Examining the effects of alternative management strategies on landscape-scale forest patterns in northeastern Minnesota using LANDIS

Spatial modeling of forest patterns can provide information on the potential impact of various management strategies on large landscapes over long time frames. We used LANDIS, a stochastic, spatially-explicit, ecological landscape model to simulate 120 years of forest change on the Nashwauk Uplands, a 328,000 ha landscape in northeastern Minnesota that lies in the transition between boreal and temperate forests. We ran several forest management scenarios including current harvesting practices, no harvests, varied rotation ages, varied clearcut sizes, clustered clearcuts, and landowner coordination. We examined the effects of each scenario on spatial patterns of forests by covertype, age class, and mean and distribution of patch sizes. All scenarios reveal an increase in the spruce-fir (Picea-Abies) covertype relative to the economically paramount aspen-birch (Populus-Betula) covertype. Our results also show that most covertypes occur in mostly small patches <5 ha in size and the ability of management to affect patch size is limited by the highly varied physiography and landuse patterns on the landscape. However, coordination among landowners, larger clearcuts, and clustered clearcuts were all predicted to increase habitat diversity by creating some larger patches and older forest patches. These three scenarios along with the no harvest scenario also create more old forest than current harvesting practices, by concentrating harvesting on some portion of the landscape. The no harvest scenario retained large, fire-regenerated aspen-birch patches. Harvests fragment large aspen-birch patches by changing the age structure and releasing the shade-tolerant understory species. More sapling forest, and larger sapling patches resulted from the shortened rotation scenario.     

Mediation of area and edge effects in forest fragments by adjacent land use

Habitat loss, fragmentation, and degradation have pervasive detrimental effects on tropical forest biodiversity, but the role of the surrounding land use (i.e., matrix) in determining the severity of these impacts remains poorly understood. We surveyed bird species across an interior-edge-matrix gradient to assess the effects of matrix type on biodiversity at 49 different sites with varying levels of landscape fragmentation in the Brazilian Atlantic Forest—a highly threatened biodiversity hotspot. Both area and edge effects were more pronounced in forest patches bordering pasture matrix, whereas patches bordering Eucalyptus plantation maintained compositionally similar bird communities between the edge and the interior and exhibited reduced effects of patch size. These results suggest the type of matrix in which forest fragments are situated can explain a substantial amount of the widely reported variability in biodiversity responses to forest loss and fragmentation.     

武夷山风景名胜区景观要素斑块特征分析

针对近年来开展生态旅游等人类活动的强烈干扰给风景区带来巨大生态影响的问题，在武夷山风景名胜区景观类型划分的基础上，从景观要素斑块特征的角度对武夷山风景名胜区的景观格局及破碎化进行初步的研究，以期为今后武夷山风景名胜区的景观生态保护提供科学的依据．研究结果表明，在武夷山风景名胜区中，马尾松林、茶园与农田是风景区中3个主要景观类型，三者面积与周长之和分别占全区的84．581％和81．669％；景观要素的面积、周长、斑块数的分布极不平衡，尤其在3类主要景观类型中，在斑块面积、周长方面差异显著；各景观要素面积与周长的分布极为相似，而斑块数的分布却没有明显的规律性；景观要素面积、周长、斑块数等斑块特征分析表明，茶园、居住地、经济林等人工或半人工经营景观的破碎化程度高，而马尾松各天然林景观的破碎化程度低，从而证明了人类经营活动的干扰是导致自然风景区景观破碎的主要因素之一．表3参18     

Are shrubland birds edge specialists?

In studies of forest fragmentation, birds of scrubby, early-successional habitats are considered edge specialists. Because these birds are assumed to thrive in fragmented, edge-dominated areas, their landscape ecology has received little attention from ecologists. With populations of shrubland birds declining throughout the eastern United States, the question of whether or not these birds really prefer edge habitats has important conservation implications. We used a meta-analysis to test how edges affect the abundance of shrubland birds in early-successional habitats. We analyzed data for 17 species from seven studies that compared the abundances of birds in the interiors and edges of regenerating clearcuts surrounded by mature forest. The meta-analysis clearly showed that shrubland birds avoid edges. All 17 species tested had higher abundances in patch centers than along edges, and edge effects were significant for 8 of 17 species. The key implication of this result is that small or irregular patches, dominated by edge, are unlikely to provide suitable habitat for shrubland birds. Thus, management for these declining species should involve providing large patches and minimizing edges. These findings demonstrate the importance of testing widely accepted ecological classifications and the need to view landscape ecology from the perspective of non-forest wildlife.     

Spatiotemporal changes and fragmentation of mangroves and its effects on fish diversity in Ca Mau Province (Vietnam)

Mangroves are important economically and ecologically, however mangrove cover has declined dramatically leading to habitat fragmentation and biodiversity loss. Information on mangrove cover change, fragmentation and impacts on fish diversity is poorly understood. The aims of this study are to detect spatiotemporal changes and mangrove status, examine fragmentation changes and associated effects on fish diversity. Landsat images in1989, 2000, and 2013 were used to classify mangrove cover in Ca Mau Province (Vietnam) and validated against high resolution Pleiades imagery. Fragmentation changes in mangrove cover were examined using series of landscape metrics evaluated against fish diversity indices (Simpson’s index, Jaccard’s coefficient and relative abundance). Results show that mangrove cover has declined 24.6% in the province. Currently, high and moderately dense mangroves distribute in southern half of the region while the low density mangroves occurs in the northern half. Over the 24 year study periods, the number of patches and edge density has increased 58% and 53.9%, respectively, while the mean patch size and mean patch edge has decreased 52.3% and 26.6%. Fish diversity in the more highly fragmented mangrove area was 1.78 times lower than the less fragmented mangrove. The study illustrates the applicability of using Landsat satellite imagery for use in mangrove fragmentation studies as well as the impact of fragmentation.     

The relative influence of habitat loss and fragmentation: do tropical mammals meet the temperate paradigm?

The relative influence of habitat loss vs. habitat fragmentation per se (the breaking apart of habitat) on species distribution and abundance is a topic of debate. Although some theoretical studies predict a strong negative effect of fragmentation, consensus from empirical studies is that habitat fragmentation has weak effects compared with habitat loss and that these effects are as likely to be positive as negative. However, few empirical investigations of this issue have been conducted on tropical or wide-ranging species that may be strongly influenced by changes in patch size and edge that occur with increasing fragmentation. We tested the relative influence of habitat loss and fragmentation by examining occupancy of forest patches by 20 mid- and large-sized Neotropical mammal species in a fragmented landscape of northern Guatemala. We related patch occupancy of mammals to measures of habitat loss and fragmentation and compared the influence of these two factors while controlling for patch-level variables. Species responded strongly to both fragmentation and loss, and response to fragmentation generally was negative. Our findings support previous assumptions that conservation of large mammals in the tropics will require conservation strategies that go beyond prevention of habitat loss to also consider forest cohesion or other aspects of landscape configuration.     

Linking edge effects and patch size effects: Importance of matrix nest predators

The edge effect is usually considered to be the proximate cause of area sensitivity in forest birds. We tested if birds nesting in large patches are less vulnerable to the edge effect using a simple model that assumes an increase in patch size reduces the probability of a matrix predator moving to the core areas of forest and that larger perimeter/area ratios result in a higher number of matrix predators per unit of area. The probability of a nest being successful decreased asymptotically with an increase in either the patch penetration distance of predators or predator density, but those effects were reduced when patch size was increased. Large patches have a lower probability of being affected by an Allee effect and they can function as sink habitats only if penetration distance and predator density are largely increased. However, the transition from an Allee effect to a sink condition occurs with a small increase in penetration distance and predator density. Since birds nesting in large patches are less vulnerable to an increase in matrix predator populations, persistence of bird populations may be possible by increasing the size of habitat patches that can act as source populations.     

黑龙江省森林景观的格局变化

运用地理信息系统分析软件ARC／INFO 8．01、ARCVIEW 3．2和基于ARC／INFO的FRAGSTATS 3．0软件，处理了1896年、1949年和1981年黑龙江省森林资源分布图，并用所得到的斑块总面积、平均斑块大小、斑块密度、斑块大小变异系数、平均斑块分数维和平均形状指数对黑龙江省森林景观格局变化和各个斑块类型的变化进行了研究．结果表明，从1896年到1981年黑龙江省森林景观的总面积急剧减少，斑块数量增多，斑块密度加大，平均斑块大小减少，斑块间的毗连程度减弱，但是斑块的形状逐渐趋于相对规则，斑块的边界趋于简单化，所有这些表明，森林景观逐渐趋于破碎化，其中以红松的破碎化最为严重．整个森林的景观多样性和景观类型分布的均匀性逐渐降低．造成这一变化的主要原因是人类的经济活动，另一原因是近一个世纪的气候变化及森林群落的自身演替，但是同人类的干扰作用相比，作用很微弱．图5表2参19     

Effects of Roads on Movements by Understory Birds in Mixed-Species Flocks in Central Amazonian Brazil

Abstract: Roads through tropical forest create linear disturbances that have unknown consequences for forest birds. We studied how a narrow, rarely used road through otherwise undisturbed Amazonian forest affected the movements and area requirements of understory birds that form mixed-species flocks. Differences in road maintenance led to two distinct treatments along the same road. Trees along the "closed" road formed a partial canopy connecting the two sides of the road, although the roadway itself was kept open. The "open" road was regularly maintained, making a complete opening 10–30 m wide.We followed 15 flocks, 5 each in interior forest, along the open road, and along the closed road. These flocks were led by Thamnomanes antshrikes, and each flock had a discreet, permanent territory. Flock territory size (mean = 8.5 ha) did not differ among the three locations. The open road formed the territorial boundary for all five flocks, although birds moved within a few meters of the edge of the road. The closed road was less of a barrier: 2 of 5 flocks used both sides of the closed road. Playback experiments showed that flocks readily crossed the closed road to approach agonistic vocalizations. Along the open road, even though birds responded to playback by becoming agitated and moving to the extreme edge of the roadside vegetation, they were less likely to cross the road and did so only after a longer duration of playback. Our results suggest that flocks respond to a road as they would to a long linear gap. They use the vegetation along the edges of the road, but because they are unwilling to cross the open area, it becomes a flock territory boundary. Similarly, as in forest gaps, successional change along the closed road produced suitable habitat for flocks. Although this suggests that roads are a trivial problem, we caution that this result applies only to narrow roads that are not accompanied by deforestation or other disturbance.     

厦门环同安湾海岸带景观空间格局动态变化分析

利用遥感和地理信息技术,运用平均斑块面积与分离度指数、多样性指数、破碎度指数、优势度指数和分维数等景观格局指数,以厦门环同安湾区1989年、1997年和2007年3个时期遥感影像解译数据作为基本信息源,对过去18年间环同安湾海岸带的景观格局的时空变化过程和演变趋势进行了研究。结果表明：1989—2007年,农田面积大量...     

Effects of Clearcutting on Habitat Use and Reproductive Success of the Ovenbird in Forested Landscapes

We studied Ovenbirds ( Seiurus aurocapillus ) in northern New Hampshire during 1992 and 1993 to determine whether edge-related changes in habitat use and reproductive success reported in fragmented landscapes exist in predominantly forested landscapes. Six study plots were placed adjacent to four recent clearcuts (2.1–5 ha) and extended 400 m into the forest interior. Nests, territories, and territorial males obtaining mates were equally distributed in edge (0–200 m) and interior (201–400 m) areas. Nest survival was higher in the forest interior in 1992 and for 1992 and 1993 combined. The proportion of pairs fledging ≥ 1 young, fledgling weight, and fledgling wing-chord did not differ between edge and interior in either year. Number of young fledged per pair was slightly lower in edge areas, but these differences were not significant. We conclude that clearcutting in extensively forested landscapes can affect Ovenbird reproductive success. Nevertheless, the effect on Ovenbird populations is moderated by the abundance of mature forest cover in the region and by the tendency of Ovenbirds to renest after initial nest failure.     

Salamander Abundance along Road Edges and within Abandoned Logging Roads in Appalachian Forests

Abstract:  Roads may be one of the most common disturbances in otherwise continuous forested habitat in the southern Appalachian Mountains. Despite their obvious presence on the landscape, there is limited data on the ecological effects along a road edge or the size of the "road-effect zone." We sampled salamanders at current and abandoned road sites within the Nantahala National Forest, North Carolina (U.S.A.) to determine the road-effect zone for an assemblage of woodland salamanders. Salamander abundance near the road was reduced significantly, and salamanders along the edges were predominantly large individuals. These results indicate that the road-effect zone for these salamanders extended 35 m on either side of the relatively narrow, low-use forest roads along which we sampled. Furthermore, salamander abundance was significantly lower on old, abandoned logging roads compared with the adjacent upslope sites. These results indicate that forest roads and abandoned logging roads have negative effects on forest-dependent species such as plethodontid salamanders. Our results may apply to other protected forests in the southern Appalachians and may exemplify a problem created by current and past land use activities in all forested regions, especially those related to road building for natural-resource extraction. Our results show that the effect of roads reached well beyond their boundary and that abandonment or the decommissioning of roads did not reverse detrimental ecological effects; rather, our results indicate that management decisions have significant repercussions for generations to come. Furthermore, the quantity of suitable forested habitat in the protected areas we studied was significantly reduced: between 28.6% and 36.9% of the area was affected by roads. Management and policy decisions must use current and historical data on land use to understand cumulative impacts on forest-dependent species and to fully protect biodiversity on national lands     

Distribution of Carabid Beetles (Coleoptera, Carabidae) across a Boreal Forest–Clearcut Ecotone

Abstract: We studied the occurrence of carabid beetles (Coleoptera, Carabidae) in boreal forest fragments, their edges, and adjacent clearcuts in central Finland. Beetles were collected with pitfall traps along transects extending 60 m from the edge into clearcuts and 60 m into forest interior. Our main findings were that (1) species richness was significantly higher in the clearcut than in the forest fragments, (2) clearcuts hosted many open-habitat species, which increased overall species richness in these sites, (3) carabid assemblages in the edges were more similar to forest assemblages than to those found in the clearcuts, (4) no edge specialists were found, and (5) open-habitat species did not penetrate into the forest fragments from the clearcut. Because forest specialists occurred all the way to the edge on the forest side, it seems that edge effects per se do not adversely affect these species, at least in the short term. In the long term, however, habitat conditions in the edges may deteriorate for interior species because of trees falling over in strong winds, thereby reducing the size of the fragments and widening the edge zone.     

Effects of Patch Size and Type of Coffee Matrix on Ithomiine Butterfly Diversity and Dispersal in Cloud-Forest Fragments

Abstract: Determining the permeability of different types of landscape matrices to animal movement is essential for conserving populations in fragmented landscapes. We evaluated the effects of habitat patch size and matrix type on diversity, isolation, and dispersal of ithomiine butterflies in forest fragments surrounded by coffee agroecosystems in the Colombian Andes. Because ithomiines prefer a shaded understory, we expected the highest diversity and abundance in large fragments surrounded by shade coffee and the lowest in small fragments surrounded by sun coffee. We also thought shade coffee would favor butterfly dispersal and immigration into forest patches. We marked 9675 butterflies of 39 species in 12 forest patches over a year. Microclimate conditions were more similar to the forest interior in the shade‐coffee matrix than in the sun‐coffee matrix, but patch size and matrix type did not affect species richness and abundance in forest fragments. Furthermore, age structure and temporal recruitment patterns of the butterfly community were similar in all fragments, independent of patch size or matrix type. There were no differences in the numbers of butterflies flying in the matrices at two distances from the forest patch, but their behavior differed. Flight in the sun‐coffee matrix was rapid and directional, whereas butterflies in shade‐coffee matrix flew slowly. Seven out of 130 recaptured butterflies immigrated into patches in the shade‐coffee matrix, and one immigrated into a patch surrounded by sun coffee. Although the shade‐coffee matrix facilitated movement in the landscape, sun‐coffee matrix was not impermeable to butterflies. Ithomiines exhibited behavioral plasticity in habitat use and high mobility. These traits favor their persistence in heterogeneous landscapes, opening opportunities for their conservation. Understanding the dynamics and resource requirements of different organisms in rural landscapes is critical for identifying management options that address both animals’ and farmers’ needs.     

Relative Importance of the Area and Shape of Patches to the Diversity of Multiple Taxa

Abstract: Although enhancing reserve shape has been suggested as an alternative to enlarging nature reserves, the importance of reserve shape relative to reserve area remains unclear. Here we examined the relative importance of area and shape of forest patches to species richness, species composition, and species abundance (abundance of each species) for 3 taxa (33 birds, 41 butterflies, and 91 forest‐floor plants) in a fragmented landscape in central Hokkaido, northern Japan. We grouped the species according to their potential edge responses (interior‐, neutral‐, and edge‐species groups for birds and forest‐floor plants, woodland‐ and open‐land‐species groups for butterflies) and analyzed them separately. We used a shape index that was independent of area as an index of shape circularization. Hierarchical partitioning and variation partitioning revealed that patch area was generally more important than patch shape for species richness and species composition of birds and butterflies. For forest‐floor plants, effects of patch area and shape were small, whereas effects of local forest structure were large. Patch area and circularization generally increased abundances of interior species of birds and forest‐floor plants and woodland species of butterflies. Nevertheless, only patch circularization increased abundances of 1 woodland species of butterfly and 2 and 6 interior species of birds and forest‐floor plants, respectively. We did not find any significant interaction effects between patch area and shape. Our results suggest that although reserves generally should be large and circular, there is a trade‐off between patch area and shape, which should be taken into consideration when managing reserves.     

Defining Forest Fragmentation by Corridor Width: The Influence of Narrow Forest-Dividing Corridors on Forest-Nesting Birds in Southern New Jersey

In studies of forest fragmentation, a fundamental inconsistency exists in the distance criterion used to define the discreteness of forest fragments. We examined three types of ubiquitous, narrow, forest-dividing corridors for effects that influence the relative abundance and community composition of forest-nesting birds. Fixed-radius (100-meter) point counts were conducted on 54 transects established along three width classes of corridors: unpaved roads (8 meters wide), paved roads (16 meters wide), and powerlines (23 meters wide). Transect locations were distributed equally among corridor edge, forest margin 100 meters from corridor edge, and forest interior 300 meters from corridor edge. Forest-interior species of Neotropical migrants had significantly reduced relative abundances on edge transects along 16- and 23-meter corridors, compared with 8-meter corridors and with forest interior points along all three corridor-width classes. At a landscape scale, the consequences of apparently small reductions in forest area by the presence of narrow forest-dividing corridors may be cumulatively significant for abundances of forest-interior species. Brown-headed Cowbirds were more abundant than 20 of 21 forest-interior Neotropical migrants. We found surprisingly high abundances of cowbirds associated with narrow forest-dividing corridors, especially those with mowed grass. Corridor widths as narrow as 8 meters produce forest fragmentation effects in part by attracting cowbirds and nest predators to corridors and adjacent forest interiors. The most serious implication of this study is that narrow forest-dividing corridors may function as ecological traps for forest-interior Neotropical migrants. We suggest that these widespread corridors may be inconspicuous but important contributors to declines of forest-interior nesting species in eastern North America.     

Response of Red-Backed Voles to Recent Patch Cutting in Subalpine Forest

We examined the response of southern red-backed voles ( Clethrionomys gapperi ) to patch cutting in a forested landscape in which 23% of the forest cover had been removed by timber harvest. We live trapped voles in and around 18 patchcuts in one watershed of southern Wyoming. Although we found a significant difference in capture rates between patchcut interior and forest habitats in 1 of 2 years, voles did not strongly avoid the interior of patchcuts. This result contrasts with results from most studies of voles in clearcut ecosystems, which report that red-backed voles are generally rare or absent from clearcuts. Capture rates were highest on both sides of the patchcut edge, which also contrasts with studies of voles at the edges of forest remnants. The use of patchcut interior and edge habitats could not be explained as a consequence of juvenile voles dispersing to those habitats or males moving through the habitat in search of mates. We suggest that, despite similar physiognomy in patchcut and clearcut sites, the differences in landscape structure in perforated versus fragmented landscapes lead to very different patterns of vole movement. Understanding the scales at which voles perceive landscapes as coarse- or fine-grained will be key to developing predictive models to aid managers in designing timber sales that maintain high vole populations. Our results emphasize the importance of the spatial pattern and scale of disturbance in determining the response of vertebrates to landscape change and the need for more refined investigations of the consequences of deforestation.     

Value of Small Patches in the Conservation of Plant-Species Diversity in Highly Fragmented Rainforest

Abstract:  We evaluated the importance of small (<5 ha) forest patches for the conservation of regional plant diversity in the tropical rainforest of Los Tuxtlas, Mexico. We analyzed the density of plant species (number of species per 0.1 ha) in 45 forest patches of different sizes (1–700 ha) in 3 landscapes with different deforestation levels (4, 11, and 24% forest cover). Most of the 364 species sampled (360 species, 99%) were native to the region, and only 4 (1%) were human-introduced species. Species density in the smallest patches was high and variable; the highest (84 species) and lowest (23 species) number of species were recorded in patches of up to 1.8 ha. Despite the small size of these patches, they contained diverse communities of native plants, including endangered and economically important species. The relationship between species density and area was significantly different among the landscapes, with a significant positive slope only in the landscape with the highest deforestation level. This indicates that species density in a patch of a given size may vary among landscapes that have different deforestation levels. Therefore, the conservation value of a patch depends on the total forest cover remaining in the landscape. Our findings revealed, however, that a great portion of regional plant diversity was located in very small forest patches (<5 ha), most of the species were restricted to only a few patches (41% of the species sampled were distributed in only 1–2 patches, and almost 70% were distributed in 5 patches) and each landscape conserved a unique plant assemblage. The conservation and restoration of small patches is therefore necessary to effectively preserve the plant diversity of this strongly deforested and unique Neotropical region.     

Road development, housing growth, and landscape fragmentation in northern Wisconsin: 1937-1999.

Roads remove habitat, alter adjacent areas, and interrupt and redirect ecological flows. They subdivide wildlife populations, foster invasive species spread, change the hydrologic network, and increase human use of adjacent areas. At broad scales, these impacts cumulate and define landscape patterns. The goal of this study was to improve our understanding of the dynamics of road networks over time, and their effects on landscape patterns, and identify significant relationships between road changes and other land-use changes. We mapped roads from aerial photographs from five dates between 1937 and 1999 in 17 townships in predominantly forested landscapes in northern Wisconsin, U.S.A. Patch-level landscape metrics were calculated on terrestrial area outside of a 15-m road-effect zone. We used generalized least-squares regression models to relate changes in road density and landscape pattern to concurrent changes in housing density. Rates of change and relationships were compared among three ecological regions. Our results showed substantial increases in both road density and landscape fragmentation during the study period. Road density more than doubled, and median, mean, and largest patch size were reduced by a factor of four, while patch shape became more regular. Increases in road density varied significantly among ecological subsections and were positively related to increases in housing density. Fragmentation was largely driven by increases in road density, but housing density had a significantly positive relationship with largest patch area and patch shape. Without protection of roadless areas, our results suggest road development is likely to continue in the future, even in areas where road construction is constrained by the physical environment. Recognizing the dynamic nature of road networks is important for understanding and predicting their ecological impacts over time and understanding where other types of development are likely to occur in the future. Historical perspectives of development can provide guidance in prioritizing management efforts to defragment landscapes and mitigate the ecological impacts of past road development.     

Landscape history, fragmentation, and patch occupancy: models for a forest bird with limited dispersal.

We developed and tested patch occupancy models for an endemic understory bird with limited dispersal ability, the Chucao Tapaculo (Scelorchilus rubecula), in two South American temperate rain forest landscapes that differed in levels and duration of forest loss. We assessed cover changes since 1961 in each landscape and surveyed patches for Chucao Tapaculo occupancy. We then developed incidence-based predictive models independently for each landscape and tested each model reciprocally in the alternative study area. We thereby assessed the domain of model applicability and identified those predictor variables with general effects and those that varied between the two landscapes. The two models were consistent regarding variable selection, and predictive accuracy of each model was high in the landscape where training data were collected. However, the models differed substantially in the magnitudes of effects related to patch size, with larger unoccupied patches observed in the landscape with the more advanced stage of fragmentation. Due to this discrepancy, each model performed poorly when applied to the alternative landscape, potentially reflecting the contrasting stages of habitat loss. Although it was impossible to dissociate effects of level and duration of forest loss, we viewed the landscapes as representing two extremes along a continuum of fragmentation, providing insights into potential trajectories for portions of the biome where deforestation is occurring. Further, our data suggest that static equilibrium models developed from distribution patterns in recently fragmented landscapes may overestimate persistence when used as a forecasting tool, or when extrapolated to alternative landscapes where fragmentation is more advanced. Thus, we suggest that landscapes used as standards for model building should be selected with caution. We recommend that distribution patterns be obtained from landscapes where fragmentation is advanced, preferably with histories of fragmentation long enough that time-delayed extinctions already would have occurred.