Why is ‘geography’ important?

The fundamental issue"The problem of pattern and scale is the central problem in ecology, unifying population biology and ecosystems science, and marrying basic and applied ecology. Applied challenges ... require the interfacing of phenomena that occur on very different scales of space, time, and ecological organization. Furthermore, there is no single natural scale at which ecological phenomena should be studied; systems generally show characteristic variability on a range of spatial, temporal, and organizational scales." (Levin 1992; italics added)

This quote equally applies to health studies, crime analysis, etc., and emphasizes the fact that geography is a natural element of any and all analyses.

A working solutionEven though there may be no single ‘natural scale’, many have argued that ecological phenomena tend to have characteristic spatial and temporal scales, or spatiotemporal domains (e.g., Delcourt et al. 1983, Urban et al. 1987).

A central tenet of landscape ecology is that particular phenomena should be addressed at their characteristic scales. Likewise, if one changes the scale of reference, the phenomena of interest change.

(Think of the relation between health, crime and poverty—interventions taken at the neighbourhood level would be very different than those taken at the provincial / national level.)

Characteristic scales?

What are some characteristic scales?

Animals (criminals, disease vectors) may select for a resource in a consistent direction or for a mixture of habitats—denoted as “simple” and “complementary” selection.

A species that is restricted in distribution to rocky tidal zones has an obvious characteristic scale (a simple selection—a patch), while a species such as a cougar, which ranges widely across a broad range of habitats (a complementary selection—patches and the matrix), makes identifying the appropriate scale to study behaviour a much more complex process.

Characteristic scales?What are some characteristic scales?

Serial criminals can have different characteristic scales as well—they can be either marauders or commuters; one commits offences primarily within their own neighbourhood (a marauder) while the other travels outside of the neighbourhood to commit their offences (a commuter). Obviously, in the one case identifying the characteristic scale of analysis is simple (i.e., the neighbourhood), while in the other a completely different scale of analysis would be required. (How to determine?)

CommuterMarauder

87% of serial sexual offenders were found to be Marauders(Australian study)

Importance of working with the correct model / scale / extent

Multiscale analysesare often

required if one trulywants to develop a

full understanding ofa place in space.

This is the study designof the BOREAS study.

Think of a child in a homein a neighbourhood in a cityin a province in a country.All will influence how that

child develops.

Source

To address the issue of multiple scales that characterize the African Monsoona multiscale approach is being taken.

Why is geography important?Issues such as:

the scale, grain and extent of a study area,

the modifiable areal unit problem,

the nature of the boundaries of a study area, and

spatial dependence / heterogeneity

are implicit in any spatial analysis.

Why geography is important.Given the above, landscape ecologists, epidemiologists, health geographers, and crime analysts all must carefully consider the 'geography' of their problem, and what effects that geography alone may have on their analyses (e.g., do more crimes occur in area A than area B simply because more people live in area A, or are there more crimes because there are higher levels of drug use in the area, or because the levels of poverty are higher?).

Simply put—are the results dependent upon the spatial nature of the data, or do they reflect the results of a process? (Most likely, a combination of both.)

Scale terminologyGrain

The minimum resolution of the data (defined by scale, the "length of the ruler"). In raster lattice data, the cell size; in field sample data, the quadrat size; in imagery, the pixel size; in vector spatial data, the minimum mapping unit.

Extent The scope or domain of the data (defined as the size of the study area, typically)

Edge / extent effects

Interior points / polygons naturally have more neighbours than do edge points / polygons.

Scale"Scale" is not the same as "level of organization." Scalerefers to the spatial domain of the study, while level of organization depends on the criteria used to define the system.

For example, population-level studies are concerned with interactions amongst conspecific individuals, while ecosystem-level studies are concerned with interactions amongst biotic and abiotic components of some process, such as nutrient cycling. (Different levels of organization)

One could conduct either a small- or large-scale study of either population- or ecosystem-level phenomena.

Conspecific: Of or belonging to the same species

Why Scale Matters

As one increases scale in a study of a system:

Fine-scale processes or constraints, average away and become constants. For example, at the scale of a quadrat (say, 10 x 10 m) in a forest, it is reasonable to ignore larger-scale variability in soil parent material: the trees within the quadrat all see the same soil type. Likewise, at the time-scale of months to years, long-term climate trends are not apparent (although fluctuations in weather might be).

Ex. 1

A large-scale map would be used in a fine-scale study.

Why Scale Matters

However, as we increase the extent of our analysis, parameters that were constant now become variable and must be accounted for. If we were to extend the forest sampling to cover a large watershed or basin, soil types would vary and we would need to address this variability. Likewise, microclimate, as it varies with elevation and topographic position, would become a real source of variability affecting forest pattern at this larger scale.

Scale

Finally, new interactions may arise as one increases the extent of inquiry. At the scale of a landscape mosaic, interactions among forest stands, such as via dispersal of plant or animal species, emerge as new phenomena for study (emergent processes).

An emergent property can appear when a number of simple entities (agents) operate in an environment, forming more complex behaviors as a collective. If emergence happens over disparate size scales, then the reason is usually a causal relation across different scales.

ScaleThe nature of relations can change as the study’s extent changes. For example, the magnitude or sign of correlations may change with spatial extent. At the scale of a single habitat patch, abundances of different species might be negatively correlated due to interspecific interactions; but if one considers a set of these habitat patches in a heterogeneous landscape, any species inhabiting similar habitat types will be positively correlated. (Think again of crime and poverty and how studies at a local level could reveal different relations than a study at the national level.)

Thus: explanatory models are scale-dependent

Scale & spatial autocorrelation-’ve correlation within each stand, +’ve correlation between stands

A stand

Spatial autocorrelation

Cliff and Ord (1973) define spatial autocorrelation: ‘If the presence of some quantity in a sampling unit (e.g., a county) makes its presence in neighbouring sampling units (e.g., adjacent counties) more or less likely, we say that the phenomenon exhibits spatial autocorrelation’.

It may be classified as either positive, random or negative. In a positive case similar values appear together, while a negative spatial autocorrelation has dissimilar values appearing in close association (or similar values maximally dispersed).

Spatial autocorrelationThe non-random distribution of organisms over the earths’ surface means that most ecological problems have a spatial dimension. Biological variables are spatially autocorrelated for two reasons:

inherent forces such as limited dispersal, gene flow or clonal growth tend to make neighbours resemble each other; organisms may be restricted by, or may actively respond to, environmental

factors such as temperature or habitat type, which themselves are spatially autocorrelated (Sokal & Thomson 1987).

Obviously describes crime and diseasepatterns as well (inherent vsextrinsic forces).

Figure 11.21 from Intro to GIS and Spatial Analysis

Geostatistical methods: KrigingKriging

stochastic, exact, smooth or abrupt, global or local method of spatial interpolation.

Natural data are difficult to model using smooth functions because naturally-occurring random fluctuations and measurement error combine to cause irregularities in sampled data values.

Kriging was developed to model those stochastic concepts.

It is based on the concept of a regionalized variable that has three components:

Components of a Regionalized Variable

data

STRUCTURAL – This may be represented by the

mean or a constant trend.

SPATIALLY CORRELATED – Data often exhibit positive

spatial correlations.

RANDOM NOISE – Measurement errors, other

errors, random fluctuations.

Topography is a reflection of many processesoperating at different scales; with Kriging we hope to develop models of some of those processes.

Components of a Regionalized Variable / of spatial autocorrelation.

The random noise component (non-fitted)

The spatially correlated component

The structural component (e.g., a linear trend)

This is what krigingattempts to model.

Environmental gradient

Biological interactions(e.g., dispersal)

Kriging

Kriging is implemented using a semi-variogram

There are many different varieties of kriging (e.g, ordinary, universal, simple, indicator), and selecting the appropriate one requires careful consideration of the data.

ArcGIS's help file--look up the term kriging—provides a lot of information on the various types of kriging (and co-kriging) that are commonly used in spatial analysis.

ArcGIS’s tutorial for the Geostatistical Analyst is also very informative (in particular consider the Geostatistical Wizard)

Spatial autocorrelation

Moran's I is a weighted product-moment correlation coefficient, where the weights reflect geographic proximity.

Values of I larger than 0 indicate positive spatial autocorrelation; values smaller than 0 indicate negative spatial autocorrelation.

Which is real?

Product-moment correlation coefficientsPearson’s r or Pearson’s product-moment correlation coefficient:

(2 variables X, Y)

Moran’s I is a spatially-weighted product-moment correlation coefficient:

(1 variable, X,

spread across space [i,j])

Moran’s I can also be derived from a regression analysis by looking at the normalized relation between the variable and lagged summaries of the variable

(see Intro to GIS and Spatial Analysis Figure 13.3)

MAUPThe Modifiable Areal Unit Problem is endemic to all spatially aggregated data. It consists of two interrelated parts.

First, there is uncertainty about what constitutes the objects of spatial study--identified as the scale and aggregation problem.

Second, there are the implications this holds for the methods of analysis commonly applied to zonal data and for the continued use of a normal science paradigm which can neither cope nor admit to its existence (i.e., how specific are the results to the specific data units used; how generalizable are they?).

Object uncertainty: ScaleThe scale effect is the tendency, within a system of modifiable areal units, for different statistical results to be obtained from the same set of data when the information is grouped at different levels of spatial resolution (e.g., enumeration areas, census tracts, cities, regions). This infers that, generally, as one changes the scale of the study there is a corresponding change in ‘grain’.

Object uncertainty: Aggregation

The aggregation or zoning effect is the variability in statistical results obtained within a set of modifiable units as a function of the various ways these units can be grouped at a given scale, and not as a result of the variation in the size of those areas.

MAUP effects

This illustratesboth scaleand aggregation effects.

?

AggregationThe problem with aggregated data comes not (only) with the data themselves or any conclusions drawn from them, but from attempts to extend the conclusions to another level of spatial resolution (usually finer, like to individual households or people). Attempting to do this is called ecological fallacy.

All the statistics and model parameters could differ between the two levels of resolution, and we have no way to predict what they are at the finer level, given the values at the coarser level.

MAUPThe second component of MAUP follows from the uncertainty in choosing zonal units.

Different areal arrangements of the same data produce different results, so we cannot claim that the results of spatial studies are independent of the units being used, and the task of obtaining valid generalizations or of comparable results becomes extraordinarily difficult.

MAUP therefore consists of two problems--one statistical and the other geographical / philosophical, and it is difficult to isolate the effects of one from the other.

Given that many policy decisions are made on the basis of statistical associations obtained from the analysis of spatial data (e.g., funding for multicultural activities to

neighbourhoods on the basis of the percentage ethnic population living there), much more attention needs to be paid to the problem.

Using the MAU effect we can create zonings

with particular statistical

aims in mind.

Another example

MAUP in action

Redrawing the balanced electoral districts in this example creates a guaranteed 3-to-1 advantage in representation for the blue voters. Here, 14 red voters are packed into the yellow district and the remaining 18 are cracked across the 3 blue districts. This is known as gerrymandering.

Gerrymandering

The MAUP is a very real issue for politicians.

One of the requirements of Civil Rights era legislation is that states that had a history of racial discrimination (generally, the states that constituted the Confederacy, including Texas) must obtain "pre-clearance" of all redistricting plans from the U.S. Department of Justice. This is because of the tendency of those states to engage in so-called "racial gerrymandering" – configuring districts in order to minimize minority representation. This can be done either by concentrating minorities in as few districts as possible (minority vote concentration), or distributing them across many districts (minority vote dilution).

Carved out with the aid of a computer, this congressional district was the product of California's incumbent gerrymandering.

Today’s news

Spatial units

We should identify that two distinct types of spatial units are commonly used in geographic analysis--artificial and natural units.

Census data collected for individuals, but aggregated and represented as artificial areas, present a major problem in interpretation to social geographers, and cannot be treated in the same way as 'natural' areal data, such as soil type, that is collected and represented as areal data.

However, even ‘natural’ units are not without their problems (e.g., fuzzy / fractal boundaries)

Spatial units

Artificial

‘Natural’

Simpson’s paradoxHowever, there are other elements which may impact any study using aggregated data.

Simpson's Paradox is commonly encountered.

If the values of the variables vary in correlation with another (e.g., areas with high unemployment rates are often associated with areas that also exhibit high rates of other social-economic characteristics), then it may be impossible to obtain a reliable estimate of the true correlation between two variables.

Example

Simpson’s paradox

The paradox in the example arises because we assume that race is the independent variable while unemployment is the dependent variable. In fact, location is the independent variable (and unavailable for examination when we only examine the totals) and unemployment and race are the dependent variables. An example of a common-response relation.

Correlation considerations

Churches

Bars

Population

Churches

Are the other variables that we aren’t consideringdriving the relation?

Why does the MAUP exist?

One reason is that geographical areas are made up not of random groupings of species / individuals / households, but of species / individuals / households that tend to be more alike within the area than to those outside of the area. Three main classes of ‘neighbourhood’ models (e.g., drivers of spatial autocorrelation) have been identified:

GroupingGroup-dependentFeedback

Neighbourhood models I

Grouping models, in which similar individuals / households choose, or are constrained, to locate in the same area / group, either when those groups are formed or through migrations.

That is to say, some process has operated and / or continues to operate such that individuals / households do not randomly move into areas. (Chinatown, Sikh neighbourhoods in Surrey)

A tendency for plants with similar ecological requirements to be located in 'communities'.

Neighbourhood models IIGroup-dependent models, in which individuals / households in the same area / group are subject to similar external influences.

For example, there may be some 'contextual' variable affecting all individuals in the area. Alternatively, some common influence may have operated in the past, the effects of which are still felt (e.g., the restrictive covenants that used to be in place in the British properties in West Vancouver).

The rain shadow effects felt in the Okanagan Valley, and the dryland communities that result.

Neighbourhood models IIIFeedback models, in which individuals / households interact with each other and influence each other, and the frequency / strength of such interaction is likely to be greater between individuals in the same area / group than between individuals in different areas. (A tendency for people living nearby to interact and as a result to develop common characteristics.)

A bog community, wherein the acid conditions are maintained by the decomposition of the plants found therein.

Neighbourhood models

Grouping

Group-dependent

Feedback

A map illustratingredlining in Philadelphia

Autocorrelation exists, but how was it established, andwhat maintains it now?

Neighbourhood modelsThese models could all be operating, and be operating at different scales (block, neighbourhood, city, province).

Therefore, attempting to achieve a perfect understanding of the reasons why MAUP occurs may be impossible. These models describe different ways in which spatial (auto)correlation may be acting on the variables of interest.

Conclusion

So, as you can see, developing an understanding of the role that geography by itself can play in an analysis is vital--before one can search for meaningful biological, environmental or sociological explanations for an observation, one should first examine the geographic explanation.

Ultimately, neighbourhoods are composed of unique combinations of biological (behavioral, social, political, economic) and physical environments (all of which might change over time), and no combination of statistical manipulations may be able to unpack such a complex set of 'actors.'