Tree and Stand Dynamics:

Unravelling the Different Effects

Of Site and Competition

The impossible dream

or an agenda for more research?

I first became interested in this question in the early 1990s when the BC Provincial Government introduced silviculture policies designed tp ensure that those with licenses to cut timber on public lands took responsibility for the non-commercial thinning of regenerated over-dense stands on public lands as part of their license obligations. Debate ranged around the issue of What is over-dense? This issue was particularly acute when it came to lodgepole pine and its tendency to manifest decreases in (dominant) tree height growth with increases in density. Clearly the traditional approach to dealing with site productivity using site index looses its foundation under such circumstances it can no longer be assumed that dominant trees are even relatively unaffected by competition. A series of adjustments are needed to set this straight, but these are just band-aids on a much deeper problem the arbitrary way in which the effects of site versus competition are partitioned in standard growth models, particularly those that use site index.

Since conceiving of this problem in the early 90s I have continued to struggle with it. In 2000 I returned to UBC to work on this as a PhD thesis in the hopes that I might make better progress. Progress has been slow or non-existent, although I like to think that I am beginning to explain the problem in a way that others can understand and think worthy of pursuing. It is for this reason that I am making this presentation to stimulate your thoughts to find out if you have any ideas of your own that might contribute to resolving the issue or - to find out if you know of someone who has similar interests. For my own part I can tell you the experience of trying to deal with the problem has been frustrating, but I also continue to believe that it is important enough to continue pursuing. I am interested to hear what you think in regards to its importance and in regard to any solutions that you may have in mind.

Ian S. Moss

forestree@shaw.ca

Outline

Explore some issues and questions relating to site, competition and the development of tree height and diameter with time.Use a systems view to illustrate how we might begin to address the issues.Draw some conclusions.Focus on growth, not mortality.

Issues Needing A Better Explanation In Growth Models

Weyerhaeuser effect coastal Douglas-firSmall vs. large tree dichotomy Height repression lodgepole pineMixed species / uneven-aged interactionsHeight and diameter responses to thinning

Our concepts of site index as an indicator of productivity and how it is used in defining competition are at the centre of these issues.

This discussion is motivated by the need for better explanations of how trees grow in relation to the above mentioned phenomena.

A Fundamental Question

Is site index a biologically meaningful concept or an overly-simple, yet convenient solution to a complex problem?

If it is the latter

we have much more work to do

What is the true biological relationship between individual tree height, diameter

and age?

How much of what we think is due to competition is due to within site, productivity variation?

This is difficult to answer unless the effects of competition are explicitly accounted for in our assessment of productivity - rather than simply assumed away as is necessary to justify the notion of site index.

Tree height, including maximum tree height is best explained by diameter in combination with at least 1 additional variable perhaps age or height to live crown.

Is height growth in fact stimulated by increased competition up to a maximum?

The challenge in answering these questions

Would such a stimulation effect operate through changes in crown characteristics?

To illustrate the point lets look at some time series data.

To develop a systems view using a minimum number of variables and equations.

Six trees are represented in terms of their height (y-axis) and diameter (x-axis) development. They represent 70 to 80 year old coastal Douglas-fir growing on the southern end of Vancouver Island. Trees were selected from a 1/10th hectare plot so as to represent the range of diameters in the stand. Stem analyses was done on each of the 21 disks using x-ray densitometry. Tree heights were (roughly) estimated for each year of growth (each year is represented by a red dot). The diagram illustrates that height tends to increase with diameter and increasingly so when the tree is suppressed (1 star, light blue line). In more open grown conditions (two stars, dark blue line) heights are much lower for a given diameter as expected. The shapes of the height versus diameter curves tends to be sigmoid for more open grown trees, becoming more linear with increased competition.

In this graph the same trees are illustrated this time in terms of height (y-axis) versus age (x-axis). On one hand this graph seems to support the idea of site index if the lines were shifted so that they more nearly lay on top of one another. Conversely, this graph may be used to suggest that increasing levels of competition actually stimulate height growth up to a maximum (single star light blue line). This latter interpretation would provide an explanation for the Weyerhaeuser effect, which well come back to in a minute.

This graph illustrates tree diameter (y-axis) versus age (x-axis). Tree diameter tends to develop more quickly at early stages of growth, slowing at later stages, with the rate of development being proportional to the degree of competition. In summary one alternative description of tree height development, relative to site index, would include the following statements

Tree Height Development

Height is strongly related to diameter.There is a maximum height given diameter.With increasing levels of competition, height growth may in fact be stimulated.Perhaps it is necessary to integrate the effects of both site and competition into one equation involving height, diameter and age.

So What?

We need to develop and test a model that encompasses these phenomena.The fundamental criteria of whether or not such a model is better than ones already in existence is:

- The degree to which it addresses more completely the issues and questions that were introduced at the beginning, with a minimum number of variables, parameters and functions.

The Weyerhaeuser Effect:How Might This be Explained?A system of equations

ht = f(dbh, hlc)dbh = f(age, ht, hlc, site)hlc = f(ht, baph)mortality = f(baph, dbh)

dbh

ht

hlc

tph / surv

++

++ , max ht | dbh

++

Tree and stand dynamics a systems point of view.

W

site

productivity

+

baph

-

-

Time interactions

S

+

++

+

+

+, self shading

Here is a systems view of one such model. A systems view encompasses positive feedback and so too negative feedbacks that cause a system to remain within certain (narrow height and diameter) boundaries. We are concerned with accurately describing tree and stand attributes through time. The challenge is to find the best explanation one that provides the most complete explanation of stand dynamics as it relates to the issues and questions discussed at the beginning of this talk.

+, ++ and - are used to indicate that following from an increase in one variable, the rate of change in the response variable is either increased (+), substantially increased (++) or decreased (-). W is used to indicate where an explanation may be found for the Weyerhaeuser effect. Increased levels of competition, increases the height to live crown, that in turn stimulates height growth. Due to the positive feedback in the system, diameter increment is also stimulated. Due to the negative response of diameter to increases in height to live crown, diameter growth is less than what it otherwise would be, leading to an overall increase in height-to-diameter ratios. When carried to its logical extent, height suppression occurs where there is a lack of mortality in dense stands, resulting in rapid basal area development that in turn stimulates height height-to-live-crown and height growth, but suppresses diameter growth. As a result trees quickly approach the maximum height given (a small) diameter.

dbh

ht

hlc

tph / surv

++

++, max ht | dbh

++

Tree and stand dynamics an alternative systems point of view.

site

productivity

+

baph

-

-

Time interaction

S

+

+

+

X

Here is an alternate view, where changes in height are governed by age instead of height to live crown. Dbh is is simply governed by height and height to live crown. Note that competition now reduces dbh as a result of increases in height-to-live crown, that in turn would have to be compensated by increases in height with age. There is no possibility of stimulating height growth through effects of competition due to removal of the previously included height stimulation through the height-to-live crown. If the time interaction between height and diameter is removed (X) then this diagram perhaps corresponds more closely with more conventional models of tree and stand dynamics.

Conclusions

The time has come the Walrus said to explore alternative explanations (models) of how site and competition influence tree and stand development patterns.Although not discussed multi-level or hierarchical modelling is an important tool in this process.Based on my experience so far, finding a system of equations to complete the systems view remains a challenge.

Thank you

Thanks for taking the time to listen

0

100

200

300

400

500

BHAGE

0

1000

2000

3000

4000

5000

BHTCM

PL

FD

SP

0

50

100

150

DBHOB

0

1000

2000

3000

4000

5000

BHTCM

PL

FD

SP

Douglas-fir Plot 1

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

age

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

13.00

14.00

15.00

16.00

17.00

18.00

19.00

20.00

21.00

22.00

23.00

24.00

25.00

26.00

27.00

28.00

29.00

30.00

31.00

32.00

33.00

34.00

35.00

36.00

37.00

38.00

39.00

40.00

41.00

42.00

43.00

44.00

45.00

46.00

47.00

48.00

49.00

50.00

51.00

52.00

53.00

54.00

55.00

56.00

57.00

58.00

59.00

height

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

50 Years

bh

age

30 m ht

*

**

***

Height

vs

Age

Douglas-fir Plot 1

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

age

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

13.00

14.00

15.00

16.00

17.00

18.00

19.00

20.00

21.00

22.00

23.00

24.00

25.00

26.00

27.00

28.00

29.00

30.00

31.00

32.00

33.00

34.00

35.00

36.00

37.00

38.00

39.00

40.00

41.00

42.00

43.00

44.00

45.00

46.00

47.00

48.00

49.00

50.00

51.00

52.00

53.00

54.00

55.00

56.00

57.00

58.00

59.00

dbh

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

**

*

***

Dbh

vs. age

Douglas-fir Plot 1

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

32.00

34.00

36.00

38.00

40.00

42.00

44.00

46.00

48.00

50.00

52.00

54.00

56.00

58.00

dbh

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

32.00

34.00

36.00

38.00

40.00

42.00

44.00

46.00

48.00

50.00

52.00

54.00

56.00

58.00

height

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

30 cm

dbh

30 m ht

*

**

***

Height

vs Dbh