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The critical concept of scale “…the problem of relating phenomena across scales is the central problem in biology and in all of science”. Simon Levin,

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Presentation on theme: "The critical concept of scale “…the problem of relating phenomena across scales is the central problem in biology and in all of science”. Simon Levin,"— Presentation transcript:

1 The critical concept of scale “…the problem of relating phenomena across scales is the central problem in biology and in all of science”. Simon Levin, ScalesScales over which humans observe the world

2 Why be concerned about scale? Characterization of biogeographic pattern involves: –Scale of the phenomena –Scale of its detection through observation –Scale at which a pattern is statistically analyzed and communicated.

3 Cartographic scale From Lewis Carroll’s Alice in Wonderland

4 Cartographic scale

5 1:250,0001:50,0001:2500 Representative fractions

6 Cartographic scale Assuming that you have two maps of the same paper size, which of the two representative fractions shows the most detail and the smaller surface area? 1:50,0001:10,000

7 Large versus small cartographic scale Large cartographic scaleSmall cartographic scale

8 Absolute and relative scaling Absolute scale –Distance is physical, measureable Relative scale –Distance is not a physical distance but a more intangible construct, often similarity

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12 Operational scale Refers to the spatial and temporal dimensions of an object or a process

13 Operational 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. Operational scale

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15 And so these men of Indostan Disputed loud and long, Each in his own opinion Exceeding stiff and strong, Though each was partly in the right, And all were in the wrong! John Godfrey Saxe 1878

16 Decreasing (finer) grain, extent is constant Increasing extent, grain is held constant Extent: spatial (or temporal) dimension of an object or process observed or analyzed Grain: level of spatial (or temporal) resolution at which an object or process has been measured or observed. Ecological scaling

17 Which map shows more grain?

18 How much grain is shown can be a subjective decision. Cartographic scale and ecological scale are often intertwined.

19 Haggett’s scale coverage problem Nature has an immense extent and a fine grain

20 Haggett’s scale coverage problem To make even small descriptions of it, we have to sample Sampling requires sacrificing grain for extent or extent for grain.

21 Fallacies of scale Individualistic fallacy: extrapolating to the broad scale based on observations conducted at small, local scales Ecological fallacy: making local-scale characterizations based on broad-scale observations.

22 Modifiable areal unit problem Two components –Aggregation problem –Zoning problem

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24 Hierarchy theory Landscapes organized into spatial and temporal domains of shaping processes Scale hierarchy is a system of vertical interconnections Higher levels constrain the lower levels

25 Hierarchy theory

26 Non-hierarchical controls also relevant Examples: Tilt, insolation, climate, photosynthesis: hierarchical Invasive species, dispersal, natural selection: non- hierarchical

27 Cartesian scale Hierarchy theory exemplifies a Cartesian scaling of the world Scales are imposed Not necessarily “true” scales Often tied to XYZ coordinate system Space as a container

28 Constructivist scale Scale emerges out the interactions of entities Scales are produced or constructed There is no fixed and unchanging hierarchy of scales.

29 Constructivist scale Boundaries in space and frequencies of environmental exposures shaped by organisms not just our observation of them.

30 Evolutionary scaling Scaling is a practice related to adaptation

31 –Scale 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?

32 Rules for ecological scale for humans 1.Patterns are dependent upon the scale of observation 2.The important explanatory variables change with scale. 3.Statistical relationships may change as scale changes. 4.Patterns are generated by processes acting over various temporal and spatial scales.

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37 Rules for ecological scale 5. Scale can be used to justify or refute certain management practices and ideas about nature

38 Example: Successional response to clearcut logging Grain and extent of post-logging sampling determine criteria for judging response –Large extent, fine grain: criteria for recovery not likely to be met –Small extent, coarse grain: criteria for recovery easier to meet

39 Rules 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.

40 How to work with scale There 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.

41 Be aware of the different types of scaling and their relatedness Don’t be too anthropocentric Employ sampling designs and methods that are sensitive to multiple scales –Nested observations –Power laws –Fractals –Networks How to work with scale

42 Power laws Summarize how relationships change with changes in scale Often expressed on a log-log plot. Y = constant (X) n Similar slopes are thought to have similar structuring processes (n = slope) Examples Species-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 process

43 Metabolic rate and body mass

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45 Fractals A 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.

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47 Networks Can represent relationships at a variety of scales at once. Structural properties of networks provide means of understanding how they work. –Nodes and links –Degree centrality and betweenness –Weak versus strong links –Directional versus non- directional graphs

48 Random and scale free networks

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50 Spatial autocorrelation A method to summarize how patterns change with scale

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