Transcript Introduction to Geog 471

"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 fundamental
element of any and all analyses.
• None-the-less, 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.
What are some characteristic scales?
• Animals (criminals?) 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), while a species such
as a cougar ranges widely across a broad range of habitats (a
complementary selection) and, thus, identifying the appropriate scale
to study cougar behaviour is much more complex.
What are some characteristic scales?
• Similarly, serial criminals can be commuters or marauders; 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 easy (i.e.,
the neighbourhood), while in the other a completely different
scale of analysis would be required. (How to determine??)
Marauder
Commuter
87% of serial sexual offenders were found to be Marauders
(Australian study)
Importance of working with the correct model / scale
Multiscale analyses
are therefore
required if one truly
wants to develop a
full understanding of
a place in space.
This is the study design
of the BOREAS study.
To address the issue of multiple scales that characterize the African Monsoon
a multiscale approach is being taken.
Source
Issues such as:
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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.
• 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?).
• 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.)
• Grain
• 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)
• "Scale" is not the same as "level of organization."
Scale refers 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
among biotic and abiotic components of some process
such as nutrient cycling.
• 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
• 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 years to decades, long-term climate trends
are not apparent (although fluctuations in weather might
be).
Ex. 1
• As one increases scale in a study of a system:
• Reciprocally, as we increase the extent of our analysis,
parameters that were constant now become variable and
must be accounted. If we were to extend the forest
sampling to cover a large watershed or basin, soil types
would indeed 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.
Ex. 1
• 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)
• 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.
• Thus: explanatory models are scale-dependent
A stand
-’ve correlation within each stand, +’ve correlation between stands
• 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).
• The 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 disease patterns as well
(inherent vs extrinsic forces).
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.
• The 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.
• The 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 as one changes the scale
of the study there is a corresponding
change in ‘grain’.
• 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.
This illustrates
both the scale
and aggregation
effects.
• The 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.
• The 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 / philosphophical, 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
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.
• 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 socalled "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.
• 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)
Artificial
‘Natural’
• However, 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
• 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.
Bars
Churches
Population
Churches
Are the other variables
that we aren’t considering
driving the relation?
• Geographical areas are made up not of random
groupings of individuals / households, but of
individuals / households that tend to be more alike
within the area than to those outside of the area.
Three main classes of models have been identified:
• Grouping
• Group-dependent
• Feedback
• 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'.
• Group-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.
• Feedback 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.
Grouping
Group-dependent
Feedback
A map illustrating
redlining in Philadelphia
Autocorrelation exists, but
how was it established, and
what maintains it now?
• These 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.
• So, as you can see, developing an understanding of the
role that geography alone can play in an analysis is
vital--before one can search for meaningful biological,
environmental or sociological explanations for an
observation, one should first eliminate 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.'