Quantitative Evidence for Increasing Forest Fire Severity in the Sierra Nevada and Southern Cascade Mountains, California and Nevada, USA

Recent research has concluded that forest wildfires in the western United States are becoming larger and more frequent. A more significant question may be whether the ecosystem impacts of wildfire are also increasing. We show that a large area (approximately 120000 km²) of California and western Nevada experienced a notable increase in the extent of forest stand-replacing (“high severity”) fire between 1984 and 2006. High severity forest fire is closely linked to forest fragmentation, wildlife habitat availability, erosion rates and sedimentation, post-fire seedling recruitment, carbon sequestration, and various other ecosystem properties and processes. Mean and maximum fire size, and the area burned annually have also all risen substantially since the beginning of the 1980s, and are now at or above values from the decades preceding the 1940s, when fire suppression became national policy. These trends are occurring in concert with a regional rise in temperature and a long-term increase in annual precipitation. A close examination of the climate–fire relationship and other evidence suggests that forest fuels are no longer limiting fire occurrence and behavior across much of the study region. We conclude that current trends in forest fire severity necessitate a re-examination of the implications of all-out fire suppression and its ecological impacts. Author Contributions: Jay Miller designed the study, performed research, analyzed data, and wrote the article. Hugh Safford performed research, analyzed data, and wrote the article. Michael Crimmins performed research and analyzed data. Andi Thode designed the study and performed research.     

The structure and dynamics of Abies magnifica forests in the southern Cascade Range,USA

Abies magnifica (Red fir) forests in the Cascade Range and Sierra Nevada of California are composed of groups, or patches, of even-sized individuals that form structurally complex stands. Patches may be even-aged, resulting from synchronous post-disturbance establishment, or multi-aged, reflecting continuous recruitment of seedlings moderately tolerant of shade. We analyze the population structure (i.e. age, size, and spatial patterning) of A magnifica, and associated A concolor, White fir, and reconstruct the disturbance history of two mature to old-growth A. magnifica forests in order to determine the relationship between disturbance and forest structure. Within both stands examined, the distributions of A. magnifica seedlings, saplings, and small understory trees were clumped, with clump sizes corresponding to the area of canopy gaps. Gaps were created by frequent wildfire (mean fire return interval of 41 yr) and by windstorms. Severe fire initiated mass establishment of Abies magnifica, whereas gaps created by windthrowreleasedalreadyestablishedindividuals. Lowinten-sity fire stimulated little recruitment, but Red fir established continuously during fire-free intervals. Thus, the complex age and structures of Red fir forests reflect both episodic and continuous recruitment, as determined by the type and severity of natural disturbance.     

The dynamics of old-growth Pseudotsuga forests in the western Cascade Range,Oregon, USA

Size and age structure, spatial analysis, and disturbance history were used to analyse the population structures and regeneration patterns of 8 conifer stands in the central western Cascade Range, Oregon, USA. Variation in forest structure reflected the effects of frequent (20–50 yr) low-intensity fires and treefalls, infrequent (100–200 yr) localised, intense fires, and extensive fires that resulted in stand replacement (every ca 400 yr?).The amount of canopy removed and the size of openings formed by fires and treefalls were important determinants of subsequent forest establishment. Single or several species stands of Pseudotsuga and/or Abies procera, or mixed species stands of Pseudotsuga, Abies procera, Tsuga heterophylla and Abies amabilis established in openings where intense fires had removed most of the canopy trees over several ha. Multi-tiered and multi-aged stands, often containing 400–500 yr-old Pseudotsuga and variously-sized more or less even-aged patches of younger shade tolerant Tsuga heterophylla and/or Abies amabilis, occurred where lower-intensity fires did not kill all overstorey trees or where treefalls occurred after the initial fire.Current regeneration processes are influenced by overstorey composition, the availability and size of canopy openings, and the availability of substrates suitable for regeneration. Tsuga heterophylla and Abies amabilis established under Pseudotsuga menziesii and Abies procera canopies and in small canopy openings (<400 m²) created by windfalls, but rarely under Tsuga. Down logs and stumps were favoured establishment sites for Tsuga.The disturbance regime of fires of low-to moderate-intensity, windfalls, and occasional fires that result in extensive stand replacement contrasts with the pattern of infrequent, catastrophic disturbances proposed for other areas of the Pacific Northwest. Although fires at stand establishment commonly determine much of the composition, structure, and subsequent stand development, canopy replacement by shade tolerant species occurs as the different life histories of the species are expressed in response to various disturbances differing in intensity and frequency. Such a non-equilibrium view of vegetation change is consistent with many other fire-dominated forests of the western United States.     

Structural characteristics and canopy dynamics of Tsuga canadensis in forests of the southern Appalachian Mountains, USA

Tsuga canadensis (L.) Carr. forests of the southern Appalachian Mountains are currently facing imminent decline induced by a nonnative insect pest, the hemlock woolly adelgid (Adelges tsugae Annand). To effectively manage these forest systems now and in the future, land managers need baseline data on forest structure and dynamics prior to large-scale Tsuga canadensis mortality. Most of our knowledge concerning the dynamics of Tsuga canadensis forests comes from more northern locations such as the Great Lakes region and New England and, therefore, may not pertain to the ecological systems found within the southern Appalachian Mountains. We examined the structure and canopy dynamics of four Tsuga canadensis forest stands within the Cataloochee watershed, in the far eastern part of Great Smoky Mountains National Park (GSMNP). We characterized the environmental settings and vertical forest layers, as well as the diameter and age-structures of each Tsuga canadensis forest stand. These environmental and structural data showed that there were indeed differences between forest stands with and without successful Tsuga canadensis regeneration. The two forest stands exhibiting successful Tsuga canadensis regeneration were located above 1,000 m in elevation on well-drained, moderately steep slopes and had the greatest canopy openness. Structural data from these two forest stands indicated a history of more continuous Tsuga canadensis regeneration. We also constructed disturbance chronologies detailing the history of canopy response to disturbance events and related these to Tsuga canadensis regeneration within each forest stand. Student t-tests adjusted for unequal variances indicated significant differences in the number of release events per tree between forest stands with and without successful Tsuga canadensis regeneration. While forest stands with successful Tsuga canadensis regeneration were more frequently disturbed by minor to major canopy disturbances, events of moderate intensity were found to be most significant in terms of regeneration. These data will be of value to land managers maintaining stands of Tsuga canadensis where treatment for hemlock woolly adelgid infestation has been successful. In areas where treatment is impractical or unsuccessful, land managers will be able to use these data to restore Tsuga canadensis forests after the wave of hemlock woolly adelgid induced mortality has passed. As of August 2008, Joshua A. Kincaid will be a member of the Environmental Studies program at Shenandoah University in Winchester, Virginia, USA     

Fire regimes and forest changes in mid and upper montane forests of the southern Cascades, Lassen Volcanic National Park, California, U.S.A.

Aim Spatial and temporal variation in fire regime parameters and forest structure were assessed. Location A 2630‐ha area of mid‐ and upper montane forest in Lassen Volcanic National Park (LVNP). Methods Two hypotheses were tested concerned with fire‐vegetation relationships in southern Cascades forests: (1) fire regime parameters (return interval, season of burn, fire size, rotation period) vary by forest dominant, elevation and slope aspect; and (2) fire exclusion since 1905 has caused forest structural and compositional changes in both mid‐ and upper montane forests. The implications of the study for national park management are also discussed. Results Fire regime parameters varied by forest compositional group and elevation in LVNP. Median composite and point fire return intervals were shorter in low elevation Jeffrey pine (Pinus jeffreyi) (JP) (4–6 years, 16 years) and Jeffrey pine–white fir (Abies concolor) (JP‐WF) (5–10 years, 22 years) and longer in high elevation red fir (Abies magnifica)— western white pine (Pinus monticola) (RF‐WWP) forests (9–27 years, 70 years). Median fire return intervals were also shorter on east‐facing (6–9 years, 16.3 years) and longer on south‐ (11 years, 32.5 years) and west‐facing slopes (22–28 years, 54‐years) in all forests and in each forest composition group. Spatial patterns in fire rotation length were the same as those for fire return intervals. More growing season fires also occurred in JP (33.1%) and JP‐WF (17.5%) than in RF‐WWP (1.1%) forests. A dramatic decline in fire frequency occurred in all forests after 1905. Conclusions Changes in forest structure and composition occurred in both mid‐ and upper montane forests due to twentieth‐century fire exclusion. Forest density increased in JP and JP‐WF forests and white fir increased in JP‐WF forests and is now replacing Jeffrey pine. Forest density only increased in some RF‐WWP stands, but not others. Resource managers restoring fire to these now denser forests need to burn larger areas if fire is going to play its pre‐settlement role in montane forest dynamics.     

Fire as a tool in the management of a savanna/dry forest reserve in Madagascar

Abstract. The possible use of fire for the management of the Ankarafantsika Reserve in the northwest of Madagascar and of its surrounding area is studied. Within this savanna landscape large parts of the remaining dry forests still exist with a unique biotic diversity, both in terms of total number of species and endemism. Unfortunately, mainly man-induced uncontrolled fires threaten these forests. Actual and former fire regimes of the local communities are analysed. The use of fire is an integrated part of land use and is also governed by socio-cultural traditions. The impact of fire on the dynamics of dry forests and grass savannas is studied considering the specifics of different fire regimes. We propose that a deliberate and controlled use of fire respecting the vegetation stage and the defined objectives could be an appropriate management tool. The strategy of a fire management is elaborated considering both the conservation of biodiversity and improvement of the livelihood of the local population depending upon the Reserve's resources. Obviously, a sustainable management of the natural resources requires a substantial participation of the community.     

Fire disturbance and forest structure in old‐growth mixed conifer forests in the northern Sierra Nevada,California

Question: This study evaluates how fire regimes influence stand structure and dynamics in old‐growth mixed conifer forests across a range of environmental settings. Location: A 2000‐ha area of mixed conifer forest on the west shore of Lake Tahoe in the northern Sierra Nevada, California. Methods: We quantified the age, size, and spatial structure of trees in 12 mixed conifer stands distributed across major topographic gradients. Fire history was reconstructed in each stand using fire scar dendrochronology. The influence of fire on stand structure was assessed by comparing the fire history with the age, size, and spatial structure of trees in a stand. Results: There was significant variation in species composition among stands, but not in the size, age and spatial patterning of trees. Stands had multiple size and age classes with clusters of similar aged trees occurring at scales of 113 ‐ 254 m². The frequency and severity of fires was also similar, and stands burned with low to moderate severity in the dormant season on average every 9–17 years. Most fires were not synchronized among stands except in very dry years. No fires have burned since ca. 1880. Conclusions: Fire and forest structure interact to perpetuate similar stand characteristics across a range of environmental settings. Fire occurrence is controlled primarily by spatial variation in fuel mosaics (e.g. patterns of abundance, fuel moisture, forest structure), but regional drought synchronizes fire in some years. Fire exclusion over the last 120 years has caused compositional and structural shifts in these mixed conifer forests.     

三工河流域荒漠绿洲植被动态及其成因分析

以三工河流域为例,讨论了植被动态及其地貌、水资源利用、河流廊道和排碱渠等景观要素的变化对植被产生的影响.结果表明,随着景观格局的变化,流域内的植丛高度、盖度及生物量均表现出较大变异性.以河流廊道为核心,通常荒漠绿洲景观格局呈带状分布,且由内向外随水热条件的改变,植被类型由乔灌木林依次向灌丛草甸、盐化草甸、荒漠化草甸和荒漠层次结构过渡.人类活动影响强烈的景观要素,其斑块多样性、破碎度、分离度和斑块密度等指数值较高,而人类活动影响较小的,其优势度和均匀度较高.各景观要素的稳定性不同,其大小顺序为:荒漠>沙砾石地>城镇用地>水体>农田>牧草地>菜地>林地>居民点>盐碱地>荒草地>水浇地>果园.梭梭群落的净生长量高峰值出现在8月,而博乐蒿、琵琶柴群落的净生长量高峰值出现时间各年度不同.博乐蒿群落与海拔相关系数最大,而琵琶柴群落则与土壤水含量、地下水位关系密切,梭梭群落与4～9月降雨量相关系数最大.     

Fire Severity in Conifer Forests of the Sierra Nevada, California

Natural disturbances are an important source of environmental heterogeneity that have been linked to species diversity in ecosystems. However, spatial and temporal patterns of disturbances are often evaluated separately. Consequently, rates and scales of existing disturbance processes and their effects on biodiversity are often uncertain. We have studied both spatial and temporal patterns of contemporary fires in the Sierra Nevada Mountains, California, USA. Patterns of fire severity were analyzed for conifer forests in the three largest fires since 1999. These fires account for most cumulative area that has burned in recent years. They burned relatively remote areas where there was little timber management. To better characterize high-severity fire, we analyzed its effect on the survival of pines. We evaluated temporal patterns of fire since 1950 in the larger landscapes in which the three fires occurred. Finally, we evaluated the utility of a metric for the effects of fire suppression. Known as Condition Class it is now being used throughout the United States to predict where fire will be uncharacteristically severe. Contrary to the assumptions of fire management, we found that high-severity fire was uncommon. Moreover, pines were remarkably tolerant of it. The wildfires helped to restore landscape structure and heterogeneity, as well as producing fire effects associated with natural diversity. However, even with large recent fires, rates of burning are relatively low due to modern fire management. Condition Class was not able to predict patterns of high-severity fire. Our findings underscore the need to conduct more comprehensive assessments of existing disturbance regimes and to determine whether natural disturbances are occurring at rates and scales compatible with the maintenance of biodiversity.     

Altered Fire Regimes Affect Landscape Patterns of Plant Succession in the Foothills and Mountains of Southern California

In the southern California foothills and mountains, pronounced and complex topographic gradients support fire regimes that vary over short distances. We used LANDIS, a spatially explicit landscape model of disturbance and plant succession, to examine the resilience of dominant plant species, representing different disturbance response strategies, to the effect of varying fire rotation intervals (FRI). The simulated fire regimes represented natural, current and very long FRIs for the foothill shrublands less than 1,400 m (90, 30 and 150 years) and montane forest greater than 1400 m (30, 150, 500 years). The 30-year FRI allowed obligate resprouting shrubs to dominate over obligate seeders, whereas the 90-year FRI resulted in a stable spatial distribution of both of these shrub functional types. This is consistent with the literature that suggests that shifts in shrubland composition are most likely to result from human-caused increases in fire frequency at the low-elevation urban-wildland interface. An ecotone conifer, Pinus coulteri, showed dramatic shifts in distribution under different FRIs, and retreated to the portion of the landscape representing its temporal regeneration niche. Both low and high frequency fire maintained the fire tolerant dominant pine (P. jeffreyi) in the montane zone. This contradicts the literature that suggests that a high frequency ground fire regime is required for the persistence of a pine-dominated forest, but is consistent with studies showing that conifer forests in the western U.S. have experienced, and are resilient to, a broad range of natural FRIs that include low frequency, high intensity crown fires.     

三工河流域荒漠绿洲植被动态及其成因分析

以三工河流域为例,讨论了植被动态及其地貌、水资源利用、河流廊道和排碱渠等景观要素的变化对植被产生的影响．结果表明,随着景观格局的变化,流域内的植丛高度、盖度及生物量均表现出较大变异性．以河流廊道为核心,通常荒漠绿洲景观格局呈带状分布,且由内向外随水热条件的改变,植被类型由乔灌木林依次向灌丛草甸、盐化草甸、荒漠化草甸和荒漠层次结构过渡．人类活动影响强烈的景观要素。其斑块多样性、破碎度、分离度和斑块密度等指数值较高,而人类活动影响较小的,其优势度和均匀度较高．各景观要素的稳定性不同,其大小顺序为：荒漠>沙砾石地>城镇用地>水体>农田>牧草地>莱地>林地>居民点>盐碱地>荒草地>水浇地>果园．梭梭群落的净生长量高峰值出现在8月,而博乐蒿、琵琶柴群落的净生长量高峰值出现时间各年度不同．博乐蒿群落与海拔相关系数最大,而琵琶柴群落则与土壤水含量、地下水位关系密切,梭梭群落与4～9月降雨量相关系数最大。     

The influence of canopy cover on understorey development in forests of the western Cascade Range,Oregon, USA

Natural disturbances, especially fire and treefalls, influence tree canopy composition in the Pseudotsuga menziesii forests of the western Cascade Range, Oregon. The composition of tree, shrub, and herb assemblages in the understorey of stands with different canopy types, such as maturing Pseudotsuga, Tsuga heterophylla, or mixed species stands, also differs.Differences in both canopy type and the prevalence of canopy openings correlated with different degrees of understorey development in stands of similar ages. This suggests that understorey assemblages also reflect disturbance history. Before understorey assemblages can be used to relate community samples to community or habitat types, the extent to which their composition reflects long term influences of stand history vs. differences in site potential must be determined.     

Insights into the Establishment of the Manila Clam on a Tidal Flat at the Southern End of an Introduced Range in Southern California,USA

Coastal ecosystem modifications have contributed to the spread of introduced species through alterations of historic disturbance regimes and resource availability, and increased propagule pressure. Frequency of occurrence of the Manila clam (Venerupis phillipinarum, Veneridae) in Southern California estuaries has increased from absent or sparse to common since the mid-1990s. Potential invasion vectors include seafood sales and aquaculture, and spread from established northern populations over decades. The clam’s post-settlement habitat preferences are, however, uncertain in this region. Our project aimed to identify factors associated with established patches of the clam within a bay toward the southern end of this introduced range. During summer 2013, we sampled 10 tidal flat sites in Mission Bay, San Diego; each containing an area with and without hard structure (e.g., riprap, boulders). We measured likely environmental influences (e.g., sediment variables, distance to ocean). Manila clam densities across the bay were most strongly associated with site, where highest densities were located in the northern and/or back halves of the bay; and weakly correlated with lower porewater salinities. Within sites, Manila clam density was enhanced in the presence of hard structure in most sites. Prevailing currents and salinity regimes likely contribute to bay wide distributions, while hard structures may provide suitable microhabitats (refuge from predators and physical stress) and larval entrapment within sites. Results provide insights into decisions about future shoreline management efforts. Finally, we identify directions for future study to better understand and therefore predict patterns of establishment of the Manila clam in the southern portion of its introduced range.     

Herder Perceptions on Impacts of Range Enclosures,Crop Farming,Fire Ban and Bush Encroachment on the Rangelands of Borana,Southern Ethiopia

This study focuses on community-based knowledge to analyze the impacts of range enclosures, crop farming, fire suppression and bush encroachment on the communal rangelands of Borana, southern Ethiopia. The knowledge of local herders is the basis for decision making in the utilization and management of grazing lands. We used Borana oral history associated with the period of the gada system to reconstruct environmental change that spans a period of 48 years. Our results show that the use of communities’ perceptions as a basis for evaluating the impacts of land use change on the environment makes an important methodological contribution. Communities’ responses to changing land use resulted in the development of range enclosures, the expansion of crop farming and the fragmentation of the communal rangelands, while the suppression of fire contributed to the expansion of bush encroachment. The overall impact was forage scarcity and greater vulnerability of stock during drought years. We conclude that policymakers could use communities’ knowledge of environmental change to improve the use of the rangelands. We propose that sustainable use of the southern rangelands in the future will require a greater focus on regulating the expansion of enclosures, crop farming and ranching, as well as reintroducing fire where necessary, to control the expansion of bush cover.

Seasonal fire effects on the diversity patterns,spatial distribution and community structure of forbs in the Northern Mixed Prairie,USA

The effects of fire season on forb diversity patterns, density, and composition were determined for a northern Mixed Prairie site, USA. Repeated spring burns (dormant season), summer burns, fall burns (dormant season), and unburned treatments were compared over a 3-yr period characterized by wet and dry moisture conditions. Alpha and beta diversity were highest on unburned and summer burn treatments, while landscape mosaic diversity was highest on fall burns. Forb density was highest on fall and spring burn sites. Nine forb species comprised 82% of total densities and were significantly affected by fire season and year to year variations in moisture. Forb composition for unburned and spring burn treatments was similar, but both treatments were different from the summer burn and fall burn treatments which were similar to each other. Fire alone did not appear to be an intense enough disturbance to initiate drastic changes in the forb component of vegetation patches. Specific fire seasons did appear to either mask or enhance forb structure arising from other disturbance(s). Fire season also affected the scales of forb organization in the landscape. Contrasting spatial characteristics of the forb component of prairie plant communities may provide a diagnostic technique for exposing the interaction of disturbances at different temporal and spatial scales.     

Climatic influences on fire regimes in the northern Sierra Nevada mountains, Lake Tahoe Basin, Nevada, USA

Aim The goal of this study was to understand better the role of interannual and interdecadal climatic variation on local pre‐EuroAmerican settlement fire regimes in fire‐prone Jeffrey pine (Pinus jeffreyi Grev. & Balf.) dominated forests in the northern Sierra Nevada Mountains. Location Our study was conducted in a 6000‐ha area of contiguous mixed Jeffrey pine‐white fir (Abies concolor Gordon & Glend.) forest on the western slope of the Carson Range on the eastern shore of Lake Tahoe, Nevada. Methods Pre‐EuroAmerican settlement fire regimes (i.e. frequency, return interval, extent, season) were reconstructed in eight contiguous watersheds for a 200‐year period (1650–1850) from fire scars preserved in the annual growth rings of nineteenth century cut stumps and recently dead pre‐settlement Jeffrey pine trees. Superposed epoch analysis (SEA) and correlation analysis were used to examine relationships between tree ring‐based reconstructions of the Palmer Drought Severity Index (PDSI), Southern Oscillation Index (SOI), Pacific Decadal Oscillation (PDO) and pre‐EuroAmerican fire regimes in order to assess the influence of drought and equatorial and north Pacific teleconnections on fire occurrence and fire extent. Results For the entire period of record (1650–1850), wet conditions were characteristic of years without fires. In contrast, fire years were associated with drought. Drought intensity also influenced fire extent and the most widespread fires occurred in the driest years. Years with widespread fires were also preceded by wet conditions 3 years before the fire. Widespread fires were also associated with phase changes of the PDO, with the most widespread burns occurring when the phase changed from warm (positive) to cold (negative) conditions. Annual SOI and fire frequency or extent were not associated in our study. At decadal time scales, burning was more widespread during decades that were dryer and characterized by La Niña and negative PDO conditions. Interannual and interdecadal fire–climate relationships were not stable over time. From 1700 to 1775 there was no interannual relationship between drought, PDO, and fire frequency or extent. However, from 1775 to 1850, widespread fires were associated with dry years preceded by wet years. This period also had the strongest association between fire extent and the PDO. In contrast, fire–climate associations at interdecadal time scales were stronger in the earlier period than in the later period. The change from strong interdecadal to strong interannual climate influence was associated with a breakdown in decadal scale constructive relationships between PDO and SOI. Main conclusions Climate strongly influenced pre‐settlement pine forest fire regimes in northern Sierra Nevada. Both interannual and interdecadal climatic variation regulated conditions conducive to fire activity, and longer term changes in fire frequency and extent correspond with climate‐mediated changes observed in both the northern and southern hemispheres. The sensitivity of fire regimes to shifts in modes of climatic variability suggests that climate was a key regulator of pine forest ecosystem structure and dynamics before EuroAmerican settlement. An understanding of pre‐EuroAmerican fire–climate relationships may provide useful insights into how fire activity in contemporary forests may respond to future climatic variation.     

Effects of environment and grazing disturbance on tree establishment in meadows of the central Cascade Range,Oregon, USA

Abstract. Within the last century there has been widespread establishment of trees in mountain meadows of the Pacific Northwest. We reconstructed patterns of tree invasion at 17 meadow sites in the central Cascade Range of Oregon, USA -sites representing diverse physical environments and vegetation types and experiencing different histories of recent anthropogenic disturbance (sheep grazing). Spatial distributions and age structures of invasive tree populations were analysed with respect to climatic records and grazing history. Patterns of establishment varied considerably among meadows, reflecting strong differences in environment and grazing history. In montane hydric meadows, tree establishment was spatially clumped beneath large old trees and on elevated microsites; however the timing of invasion differed between sites with stable versus fluctuating water tables. In upland mesic/dry montane meadows, timing of invasion corresponded with cessation of sheep grazing (early 1940s) and the onset of wetter summers (mid 1940s). In the subalpine zone, climate and aspect interacted to produce contrasting histories of invasion on north- and south-facing slopes. Establishment on north-facing slopes, concentrated in heath-shrub communities, coincided with regional warming (ca. 1920–1945) when snowpacks were lighter and melted earlier. Recruitment of trees onto south-facing slopes occurred later, when conditions were wetter (1945–1985). In many environments, the spatial distribution of recruitment suggests that once trees have established, autogenic factors become increasingly important as individual trees or groups of trees alter the physical or biotic conditions that once inhibited establishment. Knowledge of the factors that influence invasion, and of their varying importance across gradients in environment and vegetation, is critical to predicting future changes in these dynamic systems.