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BCB 322: Landscape Ecology


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Title: BCB 322: Landscape Ecology

BCB 322Landscape Ecology
  • Lecture 2 Theories Models
  • Hierarchy theory, diffusion theory percolation

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

Principal theories
  • We shall be looking at four theories in greater
  • 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

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
  • 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

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
  • Clearly, landscapes are very complex systems

Harris, 1984 (reprinted in Farina, 1998)
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)

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

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)
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
  • 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.

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
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
  • 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)
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

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
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

Eqn (3)
Farina, 1998
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)
Percolation theory resource use
  • Hence, when resources are well distributed
    (Pltpc), the organism doesnt have to move very
  • 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.

  • 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
  • Resource-gathering ( consequently home range) is
    related to resource density and landscape

  • 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,
  • 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
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