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projects > spatial and age-structured population model of the American crocodile for comparisons of CERP restoration alternatives > work plan

Project Work Plan

U.S. Geological Survey, Greater Everglades Priority Ecosystems Science (GE PES)

Fiscal Year 2006 Study Work Plan

Study Title: Spatial and Age-Structured Population Model of the American Crocodile for Comparisons of CERP Restoration Alternatives
Study Start Date: 2007 Study End Date: 2008
Web Sites:
Location (Subregions, Counties, Park or Refuge): Southern Everglades
Funding Source: GE PES
Other Complementary Funding Source(s):
Funding History: none
Principal Investigator(s): Daniel H. Slone, Kenneth G. Rice, Frank J. Mazzotti
Project Personnel: vacant post-doc position
Supporting Organizations: University of Florida

Associated / Linked Projects: Alligator Ecology and Monitoring for CERP (GE PES)

Overview & Objective(s): The American crocodile (Crocodylus acutus) is a federally endangered top consumer in south Florida, imperiled primarily by habitat loss due to expansion of a rapidly growing human population along coastal areas of Palm Beach, Broward, Dade, and Monroe counties. This loss of habitat has principally affected the nesting range of crocodiles, restricting nesting to a small area of northeastern Florida Bay and northern Key Largo by the early 1970's. When crocodiles were listed as endangered in 1975, scant data were available for making informed management decisions. Field and laboratory data suggested that low nest success, combined with high hatchling mortality, provided a dim prognosis for survival. Because of their small size, hatchling crocodiles are vulnerable to biotic and abiotic stressors, such as high levels of salinity. To grow and survive, hatchling crocodiles need to find food and benign environmental conditions (or at least avoid harsh conditions) and avoid predators. Diminished growth rates and higher mortaity or dispersal rates have been associated with areas that pose greater risk to hatchling crocodiles.

Crocodiles now occur in most of the habitat that remains for them in southern Florida. Most of the remaining habitat is currently protected in public ownership or engaged in energy production. In these areas, further loss of habitat is not an issue. However, questions of potential habitat modification through continued alteration of freshwater flow due to upstream development and potential curtailment of the range of crocodiles need to be addressed. Patterns of nesting, relative abundance and distribution, growth, and survival of crocodiles can provide insight into restoration of coastal ecosystems in Southeast Florida. For both Florida Bay and Biscayne Bay, restoring a more natural pattern of freshwater flow would provide the most benefit. Characteristics of flow patterns into Florida and Biscayne Bays that are beneficial for crocodiles include sheet flow through the fringing mangrove swamp that extends well into the dry season. Mid-to late dry season discharges of freshwater that cause a reversal of water levels in the receiving body are hypothesized to cause a dispersal of prey items, making them less available to crocodiles. If so, such discharges should be avoided. Shifting water delivery from Biscayne Bay to Florida Bay would degrade the quality of habitat in Biscayne Bay for crocodiles.

Restoration efforts in the Comprehensive Everglades Restoration Plan (CERP) will likely cause changes to salinity levels throughout the habitat of the American crocodile. Changes in salinity were seen after previous hydrologic changes in the area, when reduced freshwater flow was associated with increased salinity levels in Florida Bay estuaries, including one of the core nesting areas of the American crocodile. Large crocodiles are not significantly affected by high salinity, but previous work has shown that high salinity levels may reduce survival of hatchlings and juveniles. The detrimental effects of high salinity on hatchling and juvenile crocodiles has led to the hypothesis that increased freshwater flow to the estuaries will increase the animals' distribution, abundance, and growth.

To adequately understand crocodile populations and model population growth, existing data must be assembled and model parameters estimated. A simulation model can then be constructed and validated both with existing data and through expert opinion. A crocodile population model to simulate the south Florida ecosystem under varying management strategies is vital to evaluating and assessing restoration success under CERP.

The objectives of this project are to:

  1. Build an age and spatially structured crocodile population model suitable for comparison of CERP restoration alternatives.
  2. Couple the local age-structured models into a spatial dispersal model incorporating crocodile movement behavior.
  3. Use spatial parameter maps from the Florida Everglades as driving functions on the spatially structured model and to construct crocodile finite rate of increase maps under different management regimes.
  4. Perform sensitivity analysis on the model parameters, and release model concept and code for peer-review.

Specific Relevance to Major Unanswered Questions and Information Needs Identified:

The American crocodile has been identified as having the potential to provide a quantifiable measure of restoration success. Determination of trends and year-to-year variations in population parameters are a critical part of an expanded monitoring program to support development of ecological indicators and success criteria for the restoration effort. The relevant biological factors of this endangered species are well understood and existing databases afford good records of past and present population parameters. This provides us the unique opportunity to integrate endangered species recovery and conservation with ecosystem restoration and management in South Florida.

Specifically, a spatially explicit, stage-based model of American crocodile populations will address identified needs in the DOI science plan, including:

  • Florida Bay and Florida Keys Feasibility Study, Modeling of ecological responses to hydrologic change, emphasizing "information on the life history requirements of indicator species, including their responses to hydropattern change, will be needed to address anticipated changes in species populations. Indicator groups that should be represented in these evaluations include ... federally listed species (American crocodiles)."
  • Landscape-Scale Science Needed to Support Multiple CERP Projects, Landscape-Scale Modeling, Spatially explicit demographic models, describing the approach desired for spatial models as "stage-structured models describe population dynamics as composed of a number of life stages, each stage having different size, physiology, and environmental requirements."

In addition to the DOI science plan needs, this study addresses needs identified in the Multi-species Recovery plan for south Florida, section H2.3: "Continue habitat and population modeling to determine operational schedules for structures associated with the Program to Modify Water Deliveries to Everglades NP, Canal 111, and the Central and Southern Florida Flood Control Project that provide optimal habitat for the American crocodile."

Status: This is a new project. The crocodile model will be based on code from the ATLSS Alligator Population Model. The alligator model has been completed and has undergone expert review, calibration, and some validation.

Recent Products: This is a new project.

Planned Products: We plan on submitting manuscripts on the Crocodile Population Model to peer-reviewed journals. We will present results of our study at national and international meetings. We will also provide results of model simulations on the web.


Work to be undertaken during the proposal year and a description of the methods and procedures:

The methods we will use for the American crocodile population model will be similar to those used in the ATLSS model of American alligator growth and dispersal, authored by D.H. Slone, J.C. Allen, and K.G. Rice (Slone et al. 2003), though there will necessarily be several major changes made to accommodate the different use of habitat, different driving parameters (salinity), and different dispersal parameters for crocodiles. The ATLSS alligator model has been shown to accurately describe population size, variability, and temporal trends in calibration data (validation data and analyses are forthcoming). We prefer a stage-space based model rather than an individual-based model for this purpose because it allows us to simultaneously evaluate landscape effects on each stage of the crocodile, and predict spatial density patterns and population size with much greater computational efficiency.

We will estimate population parameters of the crocodile across hydrological and habitat gradients from available databases (Mazzotti and Cherkiss 2003). Through the development of population simulation models based on these empirical data, we will evaluate restoration alternatives and assess restoration performance measures. By applying crocodile models to restoration alternatives and predicting population responses, we can choose alternatives that result in biotic characteristics that best approach historical conditions and identify future research needs. 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 Everglades restoration projects.

In 2007, we will accomplish objectives 1 and 2:

  1. Build an age and spatially structured crocodile population model suitable for comparison of CERP restoration alternatives.
  2. Couple the local age-structured models into a spatial dispersal model incorporating crocodile movement behavior.

In objective 1, we will represent the age-structured crocodile 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, subject to the effects on crocodile parameters relative to the hydrology effects brought on by elevation changes. The net effect will be that we can still use a 2-d spatial representation of the population. We will use a size-class structured version with a Lefkovitch projection matrix having partial class development in each time step. We note that since we can construct the projection matrix at each location, then we can obtain l, its largest eigenvalue, which will indicate whether the population will increase (l > 1) or decrease (l < 1) at each location. This will enable us to make maps of crocodile population growth and decline over time.

In objective 2, we will include movement and dispersal of certain age groups in the spatial map. We introduce spatial structure into ecological models by using a discrete spatial convolution model of the form:

  n n  
Nt+1(x,y) = sum symbol sum symbol k(x - i, y - j) * f (Nt(i,j)) .
  i=1 j=1  

The function k represents the one time step dispersal kernel for the species in question (in a two dimensional spatial domain, W), and f (Nt(i,j)) is the one time step reproductive output as a function of organism density, Nt(i,j). Notice that k is any probability density function (pdf) and f may be nonlinear. The * is the 2-D discrete spatial convolution method. The dispersal filter can be directed toward attractive sources, time varying (adjusted at each time step), and with modifications to the filter for each habitat type, it can be spatially variable as well. The dispersal kernels for each size class and habitat type will be shaped by empirical measurements of movement rates under various circumstances, and directed by landscape features (e.g., shorelines or salinity levels) thought to be important for crocodile dispersal. The net result at each time step would be a rearrangement of the population from dispersal sources to attracting sites presumably driven by habitat changes and population density.

Specific Task Product(s): [List and include expected delivery date(s).] This study will develop a MATLAB-based spatial model of American crocodile populations in the southern Everglades. The code of this model will be released for peer review within one year of the date work starts. Semi-annual and annual reports will be provided to document progress.

Literature Cited:

Mazzotti, F.J. and M.S. Cherkiss. 2003. Status and Conservation of the American Crocodile in Florida: Recovering an Endangered Species While Restoring an Endangered Ecosystem. University of Florida, Ft. Lauderdale Research and Education Center. Tech. Rep. 2003. 41 pp.

Slone, D.H., K.G. Rice, and J.C. Allen. 2003. Model evaluates influence of Everglades restoration on alligator population (Florida). Ecological Restoration 21(2): 141-142

Work to be undertaken during future FY's and proposed funding:

In FY 2008, we will incorporate comments and revisions into the crocodile spatial model, and integrate the code with spatial hydrology model output from the region. The model will be calibrated with historical data, and validated with independent population survey data. A manuscript describing the model will be prepared and submitted to a peer-reviewed journal. In future work, additional funding will allow us to test and provide output for managers on CERP restoration scenarios.

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