MODELING BURROW CHOICE IN GOPHERUS POLYPHEMUS
by
Christopher Olbrych
A Thesis Submitted to the Faculty of
The Wilkes Honors College
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Arts in Liberal Arts and Sciences
with Concentrations in Economics and Environmental Studies
Wilkes Honors College of
Florida Atlantic University
Jupiter, Florida
May 2016
MODELING BURROW CHOICE IN GOPHERUS POLYPHEMUS
by
Christopher Olbrych
This thesis was prepared under the direction of the candidate’s thesis advisors, Dr. Jon
Moore and Dr. Kanybek Nur-tegin, and has been approved by the members of his
supervisory committee. It was submitted to the faculty of The Honors College and was
accepted in partial fulfillment of the requirements for the degree of Bachelor of Arts in
Liberal Arts and Sciences.
SUPERVISORY COMMITTEE:
____________________________
Dr. Jon Moore
____________________________
Dr. Kanybek Nur-tegin
______________________________
Dean Jeffrey Buller, Wilkes Honors College
____________
Date
ii
ACKNOWLEDGMENTS
I am grateful for the family, friends, and mentors who have served an integral part
of shaping me into the man I am today. The support you provided throughout my journey
does not go unrecognized. My family has always been there to support me through all my
successes and failures, especially my mother, Kristina, my father, Michael, my brothers,
Greg and Dan, my grandparents, and my Aunt Cathy. I would like all the faculty and staff
at the Harriet L. Wilkes Honors College for providing me with an unparalleled academic
experience. I especially appreciate the help provided by Dr. Jon Moore for including me
in his research and Dr. Kanybek Nur-tegin for being an excellent teacher. I would like to
extend my appreciation to all my residents who I hope realize how important they are to
me. I’d also like to thank the staff I’ve worked with while working with Jupiter Housing,
especially Sammie Linton, Donald Vanpelt, Laura Kepler, and Cathy Ray. I appreciate all
those who have worked with me in my clubs including Jeff, Kia, Erin, Alyssa, Christy,
and Kendyl. The friends I’ve found on campus will always be treasured and are too
numerous to be mentioned. Special thanks to Colton Hoffer, Zach Merschdorf, Kelly
Aucello, Andrew Li, and Genesis Buendia. Thank you to Rachel Turn for your
unwavering support and friendship and the opportunity to work with you to make the
world a better place.
iii
ABSTRACT
Author:
Christopher Olbrych
Title:
Modeling Burrow Choice in Gopherus Polyphemus
Institution:
Wilkes Honors College of Florida Atlantic University
Thesis Advisors:
Dr. Jon Moore and Dr. Kanybek Nur-tegin
Degree:
Bachelor of Arts in Liberal Arts and Sciences
Concentrations:
Economics and Environmental Studies
Year:
2016
Gopher tortoise populations, declining due to habitat fragmentation and
degradation, are in need of revised management practices that take into account the
individual site’s needs and limitations. The site of concern in this research is the
Greenway in Jupiter, FL, which is suffering habitat degradation due to overgrowth driven
by a lack of controlled burns or alternative management methods on site. A simple
econometric model is developed characterizing the effects of environmental factors that
influence the occupancy of burrows by gopher tortoises. A greater understanding of
environmental factors affecting gopher tortoise habitat will allow land management
practices to best meet the needs of this keystone species at the Greenway nature area.
iv
TABLE OF CONTENTS
Introduction ..........................................................................................................................1
Gopher Tortoises and Land Management ........................................................................3
Figure 1: Abandoned Burrow and Canopy Overgrowth in Abacoa Greenway (VIa) .....5
Prior Modeling of Burrow Distribution ...........................................................................7
Methods..............................................................................................................................10
Site Description ..............................................................................................................10
Figure 2a: Aerial Photo of the Greenway Nature Preserve............................................10
Figure 2b: Range VIa in May 2007, six months after reduction mowing .....................11
Figure 2c: Range VIa in May 2016, almost 10 years after reduction mowing ..............11
Data Collected ................................................................................................................12
Table 1: Summary of Statistics ......................................................................................13
Figure 3: Greenway Range VIa Path Outlines with Burrow Locations.........................16
Modeling Methods .........................................................................................................17
Results ................................................................................................................................20
Table 2: Statistical results of probit model .......................................................................20
Discussion ..........................................................................................................................22
Conclusion .........................................................................................................................27
References ..........................................................................................................................28
v
1. INTRODUCTION
Choice is an essential element to consider in both humans and animals attempting to
maximize utility under conditions of limited space and resources. Economic models
provide frameworks that illustrate complex processes of behavior and reasoning under
constraints, including limited time, resources, or money. Used in the field of behavioral
economics, choice modeling attempts to consider and weigh all of the relevant factors in
the decision making process of an individual. Models commonly applied to humans,
including utility optimization and demand curves, can be applied to non-human species to
yield a useful framework for policymakers with some modifications of assumptions and
reasoning. Such a framework can guide conservation policy in mapping the preferences
of different species in a habitat and how various land management practices can best be
tailored to these needs. Better structured policies can improve existing habitat and further
habitat degradation.
A major focus in many conservation policies are populations of keystone species,
as they play a critical role in the environment.1Through their interaction with the habitat
and other species, keystone species enable the ecosystem to function. The loss of a
keystone species can have major negative effects on an environment so protecting these
species serve the interests of the whole ecosystem.
An example of a keystone species in South Florida is the gopher tortoise,
Gopherus polyphemus, which is considered a keystone species because they dig large
burrows that create unique microclimates for other species (Eisenberg 1983).Gopher
1
Keystone species are a species that has a disproportionately large effect in the communities and range in
which it occurs and, if removed, would change the ecosystem drastically.
1
tortoises are listed as a threatened species in Florida primarily because of significant
habitat loss, degradation, and fragmentation (Florida Administrative Code, 2007).2
Nature preserves are commonly set aside to provide habitat and protect populations of
gopher tortoises, but such reserves require human management.The23-acre range V1a in
the Abacoa Greenway in suburban Jupiter, FL is a tract of land that is currently suffering
from habitat degradation. Municipal restrictions on controlled burns and the infrequent
mowing of the property to reduce undergrowth, called reduction mowing, decrease the
habitat’s capacity to host gopher tortoises. The overgrowth of saw palmetto and slash
pine and decline of low-growing plants cause increasingly shaded ground result in a loss
of basking and foraging areas for gopher tortoises.
This paper explores factors that affect gopher tortoises burrow preferences so land
management practices can be tailored to site-specific conditions and preferences of
gopher tortoises. Focusing on the Abacoa Greenway, I use a regression model to analyze
the rate burrow occupancy based on a number of relevant environmental factors.
Independent variables affecting burrow activity include distance to food and water
sources, distance between burrows, burrow orientation, and degree of canopy cover. The
choice of variables is grounded in existing information on life history and should
contribute the model’s ability to explain differences in activity in burrows.
The rest of the paper is organized as follows. Section 1 provides information on
the life history on the gopher tortoise and its role in the habitat as well as an analysis of
the effectiveness of current land management practices. Section 2 discusses previous
2
Habitat degradation is the process of habitat becoming less suitable while habitat fragmentation occurs
when a large continues habitat is divided into smaller isolated parts.
2
studies and methods used in modeling tortoise burrow behavior having used differing
scopes. Section 3 describes the data. Section 4 explains the construction of the
econometric model and justification for included variables. Section 5provides the results
of the model. Section 6 analyzes the effectiveness and applicability of the model, both
statistically and in its relevance to the site and policymakers. Section 7 outlines the
results of the model.
1a.Gopher Tortoises and Land Management
Gopher tortoises serve as ecosystem engineers in their ranges as they improve the
ecosystem for themselves and other species by constructing burrows (Pike and Cook,
2013).3This burrow creation is the primary reason gopher tortoises are considered a
keystone species. Their burrows are expansive, up to 10-15 feet long, and can serve as
microhabitats for other animals. Over their range, gopher tortoises can share their
burrows with members of an estimated 350 species including other threatened species,
like the eastern indigo snake, and several species of special concern, such as the Florida
gopher frog and the Florida mouse (Kent et al., 1997).In scrub habitat common to
Florida, gopher tortoises prefer sandier soils that allow for easier burrowing and drainage
that prevents extended flooding in case of rain. In terms of food sources present in the
Greenway, preference is shown for small grasses and herbaceous plants such as
bahiagrass (Pasapalum notatum) and Mexican clover (Richardia spp.), but wiregrass
(Aristida stricta) and other low-lying vegetation are also options. Large open areas with
3
Ecosystem engineers are defined as a species that actively modifies or changes their habitat and affects
the availability of resources to other species.
3
limited canopy cover maximize exposure to the sun, which is required for nesting and
basking. In the long term, gopher tortoise protection policy should maintain or improve
the ability of the land to meet the needs of the gopher tortoise population, especially
considering their role as a keystone species.
Endemic to the southeast United States, most populations of gopher tortoise have
been declining, largely due to habitat loss and degradation (Diemer, 1992). To help
prevent further population declines, gopher tortoises are now protected throughout their
range, as threatened or endangered species in Georgia, Alabama, Louisiana, Mississippi,
and South Carolina, and Florida. Elements of management plans attempt to reduce
tortoise mortality through the use of a permitting system on any land being developed
that requires construction to relocate tortoises or reimburse the state for not doing so. In
efforts to increase populations, sites also aim to exclude predators, but the primary
method used is habitat management. While larger reserves with more space may be able
to host a larger population of gopher tortoises, small sites can be just as useful in the
overall restoration plan for the species. Tract size has been shown to have no significant
effect on the variety of vertebrate organisms, so there is as much reason to support a
small reserve in an urban area as there is to work in a larger park (McCoy, 1994). For
both small and large areas, the primary focus of habitat management plans is the control
of vegetation in its various stages of growth to promote a mosaic of vegetation density.
Correctly applied, habitat management creates new habitat or improves current habitat,
increasing the area’s carrying capacity.4 Acquiring new land to put under protection may
be useful, but improving current degraded habitat already under protection poses less of a
4
Carrying capacity is defined as the total population a habitat can sustain in the long term without
degrading the habitat.
4
financial cost and has the opportunity to have a greater benefit. Determining how
tortoises respond to changes in the physical landscape will allow policy makers to
improve current policy and aid gopher tortoise populations.
When there is no natural or manmade system of reduction, trees and vegetation in
an ecosystem will grow indefinitely to surpass optimal levels, making the habitat less
livable for gopher tortoises. It is important to consider that the forest growth, or
overgrowth, occurs in levels: a canopy, which consists of the treetops, and understory,
which includes shrubs, bushes, and other medium-sized trees. To an extent, canopy
growth is beneficial as trees provide shelter for new plants and stabilize the soil, but an
excess of canopy cover can overshadow and limit growth in the understory. Ground cover
is the major source of food for gopher tortoises consists. This reduces food sources and
basking opportunities for tortoises. An example of this on site is seen in Figure 1 where
extensive overgrowth of the underbrush and canopy limits ground cover and habitat for
Figure 1: Abandoned Burrow and Canopy Overgrowth in Abacoa Greenway (Range VIa)
5
gopher tortoise by crowding out space and resources.
Controlled burns are a common land management practice conducted in efforts to
improve gopher tortoise habitat through control of vegetation using fire. Overgrown
habitat, a common result of anthropogenic fire suppression, can reduce the quality of
habitat for tortoises. Typically scheduled every five to six years in pine flatwoods,
controlled burns reduce underbrush overgrowth in a manner that mimics the natural fire
cycle. In an environment not controlled by humans, dry organic matter accumulates on
the forest floor until ignited, usually by a lighting strike. Without fire suppression by
humans, burns are generally frequent enough that organic matter never would accumulate
in excess. With little fuel to feed them, burns consist of small low heat fires unable to
harm the canopy and leaving trees unharmed. If only understory is burnt, nutrients from
the ash of the fire would immediately be absorbed back into the soil, prompting the next
cycle of growth. During a controlled burn, the beneficial effects of a natural burn are
recreated and meet historically adapted needs of the environment. Burns are prevented
from extending outside the targeted areas through extensive planning, which includes
knowledge of wind patterns, use of trenches to prevent fire from spreading, and judicious
use of water. Although it is seemingly destructive, the process of burning is followed by
period of rapid growth and many of the plants and animals have adapted to survive and
even thrive in these fires. Many animals are unharmed by fire as they use gopher tortoise
burrows to hide from the fire. Sand pines, prevalent in scrub habitat, have adapted with a
closed pine cones that only releases seeds during a fire. After a fire, ash is present on the
ground with the seeds and serves as a nutrient-rich substrate for growth. A major
6
drawback of controlled burns is that they inconvenience nearby residential areas with
large amounts of smoke, and can pose a serious threat to nearby homes and businesses.
An alternative to controlled burns that can be used in areas that are urbanized is
the use of reduction mowing. Consisting of large grinders and mulchers shredding and
knocking down any underbrush, reduction mowing accomplishes the removal of
overgrown underbrush but has the disadvantage of leaving large amounts of organic
matter on the forest floor (Signore, 2007).This interrupts the natural fire cycle that
facilitates the recycling of nutrients quickly without decomposition and even prompts
reproduction in some native plants that have evolved in that habitat. If the area was
intentionally or unintentionally allowed to burn, there is a risk that the canopy could
catch fire. A canopy burn or crown fire would prompt a much larger hotter fire and cause
the destruction of the trees that would have been able protect emerging seedlings and
anchor the soil after the fire had passed. Despite these negative effects, the urban area
surrounding the study site dictates the use of reduction mowing over controlled burns. A
closer look at the effects of mowing on burrow distribution allows land management
policy to be constructed to mimic natural systems as much as possible, reduce the threat
of unplanned fire, and support species in the area.
1b.Prior Modeling of Burrow Distribution
Modeling burrow distribution in relation to environmental factors has been attempted in
other portions of the gopher tortoises range in North America, but with different scales. A
large-scale study was conducted in Fort Benning, Georgia, by Baskaran et al. (2006). A
smaller study at Florida Atlantic University Boca Raton Campus’s nature preserve was
7
conducted by Stewart in 1992. The two serve to outline different approaches to the same
issue of modeling burrow activity in response to features of the habitat. Both papers use
binomial logistic regression to predict the probability of gopher tortoise distribution
densities. A binomial logistic regression model is limited in output to two outcomes. Both
models generated by papers took a spatial approach to the data predicting whether or not
a burrow is expected at a given location. Baskaran et al. (2006) took a large-scale
geographic view compared to Stewart (1992). Based on a close site study in the public
lands at Fort Benning, the model was extended over using private lands unavailable for
direct survey but having known topographic features. Collecting data on features on a
larger geographic scale allowed for easy measurement of variables in the model using
Geographic Information Systems (GIS) mapping. Data collected in Baskaran et al. (2006)
included distance to the nearest stream, soil profile, distance to roads, type of plant cover
and trees, and land use data. The study in Boca Raton focused on physiognomic, or
visually apparent, features of the landscape to predict gopher tortoise densities, including
the vegetative cover of the area, the degree of canopy coverage, soil composition, and
distance between burrows. Given the smaller area of the study site considered in this
thesis, there is no need for large scale mapping as the area is generally homogenous in
land use and can be surveyed in person.
The models presented by Baskaran et al. (2006) and Stewart (1992) reached
similar conclusions despite the differences in methodology of the studies and variation
between study sites. Baskaran et al.’s (2006) model predicted the densities and locations
of burrows well within their area of direct survey in Fort Benning but provided less
accurate conclusions when applied to areas outside of the directly surveyed areas. Data
8
generated through GIS software was limited in how it interpreted large-scale data and
neglected relevant differences between areas. For example, pasture land looks very
inhabitable from a large geospatial scale, with its lack of trees and plenty of grass, but the
model missed the fact that ranchers tend to exclude tortoises from their property with
fences. Although limited by use of broad scale GIS data, the Baskaran et al. (2006) model
was generally able to conclude that soils with a low percentage of clay, a short distance to
a road, a long distance to a stream, and low vegetation cover would have the a higher
density of burrows.
Stewart (1992) reached a similar conclusion in that areas with less vegetation
cover, sandier soils, and more herbaceous cover had higher rates of occupancy. There
was high density of burrows found in locations where the model predicted they would not
be so dense, which called for a correction factor. Used in statistics, a high correction
factor applied to the data serves to correct the divergence between data and the model and
usually hints at a problem in the model. In this case, the need for this corrective factor
was attributed to the idea that the population limit, dictated by available resources, had
been reached, forcing tortoises to choose sub-optimal locations for their burrows. She
suggested that the habitat had become overgrown due to both uncontrolled invasive
species and lack of land management practices. The paper emphasized that overgrown
habitats are less suitable and the carrying capacity of the site could be increased by
periodic burning or clearing of shrubs in overgrown areas.
9
2. METHODS
2a.Site Description
Located in a suburban development, Abacoa, in the town of Jupiter, FL, the
segment of the Greenway nature preserve studied in this paper does not have a regular
schedule of burning nor have a consistent reduction mowing schedule. The specific area
of study is range VI, which is located south of Fredrick Small Rd and west of Central
Blvd. With the last reduction mowing done in late 2006, considerable overgrowth of the
habitat has occurred. The only regular management the area is currently receiving is the
maintenance and mowing of walking paths throughout the reserve. As seen in Figure 2,
walking paths on the perimeter, the area surrounding the remnants of an old east to west
cattle fence, and an area above a pipeline trending southeast to northwest are the only
major areas that are not overgrown. To the south and east of this upland area are
depressed dry detention basins for food control during heavy rains.
Figure 2: Aerial photograph of the Greenway Nature preserve.
10
Fig. 2b: Range VIa in May 2007, six months after the reduction mowing.
*Image from Google Earth
Fig. 2c: Range VIa in Feb 2016, almost 10 years after the last reduction mowing.
*Image from Google Earth
11
Excluding these areas, the land is now dominated by large stands of slash pines
(Pinus elliotii), thick understory of saw palmettos (Serenoa repens), approximately six to
eight feet in height, or other dense undergrowth species, such as especially dense patches
of gallberry (Illex glabrai). The homogeneity of vegetation and overgrowth of the
preserve reduces the availability of quality habitat. Through analysis of the developed
model, we can model behavior when gopher tortoises make when presented with choice
between suboptimal overgrown habitats compared to better habitat closer to the managed
areas of the paths. This knowledge can provide a site-specific answer as to how
policymakers can best manage the land.
2b.Data Collected
Considering the methods of Stewart (1992) and Baskaran (2006) and gopher tortoise
physiology, I collected data on key factors of the site relevant to burrow activity. The five
independent variables collected in the dataset include: the degree of canopy cover,
orientation of the burrow entrance, distance to forage sites, distance to human maintained
paths surrounding the area, and distance to local roads. A summary of essential data is
included in Table 1 below. The first three variables were collected while observing the
burrow on site while the latter two were generated using latitudes and longitudes
collected and GIS software. From previous research, the general locations of more than
250 burrows, with unknown degrees of activity or accessibility, were available in the
form of a reference map of the site. Due difficulty in finding burrows, normal rates of
abandonment or collapse of burrows, and a limited time frame for data collection, a
12
Table 1: Summary of Statistics
Variable
Description
const
Densi
n/a
Canopy
Density
North
Orientation
Northeast
Orientation
Northwest
Orientation
South
Orientation
Southeast
Orientation
Eastern
Orientation
Western
Orientation
Distance to
Forage Site
Distance to
Path
Distance to
Road
N
NE
NW
S
SE
E
W
DistForage
DistPath
DistRoad
Units
Collection
%
Densiometer
covered
Binary Compass
Mean
StdDev
Max
Min
6.79
21.34
98.00
0
0
0
1
0
Binary
Compass
0
0
1
0
Binary
Compass
.01
.03
1
0
Binary
Compass
0
0
1
0
Binary
Compass
0
0
1
0
Binary
Compass
0
0
1
0
Binary
Compass
0
0
1
0
Meters
Measuring
Tape
ArcGIS
5.56
5.02
20.00
0
21.10
23.59
83.24 0.16
ArcGIS
99.62
68.77
251.84 5.77
Meters
Tens of
Meters
*SW (Southwest Orientation) dropped from model
sample of only 84 burrows was collected. A sample size of 84 exceeds a generally
accepted minimum sample size of 40 for statistical models to yield sufficient degrees of
freedom. A larger sample would have been preferred, but time constraints and difficulty
were limiting factors. The range of sampling was as wide as possible given the
distribution of burrows on the site. While surveying, some burrows covered with
overgrown vegetation were less accessible and thus were difficult to survey leading to an
inherent bias in the data collection towards more easily found burrows. Generally, the
easiest burrows to survey were on the perimeter while the burrows in the interior were
more difficult. I attempted to balance out this bias by spending more time and effort in
13
the interior which yielded approximately 36 of the 84 total burrows surveyed being in the
interior.
To build the data set, I visited each site and recorded relevant data on each
burrow. In addition, I reflagged burrows as necessary and recorded GPS tags for burrows
so that future research on the site could use them. Portions of the dataset were collected
in the summer and winter of 2015 and the spring of 2016, but since the data being
collected was focused on burrows rather than the tortoises themselves, seasonal variations
in gopher tortoise behavior were limited. To be included in the model, each variable
being considered in the model requires a sound logical backing as to why it could affect
burrow distribution. Having only the most relevant variables allows for clarity in
interpretation of results and, for these reasons, the model only considers five variables.
Omitted variable bias is possible if an important variable is not included in the model and
could lead to underestimation or overestimation of the effect of other variables on the
probability of burrow activity. The variables included encompass the extent of major
factors known to affect behavior in gopher tortoises and omitted variable bias should be
limited.
The orientation of the burrow, recorded as N, S, E, W, NE, NW, SE, and SW, was
included because it may affect sunlight distribution at the burrow site or reveal a
behavioral preference on behalf of gopher tortoises. For reptiles behavioral
thermoregulation is needed to maintain consistent internal temperatures. To do so,
basking in sunny areas is used to raise core temperatures while retreating into shady areas
or back into burrows prevents them from overheating. The sand surrounding the entrance
of a burrow, called the apron, can give tortoises a place to bask during the early part of
14
the day. If the burrow is overexposed to sun, the tortoise may have to retreat far back into
the burrow to cool down leaving their burrow vulnerable to other entrants. With the sun
following an east-to-west path, orientation of burrows can affect the distribution of
sunlight. The data was coded as eight rows so that the model could properly differentiate
between directions.
A measure the density of canopy cover, Densi in Table 1, was included because
excessive canopy cover can directly degrade habitat by limiting basking opportunities.
Density of canopy also reduces grass cover on the forest floor and is expected to
negatively correlate to burrow activity. To quantify the density of canopy cover, I held a
convex mirror with a grid of etched lines, called a spherical crown densitometer, over
each burrow. A quantitative estimate of canopy density was derived from counting the
number of squares between the etched lines filled by canopy relative to sky. The result
was recorded as a percentage of the total canopy cover compared the total available
amount of sky in the surveyed portion of canopy. This gave a reasonable baseline for how
much sunlight is available for basking at the entrance of the burrow and how overgrown
the area is surrounding the burrow. Areas on the paths generally had less dense canopy as
they are maintained for recreation.
Distance to foraging site, DistForage in Table 1, records the distance in meters to
the nearest foraging source. These sources included wiregrass, forbs, and other grasses
that a gopher tortoise would consume as part of their diet. Depending on the location of
the burrow and how dense surrounding underbrush was, a combination of a digital sonar
range finder and a measuring tape was used to measure distances. The size of the patch or
specific species was not considered in data collection due to time constraints. In general,
15
gopher tortoises are mobile creatures that can travel for food but the degree to which they
consider the location of food sources in selecting burrows may be variable. Distance to
forage and distance to path in some cases were the same because the burrow was located
on or close to the path. Grasses and forb species are concentrated on the recreational
paths and provide an open grazing area for tortoises
For each burrow, I recorded latitudes and longitudes using a portable GPS unit
(Garmin eTrex) and recorded the orientation of the burrow opening with a compass. The
GPS coordinates were uploaded into ArcGIS and distances were calculated for DistPath
and DistRoad. The burrow locations and path overlay can be seen in Figure 3.
DistPath represents the distance in meters to maintained path areas, while
DistPath incorporates multiple other variables because paths have little to no tree cover
and are generally covered in grass and other forbs. Paths are regularly mowed and
Figure 3: Greenway Range Via Paths Outlines with Burrow Locations
*Burrow Numbers are indicated beside each burrow
16
maintained throughout the year so they are not overgrown with underbrush. Also, grass
grows on these paths supplying tortoises with a greater amount of food if their burrow
was nearby. Another element that is incorporated in the DistPath variable is human
interaction. In using the paths recreationally, humans may disrupt grazing activities or
accidentally collapse or damage burrows.
DistRoad represents the distance, in tens of meters, to two local roadways
adjoining the site. DistRoad is included because the roads may be a source of significant
human interaction affecting burrow activity. While paths serve light foot traffic, roads
have cars and truck constantly passing over causing vibrations that may collapse or
disturb nearby burrows. This disturbance may limit burrow choice. DistRoad includes
variations in DistPath to some extent because both roads are parallel to the northern and
eastern parts of the path.
2c.Modeling Methods
In a general sense, regression models are used to estimate the effects of
independent variables on a dependent variable. Each independent variable explains a
portion of variance in the dependent variable and the effect is included in the model as a
coefficient attached to the independent variables. The sizes and signs of the coefficients
represent the effects of the individual independent variables on the dependent variable. A
standard ordinary least squares regression model relates changes in the independent
variables to quantity changes in the dependent variable. Such a model does not apply well
to the research question being posed as the answer is limited to a binary choice between
activity and inactivity rather than continuous range measuring degrees of activity.
17
Binary choice models offer a solution to issue of the dependent variable being
limited to two options and a branch of binary choice models allow us to further expand
on what can be drawn from the model. Two commonly utilized models, the probit and
logit models, address the issue of limited dependent variable by predicting probability.
Both extend the basic regression model to predict the probability between a positive (1)
and a null (0) state, which will be defined as an active burrow (1) and an inactive burrow
(0). In this research, the probit model is chosen over the logit model because the probit
model assumes a cumulative normal distribution function to model the probability
distribution function. Normality in error distribution is an assumption in regression
analysis that, if broken, can generate misleading or inefficient estimates in the model.
Normality in error terms is relevant to regression modeling because normal distributions
are used to determine significance of estimates.
Figure 5 – General Statistical Probit Model
𝑝 𝑌 = 1|𝑋 = (𝛽0 + +𝛽1 𝑥1 + 𝛽2 𝑥2 … + 𝛽𝑛 (𝑥𝑛 )
The general statistical form of the probit model, seen in Figure 5, relates the
effects of changes in the independent variables (x) to changes in probability in burrow
activity. Coefficients are estimated such that they best model the collected results in the
sample. These coefficients are inputted into the probability distribution function () and
a slope is produced which summarizes the effect of an independent variable on the
probability of an event occurring.
The coefficients produced in the model cannot be interpreted as changes in
probability that a burrow is occupied. The effect of an independent variable on the
dependent variable is its marginal effects calculated as the derivative of the probability
18
function with respect to the given independent variable seen Figure 6. This process yields
an interpretation of how much each unit change in an independent variable affects the
probability of a positive result in the dependent variable.
Fig 6. Derivative of Probit Model
𝑑𝑝 𝑑(t) 𝑑𝑡
=
∗
= (𝛽1 + 𝛽2 𝑥)𝛽2
𝑑𝑥
𝑑𝑡
𝑑𝑥
Significance of estimates in the model is determined through the use of z-scores.
Using the average probability while considering the degree of deviation from that mean
in the data, z-scores calculate the whether or not the probability of an event is in the
normal probability distribution. Given whether the event is more or less probable
compared to the average, z-scores can be positive or negative. The absolute value shows
how abnormal the probability of an event occurring and a higher absolute value indicates
that there is one or more independent variables driving that strong deviation from the
mean. Z-scores higher than 1.95 or lower -1.95 are considered at the 5 percent level, a
commonly accepted level of significance.
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3.RESULTS
The independent variables included in the model differ in degrees of statistical
significance, predicted influence on the probability of an active burrow and relevance to
land management practices. The results of the model created are summarized in Table 2
below. In terms of overall results of the model, the model generated correctly predicts
83.3% cases of activity so the variance in the dependent variable is well explained by the
predictors included in the model. A test of significance considering the null hypothesis of
normally distributed data reaffirms that the probit model was correctly chosen. This is
supported by a p-value of .4983, which indicates that null hypothesis that the errors are
distributed normally cannot be rejected
Table 2:Statistical Results of the Probit Model
Variable
Coefficient
z-value
1.3431
2.3740
-0.0398
-1.5505
0.2036
0.6951
-1.0761
-0.6223
-0.8886
0.7112
-0.0440
-0.0415
-3.3140
-2.4310
0.2936
0.7915
-1.6380
-0.9558
-1.4550
0.8717
-1.0670
-4.3230
-0.0135
-0.5611
0.0652
0.1954
-0.3966
-0.2290
-0.3328
0.1907
-0.0149
-0.0141
0.0120
3.5960
0.0041
const
Densi
N
NE
NW
S
SE
E
W
DistForage
DistPath
DistRoad
Cases correctly predicted: 70/84 (83.3%)
Test for Normality of Residual: p-value:0.4943
*SW dropped from model
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Slope
In terms of individual independent variables, five variables estimated in the model
have z-scores indicating significance. Density of tree canopy yielded a z value of -3.3140
indicates a strong level of significance at the 1 percent level. Each percent increase in
canopy density is associated with a 1.35 percent decrease in probability of a burrow being
active. Distance to forage sites was determined to be statistically significant with a zscore of -1.067 and distance to path held significance with a z-core of -4.3230.The model
estimates a 1.41 percent decrease in probability of activity with each meter further away
from the path. Distance to the road is also significant with a z-value of 3.5960. The
marginal effect indicates that, for every 10 meter increase in distance to the road, a 4.1
percent increase in the probability of an active burrow occurred
Considering orientation of burrows, only North-oriented and South-oriented
burrows showed statistical significance in the model, with z values equal to 3.314 and z
equal to 2.431, respectively. The marginal effect predicted for North-facing burrows is a
56.11 percent decrease in probability of an active burrow. For a South-facing burrow, a
39.66 percent decrease in probability of an active burrow is predicted. Other orientations
were not significant in the prediction of burrow activity.
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4.DISCUSSION
Considering the high degree of overgrowth, I expected Densi to be a significant variable
with a large influence on burrow activity. The model’s findings are consistent with
denser canopy reducing burrow activity by blocking light and limiting basking. Basking
is an essential element in the thermoregulation of reptiles and access to both cool and
warm areas is required. The apron, the sandy outer edge of burrow, usually provides a
warm place while tortoises can retreat into the burrows to cool down. The degree to
which increased canopy cover affects activity is core to the research as it has such a large
ecological effect if left unmanaged. Indirectly, grasses and other forest floor vegetation
cannot grow as well. The lack of foraging sites in overgrown parts of site limits the
potential habitat of gopher tortoises and forces them to travel long distances.
In terms of orientations, northern and southern orientations are preferred on the
site. Possible explanations for this include the available terrain as most of the burrows
were on exposed slopes and the orientation of these slopes may force selection rather than
individuals choosing between burrows. South-facing burrow entrances are constantly
exposed to full sun possibly limiting the tortoise’s ability to retreat into the burrow and
cool off while preventing other tortoises from entering. Large catchment basins to control
flooding have expansive open slopes are present on all except the northern side of the
site. Tortoises may build burrows into slopes as they are easier to construct and have
more stable entrances. The distribution of burrows might be biased due to the terrain
rather than behaviorally driven selection between existing burrows. Additionally, northfacing burrows could be selected against because the apron of the burrow is only partially
exposed to full sun. An apron that does not receive adequate sunlight requires the
22
tortoises to fully exit the burrow, leaving the individual more at risk to potential predators
(e.g coyotes and raccoons) or another tortoise taking over the burrow.
The other orientations included in the model did not show any statistical
significance, which does not allow for definite conclusions to be drawn to their relevance.
They may or not be preferred or have a major effect on burrow activity. The influence of
burrow entrance orientation may be limited in its overall influence or scope due to
multiple effects that contribute to the orientation of burrows on the site and the effects of
different orientations. For example, in some areas of the site, burrows in the area are all
on an east-facing slope, which does not allow for other burrow orientations.
Distance to walking path, DistPath, is significant in the model. Proximity to the
walking path surrounding the site includes access to more abundant forage sources with
grasses covering the path and decreased canopy cover due to regular clearing. It also
means the possibility for increased interactions with humans. The combined effects of the
grasses present for foraging and availability of basking areas seem to overweigh the
frequency of negative interactions with humans or predators as the tortoises treat the path
as a resource rather than a hazard.
DistRoad has a limited effect on probability of gopher tortoise inhabiting a
burrow and it is possible that significance is entangled due to the road’s proximity to the
path. While tortoises can dig out of the site, the fence provides a degree of separation
between burrows and the road. The degree to which tortoises are negatively affected by
the noise and light pollution coming from local roadways and any vibrations that may
weaken or disturb their burrows is likely matched by the decreased canopy density along
the paths near the road.
23
Distance to forage, DistForage, is a measure of the distance in meters from the
burrow to the closest visible grass or forbs and is not significant in the model.
Conclusions may be limited because the density of canopy cover affects the distribution
of foraging opportunities. Other limitations may results from being unable properly
account for all the variations and preferences in terms of gopher tortoise diet. In addition,
there was no measure of a tortoise’s willingness to move moderate distances to access
food sources. There also may have been limitations to the results in the limited species
considered as the targets for data collection. Forbs and grasses were used as the target
species as that is their preferred diet, but other vegetation may have been unseen or not
considered as edible. Further research could better describe the differences in vegetation
by conducting full vegetation surveys.
Considering the model as whole, the statistically significant variables and their
effects revealed the underlying preference towards basking opportunities and food
sources when tortoises choose to occupy a burrow. This confirms the applicability of
those life history traits to the population on this site and allows for a clearer interpretation
of this population’s needs. Additional data from other nearby populations and distant
populations is needed to draw conclusions past this one site. Uneven distribution of active
burrows on the site signals how the population is responding to habitat degradation.
While preference toward having increased basking areas and food sources is common
knowledge in the research, the adaptations tortoises have made in their behavior in
response to the site and resulting implications are the truest merits of the model. Burrow
activity showing such strong preference towards closeness to paths combined with
avoidance to high density canopy cover reveals that gopher tortoise populations in the
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greenway adapt to overgrowth of canopy cover by moving closer to paths. While land
managing authorities do not allow controlled burns at this site, steps can be made to open
up the canopy and reduce the overgrowth of the understory.
Considering the revealed preferences of the gopher tortoise populations seen in
the model towards an open canopy and less dense underbrush, policy aimed towards
these ends best meet the needs of the site. Some options available to policymakers
include selective logging to reduce canopy cover and the use of reduction mowing.
Selective logging would remove trees in the densest portions of the site to reduce overall
canopy cover. A downside of removing trees manually is the natural cycle of
decomposition and return of nutrients to the soil is interrupted and grasses and forbs may
be less abundant or take longer to grow. In the short term, this is beneficial and will allow
for growth of grasses and let in sunlight for basking and foraging. Selective logging is
also limited in that it only targets large trees while some of the main drivers of
overgrowth on the site are five to nine-foot tall stands of saw palmetto. Reduction
mowing, using large grinders and mulchers, can be used to remove these stands.
Reduction mowing leaves trees intact much like a fire would but leaves a large amount of
organic material on the ground that needs time to decompose. Naturally a layer of ash
would allow for the quick absorption of nutrients but decomposition is a longer process
that slows the process of re-growth of the site. This organic layer also quickly dries up
and poses a more severe fire hazard that could permanently damage the habitat and
surrounding area. These methods target the specific needs of gopher tortoises on this site
as revealed by the data but have their own limitations as well. These negative aspects of
these alternatives methods serve the site better than inaction and I would recommend the
25
use of these methods on the site with efforts to mitigate or reduce the negative effects of
each option.
Addition and removal of variables from the model when calculating can reveal
alternatives to the proposed model that may better explain dependent variables or reveal
interrelations between data. The model response to the removal of variables did not yield
a better predictive capacity. Including only the variables determined to be significant, the
alternative model only correctly predicted 79.8 percent of cases and the distribution of
errors, while still normal at the p-value 0.10537, signals that the distribution of errors was
more spread out than the proposed model. Variables could not be added to the model due
to time limitations though possible relevant additions are proposed below.
Further data collection on vegetation on site, development of additional variables
affecting burrow activity, and survey of additional burrows would better increase the
predictive capacity of the model. In particular, a more comprehensive vegetation study
would allow for a better understanding of what vegetation land managers would need to
promote or remove to best serve the tortoise populations in the Greenway. Other
variables that may have an effect on burrow activity that were not collected in this dataset
may include whether or not the burrow is located on a slope and the proximity to each
burrow in relation to other burrows. Slopes may provide additional stability to burrow
and be easier for tortoises to occupy. Another variable to consider is the proximity to
other burrows. Gopher tortoises may aggregate in small areas during mating periods
because of the desire to be closer to the burrows of females or may aggregate to a lesser
extent to reduce competition between individuals for the same foraging and basking
resources.
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5. CONCLUSION
The model developed explores factors that gopher tortoises consider when inhabiting
burrows through the development of a probit regression model predicting burrow activity
in the Abacoa Greenway. Statistically significant variables include burrow orientation,
degree of canopy cover, distance to path, and distance to road. Major conclusions include
that the site in particular is undergoing an overgrowth in canopy cover that is negatively
correlated to probability of a burrow being active. The model also noted a higher
probability of burrow being active closer to paths, which can be interpreted as tortoises
adapting to the overly dense interior canopies. The path area is maintained regularly and
kept clear of overgrowth while also having an excess of grass and food sources local to
supplement a gopher tortoise diet. Negative results of being close to the path are that
there is a greater probability of negative human interaction whether through harassment,
accidental burrow collapse, or poaching.
Reduction mowing and selective canopy options are some the most preeminent
options to improve the habitat by targeting the variables emphasized as the most
important in the model. Land managers have the opportunity to expand habitat naturally
while abiding by the limitations of the site by specifically targeting canopy overgrowth
and the decrease in available food resources on the forest floor major as the underlying
causes of the activity shift.
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REFERENCES
Baskaran, Latha, Virginia Dale, Rebecca Efroymson, and William Birkhead. 2006.
“Habitat Modeling Within a Regional Context: An Example Using Gopher
Tortoise.”American Midland Naturalist, 155(2): 335-351.
Del Signore, Vincent. 2007. “The Effects of Reduction Mowing on Gopher Tortoises
(Gopherus polyphemus).”Florida Atlantic University Honors College
Undergraduate Thesis.
Diemer, Joan. 1992. “Gopher Tortoise (Gopherus polyphemus).” Rare and Endangered
Biota of Florida, 3(1): 123-127.
Florida Administrative Code. 2007. 68A-27.003.
Kent, Donald. 1997. “Observations of Vertebrates Associated with Gopher Tortoise
Burrows in Orange County, Florida.”FloridaScientist,60(3): 197-201.
Laessle, Albert. 1958. “The Origin and Successional Relationship of Sandhill Vegetation
and Sand-Pine Scrub”. Ecological Monographs, 28(4): 361–387.
McCoy, Earl and Henry Mushinsky. 1994. “Effects of Fragmentation on the Richness of
Vertebrates in the Florida Scrub Habitat.” Ecology, 75(2): 446-457.
Stewart, Mary Catherine. 1993. “Habitat Structure and Dispersion of Gopher Tortoises on
a Nature Preserve.” Florida Scientist, 56(2): 70-81.
John F. Eisenberg. 1983. “The gopher tortoise as a keystone species”. In Proceedings of
the Annual Meeting of the Gopher Tortoise Council, 1(4):1-4.
Pike, David and James Cook. 2013. “Burrow-dwelling Ecosystem Engineers Provide
Thermal Refugia throughout the Landscape.” Animal Conservation, 16(6):694703.
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