BCB 322: Landscape Ecology

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BCB 322Landscape Ecology

• Lecture 2 Theories Models
• Hierarchy theory, diffusion theory percolation
  theory

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Introduction

• Landscape heterogeneity, complexity of the
  ecosystem components, resource restraints
  population behaviour all affect organisms in a
  landscape.
• The interaction of these components is estimated
  through several models and theories.
• Most of these theories evolved in different
  contexts
• All aim to interpret landscape complexity
  (systems structures), and together

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Principal theories

• We shall be looking at four theories in greater
  detail
• Island biogeography theory
• Hierarchy theory
• Diffusion theory
• Percolation theory
• Well also consider two models
• Metapopulation model
• Source-sink systems model
• Between them these models cover a lot of the
  conceptual ground of landscape ecology
• There is considerable variation in the details of
  some of the models

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Hierarchy theory

• Landscapes are intrinsically complex, with
  variation in resources at all scales
• Hierarchy theory attempts to explain how
  scale-specific components of the landscape are in
  contact with components visible at other
  resolutions
• HT considers that any system is a component of
  other systems at a larger scale, and is itself
  comprised of sub-systems.
• eg Landscape classification, with the micro-,
  meso-, macro- and megachores each comprising
  combinations of the finer-scale classifications

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Hierarchy theory

• (eg) River watersheds
• River basin comprises sub-basins, each comprised
  of smaller basins
• Similarly, different mammals are associated with
  stream order.
• River basins (geological), stream order
  (physical) and animal size (biological) all
  interact.
• Clearly, landscapes are very complex systems

Harris, 1984 (reprinted in Farina, 1998)
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Hierarchy theory

• To understand complex systems, one needs to focus
  on organizational level.
• This means choosing a relevant spatiotemporal
  scale to study the system (hence the components
  of the system)
• The horizontal structure of a hierarchical system
  comprises subsystems or holons
• Each holon is an aggregate of lower-level holons,
  and is part of a higher one
• The borders of a holon may be easily visible (the
  edge of a forest) or invisible (the edge of a
  frogs distribution)

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Hierarchy theory holon borders

• eg the structure of a grassland (higher holon)
  depends on the processes of grazing and woodland
  encroachment acting on local scales
• Finer-scale holons tend to have a faster
  behaviour rate than larger ones (grazing
  behaviour at a low level,
• Outputs from one level to another are aggregates
  of the component processes
• Consequently, holon levels and borders
  effectively act as filters for behaviour.
  Boundaries exist where there is a discontinuity
  in the rate of change of variables.
• This is the basis of the hierarchical
  understanding of systems

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Hierarchy theory signal filters

• Burning in a field occurs rarely (low frequency)
  and changes the structure of a grassland (visible
  at higher levels of organisation)
• Browsing of woodland margins by migratory animals
  occurs more frequently (annually), with reduced
  effect on the matrix (visible to a lesser extent
  at higher levels)
• Localised seed-gathering by mice in a savannah
  frequently causes local shortages of seed (high
  frequency), but from a higher level the effect
  may be seen as constant

ONeill et al, 1986 (reprinted in Farina, 1998)
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Hierarchy theory Incorporation

• Incorporation is the process by which
  perturbation is absorbed by a level of the system
• Low frequency fires in a savannah tend to
  increase soil fertility, reduce woodland
  encroachment provide high-quality fodder
• Consequently, they increase biodiversity
  complexity
• Frequent (human-induced) fires can destroy the
  seed bank reduce biodiversity, when the system
  can no longer incorporate the event
• The system becomes less complex, turning from a
  woodland-grassland matrix to simple grassland,
  then to arid semi-desert.

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Diffusion theory

• This theory describes the movement of organisms
  through a landscape.
• Describes plants animals, although they
  obviously operate on different timescales
• The principle is based on the diffusion of
  particles in a liquid.

Eqn (1)

• Npopulation size
• f(N) population growth function
• D diffusion coefficient (describes spatial
  movement rate)
• diffusion operator (describes the rate of
  change of N with distance the density gradient)

Turner et al, 2001
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Diffusion theory

• When invading a uniform landscape, the rate of
  spread (V) will reach asymptotes equal to
• where r is the intrinsic growth rate D is the
  diffusion coefficient
• Equation tested by Andow et al (1990), and was
  found to work well for
• Invasion of muskrats in Europe
• Invasion of cabbage white butterfly in North
  America
• However, in the case of the cereal leaf beetle,
  movement patterns were considered on a finer
  scale, and it appeared that D was underestimated.

uniform landscape
Eqn (2)
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Percolation theory

• Real landscapes are only uniform when considering
  very broad scales
• At finer scales, percolation theory describes
  organismal movement through the matrix.
• Differs from diffusion theory in that it
  considers the connectedness of the landscape
• Also considers movement to be similar to a that
  of a fluid
• Below a critical threshold (pc), distribution is
  patchy separated into discrete regions
• Above the threshold, movement through the region
  is free
• Experiments corroborate theory that the
  percolation critical threshold (pc) is lt0.5928

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Percolation theory

• The number size of lattices are related to P
  (probability of a cell being occupied by the
  target species)
• P 0.4 (no percolation)
• 49 clusters
• Largest cluster 18 cells
• P 0.6 (some percolation)
• 17 clusters
• Largest cluster 163 cells
• P 0.8 (fully percolated)
• 1 clusters
• Largest cluster 320 cells
• From this we can calculate landscape boundaries
  (total inner edges) useful for edge effect
  assessment in conservation.

Gardner et al, 1992
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Percolation theory uses

• The occupancy can signify any resource, and we
  can thus estimate the likelihood of many events
• resinous shrubs/trees forest fires
• carrier animals disease spread
• susceptible plants pest outbreaks
• Also useful for resource usage studies in animals
• If a landscape has a percolation value over to pc
  (0.5928), it can move throughout the landscape to
  find resources
• Chance of finding no resources in n landscape
  units is
• where P is the random distribution of the
  resource

Eqn (3)
Farina, 1998
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Percolation theory uses

• Therefore, the probability R or finding at least
  one resource is
• We know that if R0.5928 the animal can move
  through the landscape to find resources
• Substituting this into equation 4 gives us the
  relationship between n and P
• This then tells us far the animal needs to travel
  to obtain sufficient resources.

Eqn (4)
Eqn (5)
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Percolation theory resource use

• Hence, when resources are well distributed
  (Pltpc), the organism doesnt have to move very
  far
• Decreasing resource density will require an
  organism to look further afield
• When there are two or more available resources, n
  is calculated using their combined potential
• If a dominant organism consumes 90 of a
  resource, the subdominant species has much lower
  resource availability, and must consequently
  search more land units
• The likelihood of finding subdominant species in
  a given land unit is hence much smaller than for
  dominant species, even in relation to their
  densities (sample is insufficient) (ONeill et
  al, 1988)
• Furthermore, fragmented landscapes will reduce
  the viability of subdominant species first.

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Summary

• Hierarchy theory all systems and processes in a
  landscape are components of higher-level systems
• Incorporation the extent to which perturbation
  can be absorbed by a system
• Diffusion theory in a homogeneous landscape,
  population dispersion is related to the
  population growth rate and the rate at which it
  can move
• Percolation theory in a fragmented landscape,
  movement rate is related to the integrity of the
  landscape. Over a critical threshold (pc
  0.5928) organisms can move freely through the
  landscape.
• Resource-gathering ( consequently home range) is
  related to resource density and landscape
  integrity

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References

• Andow, D.A., Karieva, P.M., Levin, S.A. Okubo,
  A. (1990) Spread of invading organisms. Landscape
  Ecology 4177-188.
• Farina, A. (1998) Principles and Methods in
  Landscape Ecology. Chapman Hall, London.
• Harris, L.D. (1984) The fragmented forest. Island
  biograpgraphy theory and the preservation of
  biotic diversity. University of Chicago Press,
  Chicago.
• Gardner, R.H., Turner, M.G., Dale, V.H.
  ONeill, R.V. (1992) A percolation model of
  ecological flows. In Hansen, A.J. di Castri,
  F. (eds.), Landscape boundaries. Consequences for
  biotic diversity and ecological flows.
  Springer-Verlag, New York, pp. 259-269.
• ONeill, R.V., DeAngelis, D.L. Waide, J.B.
  Allen, T.F.H. (1986) a hierarchical concept of
  ecosystems. Princeton University Press,
  Princeton, New Jersey.
• ONeill, R.V., Milne, B.T., Turner, M.G.
  Garnder, R.I.I. (1988) Resource utilization and
  landscape pattern. Landscape Ecology 263-69.
• Turner, M.G., Gardner, R.H. ONeill, R.V.
  (2001) Landscape Ecology in Theory and Practice
  Pattern and Process. Springer-Verlag, New York
  401pp.