Fire is an important driver that shapes forested landscapes due to the interactions between the frequency, intensity, and absence of fire with forest succession which can determine species composition and stand structure at varying spatial scales [1
]. The alteration of fire regimes across the eastern United States by humans has resulted in drastic reductions in the area burned over the past century which has likely led to changes in forest species and structure compositions [4
]. There is evidence that in the future climate change could have a direct effect of increasing fire potential across the region [6
]. Recently, the use of fire as a management tool has increased as managers look for new tactics to increase forest resilience, restore desirable historical conditions, or control invasive species [6
Researchers often employ models to study the effects of fire as a management tool or stochastic natural process under novel conditions, long temporal scales, or large spatial scales [12
]. The method of modeling fire effects can determine the effective spatial and temporal scope of the results [16
]. Models which simulate fire effects directly on individuals, often called first-order fire effects [16
], use mechanistic processes or empirically-based probabilities to determine injury or death caused directly by fire. Due to their complexity, first-order fire effects models often operate at short temporal time scales (daily or sub-daily) or small spatial scales (individual tree or stand) which can limit the applicability of their predictions in long-term management or strategic planning contexts [18
]. Another class of model represents the aggregated effects of fire on individuals as changes in vegetation types or land cover classes using either mechanistic or rule based state-transition methods. These models, referred to as second-order fire effect models, can simulate larger landscapes over longer time periods, although usually at the expense of tracking site-level details of forest composition [19
]. Over the course of several decades many models have been developed that use one, or both methods of simulating fire effects in order to provide information to answer a variety of research and management related questions.
One such example are forest landscape models (FLMs) which have been developed specifically to combine the interactions between spatial processes of disturbance and dispersal with site-level community dynamics. Since the spatial component of disturbances is one of the main focuses of FLMs, it is unsurprising that model developers have focused considerable effort on the ignition and spread components of fire disturbance [2
]. The method for modeling fire effects within FLMs is often implemented using a rule-based community transition method where specific age cohorts, species, or some combination of both are removed from a site where fire occurs [21
]. Most FLMs have a main component to simulate forest succession which interacts with separate disturbance modules by means of a biological or ecological model currency, which in the case of fire effects has typically been the presence or absence of specific species or age cohorts [22
]. Fire effects are represented by a specific set of these cohorts being removed from a site following a set of user-defined rules. A few, more complex and computationally intensive, FLMs model fire mortality at the individual level using empirical logistic regression probability equations [19
]. By combining the feedback from the fire effect modules with forest succession, species dispersal, and other disturbance mechanisms researchers can use forest landscape models to examine the role that fire plays across broad spatial and temporal scales that are not often feasible in direct field studies.
One area that presents opportunities for improving the utility of model predictions for management and planning decisions is the ability of FLMs to interface with common forest management and ecological monitoring sampling practices. Forest inventories typically record the species and diameter at breast height (1.5 m) above ground for every tree on a plot which can then be scaled to per hectare estimates of basal area and densities or aboveground biomass weights using allometric equations [26
]. Researchers have used forest inventory data in order to construct initial forest community conditions as a starting point for FLMs [27
]. These initial community definitions are typically structured as quantitative information describing cohorts of similar individuals which are grouped by species, functional type, developmental stage, size, age, or some combination of multiple factors. The cohorts represented in early models were typically the presence or absence of age classes by species [29
], or forest type on each site [30
]. As computational resources improved FLMs were able to track more detailed quantitative information about cohorts within the model such as biomass [31
], number of individuals [28
], or specific individuals [24
] which allowed a more direct comparison with forest inventory data for the purposes of model initialization, calibration, and validation [32
]. This also allows for the possibility of model predictions to be directly compared with studies of forest fire ecology [10
], silvicultural management [34
], and wildlife population modeling [36
We present an approach to modeling first-order fire effects using a logistic regression probability method within a FLM, LANDIS PRO. With development of LANDIS PRO version 7.0 the presence/absence age cohort structure of tracking species over the landscape was replaced with one that could directly track number of individual stems within each age cohort [28
]. This allows the model to simulate partial effects of disturbance processes at the site-level and more realistically represent some stand dynamics [38
] while still operating at fine spatial resolutions (30–270 m) over large landscapes. We demonstrate how widely available forest inventory data is utilized to initialize forest communities within the model and calibrate the fire effects model as well as validate model predictions. The objectives of this study are: (1) Compare stem densities by size class on forest inventory plots in the eastern United States to test the hypothesis that small diameter stem densities are reduced on plots where low-intensity fire has occurred within the previous five years; (2) Test if a logistic regression based fire effects model and a rule-based model are effective predicting stem densities following a low-intensity fire within a forest landscape model.
In an analysis of over 6000 forest inventory plot records we showed that plots with fire recorded within the previous five years had lower stem densities in diameter classes less than 10 cm in the Ozark Highlands and less than 15 cm in the Gulf Coastal Plains. These results are in agreement with a number of studies conducted within the study areas we examined or within systems with similar species composition and fire regimes. In a study conducted in mixed pine-hardwood forests of the southern Appalachians following a single fire of three different intensities there were few species in which stems less than 5 cm were completely removed [54
], even under the highest observed fire intensity. In two studies conducted in southern Missouri Kinkead et al. [52
] found that mortality rates for trees less than 11 cm DBH ranged from 16% to 56% in oak-hickory forests following a single low-intensity fire while Dey and Hartman [55
] found that no species had a complete removal of seedlings and saplings following a single burn. Brose et al. [51
] found in a meta-analysis of studies from the eastern United States that mortality following a single fire in oak dominated forests mainly restricted to saplings less than 10 cm DBH, while larger size classes were less likely to be affected. Knapp et al. [10
] found a decline in mid-story sapling (3–10 cm DBH) density following periodic burns on plots located within the Ozark Highlands section. Hodgkins [56
] found that southern pine forests in Alabama had significantly reduced understory stem densities of saplings 10 cm DBH or less following low-intensity fires. Waldrop and Lloyd [57
] found that loblolly pine stands in South Carolina had significantly reduced stem densities following prescribed fire, with much of the mortality occurring in smaller diameter classes. Likewise, McNab [58
] found that low-intensity fires reduced stem densities in loblolly pine stands in Georgia and that mortality was limited to trees 10 cm DBH and smaller. Some studies have examined individual fire effects using FIA data in the western United States [59
], although to our knowledge there have been no studies in the eastern United States.
In the field studies referenced above, one common finding is that there is rarely complete mortality in small diameter cohorts following low-intensity fires, even in fire intolerant species. In our results we found that predictions using a rule-based fire mortality model were significantly lower compared to the logistic regression probability model. This behavior is likely partially a result of how fire tolerance for a given species is represented in the model. In the Ozark Highlands half of the top 10 most abundant species in the region; black oak, scarlet oak, northern red oak, sugar maple, and mockernut hickory, have a fire tolerance rating in the model of two or less, meaning they are moderately to very intolerant of fire. Even the lowest intensity fire would kill 50 to 85% of cohorts in these species using the rule-based based mortality method. For example, black oak has a fire tolerance rating of two and a longevity of 150 years. In a low severity fire, using the rule-based fire mortality model, the smallest 50% of cohorts would be removed which corresponds to black oak individuals from 1–40 cm DBH. The Gulf Coastal Plains section is predominantly composed of loblolly pine which is parameterized in the model with a fire tolerance rating of four. This means that with a fire severity of two on the landscape, only loblolly pine individuals from 1–25 cm DBH would be removed using the rule-based fire effect model while under the diameter-based mortality probability trees at 2 cm have a 60% change of being killed which declines to 1% at 12 cm. As the average fire tolerance of species increased across study areas, the difference between predictions from the two fire effects models was less severe.
By modeling fire effects using a calibrated logistic regression model we were able to predict post-fire stem densities for eight diameter classes that followed trends observed in inventory data while predictions using a rule-based fire effects model consistently under-predicted the residual stem densities following a fire. The residual small-diameter stems in stands that experience a low-intensity fire are an important component along with regeneration in determining the species composition and structure of the understory in the following years, particularly in plots that do not experience repeat fires [1
]. Within LANDIS PRO the effects of wildfire and prescribed fire are modeled using the same method, with inputs from other modules determining the location and intensity of these fire events. The results presented here represent only the effects of fire on residual stem densities and do not include resprouting or seed regeneration which occur during a later process in LANDIS PRO. This is comparable to the observations of fire effects from FIA plots, which are resampled at five year intervals, and typically would not sample post-fire regeneration if the fire occurred within five years or less since there is a 2.54 cm DBH threshold for inclusion [60
]. In addition, the observations of fire disturbance within FIA do not include information regarding the cause of fire which makes differentiating between wildfire and prescribed fire in the data difficult. The significant difference in size classes among FIA plots that were burned compared to those unburned highlights the utility of this database as a resource for parameterizing and calibrating forest landscape models and fire effect models.
These results present an argument for a more empirically-based approach to modeling fire effects where probability of mortality for individuals within a cohort can be calibrated to a fire regime rather than completely removed. As computational resources have improved, FLM developers have been able to incorporate more mechanistic or empirical processes that typically had been limited to individual-based models. By modeling the site-level first-order fire effects which are then incorporated in forest succession, FLMs produce bottom-up predictions of second-order fire effects such as changes in species composition, forest structure, or carbon dynamics over time and space [61
]. This differs from other regional scale spatial models such as dynamic global vegetation models (DGVMs) or state-transition models (STMs) which model second-order fire effects directly as represented by changes in vegetation type or reductions in carbon pools [63
]. DGVMs and STMs have been used to explore the response of vegetation to climate at regional scales, however, the coarse spatial resolution, simplified demographic information, and difficulty representing management within these models limits their utility in strategic decision making processes [65
]. A finer scale representation of first-order fire effects based on empirical or mechanistic processes can translate to improved modeling of second-order fire effects which are often more useful to managers or planners [16