13th Century model of rabbit population growth:

1
13th Century model of rabbit population
growth based on Fibonacci series (1, 1, 2,
3, 5, 8, 13, .)
Malthus (1798) Nature has scattered the seeds
of life abroad with the most profuse and liberal
hand. She has been comparatively sparing in the
room and nourishment necessary to rear them. The
germs of existence contained in this spot of
earth, with ample food, and ample room to expand
in would fill millions of worlds in the course
of a few thousand years. Given unlimited
resources, size of population increases as
geometric progression (1, 2, 4, 8, 16, .)
Verhulst-Pearl logistic equation (1839) model
of population growth in a limited environment
2
Annual Calcium Budget for an Aggrading Forested
Ecosystem at Hubbard Brook (Likens et al.
1977)
NORTHERN HARDWOOD FOREST ECOSYSTEM
ABOVE GROUND LIVING BIOMASS BOUND Ca
383 (5.4)
Inorganic fraction 2.2
LITTER FALL 40.7
THROUGHFALL AND STEMFLOW 6.7
TRANSLOCATION
JJJJJJJJJ
JJJJJJJJJJJJJJJJJJ
-5.1
INPUT
BULK PRECIPITATION 2.2
BELOW GROUND LIVING BIOMASS BOUND Ca
101 (2.7)
UPTAKE 62.2
BIOSPHERE
FOREST FLOOR BOUND Ca 370 (1.4)
ROOT LITTER 3.2
HYDROLOGIC EXPORT 13.9
ROOT EXUDATES 3.5
Inorganic fraction 3.5
SOIL AVAILABLE Ca 510
Organic fraction lt0.1
Inorganic fraction (particulate) 0.2
NET MINERALIZATION 42.4
OUTPUT
MINERAL SOIL BOUND Ca 9600 ROCK
64,600
WEATHERING 21.1
dissolved organic fraction 13.7
3
A conceptual model is a mental picture of how
something works. We have a conceptual model of
a car that allows us to drive by relating certain
actions (e.g. pressing the brake pedal) to
certain results (e.g. the car stops).
We dont have to understand automotive
engineering for our driving model to work.
But if we need to repair the engine, a different
model would be required.
4
Prototype Confessions . . . . . We did not
initiate the Prairie Cluster LTEM program with
formal planning process -- convening panels of
experts. We are reviewing monitoring components
within context of ecosystem models rather late in
the design phase.
5
Cynics View of the Interface Between Ecological
Research and Management (Hobbs, 1998)
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Common Misconceptions (Starfield et al. 1997) A
model cannot be built with incomplete
understanding. Managers make decisions
with incomplete information all the time! This
should be an added incentive for
model-building as a statement of current best
understanding. A model must be as detailed
and realistic as possible. If models are
constructed as purposeful representations of
reality, then design the leanest model
possible. Identify the variables that make the
system behave and join them in the most
simple of formal structures.
7
Modeling Confusion?

• Conceptual Models of Indicator Selection Process
• Conceptual Ecosystem Models
• Small, Focused Models -- Conceptual or predictive
  models of populations
• or communities
• Holistic Program Models -- Conceptual models of
  how monitoring
• information will feed back into
• decision-making process

8

• Conceptual Models of Indicator Selection Process

• Conceptual Ecosystem Models

9
Conceptual Ecological Models of the Major Wetland
Physiographic Regions in South
Florida Comprehensive Everglades Restoration
Project Team and the Science Coordination Team
of the South Florida Ecosystem Restoration
Working Group
Lake Okeechobee Caloosaatchee Estuary St. Lucie
Estuary Indian River Lagoon Everglade Ridge
and Slough Big Cypress Basin Southern Everglades
Marl Prairies Southern Shark Slough Mangrove
Estuary Transition Florida Bay Mangrove
10
Conceptual Model of Mangrove Estuary Transition
11

• Conceptual Models of Indicator Selection Process

• Conceptual Ecosystem Models

• Small, Focused Models -- Conceptual or
  predictive models of populations or
  communities

12
Conceptual model of influences on Missouri
bladderpod habitat quality Prairie Cluster
LTEM Program
13
Conceptual model of influences on population
dynamics of Missouri bladderpod
climate, climate change, elevated CO2
autumn weather (precipitation temperature)
spring weather (precipitation, duration of
flowering period)
seed bank persistence
fungal growth
wildfire, prescribed fire
pollinator activity
seed bank
reproduction
vegetation structure composition
mature plants
woody species removal
germination
germinated seedlings
growth survival
exotic species establishment
resource/nutrient availability
habitat fragmentation
wildlife/bird activity
soil disturbance
geology
variable soil depth
winter spring weather (freeze-thaw,heavy
rainfall)
cultural use (trampling)
14

• Conceptual Models of Indicator Selection Process

• Conceptual Ecosystem Models
• Small, Focused Models -- Conceptual or predictive
  models of populations or communities

• Holistic Program Models -- Conceptual models of
  how monitoring
• information will feed back into
• decision-making process

15
Holistic program model for the Prairie Cluster
LTEM Program
Are prairie remnants sustainable within small
parks?
Indicators of Ecosystem Health
16
Monitoring Effort
Monitoring Products
Management Feedback
Synthesis
Adjacent Land Use
External land use maps
Distribution maps population size estimates of
rare species Population models of federally
endangered species
How are changes in land use impacting the prairie?
Rare Plant
What areas harbor the highest diversity? What are
the high risk habitats?
Trends in plant community diversity, structure
composition Vegetation maps
How is the prairie changing?
Is the prairie healthy?
Plant Community
Is the prairie threatened by exotic invasion?
Distribution maps of invasive exotics
Exotic Species
How are management practices influencing the
prairie?
Are exotic control methods effective?
Management History
How is prescribed fire changing the prairie?
17

• Conceptual models are useful throughout
• the monitoring process
• formalize our current understanding of the
  context and scope of the natural processes and
  anthropogenic stressors affecting ecological
  integrity
• help expand our consideration across traditional
  discipline boundaries

• Most importantly, clear, simple models facilitate
  communication between
• scientists from different disciplines
• researchers and managers
• managers and the public

18

• Conceptual Models of Indicator Selection
  Process
• Conceptual Ecosystem Models
• Small, Focused Models -- Conceptual or
  predictive models of populations
• or communities
• Holistic Program Models -- Conceptual models of
  how monitoring
• information will feed back into
• decision-making process

19
Why Do We Need Conceptual Ecosystem Models?
Despite the complexity of ecosystems and the
limited knowledge of their functions, to begin
monitoring, we must first simplify our view of
the system. The usual method has been to take a
species-centric approach, focusing on a few
high-profile species that is those of economic,
social, or legal interest. Because of the
current wide (and justified) interest in all
components of biological diversity, however, the
species-centric approach is no longer sufficient.
This wide interest creates a conundrum we
acknowledge the need to simplify our view of
ecosystems to begin the process of monitoring,
and at the same time we recognize that
monitoring needs to be broadened beyond its usual
focus to consider additional ecosystem
components. Noon et al. 1999
20
Aspects to Consider as Conceptual Models are
Developed from Barber (1994)
1. Identify the structural components of the
resource, interactions between components, inputs
and outputs to surrounding resources, and
important factors and stressors that determine
the resources ecological operation and
sustainability.
2. Consider the temporal and spatial dynamics
of the resource at multiple scales because
information from different scales can result in
different conclusions about resource condition.
3. Identify how major stressors of resource
are expected to impact its structure and function
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Conceptual model of core abiotic and biotic
relationships within terrestrial prairie
ecosystems. Modified from Hartnett and Fay
(1998), the model has been adopted by the Prairie
Cluster LTEM Program.
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Conceptual model of core abiotic and biotic
relationships within terrestrial prairie
ecosystems, including anthropogenic stressors (in
red) affecting Prairie Cluster parks.
Modified from Hartnett and Fay 1998
Physical impact
Exotic Plant Invasion
Mycorrhizae
Grazers, Cattle
Invertebrates
Watershed and landscape patterns
Grazer selectivity and grazing patterns
Plant community structure
Plant growth demography
Prescribed Fire
Direct Effects
Insects
Birds
Local extirpation emigration and immigration
Resource Availability
Mammals
Drought
Cultural use
Standing dead litter
Fragmentation
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Monitoring implications from terrestrial prairie
model
26
Aspects to Consider as Conceptual Models are
Developed from Barber (1994)
1. Identify the structural components of the
resource, interactions between components, inputs
and outputs to surrounding resources, and
important factors and stressors that determine
the resources ecological operation and
sustainability.
27
The scale of resolution chosen by ecologists is
perhaps the most important decision in the
research program, because it largely
predetermines the questions, the procedures, the
observations, and the results. .. Many
ecologists. focus on their small scale questions
amenable to experimental tests and remain
oblivious to the larger scale processes which may
account for the patterns they study.
P.D.Dayton and M.J. Tegner (1984)
Most environmental problems are driven by
mismatches of scale between human responsibility
and natural interactions. Lee (1993)
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Spatial and Temporal Characteristics of Different
Earth System Processes (NASA, 1988)
29
An Assessment of the Spatial and Temporal Scales
of Natural Disturbances in an Arctic Tundra
Ecosystem (Walker, 1991)
Climate Fluctuations Associated with Glaciations
Climate Fluctuations Associated with Glaciations
Continental Drift and Uplift of Brooks Range
6
Climate Fluctuations During the Holocene
Growth and Erosion of Ice Wedges and Erosion of
Ice Wedges
4
EVENT FREQUENCY (log of years)
Tundra Fires
Megascale
2
Annual Fluvial Erosion and Deposition
Eolian Deposition
Major Storms and Storm Surges
Snowbank Formation and Melting
Animal Disturbances
Oil Seeps
0
Daily Freeze- Thaw Cycle
Thaw Cycle
Microsite
Mesocite
Macrosite
Microregion
Mesoregion
-2
-4
-2
0
2
4
6
8
10
12
SPATIAL SCALE (log of area in m2)
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31
Incorporating Multiple Points of View
Allen and Hoekstra (1992) stress that ecology is
in many ways a soft-system science, one in
which point of view (ecological level of inquiry,
temporal/spatial scale) is the very substance of
the discourse. They suggest there are enough
decision points in an ecological investigation
(or in the design of a monitoring program) to
require some formalization of decision -making.
32

• Checklands Soft-systems Methodology (Allen
  and Hoekstra 1992)
• 1) Recognize that there is a problem, a real mess
  
• troubled feeling an ecosystem, community or
  population ecologist may have that some
  other sort of specialist could better solve the
  problem at hand
• trying to manage water, vegetation and
  wildlife in a unit of particular size but
  realizing the temporal or spatial scales dont
  mesh with natural process scales
• 2) Actively generate as many points of view for
  the system as possible
• -- painting the rich picture
• community ecologist consider physiological
  aspects of the problem, population biologist to
  consider nutrient cycling, etc.
• 3) Find the root definitions -- develop
  abstractions that restrict the rich picture in
  hopes of finding solution.
• (key system attributes will change as scale of
  the system and point of view (ecological
  discipline) is altered
• 4) Build the model

33
Why Do We Need Conceptual Models?
1) Ecosystems (communities, populations) are
messy our ability to provide early warning of
resource decline is uncertain. We need a road
map.
2) Long-term monitoring is an iterative process
(i.e. we may not get it right the first time)
modeling will help ensure that mistakes are
instructive and not repeated.
3) A balanced monitoring program should consider
multiple spatial/temporal scales and integrate
monitoring across ecological disciplines. Models
serve as heuristic devices to foster better
communication and clarify scaling issues.
4) A balanced monitoring program should address
short-term management issues and long-term
ecological integrity. Clear models serve as
heuristic devices to foster better communication
between managers and scientists, and between
managers and the general public.
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