Yield-Density Equations

Transcription

1 Yield-Density Equations A General Model of Intraspecific Density Effects

2 Yield-Density Equations Y Y wn N max ( 1+ an ) b Total yield of the population per unit area

3 Yield-Density Equations Y w Y wn N max ( 1+ an ) b Total yield of the population per unit area average yield of an individual

4 Yield-Density Equations Y w N Y wn N max ( 1+ an ) b Total yield of the population per unit area average yield of an individual population density

5 Yield-Density Equations Y w N max Y wn N max ( 1+ an ) b Total yield of the population per unit area average yield of an individual population density maximum individual yield under conditions of no competition

6 Y w N Yield-Density Equations max Y wn N max ( 1+ an ) b Total yield of the population per unit area average yield of an individual population density maximum individual yield under conditions of no competition 1/a density at which competitive effects begin to become important

7 Y w N Yield-Density Equations max Y wn N max ( 1+ an ) b Total yield of the population per unit area average yield of an individual population density maximum individual yield under conditions of no competition 1/a density at which competitive effects begin to become important b resource utilization efficience (i.e., strength of competition)

8 The Two Faces of Yield-Density Y wn N max ( 1+ an ) b Total Yield Individual Yield Y N max ( 1+ an ) b wn X XN max ( 1+ an ) b

9 The Two Faces of Yield-Density Y wn N max ( 1+ an ) b Total Yield Individual Yield Y N max ( 1+ an ) b w max 1 ( + an ) b

10 Three General Categories of Yield- Density Relationships Y wn N max ( 1+ an ) b b < 1 : under compensation b 1 : exact compensation ( Law of constant yield ) b > 1 : over compensation

11 Three General Categories of Yield- Density Relationships Y wn N max ( 1+ an ) b b < 1 : under compensation b 1 : exact compensation ( Law of constant yield ) b > 1 : over compensation

12 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b C Y N max ( 1+ an ) Total Yield Density 10 Y N ( N ) for an>>>1 Y N x max ( 1x + anx ) Y max C a

13 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Average Individual Yield w 10 ( N ) log transform log( w ) log( max ) -blog(1 + an ) Density

14 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Average Individual Yield /a à density above which competitive effects become important w 10 ( N ) w max 1 ( + an ) b log transform log( w ) log( max ) -blog(1 + an ) Density

15 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Average Individual Yield w 10 ( N ) slope b w max 1 ( + an ) b log transform log( w ) log( max ) -blog(1 + an ) Density

16 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Total Yield Average Individual Yield Density Density Y xn max ( 1x + anx ) for an>>>1 w max 1 ( x+ an )

17 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Total Yield Average Individual Yield Density Density Y» a max for an>>>1 w» an max

18 Y N max ( 1+ an ) b Exact Compensation (b1) w max 1 ( + an ) b Total Yield Average Individual Yield Density Density Y C a» max for an>>>1 w» max an C N

19 Y N max ( 1+ an ) b Under Compensation (b<1) w max 1 ( + an ) b b 0 b 0.25 Total Yield b 0.5 b 0.8 b 1 Average Individual Yield Density Density

20 Y N max ( 1+ an ) b Under Compensation (b<1) w max 1 ( + an ) b Total Yield b b 0.25 b Density b 0.8 b 1 Average Individual Yield Density Density b 0 b 0.25 b 0.5 b 0.8 b 1

21 Y N max ( 1+ an ) b No Density Effects (b0) w max 1 ( + an ) b b b 0 Total Yield Average Individual Yield Density Density Density

22 Y N max ( 1+ an ) b Over Compensation (b>1) w max 1 ( + an ) b Total Yield Density b 1 b 1.2 b 2.0 Average Individual Yield Density b 1 b 1.2 b 2.0

23 Possible Interactions Species 1 à Species Species 2 à Species Mutualism Commensalism Herbivory/ Parasitism/ Disease Neutral Ammensalism/ Allelopathy Competition

24 Competition between different species Light Space Potentially assymetrical! H20 Nutrients Space

25 Possible Interactions Species 1 à Species Species 2 à Species Mutualism Commensalism Herbivory/ Parasitism/ Disease Neutral Ammensalism/ Allelopathy Competition

26 Experimental Studies of Competitive Interactions

27 The Design Matrix Density of species j Density of species i

28 The Design Matrix Treatment combination indicating densities of both species i and j

29 The Design Matrix

30 Commonly Used Designs Partial Additive Replacement Series Additive Complete Additive

31 The Partial Additive Design Competitor Target species

32 The Partial Additive Design Commonly used design to study the impact of weeds on a crop plant

33 The Partial Additive Design Yield drops as density of competitor increases

34 The Partial Additive Design

35 Problems with the Partial Additive Design Target species only studied at one density Effects of density confounded with a change in the ratio between the two species Density Ratio :1 Species :2 50 0:1 100 Species 1

36 The Replacement Series Design Density is fixed Ratio of two species systematically altered

37 The Replacement Series Design Treatment 1 Treatment 2 Treatment 3 Treatment 4 Treatment 5 Treatment 6 Density 5 Species 1 Species 2

38 Monoculture Experiments as a Control

39 Replacement Series Experiment Monoculture treatment

40 Replacement Series Experiment Monoculture treatment Competition treatment Impact of Competition

41 Replacement Series Experiment Monoculture treatment Competition treatment Impact of Competition

42 Replacement Series Experiment Monoculture treatment Competition treatment Avena fatua has a large competitive effect A. barbata has little competitive effect

43 Replacement Series Experiment Assessing the interaction Monoculture treatment Competition treatment Total yield in treatment

44 I J Additive Competitive Effects

45 Additive Competitive Effects I J I > J

46 Additive Competitive Effects I J I > J I < J

47 Non-Additive Competitive Effects Combined effects of competition have a greater negative effect than when plants are grown alone Species i has a bigger effect on species j than it has on itself Species j has a bigger effect on species i than it has on itself

48 Non-Additive Competitive Effects Combined effects of competition are less in combination than when plants are grown alone Both species impact themselves more than their competitor does

49 A Non-Additive Example Relative yield total Sum of yields in competition Sum of yields in monoculture

50 A Non-Additive Example

51 A Non-Additive Example

52 Predicting the Outcome of Competition Log (Output 1 /Output 2 ) Before competition Log (Input 1 /Input 2 )

53 Predicting the Outcome of Competition After competition Log (Output 1 /Output 2 ) Log (Input 1 /Input 2 )

54 Predicting the Outcome of Competition yx Log (Output 1 /Output 2 ) Log (Input 1 /Input 2 )

55 Predicting the Outcome of Competition Log (Output 1 /Output 2 ) New Input Ratio Log (Input 1 /Input 2 )

56 Predicting the Outcome of Competition etc. This is a process called cobwebbing. Log (Output 1 /Output 2 ) Log (Input 1 /Input 2 )

57 Predicting the Outcome of Competition Coexistence Log (O Panicum /O Glycine ) Extinction of Glycine Log (I Panicum /I Glycine )

58 Replacement Series Experiment Monoculture treatment Competition treatment Problem?

59 Extending the Replacement Series Approach Inclusion of more densities provides more information In this example: competitive effects on A. fatua increase as overall density increases

60 Extending the Replacement Series Approach The outcome of competition changes with density. Not an ideal technique for predicting the outcome of competition