The spatio-temporal signature of tree mortality processes

Tree mortality processes can be described in terms of the agents of mortality, spatial scale, and temporal scale (Fig. 1A). Many mortality processes have been well-studied and quantitatively described at a range of spatial scales including insect epidemics, drought, and storm events (e.g., windthrow, ice storms). The timescale of these conspicuous mortality agents can be extremely acute (e.g., storms) or span multiple years (e.g., beetle epidemic, multi-year drought), and they create patterns in mortality that are evident at both intermediate and broad spatial scales (10–10,000 ha; Raffa et al. 2008, Allen et al. 2010, Meddens et al. 2012, 2018a, Baguskas et al. 2014). Conversely, slower-acting background mortality processes, including competition, endemic bark beetle activity, and pathogens, are more evident at finer spatial scales (<1 ha) and longer temporal scales (>3 yr; Fig. 1A). The slower dynamics of these processes makes them challenging to study, often requiring long observation periods and large plots for patterns in mortality to emerge (Clark and Clark 1996, Lutz and Halpern 2006, McMahon et al. 2019). Although subtle, background mortality processes regulate forest turnover rates in the absence of severe disturbance (van Mantgem et al. 2009), and they are important determinants of fine-scale spatial dynamics within stands (Das et al. 2008, Larson et al. 2015).

Mechanisms of spatial structuring

The ecological mechanisms that give rise to spatio-temporal patterns in tree mortality may be broadly grouped into three categories: density dependence, distance dependence, and environmental heterogeneity. Density-dependent mortality emerges when tree neighborhoods mediate mortality risk (Kenkel 1988, Larson et al. 2015), and is evident as elevated susceptibility to competition (Gray and He 2009, Das et al. 2011), biotic mortality agents (Janzen 1970, Packer and Clay 2000, Johnson et al. 2014), and abiotic mechanisms (King 1986, Das et al. 2008, Yu et al. 2009, Schaedel et al. 2017) in dense tree neighborhoods. Distance dependence, in contrast, refers to the elevated risk of mortality for trees close to an affected individual, a characteristic associated with many mortality agents including pathogens, insects, and crushing (i.e., contagion; Goheen and Hansen 1993, Das et al. 2008, Raffa et al. 2008). Finally, environmental heterogeneity contributes to non-random patterns in tree mortality by introducing variability in light, water, soil resources, and habitat suitability which influence growth rate, vigor, and concomitant mortality risk (Greenwood and Weisberg 2008, Linares et al. 2011, Furniss et al. 2017). These mechanisms function simultaneously, and the spatio-temporal patterns of mortality are generally determined by a combination of all three mechanisms.

While density dependence has been used to describe patterns of both distance- and density-dependent mortality associated with competition and biotic mortality agents (e.g., insects, pathogens), we define these terms separately to decouple the distinct relationships between each mechanism and forest spatial structure. Forest spatial structure regulates density-dependent mortality directly through resource competition (Kenkel 1988), morphological constrains (King 1986), accumulation of host-specific plant enemies (Janzen 1970, Connell 1971), and by moderating trees' ability to invest in defense mechanisms (Lorio 1986, Herms and Mattson 1992, Kolb et al. 1998, Fettig et al. 2007, Hood et al. 2016, Stephenson et al. 2019). Conversely, forest spatial structure does not directly regulate distance-dependent mortality. Rather, distance-dependent mortality processes are spatially autocorrelated due simply to the contagious nature of certain mortality agents (e.g., pathogen spread, beetles dispersing from a recently killed tree).

While many mortality processes are both distance- and density-dependent, differentiating these terms is critical to understanding the ecological nuances of spatially non-random mortality processes. Distance-dependent mortality may be density-independent (i.e., mortality may be spatially autocorrelated but independent of local density), and conversely, density-dependent mortality may be distance-independent (i.e., mortality may not be spatially autocorrelated despite mortality risk being elevated in dense neighborhoods). In other words, density-dependent mortality is a pattern that emerges when forest spatial structure mediates mortality risk, while distance-dependent mortality is the consequence of autocorrelated mortality processes. This distinction may be conceptualized as opposing directions of the relationship between forest spatial structure and mortality risk: Density dependence represents the effect of forest spatial pattern on mortality risk, while distance dependence represents the effect of mortality processes on forest spatial pattern.

Spatial elements of background mortality

Perhaps the most widely recognized example of spatially structured tree mortality is competition-dominated density dependence that defines the competitive exclusion phase of forest succession models (Yoda 1963, Peet and Christensen 1987, Franklin et al. 2002). This form of density dependence is most often observed in young and even-aged forests (Kenkel 1988, Larson et al. 2015, Birch et al. 2019b), but asymmetric competition can continue to cause density-dependent mortality in mature and old-growth forests as well (Lutz et al. 2014, Furniss et al. 2017, Zhu et al. 2017). In these more structurally complex forests (Lutz et al. 2018, Jeronimo et al. 2019), mortality agents including bark beetles, pathogens, and physical damage (Franklin et al. 1987, Larson and Franklin 2010, Das et al. 2016) become increasingly important determinants of mortality, and patterns in background mortality are structured by a complex mix of both distance- and density-dependent mechanisms (Das et al. 2008, 2011, 2016, Silver et al. 2013, Gendreau-Berthiaume et al. 2016, Lintz et al. 2016).

Individual mortality agents may be both distance- and density-dependent. Bark beetles, for example, create contagious patches of mortality (i.e., distance dependence) by releasing aggregation pheromones that attract nearby beetles to a single individual and overwhelm the tree's defenses (Raffa and Berryman 1983), and successful mass attacks result in a concentrated point source of beetles that disperse to nearby trees (Raffa et al. 2008). Density dependence further contributes to spatial patterns of beetle-related mortality as local forest structure determines the intensity of competition and thus the availability of resources necessary for trees to invest in defense chemicals and resist beetle attacks (Lorio 1986, Herms and Mattson 1992, Fettig et al. 2007, Hood et al. 2016). Density dependence is also evident at broad scales as forest composition and host tree density regulate background beetle population levels which determines success rate of mass attacks, and neighborhoods with high host tree density may be preferentially selected by dispersing beetles (Raffa and Berryman 1983, Kolb et al. 2007, Raffa et al. 2008). Patterns in bark beetle mortality can also be driven by variability in drought intensity across a landscape (Baguskas et al. 2014), as susceptibility to beetle attack is closely related to drought severity (McDowell et al. 2008, Anderegg et al. 2015).

Pathogen-related mortality is determined by a similarly complex mix of spatially structured processes. For example, the widely cited pattern of conspecific negative density dependence (CNDD; Hille Ris Lambers et al. 2002, Comita et al. 2010, LaManna et al. 2017) is often attributed to host-specific pathogen accumulation (Janzen-Connell hypothesis), but this distance-dependent contagion is reinforced by the elevated intensity of intraspecific competition (Adler et al. 2018; but also see Detto et al. 2019) near conspecific host trees (i.e., conspecific density dependence). The below-ground growth form and slow spread rate of pathogens make their contagion detectable as patches or rings of mortality that manifest at intermediate to large (1–100 ha) spatial scales (Lung-Escarmant and Guyon 2004, Schmitt and Tatum 2008), but this is generally only evident over long timescales (decades to centuries, Fig. 1A; Waring et al. 1987). The spatial elements of insect activity may also contribute to the spatial structuring of pathogens as fungal spores can be transported to new host trees by the insects themselves (Goheen and Hansen 1993, Paine et al. 1997, Safranyik and Carroll 2006).

Finally, physical mortality agents including crushing and some forms of wind-related mortality (e.g., wind waves) may be regarded as distance-dependent as probability of mortality is positively related to the proximity to a falling tree (Das et al. 2008) or the edge of a gap (Taylor 1990). Patches of wind-related mortality are often associated with root- and stem-rot (Sprugel 1976), and their spatial structure is therefore additionally influenced by the distribution and spread of saprophytic decay fungi. Physical mortality agents that operate at broader spatial scales, such as wind, ice, and snow storms, are most strongly determined by environmental heterogeneity (Rebertus et al. 1997) and the spatial variability in the intensity of the weather event (Pasher and King 2006). The density dependence of physical mortality agents is perhaps most apparent in single-age stands where density directly influences tree morphology (i.e., diameter to height ratio) and thus resistance of trees to strong wind (King 1986). Physical mortality agents may be both positively and negatively density-dependent. Stand density can influence tree morphology (i.e., diameter to height ratio) and thus be positively related to susceptibility of trees to strong wind (King 1986), while high density stands can also ameliorate the localized intensity of wind and ice storms and thus reduce mortality risk (Bragg et al. 2003).

Spatial elements of direct fire mortality

Fire is an intrinsically spatial process, causing patterns in mortality that are both distance- (proximity to flames) and density-dependent (density alters fire behavior). Heterogeneity in fire effects introduces complex patterns across a wide range of spatial scales from <0.01 ha (Blomdahl et al. 2019) to >10,000 ha (Turner et al. 1997, Meddens et al. 2018a, Whitman et al. 2018, Fig. 1B). Fire behavior is spatially autocorrelated due to heat transfer from burning fuels to adjacent vegetation (Michaletz and Johnson 2006, 2008, Smith et al. 2016, 2017) that creates patchiness in patterns of cambial heating, crown scorch, and concomitant tree mortality (Loudermilk et al. 2012, Hood et al. 2018, Furniss et al. 2019). During surface fire, tree crowns are damaged primarily by convective heat transfer from plumes of heated air that quickly kill foliage, buds, and vascular tissue, while tree boles are more susceptible to conductive and radiative heat transfer from combustion of surface fuels (Hood et al. 2018). The thick bark of fire-adapted species and large-diameter trees can protect from this radiative heat to some extent (van Wagtendonk and Fites-Kaufman 2006, Belote et al. 2015), but the long residence time of heat released from smoldering duff and slow burning fuels (e.g., large woody debris) can penetrate this thick bark and warm the cambium enough to cause tissue death (≥60°C; Hood et al. 2018). By driving both fire temperature and residence time, the size and arrangement of fuels (Hiers et al. 2009, Loudermilk et al. 2012) influence both the intensity (energy release) and severity (ecological consequences) of fire (Jeronimo et al. 2020).

Weather, topography, and environmental heterogeneity can also create spatial patterns in fire effects. Areas that burn under moderate weather conditions generally burn with lower intensity compared to areas that burn under more extreme fire weather conditions (e.g., strong winds, low relative humidity; Lydersen et al. 2014). This is particularly evident during extreme weather conditions when positive feedback cycles between fire and the atmosphere create self-sustaining, plume-dominated fire behavior that results in large patches of high-severity fire effects across vast portions of a landscape (Allen 2007, Lydersen et al. 2014). Topography contributes to spatial autocorrelated fire behavior both directly through regulating fire intensity (e.g., higher intensity toward ridge tops; Turner and Romme 1994, Kane et al. 2015) and indirectly through feedbacks with forest structure (Jeronimo et al. 2020).

Forest structure regulates fire behavior at both fine (Thaxton and Platt 2006, Hiers et al. 2009, Loudermilk et al. 2012) and broad scales (Rothermel 1972, Miller and Urban 1999a, b, 2000a, Harris and Taylor 2015), and it contributes to temporal patterns by moderating fuel connectivity and regulating spread rate (Caprio and Swetnam 1995, Miller and Urban 2000b, Taylor and Skinner 2003). Conversely, repeated fire events influence the spatial pattern dynamics of trees and fuels within stands (scales <10 ha; Youngblood et al. 2004, North et al. 2007, Larson and Churchill 2012), and broad-scale patterns in fire behavior (>10 ha) create, rearrange, and refine patches of forest, unburned islands, and early-seral habitat among stands and across broad landscapes (>1000 ha; Turner et al. 1997, Hessburg et al. 1999, Taylor and Skinner 2003, Kane et al. 2014, Meddens et al. 2018a, b, Jeronimo et al. 2019). In short, heterogeneity in forest spatial structure contributes to variability in fire intensity, and variability in fire intensity perpetuates heterogeneity in forest structure. This reciprocal relationship between fire, fuels, and forest spatial structure mediates the severity of future fires, and this self-regulation renders fire foundational to the structure and function of many forest ecosystems (van Wagtendonk and Fites-Kaufman 2006, Scholl and Taylor 2010, Larson et al. 2013).

Larson and Churchill (2012) reviewed the literature regarding spatial pattern dynamics in frequent-fire forests, and they characterized spatial patterns in these forest types as a shifting mosaic of individuals, clumps, and openings. They described the iterative nature of fire spatial pattern interactions including mechanisms of pattern formation and maintenance, and this model has become an archetype for spatial pattern dynamics in frequent-fire forests (Franklin and Johnson 2012, Hessburg et al. 2015, North et al. 2019). While this model may be sufficient to describe the feedbacks between fire and forest spatial structure, there is limited consideration of how background mortality processes interact with fire to mediate the spatial pattern dynamics in post-fire forests and to moderate mortality in between fire events.

There is extensive overlap between the spatio-temporal signature of fire and background mortality agents (Fig. 1), and this suggests that background mortality processes may be important contributors to patterns observed in post-fire mortality. There are indeed many studies of interactions between background mortality processes and fire in the literature (Hood and Bentz 2007, Youngblood et al. 2009, van Mantgem et al. 2013, 2018, Kane et al. 2017b, Hood et al. 2018, Stephens et al. 2018), but these studies are focused primarily on the nature of the interaction (i.e., amplified or inhibited; Kane et al. 2017b) rather than the interactive effects of these processes on patterns in mortality.

Spatial elements of post-fire mortality

Among the most widely studied mortality process in post-fire forests is competition for water and soil resources. Stand structure mediates the intensity of inter-tree competition and creates heterogeneity in the severity of drought- and competition-related stress (Fensham and Holman 1999, Guarín and Taylor 2005, Allen et al. 2010, van Mantgem et al. 2016), and this modifies the susceptibility of trees to both direct (van Mantgem et al. 2013, Furniss et al. 2019) and indirect fire-related mortality (van Mantgem et al. 2016, 2018, Hood et al. 2018). While inter-tree competition in unburned forests is often considered to primarily inhibit seedlings and small-diameter trees, recent studies suggest that competition in post-fire forests can be an important determinant of mortality for larger trees as well (Yu et al. 2009, van Mantgem et al. 2018). The nature of drought–fire interactions is also dependent on the timing of events: Fire reduces stand density, and this can make surviving trees less susceptible to competition- and drought-related mortality post-fire (van Mantgem et al. 2011, 2016), but pre-fire drought can hinder trees' ability to tolerate fire damage and can increase probability of immediate fire-related mortality (van Mantgem et al. 2013, 2018).

Bark beetles have been long considered as an important factor in mediating post-fire mortality (Ryan and Amman 1996, Scott et al. 2002, Sieg et al. 2006, Hood and Bentz 2007), but the effects of local tree neighborhood on susceptibility to bark beetles are complex and dependent on a variety of post-fire factors (Kolb et al. 2007). As with beetle-related mortality in a pre-fire mortality regime, local neighborhood structure and composition influence the availability of resources necessary for trees to invest in defense infrastructure (i.e., resin and resin ducts; Hood and Sala 2015), and this directly contributes to resistance against bark beetle attack (Raffa 2014). As fire decreases density and competition for resources, we might expect fire to enhance resistance to bark beetle attack by increasing resource availability and thus the capacity of trees to invest in resin defenses. However, surviving trees may be temporarily weakened due to direct fire injury to their foliage, cambial tissue, and surface roots, and this may limit their capacity to defend against beetle attack immediately after fire (McHugh and Kolb 2003, Kolb et al. 2007). Fire may further intensify bark beetle pressure by creating an abundance of weakened host trees across the landscape that are susceptible to beetle attack and thus enabling beetle populations to proliferate. This increase in beetle abundance may facilitate more successful mass attacks and can catalyze a transition from endemic to epidemic beetle population dynamics (Raffa et al. 2008). Empirical studies have found evidence for both facilitated and impeded bark beetle mortality post-fire (Youngblood et al. 2009, Hood et al. 2016): Fire may initially increase susceptibility to bark beetles by weakening trees and reducing their ability to defend (McHugh and Kolb 2003, Hood and Bentz 2007, Kolb et al. 2007, Youngblood et al. 2009), but fire is also thought to increase resistance to bark beetles over longer timescales by reducing stand density, increasing the distances between conspecifics, and stimulating the production of resin (Fettig et al. 2007, Hood et al. 2015, 2016).

Pathogens also interact with fire damage to mediate post-fire mortality (Parker et al. 2006, Kane et al. 2017b), and local tree neighborhoods may affect susceptibility to pathogens post-fire through altering resource availability, overall vigor, and capacity to defend against pathogens. As with bark beetles, it is not clear whether fire will enhance or reduce the prominence of pathogen-related mortality (Kane et al. 2017b). Fire may facilitate the apparent virulence of pathogens by weakening trees (Parker et al. 2006), but it may also impede pathogens (Grelen 1983, Beh et al. 2012) by scorching the soil, reducing the number of live trees, and increasing distance between suitable host trees. Three-way interactions between pathogens, bark beetles, and drought on fire-weakened trees may further complicate the detection of pathogen-caused mortality in post-fire forests.

Applications for post-fire mortality models

There is a growing body of evidence (Youngblood et al. 2009, Hood et al. 2018, van Mantgem et al. 2018, Furniss et al. 2019) that suggests that these background mortality processes play a key role in shaping post-fire mortality, but they are absent from the most widely used post-fire tree mortality models. A recent update of the First Order Fire Effects Model (FOFEM; Hood and Lutes 2017) has improved model accuracy by incorporating bark beetle presence/absence as a predictor variable for four species-specific models (Hood and Lutes 2017), but this binary approach is not optimally suited to capture the complex nature of bark beetle population dynamics (Raffa et al. 2008). Furniss et al. (2019) found that mortality model prediction error was spatially autocorrelated, indicating that spatially structured mortality processes not only mediate patterns in post-fire mortality, they comprise some of the unexplained prediction error within fire effects models. This is supported by recent efforts to integrate background mortality agents including bark beetles, pathogens, and competition into theoretical frameworks describing the mechanisms of post-fire tree mortality at scales ranging from individual trees (Hood et al. 2018) to broad landscapes (Kane et al. 2017b).

Objectives

The considerable volume of background tree mortality literature demonstrates a variety of mechanisms by which biotic and abiotic mortality agents evoke spatial patterns in tree mortality (Fig. 1). Yet, there is not currently a cohesive framework for assessing how fire and other acute disturbance events may modify the relative importance and spatio-temporal structure of background mortality processes. We addressed this by quantifying the spatial elements of pre-fire, direct fire, and post-fire tree mortality, then developing an empirically informed framework describing how fire and background mortality processes interactively mediate mortality and collectively determine forest spatial pattern dynamics. For each mortality regime (pre-fire, direct fire, and post-fire), we examined the spatial structure of distance-dependent mortality processes using point pattern analysis, and we evaluated the intensity and spatial extent of density dependence using generalized linear models.

We tested the null hypothesis that fire and background mortality processes do not interact, resulting in a post-fire mortality regime that may be characterized simply by the additive effects of direct fire damage and background mortality processes. Alternatively, we hypothesized that fire may override and obscure background mortality processes, impeding the spatial elements of background mortality and imposing patterns in post-fire mortality that reflect only the heterogeneity in direct fire damage. In this case, we would expect the spatial patterns associated with background mortality agents (e.g., bark beetles, pathogens) to become spatially random, or to resemble the spatial pattern of direct fire damage (e.g., crown scorch). A second alternative hypothesis is that fire may interact with background mortality processes, creating patterns in post-fire mortality that do not resemble the patterns of either pre-fire or direct fire mortality alone. Finally, we hypothesized that mortality would become less density-dependent post-fire because reduced stand density may have increased above- and below-ground resource availability, thus reducing the sensitivity of surviving trees to competitive stress and contagious mortality agents within their local neighborhoods.

Study area

We conducted this study in an old-growth Abies concolor–Pinus lambertiana (white fir–sugar pine) forest in the lower-montane, mixed-conifer forest zone of the Sierra Nevada, California, USA. We used data from the Yosemite Forest Dynamics Plot (YFDP; Lutz et al. 2012, Lutz 2015), a 25.6-ha stem-mapped forest monitoring plot located between 1774 and 1911 m elevation in Yosemite National Park, with species composition and structure representative of the Sierra Nevada white fir superassociation (Keeler-Wolf et al. 2012). The YFDP was established in 2009 and 2010 when we tagged, identified, and mapped all tree stems ≥1 cm diameter at breast height (DBH; 1.37 m) within the plot (n = 34,458 live stems; Lutz et al. 2012). We considered four tree species comprising 32,989 stems ≥1 cm DBH within the YFDP: A. concolor [Gordon] Lindl. ex Hildebr. (white fir; 939 stems/ha), P. lambertiana Dougl. (sugar pine; 180 stems/ha), Calocedrus decurrens [Torr.] Florin (incense cedar; 64 stems/ha), and Quercus kelloggii Newb. (California black oak; 46 stems/ha).

Fire in the YFDP

The YFDP has been relatively unaffected by timber harvest and grazing, but a century of effective fire suppression had a profound impact on the pre-fire structure and composition of this forest. The lack of fire resulted in an abundance of surface and ladder fuels, uncharacteristically high stem density, and a compositional shift toward shade-tolerant species (Caprio and Swetnam 1995, Scholl and Taylor 2010, North et al. 2019). The high fuel loads associated with these stands can make the reintroduction of fire challenging (Lydersen et al. 2014), often requiring mechanical fuel reduction and prescribed fire treatments to develop historical structure, composition, and spatial pattern that confer resilience to wildfire, drought, and biotic disturbance (North et al. 2007, Safford et al. 2012, Stephens et al. 2018).

The YFDP was burned for the first time in 113 yr (Barth et al. 2015) as part of a management-ignited fire set to control the spread of the Rim Fire, a 104,131-ha wildfire that burned in August and September of 2013. The fire was ignited ~1 km from the YFDP on 31 August 2013, and no management action was taken within the YFDP before or after ignition. Fire intensity ranged from low- to high-intensity surface fire with patches of unburned surface fuels (primarily in draws; Lutz et al. 2017a, Blomdahl et al. 2019) and occasional crown torching (Fig. 2). Surface fuel consumption was >90% for litter, duff, and small fuels (<1000 h), and 61% for coarse woody debris (Larson et al. 2016, Cansler et al. 2019). Fire effects were heterogeneous with patches of low, moderate, and high tree mortality (Furniss et al. 2020).

Pre-fire mortality was measured through annual mortality surveys in 2011, 2012, and 2013. Each year, we re-visited every tree that was alive in the previous year and we identified new mortalities (no live foliage above DBH). We conducted pathology examinations (including removing bark to inspect the cambium) on each newly dead tree and recorded the multiple factors associated with death (e.g., beetle galleries, pathogens, ruptured stem, crushing; see Appendix S1 for comprehensive list). We also recorded notes about each live tree pertaining to unique characteristics such as old fire scars. Eight months after the fire, we conducted a mortality survey to identify newly dead trees (hereafter “immediate mortality”; trees newly dead between June 2013 and May 2014). In addition to the standard pathology procedure (Appendix S1), we also recorded fire damage (bole scorch height and percent crown volume scorched; CVS) for all live and newly dead trees. Post-fire mortality was measured through annual mortality surveys for five years following the fire (hereafter “post-fire mortality”; trees that survived ≥1 yr post-fire but died in 2015–2018). Pathology examinations were conducted by well-trained, inter-calibrated field crews under the direct supervision of the principal investigators and experienced crew leads, with four personnel present during all ten years of measurement for continuity.

Analyses

As spatially explicit mortality processes may differ among species and size classes (Das et al. 2008, Wang et al. 2012), we analyzed each species independently and grouped trees into three size classes chosen to reflect the distinct ecological roles of small (1–10 cm DBH)-, medium (10–60 cm DBH)-, and large (≥60 cm DBH)-diameter trees (sensu Lutz et al. 2018) while maintaining a robust sample of trees in each diameter class. We restricted all point pattern analyses to species-size classes that contained >100 individuals to minimize exposure to type II error (failure to reject the null when it is false; Rajala et al. 2018).

We grouped mortality into three regimes: pre-fire (background) mortality, direct fire-related mortality, and post-fire mortality. For each mortality regime, we assessed both the spatial structure of background mortality processes as well as the effects of local neighborhood structure on mortality risk. To characterize the spatial structure of mortality, we used two forms of point pattern analysis: the pair-correlation function (PCF) to quantitatively compare patterns, and maps of point pattern intensity to qualitatively describe, visualize, and compare patterns. To assess the effects of forest spatial pattern on mortality risk, we used generalized linear models based on the local neighborhood spatial structure around each tree. We implemented both types of analysis for each species, size class, and mortality regime.

Distance-dependent mortality

Pre-fire mortality

Pre-fire mortality was aggregated when all stems were pooled (Fig. 3), indicating the presence of distance-dependent mortality processes. Mortality was aggregated at the greatest distance for small-diameter stems (0–13 m), and this clustering of mortality was evident despite the initial pre-fire pattern of small-diameter stems also being strongly aggregated (Fig. 3; Appendix S1: Fig. S1). Pre-fire mortality of medium-diameter stems was similarly aggregated, but the clustering of mortality was more clearly differentiated because the initial pattern of medium-diameter stems was more regular (i.e., less aggregated) compared to the initial pattern of small-diameter stems (Fig. 3). The spatial pattern of large-diameter mortalities was generally random, but this randomness may indicate a slightly clustered pattern of mortality because the initial pattern of large-diameter trees was hyper-dispersed (Appendix S1: Fig. S1).

Mortality associated with bark beetles was aggregated for all species-size classes (Fig. 4; n for each indicated by bold in Table 1). Beetle-related mortality was aggregated from 0 to 4 m for small-diameter (1–10 cm DBH) Abies, from 0 to 6 m for medium-diameter Abies, and from 0 to 10 m for Pinus of all sizes (Fig. 4). Mechanical mortality was also aggregated for small- and medium-diameter Abies from 0 to 6 m and 10 to 22 m, respectively. Pathogen mortality was spatially random for small-diameter Abies, the only size class that had sufficient numbers of mortality to test (Fig. 4).

Post-fire mortality

Post-fire mortality of all stems ≥1 cm DBH was aggregated from 0 to 7 m, a finer scale compared to both pre-fire and direct fire mortality (Fig. 3). Post-fire mortality of small stems was random, while medium-diameter mortalities were slightly aggregated from 0 to 8 m (Fig. 3). Post-fire mortality of large-diameter trees, in contrast, was strongly clustered and at greater scales compared to pre-fire mortality (0–17 m; Fig. 3). The emergence of strongly clustered large-diameter tree mortality was readily apparent in the field and is also visually discernable from the stem maps of mortality (Appendix S1: Fig. S1). Considering species individually, post-fire mortality was aggregated from 0 to 4 m for Abies, from 0 to 17 m for Pinus, and was spatially random for Calocedrus and Quercus (Fig. 3).

Post-fire mortality was mediated by biotic and mechanical mortality processes that were spatially structured for all species and diameter classes that we tested. Bark beetle mortality was aggregated for medium-diameter Pinus from 0 to 12 m, large-diameter Pinus from 0 to 18 m, and medium-diameter Abies from 1 to 8 m (Fig. 5). Mechanical mortality was aggregated for medium-diameter Abies from 0 to 5 m and 16 to 19 m. Pathogen mortality was also aggregated for medium-diameter Abies from 2 to 3.5 m (Fig. 5).

Geographic patterns in mortality

Pre-fire mortality

Maps of mortality intensity revealed complex patterns of mortality across the YFDP. Pre-fire mortality of small- and medium-diameter stems was characterized by patches of both high and low mortality rates separated by regions of random, ambient mortality (Fig. 6; Appendix S1: Fig. S1). The spatial distribution of pre-fire large-diameter mortalities, however, was random.

Density-dependent mortality

Pre-fire mortality

Spatial variables improved predictions of pre-fire mortality for small- and medium-diameter Abies, medium-diameter Pinus, and Quercus ≥10 cm DBH (Table 2; Appendix S1: Table S2). Density of pole-sized conspecifics was the single most important variable in most cases, while BA was more important for Abies. The direction of the relationship was not consistent; density increased probability of mortality for small-diameter Abies, while density decreased probability of mortality for medium-diameter Pinus and Quercus (Figs. 7, 8; Appendix S1: Fig. S2). Pre-fire mortality of large-diameter trees was density-independent for the three conifer species (Figs. 7-9).

Table 2. Mortality rates and spatial metrics that were correlated with mortality.

DBH (cm)	Important structural variables
	Pre-fire	ΔAIC	Direct fire	ΔAIC C	Post-fire	ΔAIC
Abies
1–10	Density of conspecifics ≥10 cm DBH (10 m) (+)	−92.7	Density of conspecifics ≥10 cm DBH (30 m) (+)	−177.4	BA (5 m) (+)	−48.9
10–60	BA (30 m) (−)	−33.0	BA of conspecifics (30 m) (+)	−99.6	Density surviving stems 1 ≤ cm DBH < 10 (10 m) (−)	−125.9
≥60	Density of stems 10 ≤ cm DBH < 60 (10 m) (−)	−5.4	Density of conspecifics ≥10 cm DBH (30 m) (+)	−6.3	Density of stems ≥60 cm DBH (20 m) (+)	−15.2
Calocedrus
1–10	Density of all stems ≥1 cm DBH (20 m) (−)	−5.6	Landscape position (+)	−38.5	BA surviving conspecifics (20 m) (+)	−13.9
10–60	Density of all stems ≥1 cm DBH (30 m) (−)	−3.0	BA of conspecifics ≥10 cm DBH (30 m) (−)	−12.6	BA surviving conspecifics (5 m) (+)	−7.8
≥60	Density of stems 10 ≤ cm DBH < 60 (30 m) (+)	−1.9	BA (30 m) (−)	−5.8	BA (30 m) (+)	−2.8
Pinus
1–10	Hegyi (+)	−3.9	BA (5 m) (+)	−22.1	BA surviving conspecifics (30 m) (+)	−4.8
10–60	Density of conspecifics ≥10 cm DBH (20 m) (−)	−9.8	Density of stems ≥1 cm DBH (5 m) (−)	−9.8	BA of conspecifics ≥10 cm DBH (10 m) (+)	−37.2
≥60	BA of conspecifics ≥10 cm DBH (10 m) (−)	−6.2	Fire scar (+)	−24.0	Hegyi (+)	−76.8
Quercus
1–10	Nearest neighbor (+)	−4.6	Density of stems 10 ≤ cm DBH < 60 (15 m) (+)	−41.4	…
≥10	Density of conspecifics ≥10 cm DBH (10 m) (−)	−22.9	Hegyi (+)	−41.6	BA (30 m) (+)	−13.7

Notes

• BA, basal area; CVS, crown volume scorched; DBH, diameter at breast height. “…” stands for, no variables were significant. Correlations were identified by pairing each variable with non-spatial base models based on DBH and CVS. This table contains the single best structural variable for each species and size class; all significant variables are reported in Appendix S1: Tables S2–S4. Descriptions of each variable are in Appendix S1: Table S1. The distance values each variable indicate the circular radius at which that structural variable had the most explanatory power. The (+) or (−) next to the structural variable indicates the direction of the relationship (positive indicates greater mortality risk; negative indicates lower mortality risk). Delta Akaike information criterion (ΔAIC) represents the differential model performance compared to the base (non-spatial) mortality models; more negative numbers indicate greater improvement. Bold indicates that the spatial model was significantly better than the non-spatial base model (|ΔAIC| > 7).

Pre-fire mortality

The overall pre-fire mortality rate of 1.7% per yr was within the range of variability expected based on other long-term forest demography plots in similar forest types within the Sierra Nevada (1.5% per yr; Stephenson and van Mantgem 2005). Sample size constraints limited our assessment of pre-fire mortality for some agents, underscoring the difficulties associated with detecting slow-acting ecological processes such as tree mortality, even within large forest monitoring plots (Clark and Clark 1996, Lutz 2015, Das et al. 2016, Birch et al. 2019a, McMahon et al. 2019).

Pre-fire mortality was aggregated at fine spatial scales (0–13 m considering all stems; Fig. 3), a pattern of mortality observed in both young and old forests (Kenkel 1988, Das et al. 2008, Lutz et al. 2014, Larson et al. 2015, Furniss et al. 2017). This scale of interaction is consistent with (although slightly larger than) previous studies that have quantified the scale at which second-order (i.e., plant–plant) interactions can moderate mortality risk (4.5 m in Kenkel 1988, 5 m in He and Duncan 2000, 3 m in Little 2002, 4 m in Yu et al. 2009, 9 m in Das et al. 2011, 9 m in Lutz et al. 2014, 4 m in Larson et al. 2015, 10 m in Punchi-Manage et al. 2015, 6 m in Clyatt et al. 2016, 3 m in Furniss et al. 2017, 5 m in Birch et al. 2019b).

Mortality was clustered for stems of all sizes, but strength and directionality of density dependence varied depending on tree species and size class (Figs. 7-9). Pre-fire mortality of small Abies stems was positively related to neighborhood density of conspecifics (i.e., negative density dependence), while mortality risk of medium-diameter Abies, Pinus, and Quercus was negatively related to BA and conspecific density (i.e., positive density dependence; Figs. 7, 8; Appendix S1: Fig. S2). These opposing forms of density dependence reflect the importance of competition as a primary determinant of mortality for small-diameter trees (Das et al. 2008, 2011, Lutz et al. 2014), and the importance of external factors (i.e., pests, pathogens, and physical damage) that compose the mortality complexes responsible for medium- and large-diameter tree mortality (Franklin et al. 1987, Das et al. 2011, 2016). These results are consistent with the expectation that background mortality transitions from strongly density-dependent within young forests to density-independent among mature trees in old-growth forests (He and Duncan 2000, Gray and He 2009, Yu et al. 2009, Aakala et al. 2012, Hurst et al. 2012, Johnson et al. 2014, Larson et al. 2015), and they provide a more nuanced understanding of this transition by demonstrating that density dependence can continue to regulate mortality among small-diameter stems even within a structurally complex, old-growth forest.

A likely source of the competitive stress responsible for the density-dependent mortality of small-diameter Abies is intraspecific competition from other small-diameter Abies. These stems were strongly aggregated (Fig. 3; Lutz et al. 2012) and were most abundant in areas with high conspecific density (>1000 stems/ha; Figs. 2, 7), and we may therefore expect mortality in these sites to resemble the self-thinning characteristic of dense, young forests (Kenkel 1988, Gray and He 2009, Larson et al. 2015). Another likely source of competitive stress is strong asymmetric competition from larger trees; the physical dominance of large trees provides them with superior access to both above- and below-ground resources, and this can inhibit survival of smaller trees within their local neighborhood (Lutz et al. 2014, Furniss et al. 2017).

There are a few plausible reasons for the positive density dependence we observed among medium-diameter trees (mortality risk decreased with greater BA and conspecific density; Figs. 7, 8; Appendix S1: Fig. S2). First, the local neighborhoods around medium-diameter trees were characterized by lower densities (up to 200 stems/ha; Fig. 8; Appendix S1: Fig. S2) and more regular spacing (Fig. 3; Lutz et al. 2012) compared to small-diameter trees. The reduced crowding in these more open neighborhoods may have reduced overall competitive stress, but this does not fully explain the reversed directionality of density dependence. Second, this pattern of positive density dependence may be associated with environmental heterogeneity within the YFDP. We would expect medium-diameter trees to be most abundant in high-quality habitats within the YFDP (i.e., environmental filtering; Das et al. 2018), and we might also expect mortality rates to be lowest in these favorable sites; the combination of these two factors could elicit a pattern of positive density dependence. Finally, below-ground fungal symbionts (i.e., ectomycorrhizae; Perry et al. 1989) can confer facilitative effects that may have contributed to this pattern.

These results provide two interesting contrasts with a previous study from similar forests in the Sierra Nevada (Das et al. 2008). First, the authors observed CNDD (i.e., mortality risk increased with higher conspecific density) for P. lambertiana ≥12.7 cm DBH, while we found that mortality risk decreased with increasing conspecific BA for stems 10–60 cm DBH for that species (Fig. 8). Second, they observed a pattern of positive conspecific density dependence for A. concolor (of all sizes); our results were consistent with this for medium-diameter stems, but we observed the opposite pattern among small-diameter stems. These contrasts demonstrate that while local neighborhood structure and composition are important factors determining mortality risk, the nature of neighborhood effects may vary among forest stands. Additionally, grouping trees by diameter may have enabled us to detect neighborhood effects that may be neutralized if all sizes are analyzed together.

Spatial patterns of mortality were also driven by the distance-dependent nature of pests, pathogens, and physical damage, and each of these mortality processes had a distinct spatial structure. Bark beetle-induced mortality of small- and medium-diameter Abies was aggregated at very fine scales (0–6 m; Fig. 4), while beetle mortality for Pinus was aggregated to slightly larger scales (0–10 m). Mechanical mortality (i.e., crushing) was aggregated at the greatest scales for small- and medium-diameter Abies (0–12 m and 0–21 m, respectively; Fig. 4). This is consistent with our a priori conceptualization of these two mortality agents—both bark beetle and mechanical mortality are aggregated at very fine scales (<0.1 ha), but we expected mechanical mortality to remain aggregated at slightly larger scales due to the large height (up to 55 m) and potential propagation of large falling trees (Fig. 1A).

We did not detect a spatial structure associated with pathogen-related mortality, perhaps because the slow rate of pathogen spread may necessitate a longer time span for their spatial structure to be detected (Waring et al. 1987, Lung-Escarmant and Guyon 2004). Additionally, our analysis of pre-fire pathogen mortality was limited to small-diameter Abies (due to sample size constrains) and competition was a more important driver of mortality for small stems.

Although previous studies have quantified the spatial structure associated with these mortality agents independently (Safranyik and Carroll 2006, Das et al. 2008, Larson and Franklin 2010, Bače et al. 2015, Fig. 1A), this study is the first that we are aware of that has quantitatively compared the spatially contagious nature of endemic bark beetle mortality, pathogens, and mechanical-related tree mortality within the same study site.

Direct fire mortality

Immediate fire mortality was aggregated for small- to medium-diameter stems from 0 to 30 and 0 to 22 m, respectively (Fig. 3). This was likely driven primarily by heterogeneity in fuel loadings (Cansler et al. 2019) and topography (Fig. 2) that altered fire behavior and resulted in patches of high and low crown scorch across the YFDP (Fig. 2). Crown scorch was the strongest predictor of immediate mortality (Furniss et al. 2019), causing the spatial structure of immediate mortality to closely reflect the heterogeneity in fire intensity and flame length (Figs. 2g, 6). The spatial structure of immediate mortality was clustered at the greatest inter-tree distance of any form of mortality that we assessed (30 m; Fig. 3), distinguishing direct fire morality as a key driver of structural heterogeneity and spatial pattern at slightly broader spatial scales (0.1–1 ha) compared to background mortality (Fig. 1).

Local neighborhood structure was directly related to probability of immediate mortality, presumably because higher stem density was associated with increased fuel loadings (Cansler et al. 2019) that elevated fire intensity (Miller and Urban 1999b, Thaxton and Platt 2006) and induced greater damage to trees. Surprisingly, forest structure was also related to probability of direct fire mortality when we included crown scorch as a predictor variable to control for variability in fire intensity (Table 2), suggesting that forest spatial structure also influenced probability of direct mortality by reducing tolerance of individual trees to direct fire damage (perhaps by modifying local water availability and competitive stress; van Mantgem et al. 2018).

Local neighborhood structure was not of equal importance for all trees; landscape position was more important for immediate morality of small- to medium-diameter Calocedrus, and the presence of a previous fire scar the most important factor for immediate mortality of medium- to large-diameter Pinus. The importance of fire scars for Pinus mortality reflects their tolerance to direct fire damage due to thick bark and high crown base heights, making them less exposed to heat-induced injury (Hood et al. 2018), yet uniquely susceptible to physical failure at scars incurred from past fire events (Kolb et al. 2007, Furniss et al. 2019).

Our findings reveal an important disparity between the scales at which fire operates and the scales at which fire effects are most often monitored. Fire creates ecological mosaics at intermediate and broad scales (>1 ha; Turner et al. 1997, Hessburg et al. 2005, Yocom-Kent et al. 2015, Meddens et al. 2018a), but fine-scale (0.1–1 ha) heterogeneity in fire effects performs distinct, and similarly important, ecological functions (Meddens et al. 2018b). Low-, moderate-, and mixed-severity fire introduces spatial pattern complexity (Larson and Churchill 2012, Churchill et al. 2013, Kane et al. 2013, 2014), mitigates susceptibility to drought, competition, and beetle-related mortality (Kolb et al. 2007, Hood et al. 2015, 2016, van Mantgem et al. 2016), and confers resilience to future disturbances and climatic variability (Allen et al. 2002, Hessburg et al. 2015, Cansler et al. 2018, Stephens et al. 2018, North et al. 2019). Fine-scale heterogeneity in fire effects is an essential component of these ecological functions, yet a vast amount of fire science is based on remotely sensed severity products that are limited to the relatively coarse spatial resolution of hyperspectral satellite sensors (e.g., 30-m pixel size for the Landsat series). Our results demonstrate that traditional satellite-derived data products may not be sufficient to fully capture the fine-scale complexity in fire effects that are central to the ecological function of low, moderate-, and mixed-severity fire (Furniss et al. 2020).

Post-fire mortality

The combination of fire, drought, and background mortality processes enhanced the importance of local stand structure as a mediator of mortality risk and provoked a strong spatial structure among medium- and large-diameter tree mortalities (Fig. 10). The post-disturbance mortality regime was not simply an extension of direct fire effects, nor was it a return to the pattern in pre-fire mortality (Figs. 3, 6). It was instead a novel regime that emerged from both additive and interactive effects of fire damage, drought, and background mortality agents. Second-order ecological interactions (e.g., bark beetles, mechanical failure, competition) were important determinants of post-fire mortality (Table 1, Fig. 10), and the contagious nature of these mortality agents became evident at greater distances than pre-fire (Fig. 5). Local neighborhood structure assumed a central role in mediating overall mortality risk for all trees, and mortality risk of medium- and large-diameter trees became density-dependent (Figs. 7-9).

We speculate a few reasons for the amplified spatial structuring of post-fire mortality. First, contagious mortality processes may have been facilitated by the rapid pulse of fire-weakened trees, causing the pre-fire distribution of biotic mortality agents (bark beetles and pathogens) to become revealed. In other words, the fire may not have changed the spatial structure associated with these contagious agents, and it may have simply made their spatial structure more evident. Alternatively, the post-fire proliferation of bark beetles and pathogens may have enhanced their ability to successfully attack most trees, enabling these mortality agents to kill trees that would have otherwise been resistant. This may have reduced the relative importance of individual tree characteristics (size, vigor, and defenses) and enhanced the importance of proximity to an infected host tree (i.e., distance dependence). In this case, the contagious nature of these mortality processes may have induced a pattern of aggregated mortality that would not have emerged in the absence of fire, even given enough time.

The elevated intensity of negative density dependence (Figs. 7-9) following fire may have also contributed to the increased scale of aggregation among contagious mortality agents. Despite the increased resource availability that would be expected due to direct fire mortality, surviving trees may not have been able to immediately utilize the newly available light, water, and soil resources. It can take years for trees to recover from direct fire damage (van Mantgem et al. 2011, Hood et al. 2018), and during this recuperative period, trees may have been particularly sensitive to density-dependent stress that could have increased susceptibility to drought, competition, and insect-related mortality (Kolb et al. 2007, Das et al. 2008, Yu et al. 2009, Anderegg et al. 2015, Clyatt et al. 2016, van Mantgem et al. 2016).

Fire also altered the diameter classes in which spatially structured mortality was most evident (Fig. 10). While pre- and direct fire mortality of small-diameter stems was aggregated, post-fire mortality of these trees became spatially random (Fig. 3). Conversely, the post-fire mortality regime induced a strong spatial structure among large-diameter mortalities that was not evident based on pre-fire or direct fire damage alone (Figs. 3, 6).

Implications for fire mortality models

Existing fire mortality models (e.g., FOFEM) predict mortality with a high degree of accuracy (Woolley et al. 2012, Grayson et al. 2017, Hood and Lutes 2017), but performance is inconsistent for large-diameter trees (Hood et al. 2007, Kane et al. 2017a, Furniss et al. 2019). These models perform best when direct fire damage is the primary driver of mortality (i.e., trees with high percent crown scorch), but large-diameter trees are rarely killed by fire damage alone. Our findings concur with the widespread understanding that large-diameter trees are instead more susceptible to the physical and biotic mortality agents (i.e., drought and bark beetles) that mediate delayed mortality post-fire (Hood et al. 2018), but these background mortality processes are not represented by the independent variables (i.e., crown scorch and DBH) used in most post-fire mortality models (Woolley et al. 2012, Grayson et al. 2017, Hood and Lutes 2017). Spatially structured delayed mortality processes thus contribute to spatially autocorrelated error that manifests as patches of over- or under-predicted mortality within a stand (Furniss et al. 2019). The relative infrequency of large-diameter trees (e.g., ~1% of individuals; Lutz et al. 2018) allows total model accuracy to remain high, despite systematic error that emerges when predictions are aggregated at the stand level (Furniss et al. 2019).

Both types of error may be reduced by incorporating stand structure variables into mortality models to capture the density-dependent processes that regulate delayed mortality (Figs. 7-9, Table 2; Appendix S1: Table S4). The inclusion of structural variables would particularly enhance the capacity of fire mortality models to predict post-fire spatial pattern: The resulting mortality predictions would not only reflect the variability in first-order fire intensity, they would also capture spatial heterogeneity in mortality risk due to forest composition, structure, and spatial pattern. This would also enhance the utility of mortality models for estimating the effects of fire on carbon stocks, as large-diameter trees contribute disproportionately to forest biomass (Lutz et al. 2018), and accurately modeling their demography will reduce the uncertainty associated with landscape-scale carbon estimates (Lutz et al. 2017b, Stenzel et al. 2019).