The Science of Forestry

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The Science of Forestry

• Boris Zeide
• zeide_at_uamont.edu
• Professor of Forestry
• School of Forestry
• University of Arkansas at Monticello

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30 Years Ago
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Two Is Between the Extremes

• Of many (all) points on a curve
• and
• One

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What Has Been Done Since Then?

• In 1978
• Two-point method
• Purely an empirical finding
• No theoretical rationale.
• In 2008
• I now understand why this method works.
• As a result, it has become possible to describe
  many other things, including the entire forestry.

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A Fundamental Equivalence

• of points
• of local parameters
• of growth factors
• Equations may contain global parameters or
  constants.

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Reinforcement or Opposition?

• Do the equation terms

each other?
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Empirical Support

• Current annual increment
• first increases, then decreases.
• This fact indicates that factors of growth are
  opposites.

Increment
Age
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Two Sides

• Every complex problem has two opposing sides.
• The key is to recognize both.

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and vice versa

• Many of our errors can be traced to taking one
  side for the whole.
• The rest of my talk is an illustration of these
  simple points.

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A Description of Growth

• A complete, if coarse, description of growth
• where the increase of organism size, dy, during
  an instant of time, dt, is presented as the
  product of influences that facilitate the growth
  and those that check it.

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Growth Expansion

• Basic growth process is
• Unrestricted cell division
• The growth rate is proportional to either
• the number of cells
• or
• the size of an organism

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Complications

• The proportion of living cells decreases
• where k is the coefficient of proportionality
• and p lt 1 is the allometric coefficient
  specifying the diminishing portion of living
  tissue.

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Growth Decline

• Unlimited expansion is checked by aging and
  finite area.
• The simplest assumption is that growth declines
  linearly with age
• where q is the constant rate of decline. This
  module predicts the complete termination of
  growth at age t 1/q. Afterwards, the growth
  would be negative, which is not realistic.

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Adaptation

• The linear growth decline is counterbalanced by
  phenotypic (built-in) adaptation.
• Deceleration of growth decline is proportional to
  the current rate of decline

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Adaptation Growth

• Integration results in a non-linear growth
  decline
• The requirement that . This module can be
  viewed as the sum of the infinite number of terms
  of a Taylor series.

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Combined Model of Tree Growth

• The product of the growth expansion and decline
  modules unites two opposite trends in a model of
  tree growth

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Structure of the Growth Model
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Growth Model Legend
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Empirical Verification

• The equation favored by foresters for growth
  modeling
• It does not look like the derived model.

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Empirical Verification

• Actually, the Richards equation is identical to
  the derived model
• Integration with specific values of the parameter
  p produces the Gompertz (p 1), logistic (p
  2), and Bertalanffy (p 2/3) equations.

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Empirical Verification

• In the Richards equation
• a, b, and c are

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What Does the Identity Tell Us?

• The biological processes and their analytical
  forms have substance.
• The success of the empirical equations, reflects
  the fact that they unwittingly express the basic
  processes of growth.
• While the processes infuse meaning into the
  empirical equations, the equations give shape to
  the processes, making them tangible and
  operational.

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Why Are Two Points Sufficient?

• Because those opposites are related.
• Out of three parameters of the Richards equation,
  only two are independent.
• Parameter c is global. It is determined by tree
  structure rather than site quality, growth rates,
  or tolerance.

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Growth curves combined at 50 years

• Heights of 36 spruce trees of site class 16.4
  combined at 50 years

Guttenberg, A.R., von. 1915. Growth and yield of
spruce in Hochgebirge. Franz Deuticke, Wien. 153
p.
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Growth curves combined at inflection

• Rescaled heights and ages of 104 spruce trees
  combined at the inflection point

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Shortcoming of Growth Equations

• Growth equations cannot reflect variations in
  stand density.

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Density Module Opposites

• A total lack of competition among trees and full
  availability of resources.
• The extreme competition and density that preclude
  any growth.

The growth model describes the first opposite.
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Density Module Solution

• Given adaptation, the decrease in volume growth,
  -dy', is proportional to the product of volume
  growth and density increase, y'dS, rather than to
  the density increase dS alone
• where S is stand density and m is a parameter.

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Tree Growth-Density Model

• Incorporating the density module into the growth
  model produces a growth-density model describing
  tree growth in stands of any age, size, and
  density

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Stand Growth-Density Model

• Multiplying the volume growth of average tree,
  v, by number of trees produces stand growth
• Stand growth in terms of average diameter, age
  and density

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Forest Management

• The theory outlined above exposes the inner
  mechanisms of forest stand dynamics. It is about
  regularities inferred from past observations.
• In contrast, forest management is active and
  forward-oriented it is prescriptive rather than
  descriptive.

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Two Goals Of Management

• Preserving the environment, and
• Meeting the current and future wood products
  needs of an increasing human population.
• All the diversity of forest management is made of
  various combinations of these two opposite goals.

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Solution Spatial Separation

• Conflicting goals cannot be satisfied at the same
  time and at the same place
• But they can be satisfied in different places.

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Solution Spatial Separation

• Spatial separation reverses the conflict between
  the goals and makes sustainable intensive
  management for wood products a prerequisite for
  the existence of undisturbed forests.

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Maximizing Combined Utility

• Why not combine some use with some conservation
  on the same land?
• Why not thin stands before trees rot?
• Or leave some patches of native vegetation in the
  middle of forest plantations and agricultural
  fields?

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Maximizing Combined Utility

• Because curtailed preservation on the same land
  would detract from both environmental quality and
  production.
• Spatial separation maximizes the combined utility.

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How To Manage For Preservation

• Opposites Restoration ecology versus the
  "hands-off" approach.
• Solution Leave nature alone.

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How To Manage For Preservation

• Nature is the generator and best manager of
  biodiversity. It is counterproductive and
  supercilious to interfere with its eternal work
  of creation and destruction.

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How To Manage Wood Production

• A promising way to preserve nature is to increase
  productivity on the portion of land devoted to
  the second goal of forest management wood
  production.

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How to Manage Wood Production

• Aside from expensive and not-always-rewarding
  site alteration, this can be done by
• minimizing interspecific competition and
• optimizing intraspecific competition.

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Interspecific Competition

• Among the various benefits ascribed to biodiverse
  forests are
• higher productivity,
• beauty, and
• stable dynamics.
• None of these claims is not supported by
  evidence.

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Interspecific Competition

• In fact, interspecific competition is one of the
  most harmful factors of tree life.
• kills many trees
• prevents others from reaching their growth
  potential.
• Interspecific competition should be minimized.

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Intraspecific Competition

• Current consensus
• thinning can redistribute growth from smaller to
  larger stems but not increase its amount
• As long as the site is fully occupied (trees
  making their full use of available resources),
  the species will produce the same amount of wood
  per year at various densities. Whether there are
  many small trees or fewer large trees, a similar
  wood volume is produced
• (Spurr and Barnes 1980 p.376).

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Empirical Basis of Consensus
Langsaeter's curve
Relationship between standing volume and volume
increment by Langsaeter (1941)
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A Problem with the Consensus

• Stand growth is a function of average diameter,
  age and density

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Optimal Density m

• Differentiating this equation with respect to
  density and setting the derivative equal to zero
  allows us to determine the density at which the
  current stand volume growth reaches maximum.

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Optimal And Normal Densities

• m 67839
• For undisturbed permanent plots (control and
  initial measurements) of the Monticello study,
  normal density is 63816
• When the difference in diameter is taken into
  account, the highest growth is observed in stands
  of high, and not medium, density

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Volume Growth and Density

• Relationship between volume growth (m3/ha) and
  current density for loblolly pine stands
• equal age (20 years),
• diameter (25 cm), and
• site index (20 m) (base25 years).

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Sum of Growth Maxima Is Not Maximum

• If volume growth is maximum at the highest
  current density, then this density should
  maximize the total yield over rotation.
• But this inference contradicts forestry
  experience, which tells us that moderately dense
  stands are more productive.

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Inverse Relationship

• An inverse relationship exists between tree size
  and average density.
• Although, at a given moment, normal density does
  produce maximum growth, when it is maintained
  over an extended period, the same density
  suppresses diameter and, as a result, reduces
  volume growth and volume, itself.

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Inverse Relationship

• For this reason, the sum of maxima at each moment
  does not produce the maximum of final harvest.

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Growth-Density Model and Langsaeter's Curve

• Langsaeter's curve bundles the effect of tree
  size together with that of current density. As a
  result, the position of the optimum is misplaced
  toward middle densities.
• The model is not restricted to stands of the same
  age and site as is Langsaeter's curve. It
  includes the terms reflecting these variables and
  is applicable to even-aged stands of any age and
  site.

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Growth-Density Model and Langsaeter's Curve
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Optimization of Stand Density Trajectory

• For centuries, foresters have been searching for
  a single level of optimal density to be
  maintained throughout stand life.
• But nobody has proven that keeping density at 15
  years the same as at 35 years would maximize
  harvest.
• Now the challenge is to find an optimal
  trajectory of current density.

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Conflicting Requirements

• To maximize average tree size, we need the lowest
  density.
• To maximize stand volume growth, we need the
  highest density.
• How do we minimize the negative side of density
  (small size) and maximize its positive side
  (maximum volume of trees with a given size)?

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Resolving the Conflict
Keep the number of trees per unit area constant.

• The number should be the minimum that assures the
  density sufficient to maximize financial returns
  by harvest time.
• Such a prescription can be called the minimum
  number-maximum yield (minimax) strategy.
• Albeit unknown in forestry, it is not new for
  millennia, farmers have grown only the plants
  they intend to harvest.

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Advantages of Minimax

• Besides maximum returns from final harvest,
  minimax has several other benefits
• saving on planting and pre-commercial thinning
• minimization of root rot, insect infestation, and
  other risks associated with high density
• sturdy well-spaced trees with laterally
  symmetrical crowns which reduces damage from ice,
  wind, and other hazards.
• - before the trees close their canopies, up to
  90 of the land can be used for other purposes.

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Disadvantages of Minimax

• Minimax is one extreme.
• It may maximize final yield and profit in theory,
  but it cannot be applied without some compromises
  because of the following problems
• establishment mortality
• the lack of selection
• interspecific competition
• wood quality
• forfeiting intermediate harvest
• rectangularity.

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The Science of Forestry
The Science of Forestry
BasicOpposites
Theory of Forest Stand Dynamics Forest Management
Proximate aim Passive description of what is Active prescription of what should be
Ultimate aim Truth Good
Output General laws Specific forward-oriented actions
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Opposites of Stand Dynamics
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Management Opposites
Forest Management
Preservation
Maximum profit
Action None
Environmental control
Genetic modification
Site
Competition
Interspecific
Intraspecific
Returns
Costs
Action Minimize
Life-long
Action Improve when it pays
Current
High at the end
Low at the beginning
Optimum Maximum
Action Keep the number of trees constant
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Knowledge Means or End?

• Along with practical utility, the science of
  forestry refines research methods.
• Do we use our mind to understand things and
  improve our standard of living
• or
• we study things to clarify our thinking?
• As with much else, science is a synthesis of
  these means and ends.

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THE 1-2-1 METHOD

• It considers two opposite explanations
  simultaneously. The method organizes research
  into cycles containing three basic steps.
• Defining a problem
• Exposing two oppose explanations
• Locating a solution
• The name1-2-1 methodrefers to the sequence of
  one problem, two explanations, and one solution.