Re: OG Definitions and Criteria    Cogbill
   Sep 18, 2002 08:39 PDT 
Dear Bob et al.

    With all the whirlwind on old growth criteria, I feel a bit like
Huckleberry Finn at his own funeral.

    I am flattered several informal and anecdotal criteria suggested long
ago are now considered the "standard", but I'm afraid the original logic and
rigor have been lost, or at least taken out of context. To join the litany
of questions (actually testable hypotheses) on how the "50-50" age criteria
works, or doesn't work: which trees are included (number, species, minimum
size, condition, canopy position, spatial sampling pattern)? how is tree age
determined (field appearance, field-read cores/stumps, core preparation,
crossdated cores, pith date, breast-height recruitment, "corrected",
weighted)?; what are other age determinations (regressions against size,
reciprocal of the mortality rate, site history; canopy residence times,
non-parametric or classes)?; how is the age structure expressed (maximum,
mean, median, distribution parameters such as q or Weibull c shape; all
age-classes present)?; what is the maximum longevity (pathological age,
keyed to local conditions, a confidence interval on the tail of determined
ages, extreme ever documented)?; and what spatial pattern is represented
(stand size, spatial averaging, heterogeneity, broad-scale landscape "age"
structure)?. I'm afraid there is no simple answer, but there is lots wiggle
and research room.

    Much of the motivation for the "50-50" rule of thumb was to get an
simple objective indicator of the question of "how old is old enough"
applicable for a wide range of species and sites. The first approximation
was to use stand median tree age as a logistically efficient and
statistically interesting quantitative parameter. This was put in
perspective by comparing it to a local and conceptually logical constant,
the " maximum longevity". Both empirical data from sampled stands with
known histories and mathematical theory from different stand age
distributions (truncated even-aged, multi-cohort additive; "inverse-J"
thinning; negative exponential or age independent mortality; probability
density functions from Weibull hazard mortality) indicate that the median
age in relation to a theoretical "demi-tile" is an reasonable (and
dynamically responsive) estimator. Note that the theoretical maximum is
indeterminate (mathematically, not biologically), so that a statistical
parameterization of empirical samples must be used to estimate the "maximum
longevity". Thus two independent concepts have been combined: median tree
age is a good estimator for stand age structure and the "old" reference
curve is keyed to the observable maximum. The index was originally proposed
in its rudimentary form in 1982 (Maine Critical Areas Old-Growth Report, by
Anonymous) and later elaborated in 1996 with reference to the principles and
empirical data from red spruce stands (Spruce chapter by myself in the
Eastern Old-growth Book) with a conclusion of "In theory as well as in
practice, a median age of half the maximum longevity is a good index of
old-growth character." and I must add "in red spruce stands". I guess you
could quote me here and incidentally, I still like it as a generic rule of
thumb. In actuality, it is still a working hypothesis, and has never
received any discussion, critical comment, or indeed actually been peer
reviewed. Thus despite the tendency to accept it as dogma (or worse yet
"science"), everyone must be aware of its history, assumptions, and
limitations and realize it is only a first approximation waiting for
improvement.   I hope the reaction is not summary dismissal, but instead an
understanding of the underlying issues and complexities. As an aside, I am
unaware of more than a handful of sites where enough data are actually
available to determine either the stand age structure or the stand history
in enough detail to investigate these questions. Thus for now the
widespread use of this criteria is problematic and probably moot.

    Without revisiting the discussions of the two "old growth" definition
workshops, or more importantly the vast literature on the topic, I must
point out that we are still putting the "horse before the cart". All the
quibbling about criteria still begs the question of a real definition of
"old growth". Until we can agree (or simply state one's personal view)
about the concept and get a reasonable definition (be it verbal, conceptual,
theoretical, or typic with commonly accepted examples), there is little hope
in agreeing on any criteria which identify such an entity, or is it
entities. We also are risking tautological arguments, such as the
traditional "it is 'old growth' because I (or they) say it is". Even what I
call the Supreme Court definition, Potter Stewart's "I cannot define it, but
I know it when I see it" needs some examples and "local community
standards". Inevitably such a definition must address the history of the
area, extent and intensity of disturbance, the continuity of composition and
structures, the replacement processes, and the size and integrity of the
area at various scales. I tend to see "old growth" as a process (now there
is a conceptual definition) and doubt that specific structures, predictable
composition, or indicator species will ever be that useful as parts of a
definition. They might show up in criteria, but we first must get the
definition straight first.

Enough from the balcony, its time for Huck to float down the River, no doubt
he will return.


Charles V. Cogbill
Re: Age / Diameter Relationships    Cogbill
   Jan 11, 2003 

Bob has indicated that there might be some general interest in technical comments I had on Tom Diggins's question on size/age data.  Here is my reply to Tom.


 Although most of the work on age-diameter relationships seems to have been done on managed forests or even-aged conifer systems, there is a scattered literature on ages of eastern hardwoods in older unmanaged forests. These contain big, hard and commonly hollow trees and present a problem in dendroecology, but there are indeed some data on their age structure.  Here are some relevant references and a brief summary of the methodology and efficacy of using size as a predictor of age.

 Lorimer C.G., S.E. Dahir, & EV. Nordheim. 2001.  Tree mortality rates and longevity in mature and old-growth hemlock-hardwood forests.  J. Ecol.  89: 960-971

Hough, A.F. 1943.  Soil factors and stand history in a virgin forest valley on the northern Allegheny Plateau.  Soil. Sci. 43: 19-28.

Hough, A.F. 1932.   Some diameter distributions in forest stands of northwestern Pennsylvania.  J. For. 30: 933-943.

Hough, A.F. & R.D. Forbes. 1943.  The ecology and silvics of forests in the high plateaus of Pennsylvania.  Ecol. Monogr. 13:301-320.

Chokkalingam, U. 1998.  Spatial and temporal patterns and dynamics in old-growth northern hardwood and mixed forests of northern Maine.  Ph.D. thesis, University of Maine, Orono, ME.

Gates, F.C. & G.E. Nichols.  1930.  Relation between age and diameter in trees of the primeval northern hardwood forest.  J. For.  28: 395-398.

Lorimer C.G., 1980.  Age structure and disturbance history of a southern Appalachian virgin forest.  Ecology  61: 1169-1184.

Tubbs, C.H. 1977. Age and structure of a northern hardwood selection forest, 1929-1976.  J. For.  75: 22-25.

Leak, W.B. 1975.  Age distribution in virgin red spruce and northern hardwoods.  Ecology 56: 1451-1454.

Ross, M.S., T.L. Sharik, & D.M. Smith 1982.  Age-structure relationships of tree species in an Appalachian oak forest in southwest Virginia.  Bull. Torrey Bot. Club 109: 287-298.

Sano, J.  1977.  Age and size distribution in a long-term forest dynamics.  For. Ecol. & Mgt. 92: 39-44.

Blum, B.M.  1961.  Age-size relationships in all-aged northern hardwoods.  For. Res. Note 125, USFS, NE For. Expt. Sta. Upper Darby, PA.

Kenefic, L.S. and R.D. Nyland.  1999.  Sugar Maple height-diameter and age-diameter relationships in an uneven-aged northern hardwood stand.  Northern J. Appl. For. 16: 43-47.


All studies find a statistically significant relationship between age and diameter (no surprise as trees do grow larger with age), but the correlation coefficients between these variables within a species in the same stand for dominant hardwoods (i.e. sugar maple, beech, oak, tulip, white birch) is highly variable (growth is not constant and is relatively independent of size).  In fact, the correlation coefficient (r) has an average of 0.73 in 6 of the studies cited above (range from 0.26 to 0.94). This implies  that only 53% (maximum 88%) of the variance in the ages is explained by knowing the diameter of a tree in a specific old stand.   Many studies go on to use an age-on-diameter regression to derive a predictive relationship for age.  In some cases (e.g. Lorimer 1980, Leak 1975) this regression equation is used to expand a sampled diameter frequency (size structure) into an age frequency (age structure).  Curiously using a monotonic deterministic equation produces an age without any variability.  In essence it does not derive the age structure but only RESCALES (by converting units) the diameter distribution.  As seen above there is a  rather large error even in age determination based on diameters in the same stand. 

Predicting age from trees outside the sampled stand introduces even greater variability.  The accuracy of a generic calibration of age from size can be illustrated by a quick analysis from my eastern age database for sugar maple ages derived from actual ring counts (no corrected, estimated,  or extrapolated ages) using 94 sugar maples of measured diameter up to 91 cm dbh growing in numerous old stands in the East.  Technically this analysis is a  model 1 regression, while the more appropriate analysis could be a model 2 regression of diameter-on-age.   However the predictive equation from a linear regression of the scatter of dbh-age determinations gives y (age in years)= 2.46 x (dbh diameter in cm) + 40.95 with a correlation (r) of 0.53; that is  72% of the variance in the ages is unexplained by the regression. Specifically the standard error of any specific determination of age from  this equation (s sub Yhat) is 67.0 years.  Importantly the confidence limits around this prediction line expand with distance from the mean and, in fact, many large trees exceed the domain of the regression.  Ignored are the facts that the variability also increases if the assumptions of determining ages from ring counts at dbh and the uncertainty in treating diameter as a truly independent variable without error are accomodated by the model. Thus this analysis indicates that for a 90 cm diameter sugar maple the liberal 95% confidence interval for a single age determination is +/- 134 years around the predicted mean of 262 years.  Significantly the range of ages can be confidently placed only between 128 and 396 years for a 90cm tree!  Obviously using better fitting curvilinear regressions and more site-specific samples might narrow this range, but given the large variability in the determinations it is problematic how accurately age can be determined by any regression calibration.

 Of course much of this is argument is about statistics and they can easily mislead, but I am convinced that age cannot generally be derived by extrapolations or predictive relationships.  This is the basis of my “second rule of forestry” that “one cannot tell the age of a tree by its size”.  Since there are direct means of deriving tree ages and more importantly the age structures of stands, I encourage not compounding the errors by secondary methods.   Thus I am interested in any actual ages you might have found in the Zoar Valley.  However scanty,  these are the appropriate data that are needed for the description of the age structure of this site. 

Charlie Cogbill