Understanding natural disturbance regimes is prerequisite for designing silvicultural systems and treatments that emulate natural processes. Theoretically, 'natural' treatments favor trees adapted to the site, conserve local gene pools by relying on natural regeneration, maintain native plants in the understory, are less risky than agricultural approaches, and cheaper to implement. Because clear-cutting and other stand-regenerating systems are so often employed, it is important to determine which NPCs were maintained by stand-replacing disturbances and, further, to estimate the natural rotation.  For many NPCs the natural rotation far exceeds commercial rotation, and this requires us to look to other silvicultural strategies for harvest and regeneration.  Thus, we must also estimate the frequency and intensity of disturbances that maintain these kinds of forest communities.

Natural rotation of catastrophic and maintenance disturbances were calculated from Public Land Survey (PLS) records. The records provide a point-in-time estimate (ca. 1846-1908 AD) of just how much of the historic landscape was recently disturbed by fire, windthrow, or gap-forming events such as surface fires, disease pockets, etc. To some extent these regional trends can be applied to management at the stand-scale. The kind of natural disturbance can inform site preparation; the comparative frequency of stand-replacement and maintenance events informs canopy retention and entry schedules/rotation. 

Learn more about calculating natural disturbance rotations

Natural Disturbance Regimes

The goal of the PLS analysis was to estimate the rotation of stand-replacement and maintenance disturbances unique to each NPC class. The surveyors explicitly described burned and windthrown land when working within the forested regions of Minnesota. When in the prairie region and especially along the prairie/forest border, the surveyors used a variety of terms to describe wooded vegetation understood to be maintained by frequent disturbance. Most often this was fire, but in some regions wind was important as well. Thus, geographic context is an important consideration when trying to determine if a surveyor's comments are indicating that the corner was 1) undisturbed, 2) catastrophically disturbed, or 3) recently affected by a less intense, maintenance disturbance. Placing corners in these three categories is the critical step that allows the calculation of disturbance regimes. To get at this, we must understand the surveyor's physiognomic descriptions of the vegetation at the corners: prairie, grove, bottoms, barrens, burned lands, windthrown timber, etc. Our rules for assessing disturbance at survey corners were individually set for each physiognomic vegetation type across the state. 

Stocking (i.e., tree density) is the most important element of their physiognomic descriptions. Our initial step in the analysis was to understand how the distances to bearing trees affected the surveyor's vocabulary. For all of the types, we calculated the mean distance to bearing trees which allowed us to rank and group the types in some sensible fashion.

Wooded types	Disturbance types	Riverine types	Fire maintained types	Open types
Swamp 40	Windthrow 72	Bottomland 135	Thicket 92	Meadow 183
Forest 50	Burned land 76	Dry land 157	Pine openings 113	NOTA 192
Dry ridge 60			Oak openings 145	Prairie 236
Grove 69			Scattering oak 166	Marsh 278
Island 70			Barrens 177	Wet prairie 411

Table 1. Vegetation types mentioned by surveyors and their mean distances in links to their bearing trees. Columns roughly ranked by range of distances. (NOTA means 'no other tree around.')

Wooded and riverine types (Table 1) were assumed to be undisturbed forest. The short distances to trees in the wooded types are indicative of naturally stocked forest where tree density is largely set by competition for space among trees. The riverine types have longer distances than the wooded types because bottomland and dry land corners are intermingled with river channels and marsh at a fine scale. It is common for these linear, treeless features to occupy a full quadrant at a corner in bottomland forest requiring a bearing tree be found across the channel or meadow if possible. For each wooded type, we examined the frequency distribution of corners in 10-link distance classes to get a general sense of distances that would indicate natural stocking. Figure 1 is an example for the forest-type distribution associated with 77,506 corners. 

Figure 1. Frequency of 'forest' survey corners in 10-link distance classes by rounding mean distance (e.g., the 10-link class includes corners with mean distance of 5-15 links).

In Figure 1 about 80% of all corners fall in the first 6 classes (up to 55 links). The mean distance for all forest corners is 50 links. Our interpretation is that somewhere around the mean there is a change in the nature of the distribution. Classes under 50 links are common and likely represent the natural range of variation in stocking (perhaps due to age). Classes over 50 links are infrequent and most likely represent a corner where at least one quadrant lacked nearby trees or had damaged trees due to disturbance.  Thus, for our 'undisturbed' wooded and riverine classes, it just turns out that the mean distance usually falls in the last or one of the last abundant distance classes, and classes with longer distances were assumed to be disturbed to some extent. To make a simple rule, we arbitrarily set the minimum distance indication disturbance to the mean for vegetation that the surveyors described as swamp, forest, dry ridge, grove, island, bottomland, or dry land. 

Setting the upper limit, above which we assume stand-replacement, was also a guess. It is clear that mean distances over about 180 links are typical of open, treeless environments (Table 1.). Even at distances of about 110-180 links it is clear that trees were scarce enough that the surveyors noted that the vegetation wasn't forest. The distribution in Figure 1 is incredibly smooth over the longer mean-distance classes and there is no gap in classes to suggest a natural break for our higher distance threshold. To make a simple rule, we arbitrarily set the maximum distance indicating stand-replacing disturbance as the mean plus one standard deviation for swamp, forest, dry ridge, grove, island, bottomland, or dry land.  For most classes, this number is close to the mean distances for open types that we know had very few trees.

The frequency distributions of fire-maintained types are different from the wooded and riverine types. At distances greater than the peak class, the fall in frequency is nearly linear, an example of which is for oak openings (Figure 2.). There is no obvious point of inflection to set the lower, naturally-stocked, undisturbed limit, nor are there breaks in the distribution that can help us set the upper limit for catastrophic disturbance. It is important to remember that we are interpreting the use of terms like 'openings' and 'scatterings' to corners that we believe from modern vegetation to be capable of forest stocking. Almost certainly, these terms were used to describe recent disturbance that caused trees to be sparser than normal 'forest.' To help us interpret the use of these terms to describe forest, we returned to the coarser analysis. Corners with distances under 50 links were almost certainly in places one would describe as undisturbed forest. Corners with distances over 200 links were in places where tree density was low and comparable to open habitats like prairie and meadow. To make a simple rule for corners described as thicket, pine openings, oak openings, scattering timber, and barrens, we arbitrarily set the minimum distance indicating disturbance to 50 links, and we set the maximum distance indicating stand-replacing disturbance at 200 links.

Figure 2. Frequency of 'oak opening' survey corners in 10-link distance classes by rounding mean distance (e.g., the 10-link class includes corners with mean distance of 5-15 links).

In addition to distance, we found it important to consider also missing bearing trees as evidence of disturbance. A common survey note is 'NOTA' meaning 'no other tree around,' which was the surveyor's explanation for not marking all of the required bearing trees (i.e., 4 at section corners and 2 at quarter-section corners). Most often this note appeared at corners described as one of the fire-maintained or open community groups (Table 1.). NOTA was also used at corners described as burned or windthrown. Within the context of interpreting corners modeled as forest or woodland, NOTA almost certainly was relating to some kind of disturbance that left dead trees or trees too small to scribe. Table 2 describes our model for assigning a disturbance class based on both distance and complement of bearing trees. Within their type, survey corners were assigned their final disturbance class -- undisturbed, partially disturbed, catastrophically disturbed -- by a combination of the corner's mean distance to its bearing trees and whether it had its full complement of 2 or 4 bearing trees.

Assumed undisturbed - Wooded and Riverine groups	< mean	between mean and mean + SD	>Mean + SD
Full complement	Undisturbed	Undisturbed	Maintenance
Partial complement	Undisturbed	Maintenance	Burned
Assumed disturbed - Fire-maintained group	< 50 links	links	> 206 links
Full complement	Undisturbed	Maintenance	Burned
Partial complement	Maintenance	Maintenance	Burned

Table 2. Rules for assigning a disturbance class to survey corners not explicitly described as burned or windthrown.

Adjusting the Model -- Window of Recognition
It is obvious that several pragmatic decisions and rules were made in order to assign corners to disturbance categories. Even if these rules are reasonable, one must still set a 'window of recognition' in order to make quantitative estimates of stand-replacing and maintenance rotations. The window of recognition is the span of years for which a surveyor would have bothered to describe a disturbance. Would a surveyor recognize and care to report that a stand had been burned 5, 10, 15, or 20 years after the fact? We believe that mention of fire and windthrow was more an excuse for not marking bearing trees than any conscientious effort to alert potential buyers to fire- or wind-damaged timber. Consider the fact that quaking aspen is the early successional species for nearly all terrestrial forests in Minnesota. The surveyors actually marked and scribed some 390, 2-inch aspen bearing trees and some 3,039 three-inch trees. Clearly, surveyors would bother to scribe 2-3' trees if that was their only choice. Our age/diameter models for 2-3' aspen trees suggest that these trees were between 11 and 18 years old respectively. If commenting about fire and wind was an excuse, then the window of recognition should be somewhere in the 11-18 year range because that is when trees reach a minimum diameter for marking. 

Alternatively, a window of recognition is empirically set to 'force' the rotation model to match the estimates from studies using more reliable methods. In the Great Lakes States, there are reconstructions of disturbance regimes from fire-scar studies (Frissell 1973), stand-origin mapping (Heinselman 1996), and charcoal analysis of varved sediments (Clark 1988). When we model disturbance regimes from bearing trees in these same regions, a window of 15 years tends to yield results similar to the other methods for stand-replacing disturbance. We used a 15-year window of recognition because it yields rotations comparable to rotations calculated from fire-scars, stand-origin maps, and varved lake sediments.

Many detailed investigations of forest disturbance do not calculate rotations of maintenance disturbance, but recognize its confounding effect on estimating stand-replacing events. Trees with multiple fire-scars attest that some forest types are affected more by maintenance surface fire than catastrophic crown fires. Dendrochronological reconstructions of stand history also attest that maintenance events (fire and non-fire) are common and important, releasing cohorts of advance regeneration and providing some growing space in the canopy (e.g. Bergeron et al. 2002).  Minor peaks in varve charcoal are also more common than major ones, possibly recording maintenance fires. Calculating maintenance disturbance is more complicated than stand-replacement because the signal is weaker, reliable studies are fewer, and the cause less obvious. However, some estimate is absolutely required to provide guidance in applying intermediate silvicultural treatments to the right NPCs.

As was the case for estimating stand-replacing rotations, adjusting the window of recognition is the easiest way to adjust the model. Logic would suggest that the window should be shorter for maintenance events because the disturbance is less intense and evidence of it might be gone in 15 years. If the surveyors really used terms like burned or windthrown to explain the lack of bearing trees, it is likely that they did so less often on lands lightly disturbed because there were trees around -- they just had to go a little farther to find bearing trees and might not always find a suitable tree in all quadrants. We found that a 5-year window produced rotations that matched what one might guess from multiple-scarred trees. Also, the ratio of maintenance events to catastrophic ones seemed within the range of what one might expect from the ratio of strong charcoal peaks to minor ones in varve studies. A 5-year recognition window was used to calculate maintenance rotations because it seems to fit fire-scar and varve studies.

Calculating Rotation by Example -- Northern Mesic Mixed Forest (FDn43)
Having settled on windows of recognition and having assigned disturbance classes to the corners associated with an NPC, it is possible to calculate rotation. This is easiest to understand by example.

Northern Mesic Mixed Forest (FDn43) is a fire-dependant NPC that is the matrix vegetation for much of northeastern Minnesota. Our model assigned 11,712 PLS survey corners to this community because 1) they fall on landforms (LTAs) where we have modern samples of FDn43 forests, 2) the attending bearing trees were typical of the community (>70% frequency), and 3) they lacked trees atypical of the community (<30% frequency). 

Each corner was assigned one of 4 disturbance classes based upon the distance and complement rules set up for each physiognomic vegetation class (Table 2.). The tallies for each class are shown in Table 3. 

Vegetation Class	Fire 15-year window	Wind 15-year window	Maintenance 5-year window	Undisturbed
Barrens			11	11
Dry ridge			1	29
Forest	42		111	10168
Grove				1
Bottoms				45
Scattering pine			7	16
Scattering timber	2		24	60
Swamp (misassigned)			5	153
Thicket	21		61	143
Burned	710
Ravine				6
Windthrown		63
No other tree around	16
Island			1	5
Totals	791	63	221	10637

Table 3. Counts of survey corner assignment to disturbance classes by physiognomic vegetation class for the FDn43 community.

The FDn43 landscape of 11,712 survey corners provides the base area for calculating rotation of a NPC. In Table 3, 791 of those corners were interpreted as having been catastrophically burned, representing 6.75% of the area.
(791 burned corners/11,712 total corners)*100=6.75% of the landscape

Presumably, surveyors recognized burned lands for 15 years after the event, meaning that the annual percent of the landscape that catastrophically burned is 1/15th of 6.75%.
6.75% of landscape burned/15-year recognition window=0.45% burned annually

The rotation is the time required to catastrophically burn the entire area represented by 11,712 corners. Because we have calculated this as a percent, the time it takes to achieve that is: 
100%/0.45% burning annually=222 year rotation of catastrophic fire

There is no need to calculate acres or percent of landscape, but it makes the calculation easier to understand given the area concept of rotation in forestry. The easier formulas to use are:
(Total # corners / # corners in disturbance category)*recognition window=rotation
(11,712/791burned)*15 years=222 year rotation of catastrophic fire
(11,712/63 windthrown)*15 years=2,788 year rotation of catastrophic windthrow
(11,712/221 maintenance)*5 years=265 year rotation of maintenance disturbance

It is also useful to calculate the rotation of all fire (or wind), regardless if it was catastrophic or maintenance. To make this calculation it is easiest to sum the annual percents. 
0.45% burned catastrophically each year
0.37% burned in maintenance event
0.45%+0.37%=0.82% annual=122 year rotation for all types of fires

It is the rotation of all fires that tends to reasonably match the published estimates of return intervals. For example, in the BWCAW Heinselman (1996) reports return intervals for the common forest types: Aspen-Birch-Conifer (70-110 years), Red Pine (<100), and White Pine (>100). These cover types, especially the white pine, are predominantly the FDn43 community for which we calculate a 122 year rotation for all fires.