Notes On Threshold Models

Notes on Threshold Models

Notes
on
Threshold
Models Threshold
model
assumes
that
some
dynamics
in
ecosystems
are
not
linear,
i.e.
a
little
 change
in
environment
may
have
very
strong
effect
on
the
ecosystem’s
property,
or
vice
versa.

 A
threshold
may
occur
when
a
trigger
switches
the
pull
of
negative
feedbacks
from
a
configu‐ ration
(attractor)
to
another.

Common
triggers
include
long‐term
abiotic
perturbations
and
 short‐term
biotic
modification
of
community
structures.

As
the
theory
of
ecological
resilience
develops,
threshold
model
is
more
and
more
being
 considered
as
a
necessary
tool
in
the
studies
of
ecosystem
resilience.

The
threshold
model’s
 implication
on
sudden
“flip”
of
ecosystem
state
or
appearance
is
exactly
what
inspired
the
 originator
of
ecological
resilience
concept,
C.
S.
Holling,
who
studied
caterpillar
and
food’s
non‐ linear
dynamics.

Despite
that
ecological
resilience
theory
is
increasingly
being
adopted
by
ecosystem
re‐ searchers
and
managers
worldwide,
both
in
theory
and
in
practice,
and
as
a
result
threshold
 models
are
relevant
in
many
situations,
it
must
be
noted
that
threshold
model
cannot
be
ap‐ plied
in
all
types
of
ecosystems
uniformly.

So
what
kinds
of
ecosystems
are
suitable
for
apply‐ ing
this
kind
of
models?

Threshold
models
can
be
classified
as
conceptual
models,
or
applied
models.

If
threshold
 models
are
considered
as
conceptual,
there
are
two
major
categories,
models
without
hystere‐ sis
and
those
with
hysteresis.

Threshold
models
without
hysteresis
also
have
nonlinear
behav‐ 1 of 5

and recovery, and anticipate—or in the case of degraded systems, overcome—such thresholds.

There are several types of theoretical models that predict threshold dynamics. Particularly applicable are discontinuous threshold models without hysteresis The gap between threshold models in theory and (Figure 1b), where the same response pathway occurs application regardless of the direction of the environment change NotesTheory on Threshold Models (i.e. no hysteresis). In this case, a sudden change in one Although ecosystem dynamics can be multifaceted, one direction, although discontinuous, could be reversible and common distinction is between linear continuum responses result in a sudden recovery in the opposite direction. iour:
small
changes
cause
large
response
near
threshold,
while
in
other
places
large
change
 and discontinuous threshold responses (Figure 1). ConHysteresis threshold models (Figure 1c), by contrast, tinuous change models predict that a change in the describe a situation in which there are two or more stable environment leads to a proportional change in species point attractors (basins of attraction) for one given external may
have
limited
impact.

The
relationship
between
impact
and
response,
however,
is
of
one
 composition. Increasing or decreasing the environmental environmental condition. In this case, because multiple conditions over time will lead to responses down or up the states occur at one given environmental condition, the same trajectory. Discontinuous threshold models describe pathway to a restored system can be very different from direction,
i.e.
positive
change
causes
only
positive
effect
or
only
negative
effect.

Models
with
 the situation where changes in environmental conditions the one that led to the degraded state [5]. lead to very little change in species composition or function Ecological theory yields a rigorous and detailed set of until a threshold is reached, when a sudden change in constructs needed to determine whether a system exhibits hysteresis
reflects
a
dynamic
that
is
not
only
nonlinear,
but
also
bi‐directional:
in
some
places
 composition or function occurs. Ecological theory predicts threshold behavior [19,20]. However, many tests of these that thresholds (see Glossary) occur when a trigger constructs are hard if not impossible to apply in a practical positive
change
causes
positive
effect,
in
other
places
positive
change
causes
negative
effect.

 switches the pull of negative feedbacks from one attractor setting. For instance, theory indicates that it is important to another attractor (Figure 1b,c). These triggers are often to demonstrate long-term stability for a period that either long-term abiotic perturbations that modify site exceeds the lifespan of any one individual, which would

An
illustration
of
these
two
types
of
models
along
with
linear
models
is
given
below.



Figure 1. Alternative models of ecosystem dynamics. Gradual change (a), and two threshold models, non-hysteresis (b) and hysteresis (c). Each square defines possible relative abundances of two state characters (different species, functional groups or ecosystem processes), which we have labeled assemblage 1 and assemblage 2. Ovals represent isoclines of standard units of perturbation strength (resilience) and the stars represent attractors. The dotted line in (c) indicates boundaries of basins of attraction. Each of these isocline graphs is arrayed along an environmental axis. Changes in the isoclines across the environmental gradient represent changes in composition and stability landscape. Below the isoclines, two-dimensional relationships between the biotic community composition (vertical axis) and environment (horizontal axis) are shown. Gradual change (a) occurs when there is a linear succession of species or groups along an environmental gradient. Non-hysteresis threshold change (b) occurs where species composition rapidly changes at a given point on the environmental gradient. Changes in the environmental gradient (or other external drivers) can push a system from one state to the other. Hysteresis thresholds (c) can occur if there are multiple basins of attraction (states) within the same habitat so that the threshold where assemblage 1 will decline (collapse) differs from where assemblage 1 will increase (recovery). Human activities can change the frequency and nature of threshold events by influencing resilience, which can affect the arrangement of isoclines as well as shift the system from one to another type of dynamics (i.e. from [a] to [b] to [c], as indicated by the colored rectangles).

(Copied
from
Suding,
K.N.
&
Hobbs,
R.J.,
Threshold
models
in
restoration
and
conservation:
a
 developing
framework.
Trends
in
Ecology
&
Evolution,
In
Press,
Corrected
Proof.
Available
at:
 http://dx.doi.org/10.1016/j.tree.2008.11.012
[Accessed
March
6,
2009].) 2

If
consider
the
classification
of
applied
threshold
model,
there
are
again
mainly
two
 types:
state‐transition
model
and
two‐threshold
model.

State‐transition
model
has
been
 widely
applied
in
ecosystem
management
practices.

Often
these
models
have
a
number
of
 states
and
even
more
transitions.

Transitions
at
large
temporal
or
spatial
scales
are
often
not
 easy
to
address
in
actual
management
due
to
the
limit
of
policy’s
valid
period
and
boundaries.



2 of 5

Notes on Threshold Models The
states
are
usually
defined
by
multiple
properties
of
the
system
thus
are
multi‐dimensional.

 Two‐threshold
model
is
considered
as
more
suitable
for
ecosystem
management
in
certain
set‐ tings,
as
it
assumes
that
there
is
an
“easy”
threshold
that
is
closer
and
reversible,
and
a
“hard”
 threshold
that
is
more
difficult
to
reach
and
irreversible,
therefore
ecosystem
managers
can
 pay
more
attention
on
the
“easy”
threshold
without
losing
sight
of
the
“hard”
threshold.

Threshold
models
are
often
applied
in
systems
experiencing
heavy
environmental
 changes,
and
self‐organizing
systems,
especially
those
with
intransitive
networks.

This
of
 course
is
assuming
that
heavy
environmental
changes
may
directly
cause
the
system
to
reach
 the
threshold,
and
the
ability
of
self‐organizing
may
be
influenced
after
the
threshold
is
 crossed.

The
possibility
of
reaching
a
threshold
to
a
large
extent,
and
how
significant
the
effect
 is
after
crossing
the
threshold,
determine
how
successful
if
a
threshold
model
is
applied
to
the
 system.

Applying
a
threshold
model
in
an
ecosystem
that
is
being
changed
by
human
may
be
a
 very
fruitful
attempt.

Human
can
change
the
system’s
threshold
dynamics
in
many
ways.

They
 can
change
the
system’s
biotic
capacity,
by
changing
the
composition
of
species
or
their
abun‐ dance;
they
can
deprive
the
system
of
its
biological
legacies
such
as
fallen
trees
and
dead
 shrub;
they
can
change
the
connectivity
of
the
system;
they
can
transform
transient
thresholds
 to
permanent
ones;
and
last
but
not
least
they
can
change
climate.

These
changes
may
be
 good
or
bad,
but
all
of
them
has
impact
on
the
threshold
of
the
system.

3 of 5

Notes on Threshold Models Ecosystems,
from
a
human‐independent
perspective,
all
have
certain
functions,
such
as
 supporting
their
components
and
self‐maintaining.

In
some
of
the
ecosystems,
groups
of
spe‐ cies
can
be
identified
as
providing
certain
functions
for
the
whole
ecosystem.

These
groups
are
 therefore
called
functional
groups.

The
importance
of
functional
groups
has
also
been
em‐ phasized
in
resilience
theories.

In
a
system
with
functional
groups
that
influence
the
system’s
 ability
to
recover,
or
with
functions
that
respond
to
diversity
changes,
these
dynamics
are
im‐ portant
in
evaluating
uncertainty
of
resilience,
and
threshold
models
are
especially
applicable
 in
these
systems,
as
crossing
the
threshold
is
likely
to
cause
the
change
of
the
system’s
func‐ tion.

Considering
the
number
of
ecosystems
being
influenced
by
human,
there
seems
to
be
 many
situations
where
threshold
models
can
be
applied.

However,
a
successful
result
cannot
 always
be
expected.



Due
to
the
lack
of
data
and
proven
means
of
analyzing
them,
currently
many
threshold
 models
are
formulated
in
a
heuristic
manner.

That
means
the
researchers
develop
a
rather
 crude
model
at
first,
see
how
well
it
explains
existing
data,
what
factors
should
be
included
or
 excluded,
and
revise
the
model.

Such
model
construction
lack
rigorous
validation
of
its
as‐ sumptions
and
can
hardly
be
applied
to
other
settings.

Another
difficulty
is
due
to
lack
of
tools
of
monitoring
and
evaluation,
especially
when
we
 consider
thresholds
at
large
spatial
and
temporal
scales
that
cannot
be
addressed
in
one’s
ca‐ reer
life
or
their
allocated
area
of
management.

The
managers
thus
cannot
confidently
apply


4 of 5

Notes on Threshold Models the
result
of
threshold
model.

Ignoring
a
threshold
may
cause
severe
consequences,
while
 jumping
at
every
alarm
causes
waste
of
resources.

To
improve
the
applicability
of
threshold
models
and
the
outcomes,
the
development
of
 these
models
should
address
these
issues: Incorporating
some
stochasticity
to
address
the
uncertain
nature
of
ecosystems; Evaluating
system
mechanism
controlling
restoration
or
resilience.

This
calls
for
better
 understanding
of
ecosystems
and
resilience; Evaluating
both
uncertainty
and
evidences
of
threshold
behaviour.

This
calls
for
collect‐ ing
more
data
and
do
more
analysis
of
their
implications
on
threshold; Establishing
pattern‐based
knowledge,
incorporating
indicators,
monitoring
and
expert
 knowledge; Developing
tests
using
active
adaptive
management; Looking
into
transient
dynamics; Making
use
of
statistical
and
analytical
tools. All
these
issues
cannot
be
addressed
by
researchers
or
managers
alone.

Ecologists,
 stakeholders
and
managers,
as
well
as
researchers
from
other
disciplines
must
combine
their
 forces
to
gain
meaningful
outcomes.

Threshold
models
may
be
used
more
widely
and
wisely
in
 the
future,
and
its
development
will
enhance
our
ecological
studies.

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