The structure of regeneration models is determined by the sources of reproduction and by the biotic and abiotic factors that affect population dynamics of the ecosystem being modeled. Sources of reproduction include new seedlings, advance reproduction, and sprouts from the cut stumps of overstory trees. The micro-environment (e.g., light, temperature, and soil moisture) influences the development of reproduction. Aspect, slope position, elevation, and site index are commonly used to express the integrated effect of micro-environment on reproduction. In some upland oak ecosystems, wildlife may adversely affect stand regeneration potential. Interference species such as ferns, fire cherry, red maple, and flowering dogwood may dominate the site following harvest, thereby reducing regeneration potential. The importance of these factors in influencing regeneration potential varies among regions. Thus, regeneration models must be developed for specific regions. ACORn is an example of a regional stand-level regeneration model developed for even-aged forests in the Missouri Ozarks. It can be used to predict future stand characteristics by species and diameter classes, which in turn, can be used as input for growth and yield simulators. ACORn is a model developed for conditions slightly outside the southern Appalachian region, however there are so few regeneration simulation models available that it might be used in the driersites of the region.

• Introduction
• Regeneration Models Review
• The ACORn Simulator
• Predicting Regeneration Quality
• Regeneration Surveys

Growth and yield models can simulate the development of even-age stands that are about 20 years of age and older. In the Central States, growth models such as TWIGS (Miner and others 1988), STEMS (Belcher and others 1982) and OAKSIM (Hilt 1985) can be used to project stand changes resulting from real or hypothetical management practices. However, none of these models can predict stand structure or composition of a new stand. During the first two decades after final harvest, rapidly changing tree growth and competition relations determine the character of the mature stand.

The oak reproduction that develops after clearcutting depends on the oak regeneration potential of the parent stand. Regeneration potential refers to the capacity of a species or species-group to occupy and dominate growing space at a specified time in the new stand. For oaks, it can be determined from preharvest characteristics of the parent stand, including the advance reproduction and the overstory. To quantify the regeneration potential of a stand, the various sources of reproduction thus must be considered.

Natural reproduction after final harvest may come from new seedlings, advance reproduction, and sprouts from stumps of overstory trees (Beck 1980). New oak seedlings usually grow slowly and are not a major source of reproduction in most ecosystems (Sander and Clark 1971, Sander 1972, McQuilkin 1975). Viable acorns remain in the forest floor for 6 months or less because they are rapidly consumed by wildlife, damaged by insects and pathogens, and dessicate or freeze during the winter.

Advance reproduction and stump sprouts usually are the major sources of reproduction. The competitiveness of upland oak reproduction usually depends on the development before final harvest of a large root:shoot ratio. Oak advance reproduction can develop large root:shoot ratios through repeated shoot dieback and resprouting. Shoot dieback may result from water stress, weather damage (i.e., frost and freeze), insects, pathogens, fire, and browsing. Nevertheless, oak reproduction may accumulate and develop in the understory for decades (Merz and Boyce 1956, Tryon and others 1980). Once the overstory is removed, larger stems of advance reproduction can sprout vigorously and thus capture much of the newly available growing space (Carvell 1967; Sander 1971, 1972, 1979; McQuilkin 1975; Beck and Hooper 1986; Ross and others 1986; Johnson and Sander 1988; Loftis 1988). Thus, it is the number, size, and spatial distribution of oak advance reproduction that largely determines the oak regeneration potential of a stand.

Sprouts from cut stumps of overstory trees are usually the fastest growing form of oak reproduction (Spaeth 1928, Kuenzel 1935, Sander and Clark 1971, Smith 1979, Zahner and Myers 1984). The large food reserves and absorptive capacity of the parent root system support rapid shoot growth of stump sprouts. Stump sprouts make up variable portions of the total oak reproduction and often compensate for deficiencies in oak advance reproduction (Johnson and Sander 1988).

There are several hardwood regeneration models for predicting stand development after final harvest. Predictions are based on preharvest inventories of advance reproduction, the overstory (trees larger than 1.6 in. d.b.h.), and site factors. These models thus provide land managers the opportunity to evaluate alternative prescriptions before actual harvest. Methods for evaluating the natural regeneration potential of upland oak forests have been developed by Sander and others (1976, 1984), Johnson (1977), Johnson and Sander (1988), Lowell and others (1987), Waldrop and others (1986), Loftis (1988, 1990) and Marquis and Ernst (1988). Models for evaluating the potential contribution of planted trees to future stocking also have been developed for northern red oak (Quercus rubra L.) (Johnson 1988) and other hardwoods (Johnson 1984, Johnson and Rogers 1985).

Marquis and Ernst (1988) developed an expert system for Allegheny hardwood forests called SILVAH. It generates prescriptions based on management objectives, present stand conditions, and projections of tree growth and regeneration potential (Marquis and others 1992). To evaluate even-aged stands, critical stocking values are used to predict regeneration success. In applying the system, advance reproduction is inventoried on plots 6 ft. in radius. Whether a plot is stocked depends on species, numbers of stems, and their size. For example, a plot is considered stocked with oak if there are at least 25 stems less than 4.5 ft. tall, or if there is one stem greater than 4.5 ft. tall. Oaks in the overstory also are inventoried. The number of reproduction plots expected to be stocked with oak stump sprouts at stand age 20 are estimated using models developed by Sander and others (1984). During the preharvest inventory, limiting site factors (poor drainage and stone content), amount of interference species competition, and intensity of deer browsing also are noted. Because these factors reduce the regeneration potential of a stand, the number of plots deemed stocked with desirable reproduction are accordingly reduced. The number of plots stocked with desirable tree species thus determine whether or not the regeneration potential is adequate. In general, when 70 percent of the plots are stocked with desirable advance reproduction, successful regeneration is expected to occur.

Loftis (1990) developed a regeneration model for mixed hardwood forests of southern Appalachia. The model projects eighth-year post-harvest heights and crown classes of northern red oak advance reproduction based on preharvest measurements of advance reproduction and site quality. Heights of red oak reproduction 8 years after final overstory removal are estimated from preharvest height and basal diameter of advance reproduction and from site index. Preharvest basal diameters and site index are then used to predict the probability that a given stem of oak advance reproduction grows to dominant or codominant crown classes in the new stand at age 8. This model thus can be used to evaluate the contribution of red oak reproduction to the future stand.

Sander and others (1984) developed a regeneration model for the Missouri Ozarks. It predicts the probability of individual oaks surviving and attaining a specific future height that places them in codominant or dominant crown classes. From preharvest inventories of the overstory and advance reproduction, the model predicts the adequacy of future oak stocking. A stand is deemed to have adequate regeneration potential if projected stocking of dominant and codominant oaks at stand age 20 is at C-level or greater based on Gingrichs (1967) stocking relations. However, the model is unable to predict the diameter distribution of oaks in the new stand, and non-oaks are not considered. Although species such as blackgum (Nyssa sylvatica Marsh.), sassafras (Sassafras albidum (Nutt.) Nees, hickory (Carya spp.), and flowering dogwood (Cornus florida L.) seldom occur as dominant trees in Ozark forests once they reach 20 years of age, they do affect the development of stands during the first two decades after final harvest because of their high density and rapid growth. These species are also important to wildlife and biodiversity.

In contrast to some other deciduous forests of the eastern United States, the forests of the Missouri Ozarks regenerate primarily from sprouts of harvested overstory trees and advance reproduction. Therefore, the composition and size structure of the future stand is largely determined by the species composition and size structure of the preharvest advance reproduction and overstory. By observing these features together with measurements of site factors such as slope, aspect, and site index, model users can predict the composition and structure of the new stand.

Dey (1991) developed a regeneration model called A Comprehensive Ozark Regenerator (ACORn) to simulate the regeneration of even-aged stands in the Missouri Ozarks. It was developed from measurements of individual stems of reproduction before and after clearcutting. ACORn comprises two modules that simulate the development of the two primary sources of reproduction in that ecosystem: stump sprouts and advance reproduction. Each module, in turn, contains models for estimating future heights, diameters, and survival of individual stems by species. The probability of survival of individual stems of both advance reproduction and stump sprouts, from preharvest to a specified future stand age, is estimated from initial tree size and site factors. Species-specific models estimate future tree heights and diameters from similar predictors. The predictive models, in turn, facilitate the generation of future diameter and height distributions of surviving reproduction including stump sprouts and advance reproduction by species. Projections for hickory, flowering dogwood, blackgum, and sassafras also can be obtained.

In application, preharvest inventories of the overstory and advance reproduction provide input to survival and growth models that generate diameter distributions 21 years after clearcutting. At that age, mean stand diameter averages 3 in. d.b.h. The diameter distributions then can be used to summarize stand characteristics, such as basal area per acre, stems per acre, and percent stocking by species. From this stand summary, the adequacy of future stocking can be assessed and used to develop appropriate silvicultural prescriptions. The resulting diameter distributions also can be used as input into growth and yield simulators such as TWIGS.

Quality of reproduction is commonly defined in terms of the acceptability of growing stock. Before adequacy of regeneration potential can be assessed, it is necessary to define acceptable growing stock, which requires a consideration of species and tree characteristics. Commonly used tree characteristics are height, diameter, and crown class. Although a qualitative characteristic, crown class is a concept with which most foresters are familiar. It is a widely used descriptor of trees because it facilitates visualization of a tree's social status more easily than diameter or height measurements, per se. For example, the definition of acceptable growing stock may be limited to certain species and trees that occupy only codominant and dominant crown classes. ACORn solves that problem by projecting future diameter and survival of individual trees by diameter and crown classes to stand age 21.

Some foresters may consider only codominant and dominant trees as acceptable growing stock. Others may consider trees that are intermediate or larger as acceptable. To integrate this decision into the regeneration model, a threshold tree diameter is defined that classifies trees into one of the two user-defined crown class categories: acceptable or unacceptable. When acceptable growing stock includes only codominant and dominant trees, tree diameters equal to or greater than 3.8 in. are classified as codominant or dominant at stand age 21. When acceptable growing stock is defined as trees that are intermediate or larger, trees with diameters less than 2.6 in. are classified as suppressed, and those with larger diameters are classed as acceptable growing stock. In this way, ACORn incorporates crown class to project twenty-first-year diameter distributions.

Data from preharvest inventories of the overstory and advance reproduction provide the necessary input for ACORn projections of future stand composition and structure. To inventory a stand, the overstory (trees 1.6 in. d.b.h. and larger) is sampled separately from the advance reproduction (trees less than 1.6 in. d.b.h.). Because ACORn is an individual tree model, it projects the survival and growth of single trees and then expands this to a per-acre basis in the form of stand tables. The model thus can accommodate a variety of sampling designs.

ACORn requires an inventory of the overstory including species, d.b.h., site index (black oak, base age 50), and stand age. When the overstory is even-aged, an average stand age can be substituted for individual tree age. For advance reproduction, the required inventory includes data on species, basal diameters, and heights of reproduction, slope position (upper, middle, or lower), and aspect. A computer program is available to facilitate application of the model.

Fixed-area or variable-radius plots can be used to inventory the overstory. Sander and others (1984) recommended that the overstory be sampled on 1/20-acre plots in their regeneration guide. Small fixed-area plots were recommended for inventory of advance reproduction. The model of Sander and others (1984) requires that advance reproduction be inventoried on 1/735-acre plots. The choice of sample plot size and number should be done on a stand-by-stand basis. There are numerous sampling techniques that can be used to design efficient and effective inventories (e.g., Freese 1962).

In general, the more variation there is in species composition, tree size, and the spatial distribution of trees, the more sample plots that are needed. It is usually best to sample a large number of small plots where stand variation is great than it is to sample fewer large plots. A common rule-of-thumb is to inventory at least 30 plots regardless of stand size. The upper limit to the number of plots depends on (1) constraints such as budget, crew size, and timeframe; (2) intended use of simulation, i.e., forest planning or stand prescription development; (3) amount of stand variation; and (4) desired level of precision. Plots should be distributed randomly or systematically throughout the stand.