Monitoring disturbance intervals in forests: a case study of increasing forest disturbance in Minnesota

Abstract

Key Message

We develop analytical methods and explore trends in disturbance interval via systematic forest inventory observations at a bioregional scale.

Context

Our study spans the dynamic ecotone at the intersection of southern boreal forest, mixed hardwood forest, and tall-grass prairie ecosystems in Minnesota, USA. Disturbance-related tree mortality is a major driver of demographic and successional change in this bioregion.

Aims

We aim to provide reliable disturbance estimates for forest ecology and economic research.

Methods

We develop methods applicable to any region with systematic forest inventory observations. We assess disturbances observed by the United States Department of Agriculture-Forest Service Forest Inventory and Analysis program on permanent sample plots in Minnesota, USA.

Results

A roughly 50% reduction in disturbance interval is apparent across all forest cover types and for most disturbance categories. The largest changes are for insect damage, disease, wind events, drought, and fire.

Conclusion

Publicly available forest inventory data captures the frequency of disturbance events across bioregional landscapes and over time. Our methods serve to highlight rapid changes in rates of damage to standing trees within the study area.

1 Introduction

Disturbance plays an important role in the dynamics of natural forests. Biotic and abiotic changes can disrupt stand structure, resource availability, and/or the physical environment (Pickett and White 1985). Such disturbances can range spatially from small-scale to large-scale, stand-to-landscape replacing events. The rotation interval (RI) for disturbance (not necessarily stand replacing) varies widely with many factors including disturbance type, forest cover type, successional stage, geographic location, ownership, and management regime. Moreover, these rates of disturbance may vary with time, depending on long-term climate trends, anthropogenic land use patterns, wildlife population cycles, and other factors. In total, these disturbances drive successional change in the forest (Guyette and Kabrick 2002; Reilly and Spies 2016) by, for example, determining where and when canopy openings occur, which seedlings and sprouts grow free of browse, and the average time between disturbance events.

Increasing disturbances associated with climate change, invasive species (both plant and animal), invasive tree pests like emerald ash borer (Agrilus planipennis Fair.), and diseases like Dutch elm disease (Ophiostoma ulmi Buism) have been reported in some parts of the world, including our study area. Extreme wind and precipitation-related events (e.g., either too much or too little) also appear to be on the rise. Indeed, it seems we must now plan for increased disturbance in the forest (Seidl et al. 2017). Thus, assessment of regional patterns and trends is needed.

Disturbance rates are relevant to timber production and harvest scheduling, but also to carbon sequestration, habitat management, biodiversity, and ecosystem services considerations. (For a few examples, see Rogers (1996), Thom and Seidl (2016), and Seidl et al. (2016).) Here, we use data from the ongoing cyclical forest inventory effort of the United States Department of Agriculture (USDA) Forest Service’s Forest Inventory and Analysis Unit (FIA) to analyze recent disturbance trends. We believe this is also the first study to utilize the cyclic FIA data to estimate RIs for different types of disturbance.

Prior efforts to determine RIs have typically looked at a handful of disturbance and cover types across a modest geographic region using intensive field methods to assess dates and types of disturbance (Heinselman 1973; Frelich and Lorimer 1991; Frelich and Reich 1995). Those efforts typically examined tree data obtained using increment borer samples from the trunks of standing or downed trees. These samples allowed the assessment of fire dates, drought stress, times of release from suppression, or other indicators of disturbance across relatively long periods of one to four centuries.

However, forest inventory data can be used to assess disturbance-related mortality across large spatial extents (Reilly and Spies 2016). This research used data collected for periodic inventory efforts with a sample design unique to the Pacific Northwest Region. Others have used satellite imagery (Landsat) and light ranging and detection (lidar) to assess combined change from harvesting and natural disturbance (Vogeler et al. 2018; Matasci et al. 2018). The more recent, and nationally consistent, cyclic data collected by FIA (a 5-year cycle of data collection contributes to each estimate of forestland area in Minnesota) hold promise for informing similar analytic approaches. However, these data present various difficulties stemming from the timing and sequence of observations. We develop an approach, utilizing a broad-based representative forest inventory to inform a range of interests including estimates of natural and unplanned human-induced disturbance. While our methods are applicable nationally and elsewhere, our specific objective was to devise a method for using FIA estimates of area disturbed to study RIs and trends for various types of natural disturbances across the forest. We use Minnesota as a case study to highlight the utility of the technique. We also test the hypotheses that disturbance rates (other than harvesting, which represents a planned treatment rather than a disturbance) have increased, decreased, or remained the same during the period of observation.

2 Materials and methods

2.1 Study area

A combination of natural and anthropogenic disturbance, coupled with periods of regrowth, has shaped Minnesota’s forests over time. The exact nature of these dynamics varies widely depending upon timber markets, soils, physiography, and the specifics of disturbance leading to change. Frequent fires, windstorms, insect infestations, and diseases have all played a role in shaping Minnesota’s forested landscape.

Heinselman (1973, 1996) spent much of his career mapping historic fires which shaped the mosaic of even-aged and multi-aged coniferous forests of Minnesota’s Boundary Waters Canoe Area Wilderness. Fires also played a large role in shaping the forest following the removal of most white and red pine from accessible portions of Minnesota’s northern forest between 1890 and 1920. These fires consumed the dense slash and damaged less desirable trees left on site. Aspen responded strongly to clearcuts followed by fire (Friedman and Reich 2005), dominating regrowth across much of Minnesota.

The famous blowdown of 1999, which affected a large swath of southern boreal forest, and mixed hardwood forest stretching from Minnesota across Southern Quebec, Canada, is another example of disturbance shaping Minnesota’s forests. This massive straight-line windstorm toppled mature trees across 193,000 ha (an area roughly 48 km long and 6-18 km wide) in Minnesota alone (USDA Forest Service 2001). The blowdown released younger or smaller diameter stems of shade-tolerant species present in the understory. Regrowth in the path of the blowdown leans heavily towards northern white cedar (Thuja occidentalis L.), balsam fir (Abies balsamea (L.) Mill.), and black spruce (Picea mariana Mil.), a distinct change from the mature jack pine (Pinus banksiana (Lamb.)), red pine (Pinus resinosa Ait.), eastern white pine (Pinus strobus L.) and aspen (Populus tremuloides (Michx.), Populus balsamifera (L.), and Populus grandidentata (Michx.)) originally present on most of the landscape (Rich et al. 2007).

An explanatory mechanism for recent increases in insect outbreaks is their accelerated development rate and increased reproductive potential related to increasing temperatures (Porter et al. 1991; Ayres and Lombardero 2000). Additionally, the establishment of exotic insect and pathogen species in new locations (Aukema et al. 2010) may be more likely in a warmer climate (Virtanen and Neuvonen 1999; Lesk et al. 2017). The sporulation and colonization success of some forest pathogens may also respond to changes in temperature, precipitation, soil moisture, and relative humidity (Chakraborty et al. 1998). Hence, increasing temperatures also likely contribute to increased severity and shorter RIs for insect outbreaks, disease, fire, rot, and other events (Frelich and Reich 2010). Our methods may contribute to better understanding these processes and their implications for forest management.

2.2 FIA disturbance observations

Disturbances recorded during plot visits (FIA methods are summarized in Appendix 2) include biotic and abiotic agents such as insects, diseases, animals, fire, weather, and geologic events affecting individual trees (Appendix 1) (O’Connell et al. 2017). Following FIA procedure, we do not consider intentional disturbances such as harvesting or thinning here. In that context, human-induced disturbance includes things like tree removal not associated with a planned harvest, brush clearing that damages or removes trees, or other unplanned human activities resulting in damage or mortality of the specified threshold.

Per FIA instructions, disturbances must have occurred since the last plot visit (5 years prior in Minnesota, but 7 or 10 years for some states) or within a cycle length (a defined 5-year sample period) for new plots. FIA records the estimated year of disturbance along with the type. A disturbance must be at least 0.405 ha (1 acre) in size (clearly, this observation extends beyond the plot and includes assessment of conditions in the plot vicinity), with mortality or damage to 25% of the trees on the physical plot (e.g., the equivalent of at least one full subplot must be affected in most cases). Observations of disturbance are associated with the entire plot.

When a plot becomes inaccessible for any reason, it is replaced by a new observation (possibly from a different location) during the following field season. For this reason, observations of disturbances greater than 5 years old (Fig. 1 and Appendix 3 Table 4) can be recorded. There are two caveats: (1) Observations from five sequential panels must be used to produce estimates of total and disturbed area. (2) A temporal lag between disturbance events and their observation limits the sightability, relevance, or completeness of some observations.

Fig. 1

Distribution of time delay for observation of disturbances via FIA inventory in Minnesota. Note the observation interval corresponding to the largest number of disturbance observations (e.g., 2 years following the event). We calculate the focal year as the annum in which disturbances observed in a given year were most likely to have occurred

Recorded disturbances occurred between 1995 and 2016. Hence, we have a continuous set of observations, including any visible disturbance, spanning 21 years and ~ 7 million ha. Disturbances more than a few years old are clearly difficult to observe, with evidence of different disturbances likely persisting for different lengths of time. The record is reasonably complete for disturbance events occurring during the period 1998 to 2014 (Appendix 3 Table 4). Because most disturbances more than a few years old likely go unnoticed, disturbance RIs derived from these estimates are biased upwards (e.g., some level of disturbance went unnoticed).

2.3 Model for estimating disturbance

The standard defined by FIA is a 0.405-ha (1-acre) disturbance affecting at least 25% of the trees present on and around a subplot. Thus, our prediction capability using these data is for disturbances affecting at least 0.405 ha.

At times, more than one disturbance occurs between visits to a plot. We counted these disturbances (142 records) as unique disturbance observations. We assigned these secondary disturbances a distinct disturbance code and year and counted the disturbed area a second time in summation of disturbed area. Correlation of repeated measures was ignored, but may be an issue for these 142 observations (0.76% of our total plot observations; 142/18,789), where the nature of a first disturbance may have altered susceptibility to a future disturbance. Regardless, a downward bias in estimates of disturbed area resulting from loss of disturbance visibility over time (Fig. 2) likely makes our estimates conservative in terms of the RI calculated.

Fig. 2

Timeline for observation of disturbances by FIA in Minnesota. Percentages indicate the cumulative proportion of total observations for a given disturbance year made with each panel of a 5-year cycle

The rotation (or recurrence) interval is the usual measure used to discuss the frequency with which a defined portion of the landscape will experience one or more disturbances (Swift and Ran 2012; Pickett and White 1985). The forestry literature further provides a distinction between the disturbance return interval (a point-based concept) and the rotation interval (an area-based concept) (Bond and Keeley 2005). Our methods rely on area estimation and therefore are parallel to the rotation interval concept and terminology. Comparison of area disturbed over time against total area (e.g., for a cover type, or for the forest as a whole) enables calculation of a RI for disturbance. In this case, the RI is the expected period required for each 0.405 ha in a specified cover type, or stratum, to experience one or more disturbances. We also discuss the RI for specific types of disturbance. Those intervals reference the entire forest, rather than area of a specific cover type, unless otherwise noted.

For each cover type group, and for the forest as a whole, we calculated RI as:

$$ {\mathrm{RI}}_t=\frac{{\mathrm{Total}\ \mathrm{Area}}_t}{\mathrm{Disturbed}\kern0.5em {\mathrm{Area}}_t}, $$

where t corresponds to the focal year for reporting of disturbances, and Total Area(t) is the then current estimate for total forest. In Minnesota, the focal period for observation of disturbed area lags 2 years behind the observation period for total area. An ordinary least squares regression model using focal year as the predictor and RI as the response was developed. We used Welch’s t test (Welch 1951) and linear regression (R Core Team 2018) to test for significance of changes in disturbance frequency over the period of observation.

To assess likely the variability of disturbance rates, we use the prop.test function (R Core Team 2018) to calculate the 95% binomial confidence interval for each forest type group/disturbance type group combination, and for the forest as a whole. The size of the set of responses generated at each iteration was proportional to (disturbed area sampled / mean expansion factor) for that forest cover type. This method ensures that perceived precision of the estimate is proportional to the number of disturbance observations contributing to the estimate for a forest type. In addition to trend analysis, we present cross-tabulations of:

• 1. Disturbance RI (all disturbances combined) by forest cover type,

• 2. Disturbance RI (all cover types combined) by disturbance type group, and

• 3. Disturbance RI by forest cover type-disturbance type group combinations.

2.4 Statistical computing tools

Here, we propose a reproducible methodology for estimating disturbance RIs. We compile our scripts (Appendix 3) as R markdown documents (.Rmd) constructed and run using {knitr} (Xie 2014, 2015, 2018) in RStudio (RStudio Team 2016). Scripts used to obtain our results summarized by disturbance group (Table 2) are available upon request. Similar methods were used to compile the disturbance data by forest cover type group (Table 3) and for the cross-tabulation of forest cover type group and disturbance type group (Appendix 3 Table 5).

3 Results

3.1 Total disturbance rates: USDA-FIA inventory years 1999–2016

We have records of 1780 disturbance events from 18,759 discrete observations (1999–2016) distributed across ~7 million ha of forestland. Of these, we used 1677 disturbance observations for events thought to have occurred from 1998–2014 to develop complete estimates of disturbance and to calculate RIs (Appendix 3 Table 4, bold). After excluding incomplete observations for events occurring at the extremes of the period of interest, we have a usable set of observations (Appendix 3 Table 4, shaded and bold) to develop estimates of disturbance RIs.

We depict frequency of disturbance as a RI by focal year (2001–2014) in Table 1 and Fig. 3. The expected RI declines from almost 23 years, to roughly 8 years over the course of observation. A linear model of the trend over time yields a highly significant slope (p < 0.0000012, R² = 0.8584) suggesting an average change in overall RI of − 1.28 years per year of observation. Similarly, one-sided Welch’s t test (p = 0.01786 with 172 degrees of freedom) suggests rejection of the null hypothesis that initial RIs for forest cover type-disturbance type combinations were either less than or equal to those observed at the end of the observation period. We therefore accept the alternative hypothesis that disturbance RIs have declined since 2001. Sample size limits our ability to estimate RI and confidence bounds for disturbance/cover type pairs with very few disturbance occurrences. Those with sufficient observations appear in Appendix 3 Table 5 along with binomial confidence bounds (e.g., RI.025 and RI.975). Examination of the temporal trend (Figs. 3, 4, and 5) shows that variation in the RI observed for different disturbances and cover types has decreased along with the interval.

Table 1 Total area of forestland and disturbance for evaluation groups^* 2003–2016

Fig. 3

Disturbance rotation interval (RI) trend, 2001–2014. The trend line is calculated as: E[RI] = 26.41 − 1.28 × ΔFocal year, with variance weighted by number of plots contributing to each 5-year estimate. The expected reduction in RI for each 1-year increase in focal year is 1.28 years (p < 0.0001)

Fig. 4

Rotation interval (RI) (years) by disturbance type for focal years 2001–2014 (focal year refers to the annum in which most disturbances observed in the 5-panel evaluation group are thought to have occurred.). Geologic and unknown disturbances are omitted for visual simplicity

Fig. 5

Disturbance rotation interval (RI) for major forest cover types occurring in Minnesota

3.2 Details by disturbance and forest cover type groups

Frequency of disturbance and uncertainty associated with RIs varies greatly by disturbance type (Table 2). The most frequent disturbances were weather, animal, and human. RIs have generally declined for all disturbance types except human and geologic. The greatest decreases have occurred for disease, vegetation, insects, and fire (Fig. 4).

Table 2 Forest disturbance (1998–2014) observed by USDA-FIA in Minnesota (1999–2015)

There was an almost 3-fold difference in disturbance RIs among forest cover types (Table 3). Although the aspen-birch group has suffered the greatest amount of absolute disturbance (hectares), both the oak-hickory and lowland hardwood groups have shorter RIs for disturbance. RIs have generally decreased over the study period for all forest type groups (Fig. 5). The RIs for total disturbance in a given cover type (Table 3) are much shorter than those for a given disturbance type (Table 2). For example, in order for the entire forest to experience insect damage or mortality to at least 25% of trees across at least an acre, we would need to wait approximately 180 years (Table 2). On the other hand, for all aspen to experience any kind of disturbance, we would only need to wait about 14 years (Table 3).

Table 3 Total disturbance by forest cover type group

For reference, we estimate the RI for fire between 24 and 148 years (Appendix 3 Table 5) in the mixed pine woodlands of northern Minnesota with a mean of 60.5 years. Our overall estimate of RI for fire in the Border Lakes ecological subsection encompassing the Boundary Waters Canoe Area and Wilderness is 54.6 years.

4 Discussion

Previous research supports non-harvest tree fall recurrence intervals of 50–200+ years in mesic hardwood and mixed forests (Runkle 1982; Frelich and Lorimer 1991; Seymour et al. 2002). Frelich and Lorimer report 145–175 years for canopy residence times in sugar maple and hemlock, while at the 0.5-ha scale, recurrence intervals range from 69 years for > 10% canopy removal to 1920 years for > 60% canopy removal, also similar to results from this study (using a 25% canopy damage, not removal, threshold). Somewhat shorter RIs (~ 129 years) predominate across Canada’s western Boreal Shield (interpreted from White et al. 2017), which extends south into Minnesota’s Border Lakes ecological subsection. Intervals are even shorter (50–100 years) in the southern boreal forests of northern Minnesota (Heinselman 1973). These observations are consistent with the higher frequency of minor disturbance events compared with major events resulting in substantial tree mortality.

Results of the current study, as well as casual observation, support the conclusion that more frequent disturbances are now shaping Minnesota’s forests. For example, emerald ash borer, oak wilt, Dutch elm disease, tent caterpillar, a severe drought, and several large wind and fire events have all occurred in Minnesota during the period analyzed.

Continued characterization of disturbance patterns using spatially and temporally representative data, like FIA, is needed to interpret changes in the forest, and processes affecting the forest, across larger spatial and temporal scales. The picture we can construct from FIA will improve as the length of time with consistently spaced repeat observations increases. The upper confidence bounds for many uncommon disturbance type/cover type combinations (Appendix 3, Table 5) will likely decrease as we acquire additional observations.

Disturbance frequencies fluctuate over time, especially those for large infrequent disturbances, making variability of estimates quite high. This complicates interpretation of the observed trend towards declining RIs. Nevertheless, the trend is significant, and the change is substantial (~ 50%), reaching very low recurrence intervals in the latest 5-year period (even considering the confidence intervals). This trend may indicate a shift in response to warming climate (Dale et al. 2001; Seidl et al. 2017), or change in other factors including anthropogenic species introductions/extinctions, fire suppression/ignition, or land clearing for agriculture. These changes could also be part of a natural fluctuation. If it is a regime shift characterized by increased frequency of storms, droughts, and invasive insect pests and tree diseases, it may still be temporary and shift back to longer recurrence intervals because susceptible trees die off, in a self-regulating, homeostatic process described by Runkle (1982).

The Generic Environmental Impact Statement on Timber Harvesting in Minnesota (Jaakko Pöyry Consulting, Inc. 1992), as well as more recent cross-tabulations of cover type area (Wilson and Ek 2018), shows that there is a regular and somewhat predictable exchange of area among cover types. Disturbance interacts with age-related growth and susceptibility patterns to determine the success of individual stems and hence the direction and velocity of forest succession. This hypothesis is supported by much experimental and observational data and may be corroborated through comparison of disturbance rates against successional and demographic changes among forest cover types and ecoregions. To this end, we enable assessment of disturbance, as well as differences among forest cover types, across relevant spatial and temporal scales.

5 Conclusions

Further investigation of disturbance in other regions may corroborate the trend towards shorter disturbance intervals observed here (e.g., Reilly and Spies 2016) as part of a broader pattern, or show that they are a local phenomenon. Trends reported here appear to be both meaningful in terms of their magnitude and are significant from a statistical perspective. Methods presented are transferrable to other states or regions monitored by systematic forest inventory and may aid in illustrating the spatial and temporal scale of observed changes. Finally, regional or national application of this methodology could help estimate RIs for different forest and disturbance types across their geographic ranges.

Appendix

1.1 Appendix 1. Disturbance codes and descriptions recorded by USDA-FIA (O’Connell et al. 2014)

Code	Group	Description
0	0	No visible disturbance
10	10	Insect damage
11	10	Insect damage to understory vegetation
12	10	Insect damage to trees, including seedlings and saplings
20	20	Disease damage
21	20	Disease damage to understory vegetation
22	20	Disease damage to trees, including seedlings and saplings
30	30	Fire damage (from crown and ground fire, either prescribed or natural)
31	30	Ground fire damage
32	30	Crown fire damage
40	40	Animal damage
41	40	Beaver (includes flooding caused by beaver)
42	40	Porcupine
43	40	Deer/ungulate
44	40	Bear (core optional)
45	40	Rabbit (core optional)
46	40	Domestic animal/livestock (includes grazing)
50	50	Weather damage
51	50	Ice
52	50	Wind (includes hurricane, tornado)
53	50	Flooding (weather induced)
54	50	Drought
60	60	Vegetation (suppression, competition, vines)
70	70	Unknown/not sure/other (include in notes)
80	80	Human-induced damage—any significant threshold of human-caused damage not described in the TREATMENT codes
90	90	Geologic disturbances
91	90	Landslide
92	90	Avalanche track
93	90	Volcanic blast zone
94	90	Other geologic events
95	90	Earth movement/avalanches

1.2 Appendix 2. USDA-FIA sampling protocol and analysis

FIA conducts an inventory of forest attributes across the USA. Early inventories represented a periodic effort (e.g., FIA completed a snapshot inventory every 10–15 years). Recent methods involve an ongoing annual effort in which data collected from five overlapping panels of plots provides a complete snapshot of the state’s forests. The sampling design uses a tessellation of the land base into hexagons approximately 2428 ha in size with at least one permanent plot established in each hexagon. Tree and site attributes are observed for plots on forestland. At each plot, observations and measurements are made on four 7.32-m fixed-radius subplots (Bechtold and Patterson 2005). A bounding box around the subplots (arranged in an equilateral triangle with a central subplot) encompasses approximately 0.3 ha. A 17.96-m radius macro-plot is defined around each subplot for standardization of the area used in reporting stand and vicinity level observations. Here, we focus on observations of disturbances (Section 2.1) made between 1999 and 2016.

Over 5 years, data is collected from approximately 6000 permanent sample plots located on forest lands throughout Minnesota. Plots are divided into 5 annual panels, each of which represents a sparse, but representative sample of the forest. When combined across a full 5-year cycle, these data provide a detailed look at the regional forest resource. These data are compiled, analyzed, managed, and publicly distributed as a PostgresSQL 10 database (Miles 2017). Inventory data can be accessed via: https://apps.fs.usda.gov/fia/datamart/datamart.html. Statistical methods used by FIA to produce forest summaries are described by Bechtold and Patterson (2005) and implemented by Miles (2017). FIA methods are largely replicated here. Statistical methods described by Bechtold and Patterson (2005) detail a moving average method, which we use here to blend panels across cycles, creating a rolling estimate of forest and disturbed area.

We processed the raw FIA data in R (R Core Team 2018) for efficiency and flexibility. Total area of disturbed and undisturbed forestland was summarized for each 5-year period. We used a dual moving window analysis (in the temporal sense) to produce representative estimates of base (2003–2016) and disturbed (2002–2015) forestland area for reporting periods ending between 2003 and 2016. Bechtold and Patterson (2005) detail methods for calculation of a moving average across multiple panels and cycles. The number of disturbance events observed at each time step was also recorded to illustrate the sequence of events leading to observation of a disturbance during plot visits over the subsequent 5 years.

Auto-correlation potentially arising from repeated measurement of plots over time is not a large issue for the current analysis. We view the FIA sampling scheme for disturbance as a case of change detection involving observation of fixed permanent plots (with limited partial replacement due to inaccessibility, denied entry, or change to a non-forested condition) systematically placed across the area of interest. Thus, we assume the occurrence of a disturbance on any given plot has no effect on the probability of a future event. However, for growth and yield, and in limited cases where one disturbance might change future susceptibility to a secondary disturbance (e.g., a blowdown, beetle kill, or severe drought), correlation effects resulting from repeated measurement of plots should be considered.

1.3 Appendix 3. Brief example using the Bache/Wickham piping procedure and workflow

We take advantage of several functions and tools provided by the R user community, especially the suite of packages included in {tidyverse} (Wickham 2017a, b). This suite of interlocking packages includes {ggplot2} (Wickham 2009), {dplyr} (Wickham et al. 2017a, b), {tidyr} (Wickham 2017a, b), {readr} (Wickham et al. 2017a, b), {purrr} (Henry and Wickham 2017), and {tibble} (Müller and Wickham 2017). Tidyverse also uses custom notation from the {magrittr} package (Bache and Wickham 2014) for directing data to a specified workflow and output using efficient methods via the “% > %”, or pipe, operator. Because {tidyverse} allows us to define several processes within the “summarize” wrapper function, we can create a data output tailored to our analytical needs. A brief example showing assignment to an output, direction of data to a function, and definition of the output follows.

Table 4 Disturbance matrix for Minnesota showing observations by disturbance and inventory year. Bold shaded records were included in the analysis. Ongoing disturbances can result from longer-term events like drought, invasion by competing vegetation, or repeated deer browse over many years. The last 2 digits of the disturbance year are used across the top of the table to show timing of disturbances

Table 5 Forestland disturbance for discrete forest cover type-disturbance type pairs (n ≥ 5 disturbance observations). The lower and upper 95% confidence bounds are calculated via prop.test and reported as RI.025 and RI.975