Water, wetlands, and wood storks in southwest Florida

Material Information

Water, wetlands, and wood storks in southwest Florida
Browder, Joan Arrington ( Dissertant )
Snedaker, Samuel C. ( Reviewer )
Johnston, David W. ( Reviewer )
Bayley, Suzanne E. ( Reviewer )
Huber, Wayne C. ( Reviewer )
Odum, Howard T. ( Thesis advisor )
Place of Publication:
Gainesville, Fla.
University of Florida
Publication Date:
Copyright Date:
Physical Description:
ix, 406 leaves : ill. ; 28 cm.


Subjects / Keywords:
Birds ( jstor )
Bodies of water ( jstor )
Marshes ( jstor )
Ponds ( jstor )
Rain ( jstor )
Storks ( jstor )
Surface areas ( jstor )
Surface water ( jstor )
Water tables ( jstor )
Wetlands ( jstor )
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Ecological surveys -- Wetland ecology -- Florida ( lcsh )
Ecology -- Florida ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Wetlands -- Florida ( lcsh )
Wood stork ( lcsh )
bibliography ( marcgt )
non-fiction ( marcgt )
26.42 x -81.54


Energy circuit models were used to study an oscillating ecosystem, the seasonally expanding and contracting wetlands of southwest Florida. Analog and digital computers were used to simulate the effects of the natural rainfall pattern and of drainage on seasonal expansion and contraction of water area, production and concentration of fish, and feeding and reproduction of the Wood Stork (Mycteria americana). Information for quantification of the models was obtained from aerial surveys of storks nesting at Corkscrew Swamp Sanctuary, quantitative sampling of fish and invertebrates in a pond and marsh, measurement of wetlands area on infrared aerial photographs, topographic field surveys, and a literature search and field observation on demographic parameters of populations. There are approximately 30,000 ponds ranging in size from less than an acre to more than 100 acres in Lee, Hendry, and Collier counties. Freshwater wetlands once comprised 53% of the total area. Drainage, which has accelerated in the past 15 years, has reduced wetlands area by more than 60%, diminishing the capacity of the area to store water from wet years. Regional-scale depth-area, area-volume, and depth-volume curves were developed to relate the intensity and timing of rain to the seasonally changing area of surface water. Classical hydrologic equations were combined with the regional curves to produce a water model simulating seasonal and long-term water storage and runoff. Patterns of land area covered by water from the water model were used to drive three models relating water patterns to fish and storks. Seasonal oscillation of water area increases the efficiency of the flow of energy from prey to predator and allows a system to support more top consumer than would otherwise be possible. Concentration of the fish production of the wetlands of southwest Florida is increased approximately 25 times by the sun’s energy, acting seasonally through evaporation and the transpiration of plants to shrink water area. This extra concentration factor in the food chain give a very high “energy quality value to the Wood Stork, which may serve as an indicator of the productivity of wetlands of the region. Drainage and a downward trend in rainfall for the past 15 years have stressed ecosystems causing a decline in wading birds. Simulations suggest that drainage more than decline in rainfall was responsible for the decrease in storks. Wood Storks have shown resiliency in adapting to the drained conditions, finding new feeding areas such as the marshes at Lake Okeechobee. Plans to raise lake regulation levels will eliminate half this area. Because of the topography of southwest Florida, present drainage has greatly decreased the area flooded but only slightly decreased the range of fluctuation. Therefore, a wetlands ecosystem dependent on oscillation continues to operate. If, however, the mean water level is further lowered, the fluctuation of water area may be drastically reduced and the ecosystem seriously disrupted.
Thesis--University of Florida.
Bibliography: leaves 399-405.
General Note:
General Note:
Statement of Responsibility:
by Joan Arrington Browder.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
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03157178 ( OCLC )
AAU5731 ( NOTIS )

Full Text









Joan Arrington Browder


I am indebted to my major professor, H. T. Odum, for

providing direction, advice, encouragement, support, and

introducing me to a new way of viewing the world. Other

members of my committee: S. Snedaker, W. Huber, S. Bayley,

and D. Johnson aided in many ways. S. Snedaker provided

laboratory space and equipment for the field study. W.

Huber 'helped develop the water model. M. Duever provided

facilities and the Corkscrew Sanctuary study area. Field

work was accomplished primarily with the assictrncc of E.

Sroka, E. Carlson, M. Chancy, and P. Schroeder. Others who

helped in the field work were M. Duever, L. Riopele, D.

Stellar, J. Hansen, and E. DeBellevue. R. Hartzog and B.

Oesterling measured, weighed, and identified the specimens

from the field collections.

M. Brown, R. Costanza, and E. Debellevue prepared the

maps and provided area measurements of ecosystems that

were the basis for the relationships of water depth, water

area, and water volume developed in the study. E.

DeBellevue participated in the development of the water


Concepts of the study were discussed with F. C.

Craighead, Sr., J. Ogden, J. Kushlan, A. Sprunt, IV, M.


Duever, W. Dineen, P. Rhoads, and H. Klein. Unpublished

materials were provided by J. Kushlan, J. Ogden, J. Hansen,

S. Nesbitt, R. Chandler, and others. J. Fry conducted a

field trip over his property in southeastern Hendry County

and into the Kissimmee Billy cypress strand.

The National Audubon Society funded an aerial survey

of wading bird feeding sites in southwest Florida during

the 1973 1974 dry season. P. Schroeder, my husband, was

the pilot for the aerial survey and did many other noble

and ignoble tasks to help me complete my dissertation.

Work was supported by the following grants and

contracts administered by the Center for Wetlands of the

University of Florida, H. T. Odum, principal investigator:

Rockefeller Foundation, Grant RF-73029, National Science

Foundation, Grant AEN 73-07823 A01, and Contract

CX000130057 with the National Park Service, U. S.

Department of Interior, and State of Florida Division of

State Planning.




. . q .

. IIi

. vii


Model of Water, Fish, and Wading Birds .
Climate .. . .
Study Region . .
Corkscrew Marsh and Mud Lake Pond .
Water Patterns and Biological Responses
Modeling Theory of Oscillating Systems
Population Biology of Wood Storks .


Basis for Models .
Analysis of Rainfall .
Remote Sensing for Relating Water Area to.
Volume . .
Field Study in Corkscrew Marsh and Mud Lake
Pond . .
Aerial Survey of Feeding Wading Birds .
Characteristics of the Wood Stork Population


S 45
S 77

S 79

S 96

S 112

Rainfall Pattern . .
Relationship of Water Volume to Surface Water.
Relationship between Water Levels and Fish
Populations . .
Spatial-Temporal Aspects of Wading Bird
Feeding . .. .
Wood Stork Population Dynamics .


Water Model . . .
Water Area, Fish, and Storks Models I and II
Water Area, Fish, and Storks Model III ..


15 7/

235 i





Spatial and Temporal Patterns .
Comparison of Fish and Crayfish Production .
Energy Implications of Concentration .
Observations from Model III and the Field
Study . .
The Biological Community in a Fluctuating
Habitat . . .
Effects of Natural Storage and Impact of
Drainage . .
Survival Prospects of Wood Storks in
Southwest Florida . .
Recommendations for Wood Stork Protection .
General Recommendations for Water Management .












344 /







Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Joan Arrington Browder

August, 1976

Chairman: H. T. Odum
Major Department: Environmental Engineering Sciences

Energy circuit models were used to study an

oscillating ecosystem, the seasonally expanding and

contracting wetlands of southwest Florida. Analog and

digital computers were.used to simulate the effects of the

natural rainfall pattern and of drainage on seasonal

expansion and contraction of water area, production and

concentration of fish, and feeding and reproduction of the

Wood Stork (Mycteria americana). Information for

quantification of the models was obtained from'aerial

surveys of storks nesting at Corkscrew Swamp Sanctuary,

quantitative sampling of fish and invertebrates in a pond

and marsh, measurement of wetlands area on infrared aerial

photographs, topographic field surveys, and a literature

search and field observations on demographic parameters of



There are approximately 30,000 ponds ranging in size

from less than an acre to more than 100 acres in Lee,

Hendry, and Collier counties. Freshwater wetlands once

comprised 53% of the total area. Drainage, which has

accelerated in the past 15 yrs, has reduced wetlands area

by more than 60?, diminishing the capacity of the area to

store water from wet years.

Regional-scale depth-area, area-volume, and depth-

volume curves were developed to relate the intensity and

timing of rain to the seasonally changing area of surface

water. Classical hydrologic equations were combined with

the regional curves to produce a water model simulating

seasonal and long-term water storage and runoff. Patterns

of land area covered by water from the water model were

used to drive three models relating water patterns to fish

and storks.

Seasonal oscillation of water area increases the

efficiency of the flow of energy from prey to predator and

allows a system to support more top consumers than would

otherwise be possible. Concentration of the fish

production of the wetlands of southwest Florida is

increased approximately 25 times by the sun's energy,

acting seasonally through evaporation and the transpiration

of plants to shrink water area. This extra concentration

factor in the food chain gives a very high "energy quality"

value to the Wood Stork, which may serve as an Indicator of

the productivity of wetlands of the region,


Drainage and a downward trend in rainfall for the past

15 yrs have stressed ecosystems causing a decline in wading

birds. Simulations suggest that drainage more than decline

In rainfall was responsible for the decrease in storks.

Wood Storks have shown resiliency in adapting to the

drained conditions, finding new feeding areas such as the

marshes at Lake Okeechobee. Plans to raise lake regulation

levels will eliminate half this area.

Because of the topography of southwest Florida,

present drainage has greatly decreased the area flooded but

has only slightly decreased the range of fluctuation.

Therefore, a wetlands ecosystem dependent on oscillation

continues to operate. If, however, the mean water level is

further lowered, the fluctuation of water area may be

drastically reduced and the ecosystem seriously disrupted.



Understanding the structure, functions, spatial

patterns, and temporal variations of ecosystems subjected

to sharply pulsing climatic factors is an important general

problem in ecology. Subtropical freshwater wetlands

receiving seasonally varying inputs of rain are found on

most continents and provide interesting examples of

ecological systems under the influence of climatic pulses.

This dissertation is the study of the subtropical

freshwater wetlands located at the southwest end of the

Florida peninsula. The study simulates and evaluates the

water regimes and energy flows of the regional wetlands

ecosystem by means of analog and digital computer models

and addresses the following questions:

1) How does periodic expansion and contraction of water
area control fish and wading bird populations?

2) How are water volume and water surface area related?

3) What is the timing of the storage and release of
water in relation to the timing of the rain?

4) How does change in surface water area affect energy

5) What are the major pathways of energy flow and how
is the flow of energy organized in time and space?

6) How does productivity in a pulsing system compare
with productivity in systems with more constant
energy inputs?

7) What structural features and adaptations of the
system optimize energy flow?

The models describe the system in terms of primary

inputs, outputs, and internal components, and the major

flows of energy that connect them. The pathways of energy-

flow lead to large colonial-nesting wading birds at the top

of the food chain of the aquatic system. Field sampling

and measurements, aerial surveys, remote sensing, and

topographic surveys of the study were organized around the

design and quantification of the models.

Climatic factors such as rainfall and sunlight are the -

directing forces that orchestrate the seasonal pattern, but

the responses of the system to seasonal variations in

sunlight and rain are determined by structural

characteristics of the system at levels of organization

ranging from the geomorphology of the basins to the

population biology of the indicator species.

Structural characteristics of the southwest Florida

wetlands ecosystem were examined on three different scales

of organization: on the regional scale, considering all

the wetlands in southwest Florida as a functional unit,

with expansion and contraction of the water area and

sequential use of feeding areas by wading birds; on the

biological community scale, examining biological events

such as fish production and fish predation by wading birds

in relation to the change in water depths in a pond and its

surrounding marsh; and on the scale of the bioenergetics

and demography of an indicator species, the Wood Stork,

Mvcteria americana, with consideration of age structure,

age dependent survival rate, age of maturity, and other


Information for the models in this study on the

regional scale was obtained primarily by original work.

Information at the biological community scale was obtained

partially by original work and partially from previous

studies. Information concerning the indicator species was

obtained almost entirely from previous studies.

Demographic material was largely hypothetical, but based on

the best information available.

Model of Water, Fish, and Wading Birds

Figure 1 is a simple diagrammatic model of the

wetlands system of souLiiwest Florida that shows the

relationships between primary productivity, surface water

area, fish production, fish density, and breeding success

of wading birds. The model describes a connection between

the seasonal change in sunlight and rain and the timing of

biological events. In the model, fish production is a -

function of sunlight and total surface water area. Fish

density, as defined in this study, is total fish biomass

divided by surface water area. Both bird biomass and fish

kills are proportional to fish density rather than to

absolute fish biomass. Fish kills occur only when fish

density exceeds a certain threshold value. In the model

bird reproduction is dependent on the average weight of the

birds, which is total bird biomass divided by bird number.

Figure 1. Model of water area, fish, and wading birds.

NOTE: Key to symbols is in Methods section.


Breeding takes place only when average bird weight rises

above a threshold value. In the model, breeding success of

one species, the Wood Stork is taken as an index not only

of the condition of the area's wading bird populations but

also of the general healthy functioning and overall

productivity of the wetlands system. The model tests the

effect of seasonal and long-term variations in rainfall and

the effect of drainage on expansion and contraction of

surface water area, fluctuation of the water table, total

annual fish production, fish density, and breeding success

of Wood Storks.


Figure 2 reveals seasonal and long-term patterns in

the rainfall of southwest Florida. The record of rainfall

is for the years 1951 through 1975 collected by ALICO

(Atlantic Land Improvement Company, La Belle) at Corkscrew

grove, a commercial orchard at latitude 260 25'N, located

30 km from the coast and immediately north of Corkscrew

Swamp (see Figure 4 for location). 5.

Average yearly rainfall was 1421 mm at Corkscrew

grove, which is slightly greater than the 1372 mm average

reported by the U. S. Weather Bureau near the Gulf Coast at

Page Field in Ft. Myers, Lee County. On the average,

Corkscrew grove received 68% of its annual rain during the

5 mos from June through October.

Figure 2. Monthly and
through 1975 in southwest
(ALICO, pers. comm.).

total annual rainfall from 1951
Florida at latitude 26 o 25 N

NOTE: Rain gauge is in Corkscrew grove, a commercial grove
of the Atlantic Land Improvement Company (ALICO),
immediately north of Corkscrew Swamp (see map in Figure 4).




Figure 3 shows the long term mean monthly moisture

relations in the vicinity of the study area (Royal Palm

Ranger Station, in the Everglades near the Tamiami Trail,

latitude 25000'N). The graph demonstrates an excess of

rainfall over evaporation during the summer and early fall,

but a moisture deficit, evaporation greater than rainfall,

during the spring and summer. In south Florida, pan

evaporation appears closely related to solar radiation,

also shown in Figure 3. Transpiration, the loss of water

through plants, changes seasonally. Transpiration rates

for some plants, such as cypress, willow, and many marsh

macrophytes are greatly reduced when the plants shed their

leaves or die back in late fall, suspending photosynthesis

during winter.

The Study Region

The study region can be roughly defined as the

noncoastal parts of Lee, Hendry, and Collier counties. It

also includes the seasonally drying marshes on the western

and northwestern shores of Lake Okeechobee and parts of

Charlotte and Glades counties (Figure 4). This area, which

lies between latitudes 250 47' and 270 07' N, comprises

numerous sloughs, marshes, cypress strands, wet prairies,

and ponds that are linked by flows of energy through the

movement of water and animals such as wading birds.

Although many of these wetlands are in their natural state,

Figure 3. Mean monthly rainfall (1940-1970) and mean
monthly pan evaporation (1940-1969) in south Florida at
latitude 250 00' N (redrawn from Kushlan, 1972), and semi-
monthly mean daily solar radiation (1971-1975) in south
Florida at latitude 26 42 N (R. J. Allen, Jr., pers.

NOTE: Location of rainfall and pan evaporation data was
Royal Palm Ranger Station in the Everglades. Location of
solar radiation data was the University of Florida
Agricultural Experiment Station, Belle Glade. In the solar
radiation curve, the January values are based on 4 yrs'
date and February and March values are based on 3 yrs'
data. Ly is abbreviation for Langley, which is 1 cal/sq-cm.











. 3C



0J -- I I I I I I I I --



Figure 4.
study areas.

Map of south Florida showing boundaries of the




others have been greatly changed by drainage accompanying

agricultural or urban development.

Two distinct physiographic regions within southwest

Florida, the Big Cypress and the sandy flatlands, were

recognized and described by John Henry Davis (1943). The

Big Cypress occurs throughout Collier County and in

southern Hendry County. The sandy flatlands cover Lee

County and all but the southern part of Hendry County and

include the area known as Devil's Garden (Craighead, 1971).

In the Big Cypress, the Tamiami formation, water-bearing -

limestone of pre-Pleistocene origin, is within a foot or

two of the surface. In the sandy flatlands, the Tamiami

formation is overlain by deposits of sand, shell, gravel,

marl, and clay 10 or more feet thick. The two regions are

connected by many shallow flow-ways that transect them.

Common to both regions are shallow depressions, or ponds,--

at all elevations, and cypress swamps, swamp hammocks,

freshwater marshes, and wet prairies.

Figure 5 from Parker and Cooke (1944) delineates the

major geological formations and physiographic regions of

the three-county study area. Maximum elevations in the

study area are on "Immokalee Rise" (Parker and Cooke,

1944), which is the area defined as the Talbot Formation.

The highest point on the rise is 14 m above mean sea level

(MSL). Below and south of the rise, elevations slope from

about 6 m MSL to sea level, with a gradient of

approximately 3,75 cm/km. Numerous broad, shallow drainage

Figure 5. Delineation of major geological formations and
physiographic regions of lower southwest Florida (from
Parker and Cooke, 1944).


Palmico Formation

wi --=.= o Miami Oolite
<-> ----- -- lU
-) W
o z

a- Talbot Formation

Q Fort Thompson Formation

o Tamiomi Formation

Sandy Flatlands

Big Cypress


Coastal Marshes and Mangrove Swamps

Approximate Drainage Divides

Direction of Surficial Flow


--- -


ways connecting the sandy flatlands to the Big Cypress lead

eventually to the mangrove estuaries to the south and

southwest, or to the Everglades to the east. Some, such as

the Okaloacoochee Slough, also drain north into the

Caloosahatchee River.

Corkscrew Marsh and Mud Lake Pond

Figure 6 is a high altitude infrared aerial photograph

of Corkscrew Swamp, a major slough-strand system of

southwest Florida. Corkscrew Swamp is located in north

central Collier County, west-southwest of the town of

Immokalee, at the foot of the Immokalee Rise. In the

photograph, arrows point out (1) nearby Lake Trafford, (2)

the tall cypress trees at Corkscrew Swamp Sanctuary where a

Wood Stork population nests, and (3) a pond and adjacent

marsh that were the study site for quantitative sampling of

fish and aquatic invertebrate populations. The sampling

site is within 6.5 km of the Wood Stork nesting site, and

Wood Storks feed in the study pond late in the dry season.

Lake Trafford, 5.9 km east of the study site, has a surface-

water area of 599 ha and is the only large permanent body

of fresh water in southwest Florida.

The field study site is situated in a major flow-way of

the Corkscrew strand system (Duever, 1975). Figure 7 from

Duever (1976) shows the pattern of water movement through

Corkscrew Swamp. The study site is in the approximate

center of the figure, between the two small islands.

Figure 6. High altitude infrared photograph of Corkscrew
area, showing Lake Trafford (1), Wood Stork rookery (2),
and study site in Corkscrew marsh and Mud Lake Pond (3)
(Mark Hurd photography, 1972).

NOTE: Both the Wood Stork rookery and the study site are a
part of Corkscrew Swamp Sanctuary, owned by the National
Audubon Society.


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Figure 7. Map of Corkscrew Swamp ,showing boundaries of
sanctuary (dashed line) and pattern of water flow (arrows)
(from Duever, 1976).

NOTE: Study site is located between the two small islands
in the upper right-hand extension of the sanctuary..







I I I I I I----

5 KM





I i t f.

Approximately 0.8 ha of the study site are occupied by

an open pond and its border of vegetation. The pond is in

the deepest portion of a depression in the marsh

approximately 4 ha in extent; but, except for the pond and

its border, the depression cannot be distinguished from the

rest of the marsh by vegetational features visible on

aerial photographs. The pond is bordered on two sides by

islands of higher ground supporting tropical hardwood

trees. The rest of its margin is contiguous with the


The pond is connected to the marsh during the wet

season, when the whole area is covered by a sheet of water.

During the dry season the pond shrinks to less than 0.2 ha.

Because this pond is in a depression in the center of a

slough, under most circumstances it would contain water

throughout the year and thereby act as a holding area for

aquatic life during the dry season and a center for its

redispersal at the beginning of the wet season. A shallow

well and deisel pump operated by owners of range cattle in

the area assure that the pond never dries. The pond has a

sand bottom covered with a layer of flocculent material,

which increases in thickness during the dry season, giving

the pond its name, "Mud Lake."

The pond's eulittoral zone is covered by a mixture of

marsh temperate species dominated by pickerel weed

(Pontederia lanceolata), maidencane (Panicum hemitomom),

and water hyssop (Baco a sp.). A solid stand of Sesbania


exaltata covers approximately one quarter of the pond

border. Except for clumps of button bush (Cephalanthus

occidentalis) and cordgrass (Spartina bakerii), the

vegetation of the marsh is the same as that covering the

eulittoral zone of the pond. An oblique view in Figure 8

shows the pond, neighboring islands, and nearby areas of

marsh, with the different communities defined.

Water Patterns and Biological Responses

Heavy seasonal rains and the flatness of the land,

cause water to stand on much of the land during several

months of each year. Water fills the shallow aquifer, then

the many ponds and sloughs, before running off to the

Everglades, the estuaries, or the river. A slow flow of

water into the estuaries also takes place through the

aquifer (Parker and Cooke, 1944).

Each summer all the depressions in southwest Florida

fill and overflow and the low, wet prairies become covered

with water for at least 6 mos. Sloughs, strands, and ponds

hold water longer (U. S. Department of Agriculture Soil

Conservation Service, 1968). In wetter than average years,

or if the rainfall is intense, surrounding higher areas of

slash pine or grasses also flood and may take several weeks

to several months to dry. As the dry season progresses,

the water surface area gradually shrinks with the ponds in

the uplands the first to dry. Sloughs are the last

widespread areas to dry, and, under normal conditions,

Figure 8. Features of the field study site and adjacent
areas of Mud Lake Pond and Corkscrew marsh from an oblique
low-level color aerial photograph.

... .



A S. I..k


: : SPARTIN Cttion 190 :
... ........ *,: : .
.......... ...


ponds in the center of sloughs hold some water throughout

the year. Ponds at higher elevations may have localized

.holes, dug by alligators, which hold water through the dry

season (Craighead, 1968). During the dry season, sloughs

and ponds may receive groundwater flow from adjacent higher

land. Under other circumstances, surface water storage

may recharge soil water in surrounding areas. The flow

from ground to surface or surface to ground is governed by

relative water levels. An elevation profile through the

highest point in the study area shows that the water table

follows the general slope of the land (Figure 9). The

water table gradually flattens during the dry season.

Populations of wading birds that nest and roost in

large aggregations in scattered colonies throughout the

study region cover long distances to follow local patterns

of drying as they harvest the fish that concentrate in

numerous small, isolated pools. Wood Storks, which nest at

Corkscrew Swamp Sanctuary, coordinate their breeding season

with the dry season and are, for the most part, absent from

south Florida during the wet season. Because they locate

their food by touch as well as by sight, Wood Storks

require high concentrations of fish, particularly when

feeding young (Kahl, 1964). This species has been shown to

be very sensitive to changes in the seasonal pattern of

wetlands expansion and contraction that produces and

concentrates their food (Kushlan et al., 1975). Some

Figure 9. Elevation profile of highest point in study area
(immediately north of Immokalee), showing conformation of
water table with land slope characteristics (Florida
Department of Transportation, 1944).

NOTE: H. W. is high water fine in feet.


100 108 116 124 132 140 148


years Wood Storks do not nest in the area; other years,

nesting is aborted with the young abandoned.

Populations of the food fish of Wood Storks change --

from one year to the next, and the pattern of the variation

is not completely understood. Fish production might be

expected to be greater in wet years; but, in a study of

fish populations in the Shark River Valley of Everglades

National Park, Kushlan et al. (1975) found that fish

populations decreased over a 3-yr period of above average


There has been a decline in Wood Stork populations in -

south Florida during the past 15 yrs, perhaps because they

have been nesting less frequently. The population decrease

is coincidental with a downward trend in rainfall. It also -

has occurred at the same time major changes in the water

patterns of the area have been made by drainage and diking.

During the past 15 yrs, networks of canals in .southwest

Florida have converted large areas of wetland to suburbs,

farms, and pastures. It is difficult to separate the

effects of drainage and the effects of weather on the Wood

Stork population and on other wading birds of south

Florida, which also are declining. To complicate the

problem of analysis and prediction, the Wood Stork is a

long-lived species in which individuals do not reach sexual

maturity until they are several years old (Kahl, 1963).

The young produced by the fish stock of one year mature and

reproduce several years later. This causes a lag in the


response of the Wood Stork population to changes in water

patterns and fish production,

Modeling Theory of Oscillating Systems

For many animal populations a change in population

number such as that exhibited by Wood Storks within the

past 15 yrs is part of a long-term cycle. There are many

known animal cycles in nature, and in many cases a cycle in

one species can be related to that in another. Predator

population cycles can be dependent on prey cycles. Prey

cycles can be dependent on predator cycles or on the cycles

of alternate prey species (Bulmer, 1975). Although it

seems reasonable to think that the ultimate cause of a

series of linked species cycles would be an oscillating

climatic factor, in a number of well-known cases,

particularly the 10 (9.6) yr animal cycles of the Canadian

northwest, climatic influences, though sought, have not

been demonstrated (Bulmer, 1974).

Systems showing population cycles generally have been

studied as systems with intrinsic oscillating capabilities.

Any simple two compartment population model may oscillate.

The classic two compartment prey-predator model of Lotka

(1925) and Volterra (1926) is a well known example of model

structure that will oscillate without oscillating input.

A model with a time delay such as that imposed by

delayed breeding is almost certain to oscillate (Smith,

1974), and a model subjected to an oscillating forcing

function also can be expected to oscillate (Rykiel and

Kuenzel, 1973). Some oscillating models demonstrate

persistence; others are unstable (Holling, 1973). Time

delays longer than the natural periodicity of the system

(in the equation dx/dt = rx, the natural period, or time

constant, is 1/r) almost inevitably cause instability

(Smith, 1974). On the other hand, simple changes in the

governing equations, representing adjustments or

modifications in the basic structure of the system, can

stabilize the system (Smith, 1974).

On the basis of mathematical analysis, Oster and

Takahashi (1974) predicted that, when intrinsic oscillating

factors (periodic forcing functions) are imposed on systems

with intrinsic oscillating factors (time delays), beat

frequencies may result. If, however, the frequency of the

intrinsic oscillation is close to the characteristic

frequency of the external oscillators than a phenomenon

known as entrainmentt" may occur, and the system will

respond to the external freauency only. This allows

biological oscillators to "latch on" to the environment

(Pavlidis, 1973). In the case of the Wood Stork, if

rainfall periodicity is operating on a 5 yr cycle and there

is a 4 to 5 yr delay between fledging and breeding, then a

synchronization of the intrinsic cycle and the extrinsic

cycle may occur.

The present existence of the birds is evidence that

their population was maintained under natural conditions.


To reflect the real system, the model also must maintain

the bird population under natural conditions. The first

question that arises is what structural conditions inherent

in the natural system must be included in the model to

insure a simulation of the long-term survival of the Wood

Stork population.

The second question of consequence is how have man's

changes in the structure of the system affected its ability

to maintain wading birds; or will the Wood Stork be

eliminated from south Florida under changed conditions? If

the Wood Stork is disappearing in south Florida, it may be

a number of years before the fact is obvious, and it may

then be too late to do anything about it. Model

simulations are able to provide clues to the future. They

allow the exploration of questions of both theoretical and

practical importance.

Population Biology of Wood Storks

Population size is ultimately controlled by energy,

usually food energy. Annual variation in population size

has been related to annual variation in the energy base of

a number of bird species, including the Great Tit (Perrins,

1965; Krebs, 1970) and the Tawny Owl (Southern, 1970).

Energetic influences limit bird populations by affecting

number of breeding pairs, clutch size, hatching success,

nestling survival, and mortality rates in the first (or


first few) years. Energy factors seldom limit bird

populations by shortening the life span of adults.

The research of Kahl (1963,1964) and J. Ogden (pers.

comm.) and records from Corkscrew Swamp Sarntuary (J.

Hansen, pers. comm.) suggest that food availability---.

regulates the size of Wood Stork populations by determining

whether nesting is attempted and carried to completion in a

given year; the percentage of the adult population

participating in the nesting effort; the number of

fledlings produced per nesting female (see Kahl's 1963

discussion of the effect of asynchronous hatching in this

species); and mortality during the year following fledging.

Kahl (1964) found that the availability of food to -

nesting Wood Storks depended more upon "ecological

density," or the concentration of food in numerous small

ponds, than on "absolute density," or the total amount of

food in the feeding range of the birds. In order for large

quantities of fish to be available to storks it is

necessary first that extensive areas of land be covered

with water so that fish may reproduce and grow, and then

that surface water area be reduced to bring about fish


Kahl (1964) determined the energetic requirements for

reproduction in Wood Storks, including the daily energy

requirements of the adult birds and the total energy

requirements of growing young from hatching to fledging.

He calculated that, in the active state, mature Wood


Storks, which weigh 2 to 3 kg, require a daily food intake -

of approximately 570 kcal (95 g dry weight of fish), of

which 79 percent is assimilated. Nesting activities of the

individual pair of storks extend over approximately 130

days. Table 1 (from Kahl, 1963) shows the period of time

spent in each phase of reproduction.

During the 60-65 day nesting period (from hatching to

fledging) observed by Kahl (1962), each young stork

required a total of 2.81 kg dry weight (16,802 kcal) of

fish. As the nestlings grew, relative metabolic rates

decreased from 425 kcal/ during the first and second

weeks to 80 kcal/ during the ninth week (Kahl, 1962).

Kahl (1964) calculated that approximately 220,000 kcal

of food (34 kg dry weight of fish) are required by an

average Wood Stork family (2 adults and 2.25 fledglings)

during the breeding season. During the 1960-61 breeding

season, when the Corkscrew colony had 6,000 active nests,

the birds must have consumed approximately 200,000 kg dry

weight (1,200,000 kcal) of fish, which the adults collected

from ponds throughout the southwest Florida area.

Wood Storks range up to 130 km from their rookery on

daily food gathering flights. Whenever possible, the birds

conserve energy by taking advantage of local convection

currents from which they gain altitude for gliding, or

powerless flight. Thermal lift carries Wood Storks to 1500

m In south Florida during the latter months of the dry


Table 1. Estimated duration of stages in the Wood Stork reproductive
cycle (from Kahl, 1963).


Pre-pairing presence in vicinity of colony

Pair-formation and nest-building


Pre-flight nestling stage

Post-flight attachment to the nest


Estimated Duration
Minimum Maximum

12 25

5 8

28 32

50 55

15 30

110 150


J. Ogden's (pers. comm.) observations of Wood Stork -

nesting colonies in Everglades National Park suggest that

the length of the breeding season, particularly the period

of raising nestlings, may vary according to the

availability of food. Nestlings may survive but grow at a

slower rate at suboptimal levels of food availability. J.

Ogden (pers. comm.) also noted that mortality was high

during the first year of life (from fledging to age 1) for

fledglings leaving the nest under conditions of poor food

availability near the rookery. First year mortality is

normally believed to be about 40% for this species (Allen

et al.,' 1958), but it may be 90% or higher during marginal

years (J. Ogden, pers. comm.).

Wood Storks lay as many as five eggs (Palmer, 1962),

but three eggs are usual. Howell (1941) inspected 200

nests in an Everglades mangrove rookery in December 1933

and found that "most" nests had four eggs and five nests

had five eggs each. Kahl (1963) found an average of 3..3

eggs per nest in a rookery in central Florida in 1960.

According to Kahl (1963) the average number of young

fledged per successful nest was much more variable than the

average number of eggs laid per nest. The mean number of

young fledged in the rookeries he studied during the years

1958-1961, varied from 1.34 per nest (based on 140 nests)

at Micanopy in northcentral Florida in 1959 to 2.92 per

nest (based on 100 nests) at Corkscrew in 1960. Kahl

(1962) said that the difference in fledgling production

between rookeries in northcentral Florida and rookeries in

south Florida during the same period indicated that

conditions for raising young were enhanced by greater

fJulctuation of the water table, causing greater

-concentration of food. The probability of nesting failure

with zero production in certain years was, however, also

increased in areas where the water level fluctuation was

the greatest.

Table 2 gives the number of fledglings produced at the

Wood Stork rookery at Corkscrew Swamp Sanctuary for the

past 19 yrs. As the Corkscrew population represents

approximately one half the Wood Stork population in the

United States (J. Ogden, pers. comm.), this table provides

a good index of the variation in the size of the nation's

Wood Stork population over this period. As the table

shows, a high percentage of nests were successful in only 7

out of 19 yrs. In 7 other years out of the 19, no young

were produced, either because nesting was not attempted or

because all the nests were abandoned before the young were

old enough to support themselves. In the other 5 yrs only

a small portion of the population successfully raised


Kah1's (1964) observations, augmented by a comparison

of the fledgling production record at Corkscrew with the

weather record for the same period, suggest that successful

nesting for Wood Storks in this area depends on the

following factors: -..

Table 2. Wood Stork fledgling production at Corkscrew Swamp Sanctuary, 1957-1975.

Nesting No. of pairs of

No. of pairs of
nesting storks











Date started










No nesting attempted

All nests deserted in early Jan.
due to cold temp. and over 8" rain

Successful nesting

All but 50 pairs deserted following
heavy rainfall in late December

Successful nesting

Successful nesting

Successful nesting

No nesting attempted

About 1,000 nests with young left after
rain and high winds on Feb. 19 & 26

Successful nesting

Estimated no.
of fledglings








late November


late November

mid February

mid December

early December

early December


Table 2 continued.





Date started

No. of pairs of
nesting storks












No nesting attempted

All nests deserted in early March

All young storks died from rain and
cold in late January

Rain and wind from hurricane on June
8 killed some young

Successful nesting

Successful nesting

All young were killed by rain, cold,
and high winds on Feb. 8 and 24

Most nests deserted after a rainy
period in early Jan.

Most nests deserted after a rainy
period March 6-9. About 150 nests
left on April 15

All nests deserted after 4.9" of
rain on March 7

Estimated no.
of fledglings









mid January

late November

mid March

mid November

mid March

late November

early December

mid February

mid February





Table 2 continued.

Nestig No.of pars o

No. of pairs of
nesting storks










Date started

late November

mid January

mid March

early November


Successful nesting

Most nests deserted in mid-Feb.

Most nests deserted after 5.45"
rainfall on March 31

No nesting attempted

Successful nesting

Successful nesting

Estimated no.
of fledglings






aCompiled by James L. Hansen, with information for 1956-62 from Kahl (1964) and information for 1963-75
from unpublished notes and reports of the National Audubon Society at Corkscrew Swamp Sanctuary.

bHansen's estimate based on number of nests reported.




1) early flooding, ample rain, and a large land area
covered by water during the summer and fall prior
to nesting so that reproduction and growth of fish
are maximized;

S2))cessation of rains no later than October so that
drying commences in early winter (if the dry-down
begins too late or progresses too slowly, the birds
start their reproductive activity so late in the
season that summer rains interrupt the nesting
effort by expanding the water and allowing fish to
disperse. The reduction in fish density causes
adults to abandon their young, resulting in
death of the nestlings).

3))few or no heavy rains during the winter and early
spring (untimely rains also cause fish populations
to spread out and not be accessible to Wood Storks-;
consequently rookeries and young are abandoned);

(4) a mild winter (storms and freezes cause heavy
\ /mortalities in the rookeries).

The level of fledgling production in successful

breeding seasons and the frequency with which successful

breeding seasons must occur to assure the perpetuation of

the species are dependent upon intrinsic characteristics of

the population such as survival rates, life expectancy, and

age of first breeding. Banding of Wood Stork nestlings in

rookeries at Everglades National Park has been carried out

since 1974 by John Ogden, research biologist of the

National Audubon Society, but it will be many years before

banding returns provide needed demographic information.

Meanwhile, the small amount of data available on Wood

Storks and information on related species must be used to

formulate initial estimates to use in predictive models.

A sole record from the wild indicates that a Wood

Stork lived at least 11.7 yrs (Kahl, 1959). Another Wood


Stork that was an adult when captured lived at least 30 yrs

in captivity (Kahl, 1963). Allen et al. (1958) estimate

that mortality in the Wood Stork is probably 20% after the

firs-t- year ofl i fe.

Life expectancy and survival rates of the Wood Stork

may be close to those of the White Stork of Europe (Ciconia

ciconia). Zink (1966) estimated that 1st and 2nd yr

mortality rates for this species are "about 30% and

probably higher" and that the average mortality rate for

older birds is 21%. Wood Stork mortality during the second

year probably is no higher than that of older birds. First

year mortality of Wood Storks, however, is highly variable

and may exceed 90% (J. Ogden, pers. comm.).

Zink (1.96U6) reported that the average life expectancy

of the White Stork is 4.5 yrs, but Kahl (1963) cited Flower

as giving an average age of 25.7 yrs for 20 captive storks

of genera Ciconia, Jabiru, and Leptophilos, suggesting that

average life expectancy in -the family as a whole may be

greater than 4.5 yrs. Miller et al. (1972) proposed that

mortality in long-lived species such as the Wood Stork may

have an age dependent as well as an age independent factor

and that, after the first year or two, mortality may

increase with age.

Kahl (1963) estimated that Wood Storks first breed

when they are 3 or 4 yrs old. Time delays as in delayed

breeding can have a strong impact on the way a system


Because the Wood Stork is a long-lived species with

relatively low mortality after the first year, Wood Storks

may not need to nest successfully every year to avoid a

gradual population decline. Important questions that

should be answered are what long term average level of

productivity must be maintained by the population to

prevent a trend toward extinction, and how does the long

term production record at Corkscrew compare with this



The model diagram in Figure 1 was used to organize

available information on the wetlands system. Data

collections were organized around the model to provide

quantitative information about interactions and energy

flows. Methods for data collection included analyzing the

rainfall record; following storks in a low-flying plane;

counting ponds; measuring the area extent of ponds,.

sloughs, and marshes; making hydrologic calculations;

sampling fish and aquatic invertebrates in a pond and

marsh; and making demographic calculations for the

population of Wood Storks.

Throughout this study all measurements, calculations,

and references related to hydrology or land surveying are

given in English units, which are standard units in these

fields in the United States. All other units are in the

metric system.

Following the measurements and calculations the

initial model evolved into three slightly differing models,

all of which were simulated and tested for their behavior

under different conditions of drainage. Models I and II

were simulated on an EAI Miniac analog computer using a

repeating seasonal pattern of expanding and contracting

water area. Model III was simulated on an IBM 370 digital


computer using the results from a water model based on

actual monthly rainfall at Ft. Myers (U. S. Department of

Commerce. National Oceanic and Atmospheric Administration,

1950 1975) for the 25-yr period from June 1950 through

May 1975. All models were written in the energy circuit

modeling language of H. T. Odum (1971).

Basis for Models

Models of Water, Fish, and Wading Birds

Model I is shown in Figure 10. The diagram indicates

most important compartments storagee) of the system, major

energy sources, energy sinks, pathways of energy

interaction, and thresholds (switching functions). Figure

11 is a key to the symbols used in Figure 10 and in the

model diagrams presented throughout this study. In Table 3

components of the model in Figure 10 are isolated and

explained in order to provide an understanding of the

model's structure and relationships. The symbols relate

flows to tanks in mathematical terms. Positive values are

flows entering the tank; negative values are those flows

leaving. The tanks change with time according to

differences between inputs and outputs. Flow rates change

with time according to the sizes of the tanks. Based on

the diagram differential equations are written for each


Figure 10. Model 1. Water area, fish, and Wood Storks
with initial fish stock and potentially breeding bird stock

(1) k (2)
F = klAS k2 F/A

B = k3 F/A(3) k4 B (4) (k7 B(7)x C1)

N = (k5 B xC) k6N(6)

(1) fish growth, g/
(2) fish predation and death, g/sq-m-mo
(3) bird food intake, mg/sq-m-mo
(4) bird respiration, mg/sq-m-mo
(5) new bird production rate, birds/sq-m-mo
(6) mortality, birds/sq-m-mo
(7) energy expended in breeding effort, mg/
C1 = 1 B/N > n
= 0 B/N < n


Figure 11. Key to the symbols used In energy circuit
model diagram.

(Some energy is lost in
all interactions and from
all storage)

(storage) with inflows and


J2 = ky

(example' multiplier D or
divider )

or autocatalytic growth
J = kxQ

or crowding effect, J =

flow from E is proportional
to y.

MODULE (contains positive feed-
back for autocatalytic growth


J > 0 if x> c


Table 3. Explanation of water area, fish, and Wood Stork Model I.

Forcing functions, or environmental /W
factors of importance to the system, AREA
are represented by circles. Both A
sun and water area vary seasonally. SUN

Tanks are the symbols for stocks,
or storage, within the system. FISH
Flows of energy, water, or other F
materials are shown by connecting
lines. Arrows indicate a one-way
force. There is an energy cost
associated with all transactions.
The energy loss is accounted for
with heat sink on flow lines
and other symbols.

Table 3 continued.

Fish production is a function of
radiation and the amount of land
surface covered by water. Depen-
dence on two or more such factors
is demonstrated by the work gate.
When the action appears multipli-
cative, the work gate is a simple
multiplier function.

Fish density is fish biomass di-
vided by water surface area, de-
noted by a divider work gate. As
surface water area shrinks, fish
density increases, its limit im-
posed by minimum water area and
maximum fish biomass.

Table 3 continued.


Wood Storks feed in proportion to
fish density rather than fish bio-
mass. Fish density controls the
flow of fish to the birds.

Bird breeding is stimulated by an
abundance of food, which is reflec-
ted in the individual weights of
the birds. Bird biomass divided by
bird number yields average weight,
which, by means of a comparator
operator, is compared with a breed-
ing weight threshold to determine
whether or not breeding will occur.
Average weight rising above the
threshold value switches on the
pathway from bird biomass to bird
number to initiate breeding activity.


The coefficients, or "k" values for the equations of

the model were computed by dividing the flow by the

upstream stock. Thresholds were estimated based on

literature values and measurements from the study. The

differential equations were the basis for an analog diagram

that served as a guide for patching the analog board. Pot

settings were calculated from "k" values. Differential

equations are given in the legend to Figure 10.

Outside inputs, or forcing functions of the model,

were solar radiation and surface water area, calculated as

percent of maxima and represented by sinusoidal curves with

surface water area lagging solar radiation by approximately

3 mos. The water area curve was approximated from the

simulation for the June 1974-May 1975 year from a water

model, which will be described later in this section. It

was possible by means of the water model to determine how

drainage changed the seasonal expansion and contraction of

surface water area. This change was approximated by

adjusting the mean and the amplitude of the sinusoid.

Several other levels of drainage were also tested for their

effect on fish growth and concentration and bird biomass

and breeding.

The model in Figure 10 (Model I) represents the

simplest possible interpretation of the system. It assumes

that seasonal expansion of fish biomass is a function only

of sunlight and water area and that initial fish stock, or

the parent population at the beginning of the wet season,


is not important. It also assumes that growth of bird

biomass is proportional only to fish density, and that the

number of potentially breeding birds at the beginning of

the nesting season is not important. Note that there is no

feedback from the fish compartment to the multiplier on

fish growth or from the bird compartment on food


The structure of Model I suggests a system's

homeostasis in which fish recruitment and growth rates are

adjusted to counteract variation in initial fish stock.

When initial fish stock is low, recruitment and growth

rates are high; when initial fish stock is high,

recruitment and growth rates are lower. This model also

suggests that breeding activity is not limited by the

number of birds capable of breeding. It assumes that the

number of breeding birds is unlimited relative to the level

of breeding activity that can be supported by th.e system.

None of these assumptions is unrealistic if, in the prey

population, survival of young is inversely proportional to

the density of adults and if, in the predator population,

isolation from other breeding populations of the same

species is not complete.

In Model II (Figure 12) growth and survival rates of

fish stocks the previous year are factors in determining

the rate at which fish biomass increases. Equations for

Model II are shown in the legend to Figure 12.

Figure 12. Model II. Water area, fish, and Wood Storks,
with initial fish stock important.

F = k1 FAS(1) 2 F/A (2) + k7(7)

B = k3 F/A(3) k4 B(4)

N = (k5 B(5)C) kN(6)

(1) fish growth, g/sq-m-mo
(2) fish predation and death, g/
(3) bird food intake, mg/sq-m-mo
(4) bird respiration, mg/
(5) new bird production rate, birds/
(6) mortality, birds/
(7) immigration of fish, mg/sq-m-mo






In Model III (Figure 13) both fish history and bird

history are important. Climatic events of previous years

influence biological events of the current year. This

model includes the age structure of the birds, and only

those birds 5 yrs old or older are capable of breeding. It

also includes large populations of predatory fish (gar,

bowfin and bass) that expand in wet years, decrease in dry

years, and compete with wading birds for food fish.

Model III uses differential equations similar or

identical to those in Models I and II but makes increased

use of.discrete equations to handle logic functions such as

migration, fish kills, and the incrementation of age

cohorts. Modules on the right-hand side of the diagram

denote.age classes: 1, 2, 3, and 4 yr olds, which do not

breed; and the breeding stock, which consists of birds 5

yrs of age or older. Age cohorts are incremented once each

year, with mortalities subtracted. The number of breeding

birds increases or declines, depending on whether annual

recruitment (4-yr-olds becoming 5-yr-olds) exceeds average

mortality of the breeding stock.

The bird biomass tank empties abruptly each June and

remains empty all summer, indicating that migration out of

the region has occurred. When the birds return to the area

in the fall the bird biomass becomes the product of

"minimum weight" and "number of sexually mature birds."

Bird feeding and bird respiration switch on at that time,


Figure 13. Model III. Water area, fish, and Wood Storks with initial fish stock and breeding bird
stock important. Model includes age structure and breeding delay in the birds.

F klFAS blF2(1) k2FQ10(a2 b2F/A + c2(F/A)2)(2) -k6F/A (C2C3)(3) k5F/A(4)
k3k10B(a4 b4B/(Ny + N5)ln(c4F/A (5)

B = k3B(a4 b4B/(N + N5)n(c4F/A)(6) k4B(a4 b4(a4 4B/(N + N5)(7)

+ N5WL( C5)(8)

- BC4 (8)

G = k7G(a7 b7G)ln(l + F/A)(9) k11G(10) k12G(O.25C7 + 0.25C8 + 0.25C9 + 0.25C10)P(11)

N = N5EAC (12)

NO = ((B N5WA)/WA)C6P(13)

(1) consumption by prey fish
(2) prey fish respiration
(3) prey death in fish kill
and dry ponds
(4) general fish predation
(5) predation by storks and
other birds

N1 = NoS0Cp(14)

N2 = N1S12C6P(14)

(11 )

fish consumption by birds
bird respiration
fish consumption by gar
gar respiration
gar death in dry ponds
and fish kills

N3 = N2S23C6P(14)

N4 = N3 S34C6(14)


N5 = (N4S45 N5M)C6(15)

nesting (laying eggs)
fledgling production
incrementation of age cohorts
accumulation of breeding stock

NOTE: Numbers in parenthesis correspond to those on the diagram.


F biomass of fish
B biomass of breeding birds
and nestlings

WL minimum average weight
of birds
WA robust average weight of birds
WM robust weight plus weight of
EA average number of eggs laid

Thresholds for Controls
s summer solar radiation
f fall solar radiation
1 low water area
d fish density

survival rate, fledgling to Age 1
survival rate, Age 1 to 2
survival rate, Age 2 to 3
survival rate, Age 3 to 4
survival rate, Age 4 to 5

Egg laying Control

1 B/N>WM
C :
1 0 B/N

Migration Controls

C 1 S>s
C 6
6 0 S

1 S C5 =
0 S>f

M average mortality
rate, birds 5 years
and older
Q10function for temper-
ature effect

P pulse (=1 for 1 dt)

Prey Fish Kill Switch

1 F/A>d 1 A< 1
C = C =
0 F/A1

Predator Fish Kill

I A 0 A>1 2

1 A<14
0 A>14

I A C-=
0 A>13

1 A< 5
C0 = 6

and population biomass increases or declines according to

the balance between these two rates.

The feeding rate of the birds is a function of fish

density and bird biomass. It is an inverse function of

average bird weight, which decreases when nestlings join

the population but increases as they approach fledging. In

the model, breeding birds lay an average of 1.5 eggs each

in years when the laying weight threshold is exceeded by

average bird weight. The number of fledglings ultimately

produced in a given year is determined by the total weight

gain of the population.

In Model III, both prey fish and predator fish are

decimated when isolated ponds go dry. Prey fish, in which

recruitment and growth is a direct function of water area

and solar radiation, recover more quickly than predator

populations, in which growth is a function of prey density

and predator biomass.

Equations for Model III are shown in the legend to

Figure 13. The bases for those rate equations which differ

from those used in the simpler models are as follows.

Consumption by prey fish (rate equation 1 in

Figure 13). To the basic equation in which food

consumption is a function of solar radiation, water surface

area, and fish biomass was added a density dependent factor

to reduce fish growth when fish density becomes high. This

addition simulates the limiting of populations at high

densities by factors such as decreased fecundity or reduced

recruitment. The formula first used in Model III for the

density dependent function (normally expressed in energy

circiut language) was:

= k FAS kl F2AS (1)

This function produced instability in the model because of

the seasonally oscillating sunlight and water area. Two

variables, therefore, were dropped from the second term and

the formula became:

= kI FAS b F2 (2)

Fish respiration (rate equation 2 in Figure 13).

Respiration per unit of fish biomass in a seasonally

expanding fish population decreases with density at the

lower densities and increases with density -at higher

densities. The fish respiration rate equation and its

coefficients used in the model were similar to the

quadratic equation (equation 27 in Results section). The

respiration formula was:

= F(a2 b2F/A + c2(F/A)2) (3)

Temperature effect on fish respiration (equation 15 in

Figure 13). Respiration of all organisms is affected by

temperature. The smaller the organism, the greater the


effect of temperature on its respiration even in

subtropical climate where seasonal temperature differences

are relatively minor. "Q10," the factor by which the

respiration rate is changed by a change of 10 degrees from

a baseline environmental temperature, is the measure of the

effect of temperature on a given organism. In this model,

the Q10 of prey fish was 1.3, and the baseline temperature

(Q10 = 1) was 27 C. The Q10 equation used in the model

expressed this relationship:

Q10 = 1 + 0.03(T 27) (4)

Bird respiration (rate equation 7 in Figure 13). Bird

respiration in the model decreased as a function of average

weight of the breeding birds and their young in order to

reflect the increased energy demands of the population when

rapidly growing young are being raised. An approximate

average size and average energy demand per gram body weight

of one stork and its young were calculated for each week of

the 9-wk nesting period, based on information from Kahl

(1962, 1964). A simple linear regression of respiration

versus average weight over this period formed the basic

formula for bird respiration used in the model:

k4B(a4 b4B/(Ny + 1N5))

Fish consumption by birds (rate equation 6 in

Figure 13). Preliminary simulations by Model III

demonstrated that if stork food consumption were a simple

function of prey fish density, the tremendous difference in

fish density from year to year would cause instability.

Some measured prey-predator interactions are logarithmic

(Smith, 1974), and the natural log function of fish

density, substituted for the simple function commonly used

in energy circuit models, made the model more stable. The

basic food requirement equation of the stork population was

multiplied by the natural log of the product of prey fish

density and a constant to approximate the rate of feeding

by the birds. The food consumption formula became:

k3ln(c4F/A)B(a4 b4B/(N + N5)) (6)

Fish density was multiplied by the constant and a cut-off

was set at zero so that fractional densities would not

cause negative flows.

Fish consumption by predator fish (rate equation 9

in Figure 13). Consumption by gar was a function of the

natural log of one plus fish density in the model. The

value one was added to fish density so that negative flow

would not occur at low fish densities. The fish

consumption by gar formula was:

k7ln(1 + F/A)G(a7 b7G) (7)

Fledgling production (equation 13 in Figure 13). In

the model fledgling production was determined by the total

weight gain of the breeding population during the breeding

season. Average weight of healthy adults (2.5 kg)

multiplied by the number of breeding birds was subtracted

from total biomass of the birds and the remainder was

divided by average weight of fledglings (also 2.5 since

healthy fledglings can weigh as much as adults when they

first leave the nest according to Kahl, 1962) to determine

the number of fledglings raised. The formula used in the

model was:

= ((B N5 A )/A)C6P (8)

Death of gar in dry ponds and fish kills (equation 11

in Figure 13). A step-wise set of comparators was used to

simulate death of gar caused by drying of ponds and fish

kills because, in nature, conditions causing gar mortality

are encountered in ponds at different elevations throughout

the dry-down. The comparator value was incremented from

zero to one in 0.25 steps as surface water area dropped

below four threshold values (0.8, 0.6, 0.4, and 0.2 of

total wetland area).

The DYNAMO program for Model III is Appendix D.

Water Model

A diagrammatic representation of the model of water

volume and surface water area is shown in Figure 14.

Compartments of water storage are soil (includes ground)

and surface. Rainfall is channeled into the soil unless

this compartment is full (saturated), in which case it is

shunted directly into surface storage. Land surface area

covered by water is proportional to the volume of surface

water, according to the area-volume curve developed in this

study. Dry land area is total land area with wetlands area

subtracted from it. Water is removed from the soil and

aquifer by groundwater flow at a rate determined by the

gradient between the water table and sea level and by soil

and aquifer permeability characteristics. The water of

low-lying areas is augmented by runoff from surrounding

higher land. Input is by surface flow during the rainy

season and by horizontal flow through the ground during the

dry season. Under some conditions (i. e. when ground or

soil water level is lower than surface water level) surface

water sources restock soil water supplies. Overland flow

does not occur until surface storage areas are filled to

the lowest points on their rims. Surface water and soil

water are.subjected to evapotranspiration (ET), which is

greater during warm weather months than in winter because

of differences in wind and temperature, and also because of

seasonal physiological changes in predominant plants. In

areas where there is no standing water, ET is proportional


Model relating rainfall timing and intensity to surface water area.






- E QW


RDW = C4 {( I x AD) VDmax VD}



QDG = T B C1

hD hW
QDI = k p h hs C2


Ew = 0.75 P AW S C5
W e W 5

AW = fVW (Volume-Area curve)



ED = 0.75

Pe VDmax D S


QW= n

h 5/3 a(wW
w Wmax

(sin 9)1/2 C3

Figure 14.

Legend to Figure 14. continued.


C = 0 Ll < VDme
1 L 1 >VDme
C 0 I l-Dme

C = 0 L < VDe and hD > h
1 0 L > Dme or h < W

C = 0
3 =

C 4 0

C = 0 L < 0
C5 L2 > 0

L2 < V
L2 > VWmax
2 -Wmax

L < V Dmax
L1 Dmax

Key to Symbols

AD = area of dryland, acres
.AW = area of wetland, acres
Awmax = maximum wetland area, acrea

AT = total land area, acres

An = P JbD hwl, area normal to flow, acres

a = width of overland flow: perimeter of all
primary and secondary canals; 2(N+Ca )
B = width of the edge of the aquifer, length
of coastline and river borders

b = exponent on proportionality factor
A /Awmax

Ca = length of all major and secondary canals
D = difference between maximum thickness of
monitored ground water and average
height of land above mean sea level
dW = average distance between highest
points in uplands and nearest edge of
pond of slough
dpD = average distance between inland areas
and coast
g = specific yield (porosity), a proportion-
ality factor

Legend to Figure 14. continued.

hD = thickness of monitored portion of ground-
water (maximum 8 ft), ft
hD = hG + D, elevation of water table, ft
h' = depth of surface water at local deepest
point, ft
hW = 0.25h'
I = rainfall, ft/mo
K = hydraulic conductivity (permeability
N = length of all natural flow-ways
Pe = potential evapotranspiration
P = width of overland flow, perimeter of
sloughs, ponds, and ditches
RD = rainfall on dry land
R DW = rainfall excess on dry land (shunted to

Rw = rainfall on wetland
S = seasonality factor for plant transpir-
ation (with and without leaves)
T = transmissivity coefficient
VD = ground and soil water volume, acre ft
VW = surface water volume, acre ft
VDax = saturation volume of soil and surface
water, acre ft

VDme = moisture equivalent (field capacity)
volume of soil, acre ft
Vmax = surface water volume to lowest lip,
9 = elevation gradient from border to in-
land areas

to the degree of soil saturation. The water supply is

replenished during the rainy season but gradually depleted

during the long dry season.

Inputs to the model are the monthly rainfall record

for a 25-yr period, June 1950 through May 1975 at the U. S.

Weather Bureau, Page Field, Ft. Myers, and average long-

term monthly pan evaporation at the Royal Palm Ranger

Station at the Tamiami Trail in the Everglades (U. S.

Department of Commerce. National Oceanic and Atmospheric

Administration, 1950 1974). Pan evaporationn represents

the integrated inputs of the energy sources, solar

radiation and wind.

Two runs of the model using the same rainfall and pan

evaporation inputs were made. In the first run, natural

conditions as they existed prior to drainage (circa 1900)

were simulated. In the later run, coefficients were

adjusted to create conditions representing the present

(1976) drainage density of the area. Only three

coefficients were changed to represent the difference

between predrained and postdrained conditions.

Equations for the model, are given in the legend to

Figure 14. The model is quantified and coefficients used

in the model are listed in the-section on quantification

and simulation of the models. Following are brief

explanations of some of the flow equations used in

developing the structure of the water model.


Interflow equation. Both ground water flow to sea and

interflow between soil and surface water are governed by

Darcy's law (Lindsley et al., 1958). The equation for

Darcy's law used as the basis of the interflow equation


QDI = K i An (9)

where Q is flow rate, i is gradient, A is cross-sectional

area normal to water flow (seepage plane), and K is the

hydraulic conductivity (permeability) of the soil and

substrate. In the interflow equation of the model, both i

and A are functions of elevation of the water table and

change as the water table fluctuates. i is equal to h/dW ,

where d is the distance of water flow and h is the

absolute difference in elevation of groundwater and surface

water. An is equal to h x p, where p is the width of the

cross-sectional area normal to flow. For simulations under

primitive (predrained) conditions, p was the total gross

perimeter of the ponds, strands, and sloughs. For

simulations under present conditions, it was double the

length of drainage ditches plus the gross perimeter of the

natural drainage-ways.

Equation for groundwater flow to sea. Another form of

the equation for Darcy's law was used as the basis of the

equation for groundwater flow to sea. This form was:

QDG = T i B (10)

where QDG is flow rate, i is gradient, T is transmissivity

(hydraulic conductivity multiplied by the depth of the

aquifer), and B is the width of the cross-sectional area

perpendicular to water flow. In calculations for this

model, B was the length of the coastline plus the length of

the Caloosahatchee River. As transmiss'ivities vary

somewhat in different parts of the study region, the total

length was divided into three stretches and a different

transmissivity was estimated for each, based on Klein et

al. (1964). T x B was determined for each stretch, and the

three values were added together to give a weighted T B for

the total river and coastline of the study region. In this

equation i was calculated by dividing elevation difference,

h, by distance, d. h is the variable, (12 + D), and D is a

variable less than or equal to 8 that represents how many

of the top 8 ft of the aquifer and soil are saturated. The

maximum volume of water in the soil-substrate compartment

was the saturation volume of the top 8 ft of the soil and

substrate, because average water levels for the entire area

never fall below 8 ft. Twelve ft plus a maximum of 8 ft is

the approximate average elevation of the water table

relative to sea level when the soil is saturated. At less

than saturation, the water table is lower and the gradient

between water table and the sea is less.


Equation for surface water runoff. Runoff in the

water model is governed by the Manning equation (Lindsley

et al., 1958):

= 1.49 hw 5/3 L (sin 0)1/2 (11)

where QW is flow rate, hwis depth of the surface water, L

is the width of overland flow, and 8 is h/d, or the land

elevation gradient between upper and lower ends of the

flow-way. One quarter of the water depth at the deepest

local point (from the curve relating depth at deepest local

point to total surface water volume) was the estimate of h

used in the model. Runoff values simulated with the use of

this estimate of h were very similar to those simulated

with the use of "average depth," a value determined by

dividing total water volume by total area of surface water.

The first estimate, however, yielded a more realistic

simulation of seasonal change in surface water area. The

equation is:

hw= c h, (12)

where h' is depth at local deepest point and c is 0.25. In

the model L was a variable that changed according to a

power of the proportion of the total wetlands area

containing surface water. The equation is:

L = a (A /Awmax )b (13)

where a in the predrainage case is the perimeter of all

natural flow ways and in the present case is double the

length of all primary and secondary canals AW is surface

water area, AWmax is total wetlands area, and b is a number

between 1 and 2 that roughly relates width of the flow line

to water surface area. A /Awmax was less than 1 when

wetlands were not filled, equal to 1 when wetlands were

covered, and greater than 1 when uplands were flooded. The

maximum possible value of (A /Amax )b was 2. This allowed

for increased importance of connected shallow ditches for

removal of surface water when upland areas were flooded.

Evapotranspiration from surface water. The equation

for evapotranspiration from surface water in the model was:

Ew = 0.75 S Pe AW (14)

where Pe is long term average pan evaporation for each

month of the year, measured at Royal Palm Ranger Station in

the Everglades (U. S. Department of Commerce. National

Oceanic and Atmospheric Administration. 1974), AW is

surface water area, and S is a coefficient of plant

activity and shading that increases or decreases

evapotranspiration seasonally in correlation with leaf

senescence and regrowth of predominant vegetation cover.

This equation goes to zero as AW goes to zero.

Evapotranspiration from soil and substrate. The

equation for evapotranspiration from soil and substrate in

the model was:

ED = 0.75 S Pe (VD/VDmax ) AD (15)

where Pe is long term average pan evaporation, as above; S

is as above, VD is soil and substrate water volume to a

depth of 8 ft (generated by the model), V Dmax is saturation

volume of the soil and substrate to a depth of 8 ft, and AD

is the land area not covered by water. VD/VDmax is a

proportionality factor that reduces simulated

evapotranspiration as soil water becomes more difficult for

plants and wind to remove.

Depth and area of surface water. Both water depth at

the local deepest point and land covered by water are

variables related to surface water volume. The means by

which these relationships were determined are described

later in the Methods section. Plots of the relationships

are presented in the Results section. The plots were

translated into a table function in DYNAMO for

incorporation into the model.

Logic. In the model flows are limited by switching

functions and thresholds approximating real conditions.

For example, only gravity-flow water, or that volume of

water above the moisture equivalent volume of the soil, can

move as interflow from soil to surface water storage or as

groundwater flow to sea. Surface water runoff occurs only

when that volume is exceeded which is required to fill all

surface water areas to the estimated lowest points on their

rims. Only the top 5 ft (1.5 m) of soil-substrate water is

available to the roots of most plants and thereby subject

to removal by transpiration. Evapotranspiration from

surface water cannot remove a greater quantity of surface

water than is present. Rainfall is accepted by the soil-

substrate water tank only to the capacity of saturation

volume of the tank. Upland rainfall in excess of the

saturation volume of the soil-substrate tank becomes a part

of the surface water.

The water model was simulated on an IBM 370 digital

computer at the Northeastern Regional Data Center of the

University of Florida, using the DYNAMO modeling package.

Analyses of Rainfall

Trend Analysis

Moving 5-yr averages of annual, total wet season, and

total dry season rainfall for the 25-yr period of record at

Corkscrew grove (ALICO, pers. comm.) were graphed.

Graphing moving averages eliminates short term variation in

a periodic or noisy record so longer term periodicity or

trends, if present, can be identified. The 5-yr grouping

for the moving average was selected because Thomas (1970)


reported a 5-yr periodicity in the long term records of

some south Florida stations (although none of these

stations were in southwest Florida).

Frequency Analysis

Fourier analysis was used to look for cycles in the

rainfall record of Ft. Myers (U. S. Weather Bureau, Ft.

Myers). A fast Fourier transform program written by C.

Kylstra (pers. comm.) was used to convert both total

monthly and total annual data series to the frequency

domain so that the harmonic components of the signal could

be determined by a plot of amplitude versus frequency. The

equation used was as follows:

1 M y-j2rnm/M (16)

F = 1/2(an jb n); an = amplitude of real component; bn =

amplitude of imaginary component; M = total number of

Intervals; m = interval; n = harmonic.

Another Fourier equation, which converts a signal from

the frequency domain to the time domain, was used to

approximate the original signal as a sum of sines and

cosines. The equation is:

N j2(nm/M
ym = E Fe (17)

where N = total number of harmonics.

The fast Fourier analysis program was executed several

times on the monthly data, using different numbers of data

points (multiples of 12) in order to assure that any low

frequency components that might be present would show as

clearly defined peaks and that non-even number harmonics

would not be spread out over several adjacent harmonics and

their importance possibly obscured. Due to limits of the

computer and the program, data sets greater than 36 yrs

(432 data points) in length could not be tested. Fourier

analysis of annual total rainfall at Ft. Myers tested 82,

81, 80, and 77-yr sequences. The programs were run on an

IBM 1180 digital computer at the Department of Nuclear

Engineering at the University of Florida.

Remote Sensing for Relating Water Area to Volume

Depth-area (hypsographic), depth-volume, and area-

volume curves of the three-county study region were

developed using remote sensing techniques, plan profiles

from state road and private canal surveys, and on-site

topographic surveys. Lands covered by water several months

annually were located and mea-sured on infrared aerial

photographs by means of soil and vegetation

characteristics. Relative elevations and elevation ranges

of the different vegetation communities were determined

with the plan profiles and the topographic surveys.

In this study eight wetland areas were defined. These

are marshes through which water flows (sloughs), the

dominant vegetation 'of which comprises pickerel weed

(Pontederia lanceolata), maidencane (Panicum hemitomom),

arrowhead (Sagittaria lancifolia), and cordgrass (Spartina

bakerii); cypress strands, dominated by baldcypress

(Taxodium distichum); swamp hammocks, in which grow pond

apple (Annona ,labra), water ash (Fraxinus caroliniana),

and red maple (Acer rubrum); wet pairies, dominated by

short sedges and grasses, different species predominating

on sand and on marl; shallow ponds, open or holding pond

cypress (Taxodium ascendens), water ash, pond apple, red

maple, pickerel weed, maidencane, and arrowhead; and deep

sink holes; large shallow ponds; and lakes, all of which

are open. A cross section showing relative elevations is

given in Figure 15. Throughout the study it was possible

to use the term "slough" and "marsh" interchangeably. In

common usage the term "swamp" applies to wetlands with

trees and "marsh" to wetlands without trees.

The high water line for the average wet season was

assumed to be the line where saw palmetto, slash pines, or

live oaks began (Davis, 1943). Rings of sparse vegetation,

showing white on the photographs, also helped delineate the

outer limits of many wetland areas, particularly ponds.

Following are details of area measurements made of the

different types of habitat.

Figure 15. Relative elevations of pineland, sloughs (also
marshes), wet prairie (also dwarf cypress), strands, and

a I
!Cypress Strand or i Dwarf Wet Prairie
Swamp Hammock! Cypress

a Water in ponds

b Water in strands

c Water standing above rim of

strand when marl prairie

(or dwarf cypress) is flooded

~i i
i i i

I Pine Slough iPine ;
I I or
j Forest ; I Forest!

d Water over marl prairie

(or dwarf cypress)

e Water in sloughs

Marshes, Cypress Strands, and SwamD Hammocks

Areas of major wetlands units were obtained from land

use maps for Hendry, Collier, and Lee Counties (DeBellevue,

1976; Brown,1976; Lehman, 1976). Maximum volumes of water

retained in sloughs were approximated by estimating average

depths of sloughs from elevation profiles (ALICO, pers.

comm. and Florida Department of Transportation, pers.

comm.). The profiles are listed in Table 4. Curves of

water depth versus water surface area were developed from

cross-sections from the profiles. Water volume was taken

as the integral of (or area under) each curve, and water

surface area was plotted against water volume.

Ponds of Less than 100 Acres

Area of ponds was obtained by multiplying number of

ponds by average size of ponds. The ponds in each county

were marked and counted on a 1:250,000 scale index sheet of

Hurd infrared photographs from 1950. Average size of ponds

in sample areas was determined from 1:20,000 scale

Agricultural Soil Conservation and Stabilization (ASCS)

infrared aerial photographs (9" x 9") in Hendry and Collier

Counties. Figures 16 and 17 show the locations of the

areas covered by the sample 9" x 9" photographs. Areas of

circular or near-circular ponds were calculated by

measuring average diameters and using the equation for the

area of a circle. Areas of irregular shaped ponds were

determined by a digital planimeter (Hewlett-Packard

Table 4. Plan profiles providing relative elevation information for
the study.


State Road 833

State Road 29

State Road 84
(Alligator Alley)

North Boundary

South Boundary


Portion including 900 angle turn
in the Deer Fence area of southeastern
Hendry County

Portion in Cow Slough area, Immokalee
Rise, extreme northern Collier County

Portion in Big Cypress area, west of
Fahkahatchee in western Collier County

Devils Garden area between Ll Canal and
SR 833 in Hendry County

Devils Garden area between Ll Canal and
SR 833 in Hendry County

aFlorida Department of Transportation
bAtlantic Land Improvement Company







Figure 16. General Highway Map of Hendry County (Florida
Department of Transportation, 1969) showing location of
sample 1:20,000 scale photos used in determining area of







0 3 6 I;


20- 4 50-
121 37
3D- 833
118 84
DI I183 -
g 54


I i
I i

! ,
' I

s *

L.- -- --- ....-

Figure 17. General Highway Map of Collier County (Florida
Department of Transportation, 1966) showing location of
sample 1:20,000 scale photos used in determining area of

0 3 6 12

b I


0 3 6 12

digitizer). A total of 751 ponds in Hendry County and 192

ponds in Collier County was used to estimate average pond

size. Lee County ponds were assumed to be similar. Ponds

were counted on the sample 9" x 9" aerial photographs, and

calculations of ponds per mile from the 9" x 9" aerial

photographs were compared with those from the same general

areas on the index sheet to test the accuracy of the

original count. A small correction factor thus developed

was applied to the total count for the counties. Figure 13

shows a sample aerial photograph with ponds outlined.

Pond area was subtracted from other wetlands types to

avoid double-counting. The area of ponds in each ecosystem

was approximated from observations made during the count.

The estimated percentage of pond area in each ecosystem is

given at the bottom of the tables describing wetlands area

for each county in Appendix A. Histograms showing the size

frequency distribution of ponds in Hendry and Collier

Counties were prepared.

Maximum capacities of the sample ponds were estimated

by the equation for the volume of a cone. Total capacity

of the sample ponds was multiplied by the total number of

ponds and divided by the number of sample ponds to obtain

the total volume of water the ponds of the two counties

could hold. The total capacity of ponds in Lee County was

estimated as the product of total number of ponds in Lee

County and the average size of ponds in Hendry and Lee


Figure 18. Copy of 1:20,000 scale infrared aerial photo
BUN-10-97 (U. S. Department of Agriculture. Agricultural
Soil Conservation and Stabilization) with ponds outlined.


1 ; '

k t-