PRINCIPLES OF ECOLOGY
PRINCIPLES OF ECOLOGY BIOL 570
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Date Created: 10/26/15
The Art of Theoretical Ecology Lecture 2 Kevin Higgins Biological Sciences University of South Carolina August 26 2008 What is a theory What is the relationship of ideas or principles to empirical data in science What is an ecological principle Give an example What is a hypothesis What is a model Why are models important Is a model the same thing as a theory Why is mathematics used to state ideas in science What is the role of statistics in science 1 What is a theory 2 What is the relationship of ideas or principles to empirical data in science 3 What is an ecological principle Give an example 4 What is a hypothesis 5 What is a model Why are models important 6 Is a model the same thing as a theory 7 Why is mathematics used to state ideas in science 8 What is the role of statistics in science What Do Theorists Do Introduction to Theoretical Ecology Peter Yodzis 1989 Simplify the vast complexity of nature by abstracting out certain essential features modeling that the theorist regards as essential Deduce the consequences of these assumptions Compare these consequences with observed data to look for patterns in the data Purpose of a Model Introduction to Theoretical Ecology Peter Yodzis 1989 A model is not a literal description of some system A model provides a conceptualization representation of the system and its workings so that one can think about the system and understand something of its behavior Reasons for Mathematical Models in Ecology Introduction to Theoretical Ecology Peter Yodzis 1989 Systems being studied in ecology tend to be very complex Mathematics is ideally suited to the expression of complex relationships in a form that makes it relatively easy to examine their consequences In principle one could attempt to do all the same reasoning verbally or in some extraordinarily complicated diagram Mathematics forces one to try to say exactly what one s ideas are and it enables one to find out exactly what their consequences are On the Relation Between Theory and Observation Introduction to Theoretical Ecology Peter Yodzis 1989 Theory sharpens hypotheses pinpointing just exactly which measurements need to be made to test the hypotheses Theory often generates new hypotheses that flow from its inner logic Observations Human population k 8000 Hypothesis Population is growing Observations Human population k 8000 Hypothesis Population is growing linearly in time Observations Human population k 8000 Hypothesis Population is growing exponentially Let us assume that the growth of the human population is proportional to its size dP E rP where P is size 7 is the growth rate and t is time The solution is Pt pert where p is the initial population size Compare Model to Observations Human population Pt p6 1325 4451380860390022t Compare Model to Observations Human population pert 17 00000006 0 0 Human population size 4 4 r 0002 AH r 00014 9 9 r 0001 I r 00005 Hypothesis Rejected Population is growing faster than exponentially C O 3 2 3 D O Q C B E 3 I 858993909 429497e09 214748909 1073741824 536870912 268435456 Compare Model to Observations was zogpert1 0 0 Humans d lt r 0002 A A r 00014 Ho r 0001 I I r 00005 134217728 0 Dungeness Crab Observations A U 395 C 5 O Q q 0 U C 2 E v C O 1 U U Q U L O U U a C d O C 5 D f M 01 i N D i L 01 i L D i 01 Fort Bragg Eureka and Crescent City Brookings Gold Beach Coos Bay and Winchester Bay Newport and Depoe Bay Tillamook and Garibaldi Astoria and Warrenton Grays Harbor Willapa Bay A xv 7 A 0 1 950 1 960 Northern Ports O5 Tillamook Newport Astoria Grays Harbor U l b gt F D C a 395 C 2 3953 3 Q C Q 395 2 U U U 1 970 1 980 Year Southern Ports r a W y Mm MM 0 x i x x 1950 1960 1970 1980 1990 Year k J O Fort Bragg Eureka Crescent City Brookings Gold Beach Port Orford Coos Bay Winchester Bay 01 h 03 N gt I cn a 396 c o 1 g s o o o 396 2 as o I L Hypotheses Population is constant Population is growing linearly Population is growing exponentially Population is growing some times and declining other times Population fluctuations are caused by internal population forces life history Population fluctuations are caused by environmental forces Population fluctuations may be caused by the interaction between these forces Dungeness Crab Life History Females Age 1 Females Age 2 Females Age 3 F3 Females Age 4 F4 A 57 x O O O 1 v C 0 1d 5 O Q 5 L O U U G C d O C 3 0 Compare Dungeness Crab Model to Data b b M ndp rms 0215 163 1950 1960 Compare Dungeness Crab Model to Data O O O A O x O O O 1 V C 0 4 U 0 Using estimated parameters from Newport and Depoe Bay 89 r r y 1950 1960 1970 1980 Year Supported Hypotheses k Population is constant yes and no Population is growing linearly no Population is growing exponentially no Population is growing some times and declining other times obviously yes Population fluctuations may be caused by internal population forces life history Cannibalism supported Population fluctuations may be caused by environmental forces Population fluctuations may be caused by the interaction between these forces