Presentation on theme: "The critical concept of scale"— Presentation transcript:
1The critical concept of scale “…the problem of relating phenomena across scales is the central problem in biology and in all of science”. Simon Levin, 1992.Increasing technological sophistication now allows observations to be made across microscopic to global scales. Consequently, as there is a need to integrate our observations, there is also a need to develop and use a set of common terms related to scale.This lecture presents several of ways scale is conceptualized and applied in biogeographic research.Scales over which humans observe the world
2Why be concerned about scale? Characterization of biogeographic pattern involves:Scale of the phenomenaScale of its detection through observationScale at which a pattern is statistically analyzed and communicated.Tuna exampleBirds – temperature or calendar dates?Flesh out examples more
3Cartographic scaleFrom Lewis Carroll’s Alice in Wonderland
12Operational scaleRefers to the spatial and temporal dimensions of an object or a process
13Operational scaleOperational scale may not be independent of our observations, and in fact may be very dependent upon them.Operational scale can be constrained by our technology and our senses.How did we define the world before our understanding of astronomy, or biology?
15And so these men of Indostan Disputed loud and long,Each in his own opinionExceeding stiff and strong,Though each was partly in the right,And all were in the wrong!John Godfrey Saxe1878
16Decreasing (finer) grain, extent is constant Ecological scalingExtent: spatial (or temporal) dimension of an object or process observed or analyzedGrain: level of spatial (or temporal) resolution at which an object or process has been measured or observed.Increasing extent, grain is held constant
18How much grain is shown can be a subjective decision How much grain is shown can be a subjective decision. Cartographic scale and ecological scale are often intertwined.
19Haggett’s scale coverage problem Nature has an immense extent and a fine grain
20Haggett’s scale coverage problem To make even small descriptions of it, we have to sampleSampling requires sacrificing grain for extent or extent for grain.
21Fallacies of scaleIndividualistic fallacy: extrapolating to the broad scale based on observations conducted at small, local scalesEcological fallacy: making local-scale characterizations based on broad-scale observations.To an extent, humans have to commit the individualistic fallacy and the ecological fallacy to certain extents in order to navigate the world
22Modifiable areal unit problem Two componentsAggregation problemZoning problem
24Hierarchy theoryLandscapes organized into spatial and temporal domains of shaping processesScale hierarchy is a system of vertical interconnectionsHigher levels constrain the lower levelsSlow large at top; fast, local at bottomHighest level variable: constantLowest level variable: noise
27Cartesian scaleHierarchy theory exemplifies a Cartesian scaling of the worldScales are imposedNot necessarily “true” scalesOften tied to XYZ coordinate systemSpace as a container
28Constructivist scale Scale emerges out the interactions of entities Scales are produced or constructedThere is no fixed and unchanging hierarchy of scales.
29Constructivist scaleBoundaries in space and frequencies of environmental exposures shaped by organisms not just our observation of them.
30Evolutionary scalingScaling is a practice related to adaptation
31Scale and scaling are practiced by all forms of life Are our observational scales relevant to the organism of interest?How do other organisms scale the world and how does it influence what they (and we) can know and act upon?Tuna exampleBirds – temperature or calendar dates?Flesh out examples more
32Rules for ecological scale for humans Patterns are dependent upon the scale of observationThe important explanatory variables change with scale.Statistical relationships may change as scale changes.Patterns are generated by processes acting over various temporal and spatial scales.
36Scale dependence of the correlation between human population presence and vertebrate and plant species richnessECOLOGY LETTERS, 10 (1): 16-24; JAN 2007Human presence is generally negatively related to species richness locally, but the relationship is positive at coarse scales. An increase in the strength of the latter correlation with increasing study resolution has been documented within studies, but it is not known whether such a scale dependence is present across different studies. We test this with data on the spatial co-occurrence of human beings and the species richness of plants and vertebrates from a continuum of scales. The correlation coefficient between human presence and species richness is positively related to study grain and extent. The correlation turns from positive to negative below a study grain of c. 1 km and below a study extent of c km(2). The broad-scale positive correlation between human presence and species richness suggests that people have preferentially settled and generally flourished in areas of high biodiversity and/or have contributed to it with species introductions and habitat dive! rsification. The scale dependency of the correlation between people and biodiversity's presence emphasizes the importance of the preservation of green areas in densely populated regions.
37Rules for ecological scale 5. Scale can be used to justify or refute certain management practices and ideas about nature
38Example: Successional response to clearcut logging Grain and extent of post-logging sampling determine criteria for judging responseLarge extent, fine grain: criteria for recovery not likely to be metSmall extent, coarse grain: criteria for recovery easier to meet
39Rules for ecological scale 6. The scales experienced by an organism define what it sees and responds to. For example, what might constitute a patchy resource to an insect, could be perceived by a larger vertebrate as homogeneous.
40How to work with scaleThere is no single correct scale or level at which to describe a system.This does not mean that all scales serve equally well or that there are not rules or guidelines.
41How to work with scaleBe aware of the different types of scaling and their relatednessDon’t be too anthropocentricEmploy sampling designs and methods that are sensitive to multiple scalesNested observationsPower lawsFractalsNetworks
42Power laws Summarize how relationships change with changes in scale Often expressed on a log-log plot.Y = constant (X)nSimilar slopes are thought to have similar structuring processes (n = slope)ExamplesSpecies-area relationships (left)Animal metabolic rates and body mass (next slide)However, a valid criticism of power laws is that they often lack an explanatory processS=cAzMetabolic rate = constant (mass).75
45FractalsA fractal pattern appears the same across all scales. It is scale invariant.The relationship between size of box and pattern in it is constant.Fractals follow their own power law relating how number of boxes needed to cover a shape change in relation to their size.A fractal is a pattern that can be split into parts, each of which is a reduced-size copy of the whole, a property called self-similarity.
47Networks Can represent relationships at a variety of scales at once. Structural properties of networks provide means of understanding how they work.Nodes and linksDegree centrality and betweennessWeak versus strong linksDirectional versus non-directional graphs
48Random and scale free networks A few nodes highly connected, most are not.If this pattern holds for all observations, the distribution is said to “scale” as a power law and be “scale-free”.