4. Generalizing the Yield- Density Relationship

5. Empirical Data on Yield Density Relationships

7. Three General Categories of Yield- Density Relationships b < 1 : under compensation b = 1 : exact compensation (“Law of constant yield”) b > 1 : over compensation

8. Exact Compensation (b=1) for aN>>>1

9. Under Compensation (b<1) b = 1 b = 0.8 b = 0.5 b = 0.25 b = 0

10. Under Compensation (b<1) b = 1 b = 0.8 b = 0.5 b = 0.25 b = 0 b = 1 b = 0.8 b = 0.5 b = 0.25 b = 0

11. Under Compensation (b<1)

12. No Density Effects (b=0) b = 0

13. Over Compensation (b>1) b = 1 b = 1.2 b = 2.0 b = 1 b = 1.2 b = 2.0

14. Reassessing the Empirical Evidence What processes lead to this result?

15. Initial Planting Densities Low to High Assessment of Outcome (Yield) Time Plant Harvest ?

16. Glycine max (L.) Merr

17. Day 0 slope ≈ 0 ?

18. Glycine max (L.) Merr Day 12 effects of competition

19. Glycine max (L.) Merr Day 21

20. Glycine max (L.) Merr Day 31

21. Glycine max (L.) Merr Day 45

22. Glycine max (L.) Merr Day 84

23. Glycine max (L.) Merr Day 119

24. Glycine max (L.) Merr Day 119

25. Glycine max (L.) Merr Day 119 Constant Yield slope ≈ -1

26. Glycine max (L.) Merr Day 119 What is the role of individual variability?

27. Individual Development over Time An experiment with Tagetes patula (marigold)

28. Individual Development over Time Age Survivorship Approximately a normal distribution

29. Individual Development over Time Population Density Declines through Mortality

30. Individual Development over Time Lots of small individuals A few large individuals

31. Individual Development over Time A Size Hierarchy Develops over Time

32. Density Effects on the Development of Size Hierarchies

34. Size Hierarchies many small plants a few large plants Reasons for differential rates of growth? Flax

35. Size Hierarchies many small plants a few large plants Flax Microhabitat differences Genetic differences Priority Effects Sources of Differential Growth Rate

36. Priority Effects Androsace septentrionalis L. Northern Rock Jasmine Survival of successive cohorts of seedlings Emergence date (after emergence of 1 st cohort)

37. Priority Effects among Cohorts Androsace septentrionalis L. Northern Rock Jasmine Emergence date (after emergence of 1 st cohort) Day 0 Survival of successive cohorts of seedlings Day 1 Day 2 25% less likely to survive with 2 day delay in emergence

38. Priority Effects among Cohorts Tragopogon heterospermus Schweigg. Sand Goat’s Beard Survival of successive cohorts of seedlings Emergence date (after emergence of 1 st cohort)

39. Dactylis glomerata L. Sweet Orchard Grass Priority Effects among Individuals

40. Dactylis glomerata L. Sweet Orchard Grass Priority Effects among Individuals >1000x size difference depending on emergence date!!!!