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Hierarchy theory


Hierarchy theory is a useful tool created in order to understand natural systems. It is considered a part of systems theory. Hierarchy theory emerged when the idea of holons was brought into ecology by Scott Overton in 1974. A holon is a self-organized system that belongs to a hierarchical level. It can either be considered as a whole or as a part of the larger structure. This duality takes into account that individual entities are tied to the entire structure, but allows us to focus on specific levels. There are two types of structures in hierarchy theory: nested and non-nested. A nested system contains all holons of the levels below, so there is overlap. A non-nested system does not contain holons of the lower levels, so they cease to exist at higher levels.
In landscape ecology, biotic interactions happen at multiple scales, and there is interplay between fine and broad scale patterns. It is difficult to put effects and processes into linear models when scales change, and cross critical thresholds. This is why we have holons in order to focus on individual levels of the hierarchy: harnessing a focus, and organizing a system of interactions for research.


Cross-scale interactions


Cross-scale interactions are the interaction of processes at multiple spatial or temporal scales that results in nonlinear dynamics with thresholds. The interaction of these processes can lead to emergent behaviours, which are not possible to forecast when cross-scale interactions are not considered. Furthermore, these cross-scale interactions are important to consider because the emergent behaviours often cannot be predicted solely by observation at independent scales.
driven by two processes: positive feedback or direct environmental effects. Positive feedback when there is a change in patterns at a fine scale that induces new processes and exceeds thresholds. Direct environmental effects are large regional processes that are powerful enough to overwhelm any fine-scale processes.


Trophic cascades and landscape ecology (arctic)


describe how the presence of predators has cascading impacts on the lower trophic levels of the food chain and can ultimately affect landscape patterns and processes. Predators can influence the abundance and distribution of forage plants through directly reducing herbivore populations or by scaring herbivores into avoiding certain habitats. The trophic cascade theory suggests that if a predator was removed from an ecosystem, herbivore populations would increase leading to a decrease in vegetation presence. Tundra ecosystems have a relatively simple tri-trophic food web with predators, small mammal herbivores (lemmings and voles) and plants. Arctic tundra ecosystems are primarily top-down controlled and herbivores are influenced more by predation than by plant growth.


Diversity and dominance


Diversity, or relative evenness, refers to how evenly the proportions of cover types are distributed (Turner, 2015). It can describe the vegetational mosaic of a landscape (Romme, 1982). This means that diversity can give an indication of how much of each cover type there is on a landscape. For example if there are three cover types present, each could occupy 33% of the landscape or one could occupy 90% and the others each only 5% (Turner, 2015). A high value indicates that there is high evenness on the landscape, whereas a small value indicates that there is less evenness. This index is only effective when there are two or more cover types on the landscape, as homogenous landscapes result in a value of zero (Turner, 2015). The value in the equation given is normalized to range between 0 and 1 so that it will scale properly and are not dependent on a maximum
value when the number of cover types varies (Turner 2015). Diversity is the inverse value to the dominance (Turner, 2015).

Dominance is expressed as the deviation from the maximum value of diversity. The number of land cover types present determines the maximum value, upon which the dominance index depends. Including the maximum term serves to produce a normalized version of the landscape dominance metric, rendering it useful for different landscapes with different numbers of land cover types (O’Neill et al., 1988; Turner, 1990). The index is only useful for landscapes with two or more cover types; homogeneous landscapes result in a dominance value of 0 (Turner, 2015; Turner 1990). The index values range from 0 to 1, where large values are associated with only one or a few cover types dominating the landscape and small values are associated with many cover types in relatively equal proportion dominating the landscape pattern (O’Neill et al., 1988; Turner, 2015).


Contagion metric


measure of spatial configuration, a quantitative description of the spatial arrangement of cover types on the landscape.
extent to which landscape elements are aggregated or clumped, where low values indicate landscapes with many small patches and high values may be associated with a few large, contiguous patches. used lfor measuring landscape fragmentation and carries information on both the proportion of land cover types and their geographical distribution within a landscape. The metric ranges from zero to one, with high values indicating more clumped patterns of cover types across the landscape, and low values indicating a landscape with a dispersed or fragmented pattern of cover types.
useful in capturing fine-scale variation in patterns that relate to the “graininess” of the map. know what cover types are present, as the index can return a similar numerical value for landscapes that are functionally different. derived from information theory, computed from a set of probabilities, and returns a single value that applies to the whole landscape and in this case, the values are the probabilities of adjacency—i.e., the probability that a grid cell of cover type i is adjacent to a grid cover type j. These probabilities are thus sensitive to the fine-scale (i.e., cell-to-cell) spatial distribution of cover types. High q i, i values indicate a highly aggregated cover type and low q i, i values indicate that the cover type tends to occur in isolated grid cells or small patches.


Lidar and how can it be used in landscape ecology


remote sensing technology that obtains geospatial data that provides fine-grain information on terrestrial and aquatic structures across a broad spatial extent. Where conventional sensors have lacked in ecological application due to their limited two-dimensional images, LiDAR has emerged as a leading technology in landscape ecology for its ability to directly measure the three-dimensional structure of vegetation and subcanopy topography at a landscape level. thus producing highly accurate estimates of aboveground biomass and high-resolution topographic maps. LiDAR has reduced the time and effort previously required to collect data on physical attributes of vegetation canopy structure and incorporated a wider perspectives into ecological research.




Variography is one of the most common tools for describing spatial dependence and relationships over a landscape, and was used as early as the 1970s. Variography is the process of examining the tendency for pairs of observations to influence one another at different lag distances, allowing for spatial interpolation across a landscape. Variography can utilize both correlograms and variograms to describe autocorrelation and the distribution of spatial variables.
Semivariograms are a type of variogram. They are used to characterize spatial dependence, and can interpolate values at unsampled locations using sampled points. An important use of the semivariogram is performing the spatial interpolation method of kriging. Imagine a landscape with the pairing of one point (central point) with other measured locations (surrounding points). Each pair of points has a unique distance. Instead of plotting the distance of all pairs of points, a semivariogram groups pairs into “lags”. The x-axis plots distance in lags, and the y-axis plots the variance of the response variable (e.g. if you were measuring water content in soil) between two points.
Correlograms graph autocorrelation by lag distance, showing the direction and magnitude of spatial variation. They are useful for measuring spatial correlation by comparing the similarity between two points, differing from semivariograms which measure variance. The y-axis plots autocorrelation (the degree of statistical correlation; evaluating randomness) with values ranging from -1 to 1. The autocorrelation values would be near zero at all time lags if the data is completely random with no correlation6. Greater absolute values on the y-axis suggest stronger linear relationships, the strongest being -1 or 1.


Relationship between grain, extent, and variance


Scale is characterized by grain and extent, both of which are co-dependent variables that dictate the tools and methods employed by landscape ecologists.
Grain is the finest level of spatial resolution possible within a given dataset or the size of individual units of observation, usually expressed as pixels of a dataset or quadrats of a field ecologist. For example, this can be illustrated by the 30m resolution of Landsat thematic mapping imagery, which dictates the finest limit of a study.
Extent is simply the overall size of the study area, which is determined by the researcher and what we often think of as the sampling area. Grain defines the lower limits of a study, while extent defines the upper limits.
Both grain and extent have an effect on variance, which is a measure of dispersion or difference in a variable across space. A fine grain will preserve spatial heterogeneity, since it captures the most detail and nuance over an area. So if extent were held constant, an increase in grain would aggregate units together and result in a more homogeneous and less detailed area. This decreases spatial variance since there are fewer data units and less detail, thereby reducing the complexity of the area. Similarly, an increase in temporal extent will incorporate more variability over time, ultimately increasing variance.


Edge length and edge density


Edge length
an edge is something that divides two different land cover types. related to the size of the patch, where a small patch has a small edge length and a large patch has a large edge length when the shape is kept the same. The shape of the patch also affects edge length, where regular patches have a small edge length and irregular patch edges have a larger edge length, when the size is kept the same.
Edge density is a metric that uses the edge length of a patch and incorporates the area of that same patch. It is represented by the ratio of patch edge and patch area, often expressed in meters per hectares (m/ha) (Hargis, Bissonette & David, 1998). Each of these two variables affects the edge density where a larger patch edge, while maintaining the patch area, increases edge density, and an increase in patch area while maintaining the patch edge, decreases edge density. Edge Density (m/ha) = (patch edge)/(patch area)


Perimeter to area ratio


Perimeter or Edge to Area Ratio (PAR) is a form of patch based metric that places a landscape in a gridded matrix with individual patch seen as an assigned homogenous area.
This Ratio is calculated by the formulas (P/A, P represents perimeter and A represents area)
The basics Idea is that an area unit with higher perimeter to area creates a more complexed shape indicated by a greater PAR
A drawback to this metric is that if the shape of the patch is held constant but there are two different sized the patch with the smaller size will exhibit a higher PAR to that of a larger sized patch due to the geometric relationship between area and perimeter


Network analysis


Network Analysis is a branch of mathematics based on graph theory. Networks are used by a variety of disciplines to model, predict and identify theoretical movement, dispersal patterns, and flow rates. In Landscape Ecology Network Analysis is used to assess connectivity of habitat patches, potential flow and dispersal of objects over space. Network Analysis defines a landscape, as a series of nodes and links, or habitat patches and dispersal corridors. Nodes can be weighted based on any set of characteristics of that node. Groups of connected nodes, or patches, on a landscape form a component and the number or density of components in a network is indicative of its overall connectivity. Networks can be used to model a variety of ecosystem types, and can include variable complexity with minimal data inputs. As Networks are a theoretical model they come with several limitations and assumptions. Network analysis tends to overestimate connectivity which can lead to incorrect and dangerous assumptions for metapopulations vulnerability and habitat use. The Gamma index (shown in lecture) is the most basic formula used to calculate