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13th Century model of rabbit population growth: based on Fibonacci series (1, 1, 2, 3, 5, 8, 13, ….). Malthus (1798)

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13th century model of rabbit population growth

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


13th century model of rabbit population growth

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

BELOW GROUND LIVING BIOMASS BOUND Ca 101 (2.7)

BULK PRECIPITATION 2.2

UPTAKE 62.2

FOREST FLOOR BOUND Ca 370 (1.4)

BIOSPHERE

ROOT LITTER 3.2

HYDROLOGIC EXPORT 13.9

ROOT EXUDATES 3.5

Inorganic fraction 3.5

SOIL AVAILABLE Ca 510

Organic fraction <0.1

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


13th century model of rabbit population growth

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 don’t 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.


13th century model of rabbit population growth

Why Aren’t Conceptual Models Routinely Used

to Develop Ecological Monitoring?

Cynicism regarding utility of modeling

Incomplete understanding of ecosystem function

Confusion over modeling objectives

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.


13th century model of rabbit population growth

Sparse and Infrequent Observations

Observational Errors

Incorrect Interpretation

Theoretical Misunderstanding

Management Decisions

Oversimplified Models

Further Refinement of Unimportant Details

Computer Models

CONTROVERSY

Unrealistic Assumptions

CONFUSION

Further Misunderstanding

Crude Diagnostic Tools

Coincidental Agreement Between Theory and Observations

PUBLICATION

Cynic’s View of the Interface Between Ecological Research and Management (Hobbs, 1998)


13th century model of rabbit population growth

Tactical ModelsversusStrategic Models

(May 1973)

attempt to measure all relevant factors way of formalizing generalizations

and determine how they interact about the ecological system of interest

“a purposeful representation of reality” (Starfield et al. 1994)

  • 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.


  • 13th century model of rabbit population growth

    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


    13th century model of rabbit population growth

    • Conceptual Models of Indicator Selection Process

    • Conceptual Ecosystem Models


    13th century model of rabbit population growth

    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


    13th century model of rabbit population growth

    Exotic Plants

    Sea Level Rise

    Reduced Freshwater Flow Volume & Duration

    Exotic Fish

    Altered Nutrient Mixing & Estuarine Productivity

    Altered Salinity Gradient

    Coastal Embankment Erosion Exceeding Accretion

    Altered Hydroperiod & Drying Patterns

    Invasion of Schinus & Colubrina

    Altered Mangrove Production Community Structure & Organic Sediment Accretion

    Invasion of Mayan Cichlid

    Estuarine Fish Communities & Fisheries

    Estuarine Geomorphology

    Mangrove Forests & Plant Communities

    Woodstork & Roseate Spoonbill Nesting Colonies

    Estuarine Crocodilian Populations

    Conceptual Model of Mangrove Estuary Transition


    13th century model of rabbit population growth

    • Conceptual Models of Indicator Selection Process

    • Conceptual Ecosystem Models

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


    13th century model of rabbit population growth

    spatial variability at very small scales

    geology

    shallow soils, prone to drought and frost heave

    climate,

    climate change, elevated CO2

    temporal variability at multiple scales

    woody overstory development

    resource/nutrient availability

    woody species removal

    vegetation structure & composition

    habitat quality highly variable in time & space

    wildfire,

    prescribed fire

    spatial & temporal variability

    exotic species establishment

    increased

    edge effect

    differential germination, survival & reproduction

    reduced recolonization by native species

    habitat fragmentation

    Conceptual model of influences on Missouri bladderpod habitat quality

    Prairie Cluster LTEM Program


    13th century model of rabbit population growth

    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)


    13th century model of rabbit population growth

    • 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


    13th century model of rabbit population growth

    Threats

    Resource Actions

    How is external land use

    Is the proximity or size of

    Landscape

    changing?

    nearby prairie remnants

    How is prescribed fire

    Are land-use changes

    changing?

    affecting prairie plant

    affecting prairie remnants?

    communities?

    Do prairie streams support

    diverse

    macroinvertebrate

    Are restoration

    Is the water quality of

    communities?

    methods working?

    prairie streams declining?

    Community

    Do small prairie remnants

    Is rare species habitat

    support diverse native plant

    Where are are invasive

    protection &

    communities?

    exotics distributed within

    restoration working?

    and adjacent to the

    Do small prairie remnants

    park?

    support diverse butterfly

    Are exotic control

    and bird communities?

    efforts effective?

    Are rare species re-

    Population

    colonization sources

    Are rare species populations

    disappearing?

    stable?

    Holistic program model for the Prairie Cluster LTEM Program

    Are prairie remnants sustainable within small parks?

    Indicators of Ecosystem Health


    13th century model of rabbit population growth

    Monitoring Products

    Management Feedback

    Monitoring Effort

    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?


    13th century model of rabbit population growth

    • 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


    13th century model of rabbit population growth

    • 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


    13th century model of rabbit population growth

    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


    13th century model of rabbit population growth

    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 resource’s 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


    13th century model of rabbit population growth

    Physical impact

    Mycorrhizae

    Grazers

    Invertebrates

    Soil N

    storage

    Watershed and

    landscape

    patterns

    Grazer selectivity

    and grazing

    patterns

    Plant community

    structure

    Plant growth & demography

    Fire

    Direct Effects

    Insects

    Birds

    Local extirpation

    emigration and

    immigration

    Resource

    Availability

    Mammals

    Drought

    Standing dead

    & litter

    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.


    13th century model of rabbit population growth

    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


    13th century model of rabbit population growth

    Monitoring implications from terrestrial prairie model


    13th century model of rabbit population growth

    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

    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 resource’s ecological operation and sustainability.


    13th century model of rabbit population growth

    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)


    13th century model of rabbit population growth

    Global

    Global Weather Systems

    Carbon Dioxide Variations

    Atmospheric Composition

    Origin of Earth and Life

    Climate

    104

    Glacial Periods

    Plate Tectonics

    El Niño

    Ocean Circulation

    Mantle Convection

    Upper Ocean Mixing

    103

    Synoptic Weather Systems

    Soil Development

    SPATIAL SCALE (km2)

    Extinction Events

    Soil Moisture Variations

    102

    Earthquake Cycle

    Soil Erosion

    Metallogenesis

    Seasonal Vegetation Cycles

    Volcanic Eruptions

    101

    Atmospheric Convection

    Nutrient Cycles

    100

    Atmospheric Turbulence

    Local

    Minute

    Day

    100 yr

    102 yr

    104 yr

    106 yr

    109 yr

    Second

    TEMPORAL SCALE

    Spatial and Temporal Characteristics of Different Earth System Processes(NASA, 1988)


    13th century model of rabbit population growth

    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)


    13th century model of rabbit population growth

    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.


    13th century model of rabbit population growth

    • Checkland’s “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 don’t 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


    13th century model of rabbit population growth

    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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