ surviving/fledging young. If the mean clutch size is smaller than the \ predicted Lack clutch size, how could this be explained? What factors could \ we have missed in our basic model?\ \>", "Subsection", CellChangeTimes->{{3.432669383328125*^9, 3.43266938340625*^9}, { 3.43267042596875*^9, 3.432670444484375*^9}, {3.432670479796875*^9, 3.43267068290625*^9}, {3.432671107015625*^9, 3.432671129375*^9}}, FontWeight->"Bold"], Cell["\<\ The proportion of young that fledge p as a function of clutch size C :\ \>", "Text", CellChangeTimes->{{3.432669730515625*^9, 3.432669749390625*^9}, { 3.4326698036875*^9, 3.432669804609375*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"p", "[", "C_", "]"}], "=", RowBox[{"0.84", "-", RowBox[{ RowBox[{"(", RowBox[{"8.0", "*", RowBox[{"10", "^", RowBox[{"-", "6"}]}]}], ")"}], "*", RowBox[{"C", "^", "9.45"}]}]}]}], ";"}]], "Input", CellChangeTimes->{{3.4326693878125*^9, 3.432669403015625*^9}, { 3.432669501203125*^9, 3.432669519875*^9}, {3.4326695655625*^9, 3.43266964528125*^9}, {3.43266980771875*^9, 3.43266980803125*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ 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