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Parameter Estimation and Population-Based Simulation Modeling of American Alligator Populations in Support of ATLSS

Project Proposal for 2001

Continuation Research Plan [Year 3 of 3 Years]

PROJECT TITLE: Parameter Estimation and Population-Based Simulation Modeling of American Alligator Populations in Support of ATLSS

Principal Investigator: Dr. Kenneth G. Rice
USGS- Biological Resources Division
Florida Caribbean Science Center
Email: ken_g_rice@usgs.gov
Mail address:
USGS
Everglades National Park Field Station
4001 SR 9336
Homestead, FL 33034
Phone: (305) 242-7832

Co- Principal Investigator: Dr. H. Franklin Percival, Leader
Florida Cooperative Fish and Wildlife Research Unit
USGS- Biological Resources Division
Email: percivalf@usgs.gov
Mail address:
USGS
University of Florida
117 Newins-Ziegler Hall
Gainesville, FL 32611-0450
Phone: (352) 392-1861

Co- Principal Investigator: Dr. Jon C. Allen
Mail address:
Entomology & Nematology Department
University of Florida
Gainesville, FL 32611-0620

BACKGROUND:

The American alligator (Alligator mississippiensis) is not only a top consumer in south Florida, but also physically influences the system through construction and maintenance of alligator holes and trails (Mazzotti and Brandt 1994). The existence of this species is important to the faunal and floral character of the Everglades as it has evolved. Despite its prominence biologically and publicly in the system, many important questions about basic population parameters and strategies of alligators remain unanswered. In order to adequately understand alligator populations to model population growth, existing data must be assembled and new data collected for many parameters. A simulation model can then be constructed and validated both with existing data and through expert opinion. The ATLSS (Across Trophic Level System Simulation) project requires an alligator population model to simulate the south Florida ecosystem under varying management strategies. This project will provide estimation of population parameters and modeling frameworks for this simulation process.

The estimation of population parameters will require all existing data on population size, alligator growth, nesting, egg viability rates, nest survival and flooding, mark-recapture of alligators, and any other collections to be assembled. Appropriate statistical estimation techniques (mark-recapture analysis, trend analysis, etc.) will be used to estimate or construct parameters and variances for inclusion into the simulation model.

Objectives:

  • To estimate population parameters of south Florida alligator populations utilizing existing data sets for use in a population simulation model.
  • To estimate growth rates, contaminant loads, and reproductive potential of south Florida alligator populations.
  • To estimate population size of alligator populations in Everglades National Park for use in a population simulation model.
  • To construct an ATLSS alligator production index model.
  • To construct an ATLSS alligator population simulation model.

INFORMATION NEEDS AND USES

  • This study encompasses 2 of the critical projects for restoration of crocodilian populations determined by a meeting of over 40 biologists, managers, and administrators held in Homestead in December, 1998.
  • Alligators are a key indicator component and are used as ecological attributes and measures in the Everglades Ridge & Slough and Marl Prairie/Rocky Glades Conceptual Ecosystem Models.
  • This study directly addresses the critical ecological pathways outlined in the Everglades Ridge & Slough Conceptual Ecosystem Model.
  • This study provides an ecological study tool and population model deemed critical in the Federal Objectives for The South Florida Restoration by The Science Sub-Group of The South Florida Management and Coordination Working Group.
  • In the Everglades Ridge & Slough Conceptual Ecosystem Model, a link between water management practices and reduced production and survival of alligators is proposed. This study addresses hypotheses concerning this proposed linkage.
  • This study addresses critical information needs such as restore ecosystem structure and function, recover populations of selected indicator species, and identification of ecological assessment indicators identified in South Florida Ecosystem Restoration: Scientific Information Needs by the Science Subgroup of the South Florida Ecosystem Restoration Task Force.
  • We investigate the decline in numbers and shift in distribution of the American alligator identified as an Everglades National Park Major Issue and information need in South Florida Ecosystem Restoration: Scientific Information Needs by the Science Subgroup of the South Florida Ecosystem Restoration Task Force.
  • Specific proposed performance measures relate to the alligator such as reduce frequency of water dry-outs during courtship period and duration of below ground water depths to increase alligator nesting and re-establish hydrological predictability for relationship between peak early wet season water levels and late wet season levels to reduce alligator nest flooding.
  • This study develops an ATLSS American alligator production index and an ATLSS alligator population model for comparison of restoration alternatives during implementation as outlined in South Florida Ecosystem Restoration: Scientific Information Needs by the Science Subgroup of the South Florida Ecosystem Restoration Task Force.

KEY FINDINGS

  • As an interim model and to provide guidance to currently ongoing restoration initiatives, we have constructed an Alligator Reproductive Potential Index (API). This index uses hydrological, elevation, and habitat layers of the ATLSS model series to predict the reproductive potential of alligators across the south Florida landscape. We use predictions of breeding potential, proportion of females nesting, habitat suitability, and flooding potential to construct the overall index.
  • The index has been used to compare restoration alternatives for the Restudy and the Mod Waters project.
  • Very little data exist on present alligator population size in Everglades National Park. Since this population represents a substantial portion of the alligator=s range in south Florida and data exist for estimation of many other parameters, it is essential that an accurate portrayal of the existing population be used in the simulation model. Currently, we have used night-light surveys conducted on representative habitats as an index to population size and size/age distributions.
  • We have constructed the initial framework for the alligator population model. The simulation model essentially consists of a Leslie-type projection matrix modified to allow some proportion of animals to remain in a given stage over several time-steps. The population is aggregated into 7 basic life stages [egg, hatchling, juvenile (0.3 - 1.2 m), subadult (1.2 - 1.8 m), adult female (> 1.8 m), adult male (1.8 - 2.7 m), and mature male (> 2.7 m)]. The stages are further modeled into age/year classes to account for area-specific growth rates. Within stage survivorship and growth is presently assumed equal across individual animals
  • Alligators were captured and sacrificed from representative alligator populations in south Florida (Everglades National Park, Conservation Area III, Conservation Area II, Loxahatchee NWR, and Big Cypress National Preserve) to measure instantaneous growth rates, contaminant loads (mercury, organochlorines, etc.), hormonal concentrations, blood chemistry, and stomach contents.

PROJECT DESCRIPTION

Purpose and Goals

From the Federal Objectives for The South Florida Restoration by The Science Sub-Group of The South Florida Management and Coordination Working Group in 1993:

"The restoration process will require a new generation of ecological study tools to monitor, model, and assess the results of restoration. These will build upon the natural system models of hydrology. A coupling between the hydrologic models and future models of water quality, ecology, and plant and animal populations will allow examination of differences between predrainage and present-day conditions. These models should be developed at several scales, spanning the range from regional landscape models to models of constituent ecosystems and communities. These models must have scientific credibility and acceptability by the scientific community".

USGS-BRD and its cooperators are using a system of empirical data collection and simulation modeling to apply information on wildlife community patterns in guiding the restoration process. We will estimate population parameters of the alligator across hydrological and habitat gradients. Through the development of population simulation models based on these empirical data, we will evaluate restoration alternatives and assess restoration performance measures. By applying the alligator models to restoration alternatives and predicting population responses, we can choose the alternatives that result in biotic characteristics that approximate historical conditions and identify future research needs. Further, several other ATLSS models would benefit from linkage with the alligator population model. At some point, ATLSS fish and reptile models can be used as inputs to the alligator model. The benefits to restoration would arise by having more confidence in improved tools, like the ATLSS models, that are used to evaluate alternatives for ecological effects of the Central and Southern Florida Project Restudy, C-111 Project, and Modified Water Deliveries Plan to Shark Slough.

Everglades restoration requires an understanding of the ecological impact of various restoration alternatives. This study not only provides keys to this understanding through contribution to ecological modeling but is designed to answer questions related to the growth potential, contaminant burden, and health of alligator populations in the Everglades.

Objectives:

  • To estimate population parameters of south Florida alligator populations utilizing existing data sets for use in a population simulation model.
  • To estimate growth rates, contaminant loads, and reproductive potential of south Florida alligator populations.
  • To estimate population size of alligator populations in Everglades National Park for use in a population simulation model.
  • To construct an ATLSS alligator production index model
  • To build an age and spatially structured alligator population model using the MATLAB simulation package.
  • To couple the local age-structured models into a spatial dispersal model incorporating alligator movement behavior.
  • To use spatial parameter maps from the Florida Everglades as driving functions on the spatially structured model and to construct Alligator finite rate of increase maps under different management regimes.
  • Return the model as MATLAB code to the ATLSS project for incorporation into the overall model.

Urgency or Timelines

This study provides the construction of the ATLSS American alligator population model which will be used as a tool for evaluation of restoration alternatives during adaptive implementation of the Comprehensive Ecosystem Restoration Plan. We also provide other timely investigations involving contaminant levels, growth, and health of alligator populations in the Everglades. The alligator is both a keystone and indicator species in the Everglades ecosystem. Therefore, it is critical to understand the effects of restoration alternatives on this species and to include the alligator in restoration alternative selection, evaluation, and monitoring.

Effectiveness

  • This study provides parameter estimates, model construction, and validation to the ATLSS modeling program.
  • We provide blood and tissue samples to other ongoing projects on mercury levels and blood chemistry of the alligator.
  • We have provided written and oral comments on restoration alternatives based on the findings of this project to several Restudy groups, NPS, FFWCC, and USGS.
  • We have produced posters, model outputs, and comments on restoration alternatives to governmental, environmental (both local and international), and educational groups.
  • We have used graduate students and university OPS personnel for this study for cost effectiveness and to provide educational opportunities to future researchers and management personnel.
  • We have cooperated throughout this project with the Florida Fish and Wildlife Conservation Commission, South Florida Water Management District, the University of Florida, and the National Park Service to use equipment, personnel, and expertise for alligator capture and data collection especially during peak capture and monitoring periods at no cost to this project.

Synopsis of Research Methods

Current water management practices have resulted in a high and unpredictable rate of nest flooding. Historically, maximum summer water levels were positively correlated with water levels during alligator nest construction. This natural predictability has been lost (Kushlan and Jacobsen 1990). Historically, alligators were abundant in prairie habitats of the eastern floodplain, along the edge habitats of the central sloughs. Pre-drainage occupancy of the deep water, central sloughs was relatively low. Marsh alligator densities are now highest in the central sloughs and canals (Kushlan and Jacobsen 1990) and relatively low in the edge habitats. Canal habitats contain high concentrations of adult alligators. Nest densities are also relatively high on levees and associated spoil islands. Less flooding of nests occurs on these higher elevations. However, survival of young may be very low due to a decrease in the number of alligator holes or possible brood habitat proximal to canals. Modified hydrological conditions might be expected to increase nesting effort, nesting success, and abundance of alligators in the aforementioned edge habitats. There may also be a corresponding increase in the number and occupancy of alligator holes to serve as drought refugia.

The Everglades is believed to be a harsh environment for alligators. Everglades alligators weigh less than alligators the same length from other parts of their range (Jacobson and Kushlan 1989, Barr 1997). Further, maximum length is decreased, and sexual maturity is delayed (Kushlan and Jacobsen 1990, Dalrymple 1996). Jacobsen and Kushlan’s (1989) model for growth in the Everglades of Southern Florida predicted alligators reaching a mere 1.26 meters in 10 years and requiring at least 18 years to reach sexual maturity. It is currently suspected that the reason for this poor condition is a combination of low food availability and high temperatures (Jacobson and Kushlan 1989, Dalrymple 1996, Barr 1997).

Data collection. -- Five alligators were captured from representative alligator populations in south Florida (Everglades National Park, Conservation Area III, Conservation Area II, Loxahatchee NWR, Big Cypress National Preserve, and others) and sacrificed to estimate instantaneous growth rates. A femur was removed from each animal and a mid-diaphysis segment removed for processing (2-3 sections were removed from several bones to determine variance). The segments were further sliced into 2 transverse sections (14 micron thickness), mounted on a microscope slide, and stained with hematoxylin to demonstrate growth layers (Matson’s Laboratory, Milltown, MT 59851). The layers were then counted to estimate the age of the associated alligator and growth rate determined. Stomach contents and condition of captured animals will be examined to estimate instantaneous food availability and to calibrate food habit techniques used in historical studies.

We will establish critical baseline data for contaminant body burdens in alligators in south Florida and assess potential correlations to alterations in general and reproductive health. These parameters will be used in construction of the simulation model outlined above. The hypotheses to be tested are: (1) that contaminant body burdens in alligators will reflect land use and habitat parameters; 2) there will be a strong correlation between tissue types (i.e.) blood, liver, fat, skin etc) for contaminant concentrations and profiles enabling the development of low-invasive monitoring procedures; 3) adverse effects on general and/or reproductive health will be strongly correlated to contaminant body burdens in alligators.

The proposed work will focus on directly relating specific habitat exposures to contaminant body burdens, and adverse health effects in alligators from south Florida. We will utilize the animals captured for the growth studies outlined above (n = 30 animals). Water and sediment samples (2 each per site/region) will be collected as well as a site description recorded. Upon sacrifice, samples of liver, fat, skin and blood will be collected (100 g for each tissue and 200ml of blood) and stored frozen until analysis. Blood will also be collected from each animal for analysis of plasma sex steroids, stress steroids and thyroid hormones. Whole blood will be analyzed for general blood chemistry.

Tissue and environmental samples will be analyzed for organochlorine compounds and residues, water soluble herbicides, organophosphates, and carbamates. Screening for mercury and other heavy metals also will be included. Tissues will be homogenized and extracted for recovery of organochlorine pesticide residues. Analyses of organochlorine pesticides, polyaromatic hydrocarbons, and PCBs will be done using HPLC, GC-MS, and electron-capture procedures. Currently available information concerning potential contaminant effects and body burdens in alligators is very limited. These data are critical to future assessments of risk and ecosystem health for south Florida.

ATLSS American alligator production index. -- The ATLSS American Alligator Production Index (API) Model was developed as a coarse indicator of the yearly production potential (probability of producing nests and offspring successfully) for the American Alligator in South Florida based upon local habitat and hydrologic conditions. The production potential of this species is directly influenced by unique environmental conditions occurring throughout its range in Florida. The API model addresses only the effects of relative local habitat quality and hydrological dynamics. Consequently, this model should not be interpreted as providing estimates of population dynamics or viability. Further, the temporal extent of the model is not likely to encompass long-term changes in habitat quality. Particularly, stabilized hydrologic regimes may result in slow degradation or improvement of habitat not included in this model. Little verification of the model's performance was possible except for those populations in Everglades National Park and Water Conservation Areas 2 and 3.

The spatial resolution for the model is 500 meters by 500 meters, corresponding to the home-range of nesting female alligators (Percival et al. 2000). All data (water depth, vegetation type, ground elevation, breeding indices) represent values for a 500x500 meter area. The temporal resolution for the model is one day for all water data (height and depth) and is static for the vegetation habitat types. The model produces a single yearly value for each spatial cell that takes account of the daily water data affecting the nesting and offspring production during that year.

The mean water depth during the peak of the mating season from April 16 through May 15 is used as an indicator of the probability that mating and nest construction will occur in a given area. Two linear functions are applied to indicate the value of this model component such that the highest probability of nest construction occurs at a mean level of 1.3 feet. Mean water depth values higher or lower than this reduce the probability of nest construction. The probability of a nest being flooding is calculated from a combination of the mean water level during nest construction and the maximum water level during egg incubation. Field observations indicate that the mean water level between June 15 and June 30 will determine the elevation at which a nest will be constructed. A linear function is applied to the difference between the maximum water level during the egg incubation period (July 1 through September 1) and the mean water level during nest construction to give the probability of nest flooding.

Available evidence suggests that the type of vegetative cover and elevation within an area greatly influence the probability of nesting. This model uses a static ranking of the dominant vegetation type within a 500 meter spatial cell as a measure of habitat quality. Water levels encountered during the period ranging from May 16 of the current nesting year to April 15 of the previous year are used as an indicator of the probability of breeding occurrence in an area. The probability that nesting will occur correlates positively with the amount of time spent in flooded conditions during this period. This model component is defined to be the proportion of this period for which there was water depth greater than 0.5 feet.

The overall API is calculated as a weighted product of the described model components. This uses (1 - the probability of nest flooding) in the product and applies highest weight to the nest flooding component, a lower weight to the breeding and nesting components, and the lowest weight to habitat quality factor. Output consists of a map of the predicted index values for a restoration alternative (Alternative D13R4 in the figure below), the base condition (F2050 in the figure below), and a central map describing the difference in performance between the alternative and the base.

ATLSS American alligator population model. -- This project will provide a large-scale spatial and age-structured modeling framework for this simulation process. To this end we will utilize the Matlab Simulation Package since it is high-level optimized code which incorporates vectorized statements. Within this package we can execute model statements on whole data arrays element-by-element with just one statement in an environment optimized for speed. The advantage is that we can represent the spatially distributed alligator population and its parameter maps by arrays in which all of the information in each spatial cell is represented by a series of maps (matrices). The model simply calls these data arrays in element-by-element fashion greatly simplifying the programming process. The end result is that we can think more about ecology and less about programming.

We will represent the age-structured alligator population as a 3-dimensional array, N(i, j, k), indexing the number in age group k at spatial location (i, j), with space assumed to be 2-dimensional (the ‘flat earth’ assumption). We will later relax this assumption somewhat by incorporating hydrology effects (which may be subject to small elevation changes) into alligator parameters in a phenomenological way. The net effect will be that we can still use a 2-d spatial representation of the population. In subsequent model development we will use a size-class-structured version with a Lefkovitch projection matrix having partial class development in each time step. Dispersal of appropriate size classes will be included using a dispersal kernel or other dispersal methods.

Since the models will be nonlinear (density-dependent) due to cannibalism and competition for nest sites, we will also look for stable or unstable local population behavior as well as total population dynamics on annual and multi-year time scales. In this regard, the intensity of the density dependent parameters will be important. This is one of the most difficult areas in which to estimate parameters since it is very difficult to directly measure the strength of density dependence in the field. We will model the density dependence as ‘Ricker’ negative exponential functions of density. For example a constant fecundity at age k, Fk, would become a negative exponential function of density of age group k, Fk(n), and higher age groups such that

Equation

The rationale behind the summation of age group k and those above is that those will be the groups that cannibalize and compete most strongly with age group k. Note that while we are using age classes here for simplicity, these will become size classes in later versions of the model. For carrying capacity (K), this will involve some estimate of the potential number of nest sites that an area can support in terms of both space, type of habitat and food supply. The parameter, r, can be estimated for a particular location as r = ln(lambda) where lambda is the finite rate of increase calculated above as the dominant eigenvalue of the projection matrix at any location. In addition to this density dependent effect, the fecundity, survival or other parameters will be directly affected by the habitat such that, for example, Fk itself will depend on habitat. This will be done by multiplying a ‘maximum’ value for the parameter by a 0-1 habitat suitability factor.

Key Results

  • As an interim model and to provide guidance to currently ongoing restoration initiatives, we have constructed an Alligator Reproductive Potential Index (API). This index uses hydrological, elevation, and habitat layers of the ATLSS model series to predict the reproductive potential of alligators across the south Florida landscape. We use predictions of breeding potential, proportion of females nesting, habitat suitability, and flooding potential to construct the overall index.
  • The index has been used to compare restoration alternatives for the Restudy and the Mod Waters project.
  • Very little data exist on present alligator population size in Everglades National Park. Since this population represents a substantial portion of the alligator=s range in south Florida and data exist for estimation of many other parameters, it is essential that an accurate portrayal of the existing population be used in the simulation model. Currently, we have used night-light surveys conducted on representative habitats as an index to population size and size/age distributions.
  • We have constructed the initial framework for the alligator population model. The simulation model essentially consists of a Leslie-type projection matrix modified to allow some proportion of animals to remain in a given stage over several time-steps. The population is aggregated into 7 basic life stages [egg, hatchling, juvenile (0.3 - 1.2 m), subadult (1.2 - 1.8 m), adult female (> 1.8 m), adult male (1.8 - 2.7 m), and mature male (> 2.7 m)]. The stages are further modeled into age/year classes to account for area-specific growth rates. Within stage survivorship and growth is presently assumed equal across individual animals.
  • Alligators were captured and sacrificed from representative alligator populations in south Florida (Everglades National Park, Conservation Area III, Conservation Area II, Loxahatchee NWR, and Big Cypress National Preserve) to measure instantaneous growth rates, contaminant loads (mercury, organochlorines, etc.), hormonal concentrations, blood chemistry, and stomach contents.

Graph charting age of alligators vs. SV Length
Figure 1. Age of subadult alligators captured from several south Florida populations during September, 1999. Age determined by femur growth layer count.

INFORMATION PRODUCTS

Technical Reports

See www.fcsc.usgs.gov. (see http://cars.er.usgs.gov/)

ATLSS American Alligator Production Index Model description and use in comparison of Restudy alternatives and other restoration projects: http://www.atlss.org/.

Data & Models

All data are currently maintained at the USGS-BRD, Florida Caribbean Science Center, Restoration Ecology Branch, Everglades National Park Field Station in Homestead, Florida. We are using MATLAB software to structure the simulation model. The Breeding Potential Index results and source code are maintained with the ATLSS group in Knoxville, TN. All data requests should be forwarded to Kenneth G. Rice (305-242-7832 or ken_g_rice@usgs.gov).

Permits

Permits for alligator capture, blood and tissue collection, and survey were obtained annually from the following agencies:
1. Loxahatchee National Wildlife Refuge.
2. Florida Fish and Wildlife Conservation Commission.
3. Everglades National Park.
4. Big Cypress National Preserve.

Publications and Presentations

1. Rice, K.G., M.R. Palmer, and L.J. Gross. 2000. Modeling crocodilian production probabilities on a regional scale. 15th Working Meeting of the Crocodile Specialist Group, IUCN, Varadero, Cuba. Poster.

2. Rice, K.G. 2000. ATLSS American alligator production index model. FFWCC Alligator Section Meeting. Bokeelia, Fl. Invited Presentation.

PLANNED ACTIVITIES – 2000/2001:

  • Final application of the Alligator Production Index to restoration alternatives.
  • Five alligators will be captured from representative alligator populations in south Florida (Everglades National Park – Shark Slough and Estuarine Areas, Conservation Area III, Conservation Area II, Loxahatchee NWR, Big Cypress National Preserve, and others) and sacrificed to estimate instantaneous growth rates. A femur will be removed from each animal and a mid-diaphysis segment removed for processing (2-3 sections will be removed from several bones to determine variance). The segments will be further sliced into 2 transverse sections (14 micron thickness), mounted on a microscope slide, and stained with hematoxylin to demonstrate growth layers (Matson=s Laboratory, Milltown, MT 59851). The layers can then be counted to estimate the age of the associated alligator and growth rate determined.
  • Stomach contents and condition of captured animals will be examined to estimate instantaneous food availability and to calibrate food habit techniques used in historical studies.
  • We will continue to modify the model framework to include newly defined and estimated parameters such as movement, area specific age/size, and nesting/reproductive potential with the assistance of the University of Florida.
  • The model will be further modified with the assistance of ATLSS personnel from the University of Tennessee to accept inputs from hydrology, vegetation, and other GIS layers (Herp model, Fish model) and test simulations will be conducted.

SCHEDULE OF ACTIVITIES AND DELIVERABLES – 2000/2001:

Reports and Deliverables:
Type of Product* No. of Copies Due Date
1. Brief letter report with the following: [1] date of receipt of executed contract (i.e. start date), [2] this "table" with specific due dates, [3] status of progress made towards providing data/metadata/model-source-code, [4] draft text w/ graphics/slides for 2-pager Fact Sheet. Original + 2 + electronic copy 60 days after award of contract.
2. 1st Trimester Report – a brief report updating progress/problems to date and all data and metadata file, & model source code to date. Plus, final of 2-pager Fact Sheet. Original + 2 + electronic copy 120 days after award of contract.
3. 2nd Trimester Report - with updated data/metadata file[s] & model source code. Plus, "Request for Continued Funding" for the next year funding. Original + 2 + electronic copy 240 days after award of contract.
4. Annual Report with all data to date with metadata file[s], fully documented model source code. Original + 2 + electronic copy 1 Year after award of contract.
* Note: Manuscripts, peer reviewed publications, book chapters, graduate student thesis/dissertation, etc. are both acceptable and desirable as chapters or sections of annual/final reports. At least one 2-page fact sheet is required for each of these major types of publications.

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