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Forest health is a complex concept including many ecosystem functions, interactions and values. We develop a quantitative system applicable to many forest types to assess tree mortality with respect to stable forest structure and composition. We quantify impacts of observed tree mortality on structure by comparison to baseline mortality, and then develop a system that distinguishes between structurally stable and unstable forests. An empirical multivariate index of structural sustainability and a threshold value (70.6) derived from 22 nontropical tree species’ datasets differentiated structurally sustainable from unsustainable diameter distributions. Twelve of 22 species populations were sustainable with a mean score of 33.2 (median = 27.6). Ten species populations were unsustainable with a mean score of 142.6 (median = 130.1). Among them,

The search for an objective definition of forest health and a framework for its assessment have been elusive [

How does one define forest sustainability? Like forest health, sustainability has been difficult to define and to measure because people have differing and often competing priorities that reflect their values at a particular point in time and often come at the expense of others. For example, stakeholders (e.g., landowners, government agencies and forest ecologists) often disagree on what specific resources should be sustained and how forests should be managed. Furthermore, forest ecosystems are complex and develop slowly, confounding measures of sustainability [

We support an uncomplicated definition of forest sustainability simply as structural stability, and fully recognize that forests are dynamic, not static ecosystems as our definition may infer. We do not imply that forest structure or composition must remain unchanged for that forest to be considered sustainable or indeed, healthy. Rather it is the equivalence of baseline and observed mortality that must remain stable for the forest to be considered structurally sustainable. This approach gives us a frame of reference within which to evaluate changes in structure. It gives us the ability to objectively determine the scope and direction of change in structure and composition, which provides the ecological framework for objective management decisions. It sets the stage for the quantification of forest stability or change that hinges on a comparison of the current, observed mortality with a context-specific, theoretical value termed baseline mortality. The calculation of current baseline mortality values are independent of prior BM values. Therefore, it is irrelevant whether forests are managed or not because the approach we developed applies to both systems.

The comparison of baseline to observed mortality is possible due to the q-ratio or its special case known as the Law of de Liocourt that describes the size structure of a forest (density of stems) as a function of stem diameter [

Log-linear plot of a hypothetical diameter distribution (▲), the baseline mortality calculated from the log-linear plot (- - -), and hypothetical currently observed mortality by diameter class (solid line without triangles).

Baseline mortality is the percent of trees in each diameter class that will normally die in a structurally sustainable forest in the time it takes for the trees to grow into the next larger diameter class. The width of the diameter classes, therefore, must correspond to the time frame in which the observed mortality occurred in order to provide a basis for the evaluation of mortality from all causes. For example, if dead stems are identifiable and measureable for a maximum of 20 years, then the diameter class width (DC bin size) in a baseline mortality analysis must represent 20 years of growth. The subjects of this paper are the precise relationship between observed and baseline mortality and how much observed mortality must deviate from the baseline before we can expect a change in the size structure of the forest.

Here, we use available forest inventory datasets to assess the structural sustainability of 22 tree species in disparate geographic regions using the baseline mortality approach. We hypothesize that the structural sustainability of forest tree species populations and the impacts of known and unknown disturbances on their sustainability can be objectively and quantitatively assessed. Our objectives were to develop a quantitative index using a statistical approach to objectively distinguish between sustainable and unsustainable diameter distributions for 22 species and populations, and to evaluate the impacts of known disturbances on four of them. We used logistic regression to provide an unbiased threshold estimate. All sustainability scores above and below this estimate were deemed unsustainable and sustainable, respectively. We also developed a computer software package that performs all of the calculations necessary to conduct these analyses, and it is available on the SUNY-ESF website.

The datasets of 22 forest tree species were obtained from New Zealand (NZ) and the United States in this study.

Scientific and common names, sampling site locations, number of trees, total area sampled, and mean plot size for each of the 22 species populations utilized for baseline mortality analysis.

Species | Common name | Region ^{1} |
No. of Trees ^{2} |
---|---|---|---|

Balsam fir | AFP | 51,656 | |

Red maple | AFP | 50,571 | |

Sugar maple | AFP | 33,998 | |

Yellow birch | AFP | 9,822 | |

American beech | AFP | 49,246 | |

Red spruce | AFP | 23,403 | |

Eastern white pine | AFP | 3,380 | |

Black cherry | AFP | 16,393 | |

Eastern hemlock | AFP | 12,701 | |

White spruce | AK | 415 | |

Subalpine fir | IM | 1,141 | |

Engelmann spruce | IM | 933 | |

Mountain beech | NZ | 8,645 | |

Pacific silver fir | PNW | 5,569 | |

Pacific yew | PNW | 1,057 | |

Western red cedar | PNW | 1,076 | |

Western hemlock | PNW | 7,502 | |

Ponderosa pine | PNW & IM | 5,604 | |

White fir | SN | 6,230 | |

Red fir | SN | 3,642 | |

Incense cedar | SN | 2,383 | |

Sugar pine | SN | 1,495 |

^{1}: AFP=Adirondack Forest Preserve, NY; PNW=Pacific Northwest Region, SN=Sierra Nevada Region, AK=Alaska, IM=Intermountain Region, NZ= New Zealand; ^{2}: AFP plot data originate from expanded counts on 462 prism plots, AK data from one 20 ha stand, IM data from 26.8 ha total sampling area with a mean plot size of 3 ha, NZ data from 4.3 ha total sampling area from 107 plots of 0.04 ha each, PNW data from 51 ha total sampling area (mean plot size 1.1 ha), PNW and IM data from 77.8 ha total sampling area (mean plot size 1.4 ha), and the SN data from 23.2 ha total sampling area (mean plot size 1.2 ha).

The datasets for the 11 conifer species in old-growth stands of the Intermountain (IM), Pacific Northwest (PNW), and Sierra Nevada (SN) regions of the western US included growth and mortality measurements for trees monitored for 25–72 years dependent upon region [

Each dataset included the number and diameter at breast height (dbh) of every live and dead tree of the species of interest on the sampled plots. The total sampled area for each species was greater than 1 ha because complete and reliable negative exponential diameter distributions cannot be generated in most cases from a smaller sampling area [

The baseline mortality method is based upon certain assumptions [

The baseline mortality of each species population was calculated from the diameter distribution of the living trees using previously described methods [_{0} + α_{1} × D_{0} and α_{1} are regression coefficients to be estimated from the data. If the ^{2} of the log-linear model is 0.80 or greater, the resulting model is considered to satisfactorily fit the diameter distribution of that species population.

Then, the baseline mortality (BM) rate is calculated as follows:
^{−α1 × ∆D}_{1} is the estimated slope coefficient of Equation (1), and ΔD is the DC bin size for the species. Expected mortality can be calculated for each DC by multiplying the number of trees in each DC by BM, which represents the desirable mortality in a structurally stable forest. The difference between the observed and expected mortality indicates the disparity of structural sustainability for a given species. Whether or not the difference is statistically significant in one or more DC classes can be determined by a chi-square test using the observed and expected mortality for the species distribution, as well as for each diameter class. When the expected mortality is less than five trees in a DC, adjacent DCs can be combined to satisfy the assumptions of chi-square test.

Observed mortality is determined by counting all dead trees on the site regardless of the cause of the mortality and when it occurred. This mortality includes standing, leaning, and downed dead trees, as well as stumps. The diameter of all the dead trees and stumps is recorded. This number then is divided by the total number of trees in that diameter class and multiplied by 100 to generate percent observed mortality values by diameter class.

We believe it is essential to provide a forward-looking dimension to the mortality analyses described below. Therefore, we utilized an iterative procedure to evaluate the potential impacts of the currently observed mortality on the future diameter structure, if the current mortality were to remain constant. We assumed that in-growth was constant,

The structural sustainability of these 22 species was assessed using multivariate statistical procedures based on the following five metrics derived from the patterns of observed mortality in the diameter distributions, and their effects on future diameter distributions as discussed in the above section.

(1) Distribution of mortality (DM) is the distribution of DCs in which the observed mortality significantly differed from the expected mortality. DM is coded as 5 if the significant difference is in <25 cm DCs, 4 if in 25–38 cm DCs, 3 if in 38–64 cm DCs, or 2 if in >64 cm DC. These DM codes are based loosely on pole, small, medium, and large sawtimber size classes in the northern hardwood forest. It reflects the assumption that excessive or insufficient mortality in the smaller size classes disproportionately impacts the future diameter distributions relative to the larger size classes.

(2) Aggregation (AGG) is the clustering of significantly different DCs. AGG is coded as (1) if there are 2–3 consecutive DCs with significant differences between the observed and expected mortality, (2) if 4–5 consecutive DCs, (3) if 6–7 consecutive DCs, or (4) if >8 consecutive DCs. It reflects the greater effect of mortality clustered in adjacent DCs compared to non-aggregated mortality. Distributions without consecutively different DCs were assigned a value of zero.

(3) Magnitude (MAG) is the size of the differences between the observed and expected mortality for the species. MAG is the summation of the absolute values of the differences between the observed and expected mortality for each DC.

(4) Relative abundance (RA) is the percentage of DCs that showed significant differences between the observed and expected mortality. It is scored by dividing the number of DCs with significant differences by the total number of DCs in the species distribution.

(5) Change (CHG) is how the control and predicted diameter distributions change from the first to the last iteration. It is evaluated by using chi-square analysis to compare the distribution of predicted living trees (based on the observed and expected mortality—see above) to the control distribution (based on the baseline mortality). The total number of DCs with significant differences between the observed and expected mortality is tallied for each distribution and the difference divided by the total number of DCs, which was then arcsine transformed. This variable was created as stated previously to provide a forward-looking dimension to the mortality analyses.

Based on the five metrics above, hierarchical cluster analysis with the average linkage clustering method was conducted. The 22 species were clearly divided into two clusters. Then, a bootstrapped discriminant analysis using the same five metrics with 1000 iterations was conducted to generate a discriminant function (DF) as follows [_{1} × DM + γ_{2} × AGG + γ_{3} × MAG + γ_{4} × RA + γ_{5} × CHG_{1} – γ_{5} are discriminant function coefficients estimated from the data. Given the values of the five metrics, the score of the DF equation (Equation (3) was computed for each species, which was considered the “Sustainability Score”).

Further, given the fact that these 22 species were clustered into two distinguished groups (coded as S (sustainable) and U (unsustainable)), a logistic model was used to regress the probability of a species _{i} = _{r} (Species_{i} = S), against its “Sustainability Score” as follows:
_{0} and β_{1} are the regression coefficients to be estimated from the data. Thus, the natural log-transformation of the odds

If we assume that the probability of species belonging to the sustainable or unsustainable group is 0.5 (equal chance), _{i}_{r} (Species_{i}

Therefore, the sustainability threshold is:

If the sustainability score of a species calculated using Equation (3) is smaller than the “threshold”, the species belongs to the sustainable group, otherwise, it belongs to the unsustainable group.

All of the species that we evaluated showed negative exponential diameter distributions with model ^{2} > 0.82. Therefore, baseline mortality (BM%) was constant across all diameter classes for each of the 22 species (

Baseline percent mortality, correlation coefficient of regression of natural log of diameter distribution fit to the negative exponential model, diameter distribution metrics, discriminant function score, and cluster category for each of the 22 species populations

Species | BM (%) ^{1} |
^{2} |
MAG ^{3} |
AGG ^{4} |
DM ^{5} |
CHG ^{6} |
RA ^{7} |
DF Score ^{8} |
Cluster ^{9} |
---|---|---|---|---|---|---|---|---|---|

18.1 | 0.98 | 4.7 | 0 | 5 | 0.70 | 0.036 | 4.3 | S | |

11.3 | 0.86 | 19.4 | 1 | 5 | 0.70 | 0.071 | 12.9 | S | |

30.2 | 0.88 | 29 | 0 | 5 | 0.52 | 0.167 | 17.6 | S | |

11.3 | 0.89 | 31.3 | 1 | 5 | 0.61 | 0.075 | 19.4 | S | |

18.1 | 0.96 | 38.9 | 2 | 12 | 0.61 | 0.179 | 27.2 | S | |

31.6 | 0.96 | 46.0 | 1 | 5 | 0.34 | 0.222 | 27.6 | S | |

13.9 | 0.92 | 65.8 | 2 | 7 | 0.67 | 0.172 | 39.6 | S | |

23.7 | 0.82 | 91.6 | 2 | 5 | 0.44 | 0.357 | 52.9 | S | |

20.5 | 0.96 | 89.1 | 2 | 9 | 0.69 | 0.267 | 53.0 | S | |

18.1 | 0.95 | 89.9 | 2 | 12 | 0.58 | 0.226 | 54.7 | S | |

20.5 | 0.95 | 98.1 | 2 | 5 | 0.54 | 0.31 | 56.3 | S | |

13.9 | 0.82 | 144.4 | 2 | 12 | 0.63 | 0.296 | 84.1 | S | |

21.3 | 0.91 | 107.3 | 3 | 9 | 0.38 | 0.375 | 63.8 | U, + | |

25.9 | 0.95 | 110.5 | 3 | 9 | 0.48 | 0.333 | 65.4 | U, − | |

33.0 | 0.86 | 144.7 | 3 | 12 | 0.48 | 0.54 | 85.2 | U, − | |

13.9 | 0.89 | 175.7 | 5 | 14 | 0.30 | 0.351 | 104.2 | U, − | |

21.3 | 0.92 | 192.2 | 5 | 12 | 0.37 | 0.56 | 112.3 | U, +, − | |

40.5 | 0.98 | 228.1 | 4 | 9 | 0.42 | 0.60 | 129.7 | U, − | |

26.7 | 0.95 | 224.5 | 6 | 12 | 0.28 | 0.64 | 130.5 | U, − | |

38.1 | 0.96 | 246.7 | 4 | 14 | 0.19 | 0.56 | 141.9 | U, − | |

30.2 | 0.96 | 334.9 | 6 | 12 | 0.39 | 0.71 | 190.0 | U, +, − | |

14.8 | 0.82 | 438.0 | 7 | 14 | 0.28 | 0.72 | 247.2 | U, + |

^{1} baseline percent mortality; ^{2} correlation coefficient of regression of natural log of diameter distribution fit to the negative exponential model; ^{3} magnitude metric value; ^{4} aggregation metric value; ^{5} distribution metric value; ^{6} change metric value; ^{7} relative abundance metric value; ^{8} discriminant function score=sustainability score; ^{9} S: sustainable, U: unsustainable, +: excessive mortality, −: insufficient mortality; * misclassified by discriminant function analysis.

Cluster analysis using the five mortality metrics classified the 22 species populations into two clusters. The discriminant analysis on the two clusters yielded one significant canonical root (Wilk’s lambda = 0.2194;

We view the bootstrapped discriminant function as a “structural sustainability index” because the five metrics were based on patterns of observed mortality and existing diameter distributions, and were designed to compare mortality among different populations of trees, and to reflect potential future changes in the size structures of the species populations. For the sustainable group, the lowest sustainable score was 4.27 and the highest score was 56.3 (mean = 33.2 and median = 27.6). For the unsustainable group, the lowest unsustainable score was 85.2 and the highest score was 247.2 (mean = 142.6 and median = 130.1). The threshold score (Equation 7), defined as the sustainability score with an equal chance of being designated sustainable or unsustainable, was derived from logistic regression model parameters in Equation (4) (_{0}/−β_{1} = −7.1002/0.1006 = 70.58) Thus, species with scores less than 70.58 were sustainable and those with scores over this threshold were unsustainable.

Discriminant analysis had an apparent total error rate of 0.14 (0.08 for sustainable group and 0.20 for unsustainable group).

Sustainability problems were evident in each temperate forest type, and in each of the three old-growth western coniferous forest regions (PNW, IM, and SN), although most of the unsustainable species were located in the Adirondack Forest Preserve of New York (

In total, 12 of the 22 species populations were categorized as structurally sustainable and 10 as unsustainable (

Calculated distributions illustrating the impact of currently observed mortality on sustainability of

Structural unsustainability can be caused by either excessive or insufficient mortality (

Calculated distributions illustrating the impact of currently observed mortality on sustainability of (

Excessive mortality (

In the northern hardwood forests of the AFP, our analyses identify five structurally unsustainable species populations including

Increasing rates of mortality detected in the sampled old-growth coniferous forest stands of the western U.S. was attributed to climate change by van Mantgem

Structural stability (

The multivariate structural sustainability index and threshold value are empirically derived from 21 temperate and one boreal forest tree species. It may eventually be possible to develop a global sustainability index once more forest species from the temperate, boreal, tropical and subtropical forests of the world are evaluated. At that time it may be possible to compare the impact of global disturbances (e.g., climate change) on forest structural sustainability both spatially and temporally. Until then, we propose that a regionally derived structural sustainability index score be included as one more additional and important consideration when forestland managers or landowners assess the sustainability/health of their forests.

Although the baseline mortality concept and associated index may not be appropriate for certain species (e.g., those with diameter distributions other than negative exponential), the ramifications of our proposed methods are significant. A standardized analysis that permits the objective and quantitative assessment of the structural sustainability of a forest provides the ability to determine the impact of natural and anthropogenic disturbance agents, including management activity, on that forest. We have used the method to verify the impacts of known disturbance agents on four species, and the results support our hypothesis that the method can identify or elucidate structurally unsustainable forests. Plus, it provides the ability to recognize a potential sustainability problem before the cause is known,

A software package is available at the following URL [

Structural sustainability is a key criterion to an objective and quantitative assessment of forest health. Forest structure is an ecologically and demographically sound and comparatively easily measured feature of all forests using readily available inventory data upon which to base a method for assessing sustainability. Here, we present a quantitative index of structural sustainability that objectively distinguishes sustainable from unsustainable diameter distributions, and propose it as one additional but critical criterion for the assessment of forest health.

We gratefully acknowledge the following individuals for providing the datasets that made our analyses possible: Phil Van Mantgem (USGS, Redwood Field Station, Arcata, CA) and Nate Stephenson (USGS, Sequoia and Kings Canyon Field Station, Three Rivers, CA) for all of the western old growth coniferous forest data; Rob Allen (Landcare Research, Lincoln, NZ) for the New Zealand mountain beech data, John Lundquist (USDA Forest Service, Forest Health Protection, Anchorage, AK) for the white spruce data, and Paul Manion (Professor Emeritus, SUNY-ESF) for the Adirondack northern hardwood forest data. We additionally thank Cortney D’ Angelo for assistance with data analysis and three anonymous reviewers for their helpful comments on the manuscript.

Jonathan A. Cale, Justin L. West, and David R. Castello conducted all of the baseline mortality analyses in this study. David R. Castello and Peter Devlin developed the computer software package to facilitate the use of the method by others. Jonathan A. Cale, John D. Castello and Stephen A. Teale developed the quantitative baseline mortality method itself. Lianjun I. Zhang provided all of the statistical expertise. The concept of a structural sustainability index was conceived by John D. Castello and Jonathan A. Cale.

The authors declare no conflicts of interest.