13 th Century model of rabbit population growth

13 th 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

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) TRANSLOCATION JJJJ J UPTAKE 62. 2 SOIL AVAILABLE Ca 510 JJJJJJ -5. 1 JJJJJJ THROUGHFALL AND STEMFLOW 6. 7 LITTER FALL 40. 7 Inorganic fraction 2. 2 INPUT BELOW GROUND LIVING BIOMASS BOUND Ca 101 (2. 7) ROOT LITTER 3. 2 ROOT Inorganic EXUDATES fraction 3. 5 NET MINERALIZATION 42. 4 WEATHERING 21. 1 dissolved organic fraction 13. 7 BULK PRECIPITATION 2. 2 FOREST FLOOR BOUND Ca 370 (1. 4) Organic fraction <0. 1 Inorganic fraction MINERAL SOIL (particulate BOUND Ca ) 0. 2 9600 ROCK 64, 600 BIOSPHERE HYDROLOGIC EXPORT 13. 9 OUTPUT

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.

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. 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

Cynic’s View of the Interface Between Ecological Research and Management (Hobbs, 1998) Sparse and Infrequent Observations Observational Errors Management Decisions Incorrect Interpretation Theoretical Misunderstanding Oversimplified Models Computer Models CONTROVERSY Further Refinement of Unimportant Details CONFUSION Further Misunderstanding Unrealistic Assumptions Crude Diagnostic Tools Coincidental Agreement Between Theory and Observations PUBLICATION

Tactical Models attempt to measure all relevant factors and determine how they interact versus Strategic Models (May 1973) way of formalizing generalizations 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.

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

• Conceptual Models of Indicator Selection Process • Conceptual Ecosystem Models

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

Conceptual Model of Mangrove Estuary Transition Exotic Plants Invasion of Schinus & Colubrina Sea Level Rise Reduced Freshwater Flow Volume & Duration Altered Nutrient Mixing & Estuarine Productivity Coastal Embankment Erosion Exceeding Accretion Altered Salinity Gradient Exotic Fish Altered Hydroperiod & Drying Patterns Invasion of Mayan Cichlid Altered Mangrove Production Community Structure & Organic Sediment Accretion Estuarine Geomorphology Estuarine Crocodilian Populations Mangrove Forests & Plant Communities Estuarine Fish Communities & Fisheries Woodstork & Roseate Spoonbill Nesting Colonies

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

Conceptual model of influences on Missouri bladderpod habitat quality Prairie Cluster LTEM Program geology spatial variability at very small scales climate, climate change, elevated CO 2 temporal variability at multiple scales shallow soils, prone to drought and frost heave resource/nutrient availability woody overstory development woody species removal vegetation structure & composition wildfire, prescribed fire spatial & temporal variability increased edge effect habitat fragmentation habitat quality highly variable in time & space exotic species establishment reduced recolonization by native species differential germination , survival & reproductio n

Conceptual model of influences on population dynamics of Missouri bladderpod climate, climate change, elevated CO 2 autumn weather (precipitation & temperature) spring weather (precipitation, duration of flowering period) wildfire, prescribed fire woody species removal habitat fragmentation pollinator activity wildlife/bird activity geology cultural use (trampling) reproduction mature plants vegetation structure & composition exotic species establishment variable soil depth seed bank persistence fungal growth resource/nutrient availability growth & survival soil disturbance winter & spring weather (freeze-thaw, heavy rainfall) seed bank germination germinated seedlings

• 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

Holistic program model for the Prairie Cluster LTEM Program Population Community Landscape Are prairie remnants sustainable within small parks? Threats How is external land use changing? Are land-use changes affecting prairie remnants? Is the water quality of prairie streams declining? Where are invasive exotics distributed within and adjacent to the park? Are rare species recolonization sources disappearing? Indicators of Ecosystem Health Is the proximity or size of nearby prairie remnants changing? Do prairie streams support diversemacroinvertebrate communities? Do small prairie remnants support diverse native plant communities? Do small prairie remnants support diverse butterfly and bird communities? Are rare species populations stable? Resource Actions How is prescribed fire affecting prairie plant communities? Are restoration methods working? Is rare species habitat protection & restoration working? Are exotic control efforts effective?

Monitoring Effort Adjacent Land Use Rare Plant Community Exotic Species Management History Monitoring Products Management Feedback Synthesis External land use maps Distribution maps & population size estimates of rare species; Population models of federally endangered species Trends in plant community diversity, structure & composition; Vegetation maps Distribution maps of invasive exotics What areas harbor the highest diversity? What are the high risk habitats? How are changes in land use impacting the prairie? How is the prairie changing? Is the prairie healthy? Is the prairie threatened by exotic invasion? Are exotic control methods effective? How is prescribed fire changing the prairie? How are management practices influencing the prairie?

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

• 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

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

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

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. Physical impact Mycorrhizae Grazers Soil N storage Grazer selectivity and grazing patterns Plant growth & demography Fire Plant community structure Watershed and landscape patterns Direct Effects Insects Resource Availability Drought Invertebrates Birds Mammals Standing dead & litter Local extirpation emigration and immigration

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 Grazers, Cattle Mycorrhizae Invertebrates Grazer selectivity and grazing patterns Prescribed Fire Exotic Plant Invasion Plant growth & demography Direct Effects Insects Resource Availability Drought Plant community structure Watershed and landscape patterns Cultural use Birds Local extirpation emigration and immigration Mammals Standing dead & litter Fragmentation

Monitoring implications from terrestrial prairie model

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

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)

Spatial and Temporal Characteristics of Different Earth System Processes (NASA, 1988) Global Weather Systems Carbon Dioxide Atmospheric Variations Composition Climate 104 Glacial Periods SPATIAL SCALE (km 2) El Niño 103 Synoptic Weather Systems 102 Earthquake Cycle 101 Local Second Soil Moisture Variations Plate Tectonics Ocean Circulation Soil Development Soil Erosion Mantle Convection Extinction Events Metallogenesis Seasonal Vegetation Cycles Volcanic Eruptions Atmospheric Convection 100 Upper Ocean Mixing Origin of Earth and Life Nutrient Cycles Atmospheric Turbulence Minute Day 100 yr 102 yr TEMPORAL SCALE 104 yr 106 yr 109 yr

An Assessment of the Spatial and Temporal Scales of Natural Disturbances in an Arctic Tundra Ecosystem (Walker, 1991) Climate Fluctuations Associated with Glaciations with Continental Drift and. Glaciations Uplift of Brooks Range 4 Climate Fluctuations During the Holocene Growth and Erosion of Ice Wedges Tundra Fires 2 Eolian Deposition Animal Disturbances 0 -4 Snowbank Formation and Melting Oil Seeps Daily Freeze. Thaw Cycle -2 Major Storms and Storm Surges Annual Fluvial Erosion and Deposition Megascale EVENT FREQUENCY (log of years) 6 -2 Microsite 0 Mesocite 2 Macrosite Microregion Mesoregion 4 SPATIAL SCALE (log of area in m 2) 6 8 10 12

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.

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

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.