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Lab 1: Population Growth Practical Matters Practical
• Before lab, read the chapter, notes, and Before lab read questions. Review. Show up prepared, e.g., with a list of relevant equations. with • Class exercises: good to keep and study from; completion will count toward grade from; • Questions that will be graded are on Blackboard (Assignments, Course Documents) Blackboard Today Today Exercises 1.1, 1.2, 1.3 We’ll all work together, more or less Help others when you are done Show me your work before you leave at Show
the end the Answers to the Blackboard lab homework Answers questions (typed!) due at the beginning of next week’s lab meeting next Population Growth Population “Growth” could be negative; populations Growth”
can shrink; that’s how they go extinct can Growth determined by 4 factors: • Birth (+) • Death () • Immigration (+) • Emigration () Growth, cont. Growth, N(t+1) = N(t) + B – D + I – E This is our most basic model equation Models discrete time steps Models discrete Interested in continuous time growth? Interested continuous Although it’s very nifty, we won’t work with it in this class. See pp. 2627 for a short overview. this N(t) N(t) Assume no migration (I and E both =0) both N(t+1) = N(t)R
N(t) = N(0)Rt R = s (survivorship) + f (fecundity) In an annual species, all die after reproducing In so s = 0 and R = f. In a longlived species, s is greater than 0 and In less than 1. less R R > 1, population increases 1, R < 1, population decreases 1, R = 1, population remains stable 1, How do we find R? N(t+1) = N(t)R N(t+1)/N(t) = R Calculate for each pair of data points Over a long time period, you will actually Over
find an average R You are finding a geometric mean – not an You arithmetic mean (populations grow geometrically not arithmetically) geometrically To average R – multiply all values and find To the nth root (e.g., for 6 values, find the 6th root). root). Example Example
Year 1989 1990 1991 1992 1993 1994 1995 N R = N(t+1)/N(t) 100 N/A 116 139 160 191 225 270 1.16 1.2 1.15 1.19 1.18 1.2 Each R = N(t+1)/N(t) Each N(t+1)/N(t) Average R = Average
(1.16*1.2*1.15*1.19* (1.16*1.2*1.15*1.19* 1.18*1.2)^(1/6) Other ways to find R You may need to adjust R if your data was You
not taken at equal time steps. N(t) = N(0) Rt So, if you have data from 1995 and 1990 N(1995) = N(1990)R5 Giving you the annual intrinsic rate of increase. When you are comparing R values, you want to When
make sure that they are over the same time period. period. Other Rrelated Matters
• Remember: N(t)=N(0) x Rt • Doubling Time: N(t)=N(0) x Rt is equilavent to Rt=N(t)/N(0); doubling means that N(t)/N(0)=2 or that Rt=2; to solve for this, we need natural logs, i.e.: tdoubling = ln(2)/ ln(R) (See pp. 1213 for more details) How would we find tripling times, quadrupling times, etc.? ...
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 Spring '10
 HOLLINGSWORTH
 Mean, population growth Population

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