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ARTICLE
Hidden in plain sight: Integrated population models to
resolve partially observable latent population structure
Abigail J. Lawson
1
| Patrick G. R. Jodice
2
| Thomas R. Rainwater
1,3,4
|
Kylee D. Dunham
5
| Morgan Hart
6
| Joseph W. Butfiloski
6
|
Philip M. Wilkinson
4
| K. W. McFadden
2†
| Clinton T. Moore
7
1
Department of Forestry and
Environmental Conservation,
Clemson University, Clemson,
South Carolina, USA
2
U.S. Geological Survey, South Carolina
Cooperative Fish and Wildlife Research
Unit, Clemson University, Clemson,
South Carolina, USA
3
Baruch Institute of Coastal Ecology and
Forest Science, Clemson University,
Georgetown, South Carolina, USA
4
Tom Yawkey Wildlife Center,
Georgetown, South Carolina, USA
5
U.S. Geological Survey, Eastern
Ecological Science Center, Laurel,
Maryland, USA
6
South Carolina Department of Natural
Resources, Columbia,
South Carolina, USA
7
U.S. Geological Survey, Georgia
Cooperative Fish and Wildlife Research
Unit, Warnell School of Forestry and
Natural Resources, University of Georgia,
Athens, Georgia, USA
Correspondence
Abigail J. Lawson
Email: ajlawson@nmsu.edu
Funding information
South Carolina Department of Natural
Resources, Grant/Award Numbers:
2009094, 20100899
Handling Editor: Robert R. Parmenter
Abstract
Population models often require detailed information on sex-, age-, or
size-specific abundances, but population monitoring programs cannot always
acquire data at the desired resolution. Thus, state uncertainty in monitoring
data can potentially limit the demographic resolution of management
decisions, which may be particularly problematic for stage- or size-structured
species subject to consumptive use. American alligators (Alligator
mississippiensis; hereafter alligator) have a complex life history characterized
by delayed maturity and slow somatic growth, which makes the species
particularly sensitive to overharvest. Though alligator populations are subject
to recreational harvest throughout their range, the most widely used monitor-
ing method (nightlight surveys) is often unable to obtain size class-specific
counts, which limits the ability of managers to evaluate the effects of
harvest policies. We constructed a Bayesian integrated population model
(IPM) for alligators in Georgetown County, SC, USA, using records of
mark–recapture–recovery, clutch size, harvest, and nightlight survey counts
collected locally, and auxiliary information on fecundity, sex ratio, and somatic
growth from other studies. We created a multistate mark–recapture–recovery
model with six size classes to estimate survival probability, and we linked it to
a state-space count model to derive estimates of size class-specific detection
probability and abundance. Because we worked from a count dataset in which
60% of the original observations were of unknown size, we treated size class as a
latent property of detections and developed a novel observation model to make
use of information where size could be partly observed. Detection probability
was positively associated with alligator size and water temperature, and nega-
tively influenced by water level. Survival probability was lowest in the smallest
size class but was relatively similar among the other five size classes (>0.90 for
†
Deceased October 28, 2014.
Received: 4 March 2022 Revised: 29 July 2022 Accepted: 4 August 2022
DOI: 10.1002/ecs2.4321
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properly cited.
© 2022 The Authors. Ecosphere published by Wiley Periodicals LLC on behalf of The Ecological Society of America. This article has been contributed to by U.S.
Government employees and their work is in the public domain in the USA.
Ecosphere. 2022;13:e4321. https://onlinelibrary.wiley.com/r/ecs2 1of22
https://doi.org/10.1002/ecs2.4321
each). While the two nightlight survey count sites exhibited relatively stable
population trends, we detected substantially different patterns in size
class-specific abundance and trends between each site, including 30%–50%
declines in the largest size classes at the site with greater harvest pressure. Here,
we illustrate the use of IPMs to produce high-resolution output of latent popula-
tion structure that is partially observed during the monitoring process.
KEYWORDS
Alligator mississippiensis, Bayesian, harvest, hierarchical model, integrated population
model, population dynamics, population structure, South Carolina, state uncertainty
INTRODUCTION
In wildlife populations, demographic variation in repro-
ductive output, predation risk, or harvest pressure is fre-
quently reflected in sex-, age-, or size-specific abundances
and vital rates (Servanty et al., 2011; Tuljapurkar
et al., 2009). Management decision-making often relies
on monitoring data, which is thereby limited in its pre-
dictive power by the data’s demographic resolution—the
scale at which individuals can be assigned to a demo-
graphic group (Lyons et al., 2008; Sauer & Knutson,
2008). Demographic data with high resolution may con-
tain sex, age, or size specificity, whereas low-resolution
data collapse multiple demographic groups. While inten-
sive forms of monitoring (e.g., mark–recapture studies)
are likely to produce high-resolution demographic data
in which the state of interest (e.g., sex, size) can be
precisely observed, such options may be too costly or
time-intensive to implement on broad spatiotemporal
scales (Kendall et al., 2019; Saracco et al., 2008).
Alternatively, survey-based monitoring methods (e.g.,
counts, occupancy) or opportunistic data collection offer
the potential for lower expense and increased spatial cov-
erage but may come at the cost of added uncertainty for
some or all states of observed individuals (Fischer
et al., 2021; Saracco et al., 2008; Tenan et al., 2017). A
common manifestation of state uncertainty is partial
observability, in which the demographic state (e.g., sex,
age, reproductive status) cannot be determined to the
desired level of resolution for all observed individuals
(Conn & Cooch, 2009). Managers of monitoring pro-
grams with extensive partial observability may resort to
reducing the data’s demographic resolution to avoid
extensive censoring or to reduce bias in population pro-
jections (Caswell, 2001), which may ultimately constrain
the desired demographic resolution of management
actions (e.g., size-structured vs. total individual harvest
quotas) and increase uncertainty in their outcomes.
Leveraging data with a relatively low resolution to iden-
tify latent population structure within populations is an
emerging area of interest, as it has the potential to produce
higher resolution results for a lower cost. For example,
Link et al. (2003) developed a model to derive age-
structured abundance and survival estimates from a
64-year census of endangered whooping cranes (Grus
americana) using aggregated, low-resolution data that dis-
tinguished only two classes of birds: first-year individuals
and adults. In an extension of the N-mixture model frame-
work (Royle, 2004), Zipkin et al. (2014)incorporatedaclas-
sification probability term into the detection process to
account for state uncertainty when assigning individuals to
one of two demographic groups (e.g., adult/juvenile, male/
female) during sampling. Though each approach offers a
different mechanism to enhance low-resolution data, both
require relatively large sample sizes of low-resolution
datasets (Link et al., 2003;Zipkinetal.,2014)thatmaynot
be feasible for many monitoring programs.
Integrated population models (IPMs) offer a flexible,
efficient tool to jointly analyze multiple data streams,
thus increasing the precision of parameter estimates and
providing a standardized error structure to reduce uncer-
tainty (Besbeas et al., 2002; Schaub & Abadi, 2011).
Incorporating multiple data streams enables the IPM to
account for all demographic processes that influence
changes in population growth rate. A comprehensive
demographic model allows the estimation of additional
parameters, both ecological (e.g., immigration) and
observational (e.g., classification rate), that would be
inestimable for any of the individual model components
in isolation (Arnold et al., 2018; Schaub & Abadi, 2011;
Zipkin & Saunders, 2018). Therefore, IPMs present an
opportunity to synthesize multiple datasets, often of dis-
similar demographic resolutions, in a common frame-
work to identify latent population structure.
The American alligator (Alligator mississippiensis)isa
species of ecological and economic importance in the
southeastern United States (Mazzotti & Brandt, 1994).
Throughout their life span, alligators undergo an approxi-
mately 10-fold increase in body length paired with onto-
genetic shifts in diet and habitat use (Nifong et al., 2015;
2of22 LAWSON ET AL.
Subalusky et al., 2009; Wilkinson et al., 2016), allowing
the species to fill different ecological roles (e.g.,
meso- vs. apex-predator) as they grow (Rootes &
Chabreck, 1993a; Somaweera et al., 2013,2020).
Alligators require 11–16 years to reach sexual maturity
and continue to reproduce throughout their life span,
which likely exceeds 65 years (Wilkinson et al., 2016).
However, substantial uncertainty exists regarding both
the factors that influence asymptotic body size and the
influence of body size on fecundity (Larriera et al., 2004;
Thorbjarnarson, 1996; Wilkinson, 1983; Wilkinson
et al., 2016; Zajdel et al., 2019).
Following two decades of protection by the Endangered
Species Act triggered by overharvest, alligators are currently
managed under consumptive use programs throughout most
of their range (Rhodes, 2002). For size- or age-structured
species, like alligators, harvest decisions may cause signifi-
cant changes to population structure and ultimately, popula-
tion growth (Hauser et al., 2006; Koons et al., 2006). In
addition to detecting changes in population structure,
high-resolution monitoring data may also be useful for
developing more biologically realistic predictive models to
evaluate the consequences of harvest decisions and inform
finer resolution harvest policies (e.g., size class-specific
quotas). Nightlight surveys (also known as spotlight surveys)
are the most widely used method to monitor crocodilians
(Bayliss, 1987; Strickland et al., 2018;thisstudy).However,
nightlight surveys often produce low-resolution count data
in which the majority of detected individuals cannot be
assigned to a specific age or size class (Balaguera-Reina
et al., 2018;Gardneretal.,2016;Skupien&Andrews,2017;
Strickland et al., 2018). For alligators in particular, a lack of
data regarding size class-specific population trends may
leave alligator populations particularly vulnerable to
harvest-induced population declines due to their complex
life history, delayed maturity, and long life span
(McIllhenny, 1935; Wilkinson et al., 2016).
We developed an IPM for an alligator population sub-
ject to spatially variable harvest pressure on the middle
coast of South Carolina, USA (Figure 1), near the northern
limit at which high densities of alligators occur. Specifically,
we synthesized data from a long-term, mark–recapture
study (1979–2017) and from low-resolution nightlight sur-
veys (counts; 2011–2016) with prolific uncertainty about
size class assignment of detected alligators, as well as clutch
size and harvest data (2011–2016). Our goal was to reduce
state uncertainty in count data through integration with a
high-resolution dataset within an IPM framework to pro-
duce abundance estimates that were specific for size classes
that spanned the entire size range. We also sought to obtain
size class-specific survival estimates and evaluate environ-
mental variables that influence detection probability in
nightlight surveys.
METHODS
Alligator management
The South Carolina Department of Natural Resources
(SCDNR) has administered alligator harvest (hunting) pro-
grams for private lands since 1995 and public waterways
since 2008 (SCDNR, 2017). Boat- and truck-based
nightlight surveys are the primary method used by SCDNR
to monitor alligator populations within the state. We used
SCDNR private and public harvest data from Georgetown
County (GXN) and a portion of Charleston County
(Figure 1) for 2011–2015 only, to overlap with the time
range of nightlight survey data. The SCDNR also adminis-
ters a nuisance removal (euthanasia) program that was
established in 1988. However, the vast majority of nuisance
take occurs near human population centers (SCDNR,
unpublished data), meaning that the nuisance alligators
were unlikely to be encountered on the nightlight counts
or mark–recapture study. See Appendix S1 for detailed
descriptions of the harvest programs, handling of harvest
records in the IPM.
Study area
We studied a coastal population of alligators in Georgetown
County, SC, USA (Figure 1; 2681 km
2
). The city of
Georgetown receives 78–184 cm of annual precipitation;
the dry season occurs during October–March, and the wet
season is during June–September. Mean temperatures dur-
ing the alligator’sactiveseason(April–October) range
between 17–27Cand8–14C during brumation
(November–March) (Wilkinson et al., 2016). GXN is com-
prised of extensive and diverse alligator habitat that
includes coastal marsh, wooded wetlands, and impounded
(diked) wetlands on a mixture of private and public lands.
For our analysis, we synthesized alligator private and public
harvest data, nightlight survey counts from multiple coastal
rivers, and mark–recapture–recovery and clutch size data
from the Tom Yawkey Wildlife Center (YWC; 6033 ha;
33.217N, 79.236W), all within or bordering GXN.
Tom Yawkey Wildlife Center
We captured alligators and surveyed for nests on South
and Cat Islands within the state-operated YWC, which has
been closed to alligator hunting since the early 1900s.
YWC is part of the headland that separates two river deltas
in GXN and is surrounded by marine (>35 salinity parts
per thousand; ppt) and brackish water habitats (5–35 ppt)
(Figure 1), where the mean tidal range is 116 cm
ECOSPHERE 3of22
FIGURE 1 Legend on next page.
4of22 LAWSON ET AL.
(https://www.saltwatertides.com/dynamic.dir/scarolina
sites.html). Our sampling area included tidal marsh
(2524 ha) and managed impounded wetlands (hereafter
impoundments; 1012 ha) in which the salinity ranged
from 0 to 35 ppt (Wilkinson et al., 2016). See Lawson et al.
(2020) for a complete description.
Coastal rivers
We conducted nightlight surveys (Bayliss, 1987) in coop-
eration with SCDNR along two routes: (1) a combination
of the Great Pee Dee and Waccamaw Rivers and (2) the
South Santee River (Figure 1). The Great Pee Dee and
Waccamaw route (GPD; 38.4 km) began at the Samworth
Wildlife Management Area boat ramp (33.475N,
79.186W) and formed a circuit, which included sections
from each river, and two excavated connecting channels.
The Great Pee Dee is a fairly narrow (30 m at the boat
launch in Figure 1)“red water”river indicative of high
nutrient loads, contrasted with the Waccamaw, which is
much wider (300 m at the stream gauge in Figure 1) and
classified as a “black water”river with fewer nutrient
inputs. The GPD survey route is surrounded by a combi-
nation of suburban homes, flooded forests, and naturally
tidal freshwater marsh in which salinities are <0.5 ppt
(Bennett et al., 1989; Conrads & Roehl, 2007). The South
Santee River route (SAN) started at the Santee Coastal
Reserve Wildlife Management Area boat ramp
(33.154N, 79.354W) and extended 12.8 km upstream.
The South Santee River is surrounded by a series of fresh
and brackish water impoundments like those contained
on YWC. Within each survey route, salinity typically
ranges from 0.0 to 26.7 for SAN and 0.0 to 4.9 for GPD
from early May to mid-August (A. J. Lawson,
unpublished data).
Demographic data collection
Mark–recapture and nesting studies
We captured alligators of all size classes to evaluate
demographics as part of a long-term (1979–2017)
mark–recapture study on YWC (Appendix S1: Table S1a).
Alligators were captured using a combination of modified
baited trip-snares (Murphy & Fendley, 1973),
walk-through snares placed on trails or nest sites
(Wilkinson, 1994), camera traps placed at nest sites (for
recaptures), snare poles, snatch hooks (Cherkiss
et al., 2004), and hand captures (for small alligators only).
Annual capture effort (CE) and techniques varied to
accommodate different research foci over the 39-year
time span, which targeted different demographic groups
or individuals (description in Wilkinson et al., 2016).
Except for incidental carcass discoveries or poaching of
marked individuals, no data were collected during
1983–1992, 1994–2004, and 2008 (Appendix S1:
Table S2).
Captured adults (>180-cm total length [TL]) were
uniquely marked using the methods and materials
described in Lawson et al. (2020). For individuals
>120-cm TL, we determined the sex through cloacal
examination (Chabreck, 1963) and recorded two standard
body measurements (0.5 cm): TL and snout-vent length
(SVL). Hatchlings (≤30-cm TL) captured at nests were
marked with individually identifiable web tags
(1979–1982: Conservation Tags 1005-1) and a
scute-notching (1979–1993) and toe-clipping (1979–1993)
combination that reflected their hatch year (tail scute)
and nest number (toe), whereas nonhatchling alligators
were assigned individually identifiable scute-notching
and toe-clipping patterns. Alligators <120-cm TL were
measured for TL only and were released without deter-
mining sex (P. M. Wilkinson, personal communication).
After marking and measurements, all alligators were
released to their capture sites.
Concurrent with the mark–recapture study, we
conducted aerial surveys using a helicopter (MD 500 and
R44) to locate alligator nests (2011–2016). Helicopter sur-
veys (2–3) were conducted approximately one week apart
between 10 June and 30 June each year. Upon discovery
from the air, personnel located each nest on foot within
3–72 h and opened the cavity to record the number of
eggs (clutch size). Empty nest mounds were revisited
daily until oviposition occurred or until the nest was
determined to be false or abandoned (i.e., no visits by the
female after 7–10 days).
FIGURE 1 Map depicting the location of an American alligator capture–mark–recovery study (1979–2017) at the Tom Yawkey Wildlife
Center (YWC; indicated by the dashed border), and two nightlight survey routes (thick black lines) on the Great Pee Dee and Waccamaw
Rivers, and the South Santee River (2011–2016), which forms the border between Georgetown (GXN) and Charleston Counties (black star in
inset) in South Carolina, USA. The black squares represent boat launches (BL) or stream gauges (SG) that recorded water levels (WLs) and
water temperature (WT) for each survey route. The upper inset shows South Carolina in relation to the alligator’s distribution, whereas the
lower inset shows the four alligator management units in South Carolina subject to a public harvest program: 1, Southern Coastal; 2, Middle
Coast; 3, Midlands; and 4, Pee Dee (GXN shaded dark gray).
ECOSPHERE 5of22
Nightlight survey counts
We conducted nightlight surveys on the two routes from
2011 to 2016, excluding 2012, using flat-bottomed boats
equipped with 44,700–85,700 W (60–115 horsepower) out-
board motors. Surveys were initiated ≥30 min after sunset
and completed ≥90 min before sunrise. We did not conduct
surveys the night of a full moon or within 1 day, during
extreme water-level (WL) events, or during heavy rain or
wind (>15 km h
1
). We generally restricted surveys to
weekdays to avoid increased recreational boat traffic on
weekends. Each year we conducted two to eight replicate
surveys for each route from early May to mid-August, prior
to the onset of alligator nest hatch. At the beginning and
end of each survey, we recorded the date, time, personnel
present and their designated roles, and environmental con-
ditions. We recorded air temperature (0.1C) and wind
speed (0.1 km h
1
) using a Kestrel 4000 weather meter,
and measured water temperature (WT) (0.1C) at approxi-
mately 3.2-km intervals using YSI EcoSense 300A with a
1-m probe. While conducting each survey, we recorded
waypoints for our start and end locations, water measure-
ment sites, alligator locations, and route deviations using a
GPS unit (Garmin GPSMap 62).
During each survey, the boat traveled 5–24 km h
1
along the river centerline as two personnel (observers)
shined spotlights (Brinkman Q-Beam Max Million III
Spotlight, 3 10
6
candlepower) into the adjacent water
to detect alligator eyeshine (Bayliss, 1987), which reflects
a distinct red-orange color from the tapetum lucidum.
Each survey used two or more trained observers to detect
eyeshine (see Lawson, 2019 for additional details regard-
ing observer roles and training). When safe and logisti-
cally feasible, we approached observed alligators (≥10-m
distance) to estimate snout length and assign individuals
into one of six size classes (Table 1) based on TL:
(1) hatchling: ≤30 cm; (2) juvenile: 30–121 cm; (3) sub-
adult: 122–182 cm; (4) small adult: 183–243 cm; (5) large
adult: 244–304 cm; or (6) bull: ≥305 cm. Size classifica-
tions were assigned based on an allometric relationship
between snout length and TL (Chabreck, 1966), where
2.54 cm (1 in.) snout length equates to 30 cm (1 ft)
TL. When a size classification could not be confidently
made, the individual was classified as either one of two
general age classes that approximately distinguish repro-
ductively mature from immature animals, that is,
“unknown adult”(≥183-cm TL) or “unknown immature”
(<183-cm TL). Because of their correspondence with age,
we refer to these groupings as age classes for ease of pre-
sentation. If the alligator could not be confidently placed
into any size or age category, we classified the alligator as
“unknown.”
TABLE 1 Summary information for American alligators (Alligator mississippiensis) by size class and sex.
Size class, jName
TL
range (cm)
Female proportion,
FP
j
(mean SD) Sex
SVL
range (cm)
Growth
prob., ψ
ja
Immature
1 Hatchlings ≤30 0.72 0.02 F ≤15.51 1.00
M≤15.60 1.00
2 Juveniles 31–121 0.37 0.02 F 15.51–63.03 0.16
M 15.60–63.40 0.17
3 Subadults 122–182 0.47 0.02 F 63.03–94.55 0.19
M 63.40–95.10 0.26
Mature
4 Small adults 183–243 0.47 0.07 F 94.55–126.06 0.09
M 95.10–126.80 0.19
5 Large adults 244–304 0.35 0.10 F 126.07–157.58 0.01
M 126.80–158.50 0.12
6 Bulls ≥305 0.00 F ≥157.58 0.00
M≥158.50 0.00
Note: Size classes were divisions of total length (TL), the distance from snout tip to tail tip. Ranges of TL were the basis of classifying detected alligators during
nightlight surveys conducted in coastal South Carolina, USA (2011–2016). In a mark–recapture–recovery study at the Tom Yawkey Wildlife Center (Figure 1;
1979–2017), assignments into TL size classes were based on a measurement of snout-vent length (SVL), the distance from the snout tip to the vent posterior,
expressed as TL through a sex-specific allometric relationship between SVL and TL (Wilkinson et al., 2016). Growth probability (prob.) reflects the sex-specific
probability of an individual in size class jat time ttransitioning to j+1att+1, conditioned on survival.
Abbreviations: F, female; M, male.
a
Growth probabilities for j=2, …, 5 were estimated though Markov chain Monte Carlo simulation (Appendix S3), whereas all others were fixed values.
6of22 LAWSON ET AL.
Auxiliary data
We used breeding and nesting productivity data from
multiple studies conducted in coastal South Carolina
from 1980 to 1982 (Wilkinson, 1983), and sex ratio infor-
mation derived from the YWC mark–recapture data and
previous studies (Rhodes & Lang, 1996; Woodward, 1996)
to parameterize our models. Appendix S2 contains an
expanded methodological description and auxiliary data
summary.
Integrated population model
Multistate mark–recapture–recovery model
We used a multistate mark–recapture–recovery model
(Lebreton et al., 1999,2009) to estimate size class-specific
demographic parameters. Multistate models enable
state-specific estimation of apparent survival (φ), detec-
tion probability (p.m), recovery probability (r), and the
probability of transitioning among states (ψ) conditioned
on survival. Our model included six live states (size clas-
ses) and two dead states (Figure 2), in which the parame-
ters were estimated through a marginalized likelihood
(Yackulic et al., 2020).
We constructed capture histories for all marked indi-
viduals from the YWC study population and assigned
each individual to a size class used in the classification of
nightlight survey counts. However, we inferred TL for
size class assignment from measurements of SVL
(Table 1), as alligators often lose portions of their tail as
they age; classification by converting from SVL thus
prevented the artifact of size shrinkage of animals in sub-
sequent captures. Because the allometric relationship
between SVL and TL (among individuals with intact
tails) differed by sex in our study population (females:
TL =SVL 0.517; males: TL =SVL 0.520; Wilkinson
FIGURE 2 Life cycle diagram of the American alligator that served as the basis of the multistate mark–recapture–recovery estimation
model and the abundance state process of the integrated population model. Each circle consists of a single state ( j). States 1–6 represent live
states as defined by different size classes (Table 1), in which the dashed circles represent immature (nonbreeding) size classes (1, hatchlings;
2, juveniles; 3, subadults) and the solid circles reflect mature (breeding) size classes (4, small adults; 5, small adults; 6, bulls). The closed,
solid gray circles reflect additional states recognized in the mark–recapture–recovery estimation model: A recently dead state ( j=7) and an
absorbing, terminal, dead state (j=8). The bolded ψ
j
terms reflect growth or transition probabilities that were fixed to 1.0. Each year,
surviving individuals (φ
j
) could remain in the same size class (1 ψ
jSex
; self-looping arrows) or graduate to the next sequential size class
(ψ
jSex
; straight right-pointing arrows). Individuals that did not survive (1 φ
j
; lower arcs) could either enter the recently dead state if their
carcass was recovered (e.g., incidental carcass discovery of a marked individual) with probability r, and then compulsorily transition to the
absorbing state in the following year, or directly enter the absorbing state if their carcass was not encountered (1 r). Note that rwas set to
0 for the hatchlings and juveniles because we did not observe any dead recoveries of these size classes. The upper arc arrows show the
reproduction mechanism of the abundance state process as reproductive contributions of females in size classes 4 and 5. Fecundity (f
j,i,t
)is
the product of size class and site-specific (survey route; i) abundance at time t(N
j,i,t
); female proportion in the size class (FP
j
; Rhodes &
Lang, 1996; Woodward, 1996); proportion of breeding females (BR; Wilkinson, 1983); and nest survival (NS) and the average annual clutch
size (CL
t
) at the Tom Yawkey Wildlife Center (Wilkinson, 1983), summed for each reproductive size class. Alligators that emerge from the
nest must survive 0.75 of the year to enter state 1 by the time of the subsequent nightlight survey.
ECOSPHERE 7of22
et al., 2016), we created a series of SVL-based
(in centimeters) size class thresholds for each sex
(Table 1). For capture events in which SVL was not mea-
sured, we predicted SVL based on allometric relation-
ships with other measurements taken or on estimated
somatic growth from a previous capture, or we used TL
directly if the tail was intact.
Captures of alligators at a size at which sex could
not be determined through cloacal examination
(TL < 120 cm; Chabreck, 1963) were treated in one of
three ways in the preparation of data for analysis. If the
alligator was later captured or found dead at a size at
which sex could be determined, the sex determined at
that final encounter was assigned to all previous encoun-
ters. If the alligator was never reencountered at a size at
which sex could be determined and if size class assign-
ment at the time of capture was ambiguous without
knowledge of the animal’s sex (e.g., the size class assign-
ment of an animal measuring 15.55-cm SVL is
sex-dependent; Table 1), then the alligator was excluded
from the analysis. However, if size class assignment at
the time of capture was unambiguous, then sex was ran-
domly assigned to all captures of the alligator by drawing
a value from a Bernoulli distribution in which the success
parameter represented the proportion of females for each
size class from the literature (hatchlings: 0.72—Rhodes &
Lang, 1996; juveniles 0.37—Woodward, 1996).
Mortality (recovery) observations were assigned to an
observable, “recently dead”state in the year that they
were detected, which allowed for correct accounting of
the fact that the animal had lived up to that point.
Animals either probabilistically (not observable) or deter-
ministically (observed dead recoveries) transitioned to an
absorbing “dead”state that persisted for all subsequent
occasions in the animal’s state history. Note that we only
included mortality observations from incidental carcass
encounters, adverse trapping events, or poaching in the
multistate model, and we did not include public or pri-
vate lands harvest records. Though YWC is closed to
hunting, over the course of the study four individuals left
the study area and were harvested in the private and pub-
lic hunts, though these events were not reflected in the
individual’s capture history. As legal harvest was likely a
negligible source of mortality of YWC alligators, we
accounted for harvest in the IPM by incorporating
the broadscale harvest data into the abundance model
(h
j,i,t1
in Figure 3) rather than the multistate model. As
a result, the multistate mark–recapture–recovery model
estimates apparent survival, in which mortality and per-
manent emigration are confounded, that is reflective of a
protected population, in which legal harvest exposure is
greatly reduced, but not eliminated. Our model assumes
that population vital rates were similar for YWC and our
two nightlight survey sites, with the exception of harvest
outside YWC, which we modeled as additive to natural
mortality (see Abundance state process).
Alligator somatic growth patterns differ between
sexes (Wilkinson et al., 2016; Wilkinson & Rhodes, 1997);
therefore, we parameterized transition (somatic growth)
probabilities from each size class (j) according to sex
ðψSex
jÞ. However, we captured relatively few hatchlings or
juveniles for which we could eventually determine sex
based on a later recapture (Appendix S1: Table S1b), lead-
ing us to assume that sex-specific transition probabilities
for smaller size classes would be poorly estimated if
derived solely within the multistate model. Therefore, in
a separate analysis, we estimated sex-specific size class
transition probabilities by fitting a somatic growth model
to an expanded mark–recapture dataset and simulating
growth of individual alligators (Appendix S3). Values
from this simulation then served as fixed values of ψSex
j
in the multistate model (Table 1).
The state process component of our multistate
framework represented a typical life cycle model in
which individuals could initially be encountered in one
of j=1, …,6sizeclasses(Figure2). From time tto t+1,
the state process allowed for four possibilities, in which an
individual alive in size class jcould survive with probability
φ
j
and either (1) remain in the same size class with proba-
bility (1 ψSex
j) or (2) transition to the j+1 size class
with probability ψSex
j. Alternatively, an individual could
not survive (1 φ
j
) and either (3) transition into the
recently dead state (j=7) in which they were recovered
through a carcass discovery with probability r
j
, or (4) tran-
sition to the absorbing dead state (j=8) in which they
were not recovered (1 r
j
). The probability of remaining
within the bull size class (j=6), conditioned on survival,
was fixed to 1.0, as were transitions from hatchling to
juvenile size class (given survival), the recently dead state
to the absorbing dead state, and the probability of
remaining in the absorbing dead state. The structure of
our model rendered some transitions impossible, includ-
ing “skipping”a size class (i.e., nonconsecutive growth
transitions), “shrinking”(i.e., moving from larger to
smaller size classes), or “resurrection”(i.e., moving from
a dead state to one of the live states). Lastly, we used an
identity link to model time-invariant survival probability
(φ
j
) for each specific size class and for recovery probabil-
ity (r) for size classes 3–6, both of which used vague
priors from a uniform distribution (0,1). The full transi-
tion matrix is provided in Appendix S4.
For the observation process component of the multi-
state model, an individual alive in size class jcould either
be detected with probability p.m
j
or not detected with
probability 1 p.m
j
. We placed additional constraints on
both the process and state components to improve
8of22 LAWSON ET AL.
parameter estimation and model convergence. We fixed
r
1
,r
2
,p.m
1
,andp.m
2
to zero because the variation in CE
for the smallest immature size classes ( j≤2) over our
study precluded us from recapturing tagged alligators in
the hatchling or juvenile state in subsequent occasions,
and we did not observe any dead recoveries of these size
classes. We encountered relatively few dead alligators in
the larger size classes (j≥3; Appendix S1: Table S1);
therefore, we constrained the r
j
for those size classes to
asinglerecoveryparameterr. Due to the inconsistent
CE over time (Appendix S1: Table S2), we did not con-
sider temporal- or individual-level (beyond size class)
variation in the survival parameters of the state process,
though we did consider a covariate that allowed
temporal as well as size class specificity of detection
probability (p.m
j
).
FIGURE 3 Directed acyclic graph of an integrated population model (IPM) for American alligators in Georgetown County, SC, USA.
Parameters for which we computed posterior distributions are represented by circles, whereas observed data and extrinsic variables
(nonupdated; shaded gray) are rectangular, with indexing for size class (j), site (survey route; i), temporal survey replicate (k), and year (t). The
growth formula represents an alligator growth dataset (g; Wilkinson et al., 2016) that was used to derive transition probabilities for sex-specific
growth (ψ
jSex
) outside of the IPM framework (Appendix S3). The large, dashed box represents the multistate mark–recapture–recovery model
that used a mark–recapture dataset with dead recoveries (m), ψ
jSex
, and a capture effort covariate (CE
j,t
) to estimate probabilities of recovery (r),
detection (p.m
j,t
), and apparent survival (φ
j
)—a shared parameter within the integrated likelihood for the state-space abundance model. Input
to the fecundity formula included the proportion of females in each size class (FP
j
; Rhodes & Lang, 1996; Woodward, 1996), the proportion of
breeding females (BR; Wilkinson, 1983), and nest success (NS) and average annual clutch size (CL
t
) at the Tom Yawkey Wildlife Center
(Wilkinson, 1983). The bottom row of boxes within the state-space model reflect different types of nightlight survey data: Sized (c
j,i,k,t
), Aged
(immatures: age.im
i,k,t
, adults: age.ad
i,k,t
), or Unknown age (unk
i,k,t
). These data were used to estimate two latent quantities specific to size class,
the number of individuals encountered of known or unknown size (Detections; d
j,i,k,t
) and those encountered with size determined to at least
immature/adult specificity (Aggregated; a
j,i,k,t
), with their associated detection probabilities (p.d
j,i,k,t
)and(p.a). Detection probability p.cwas
conditioned on the size-classified counts. We modeled the effects of water level (WL
i,k,t
) and temperature (WT
i,k,t
)assurveyreplicate-level
covariates on p.d
j,i,k,t
. The true number of individuals in each size class (N
j,i,t
) was estimated in the process component of the state-space model
by fecundity (f
j,i,t
), ψ
jSex
,andφ
j
, as well as the previous year’s true number of individuals (N
j,i,t1
) and harvest (h
j,i,t1
). We note that the true
number of individuals in the first timestep (N
j,i,1
) is not part of the state-space model, so the dashed arrow between N
j,i,1
and N
j,i,t1
reflects
these collapsed dynamics.
ECOSPHERE 9of22
Count observation model
We developed a state-space model to estimate size
class-specific abundance and detection probability, in
which the observation component incorporated the count
data from temporally replicated nightlight surveys.
Nightlight survey data were comprised of three different
observation types that represented increasing levels of
demographic resolution: (1) “Unknown”includes indi-
viduals that were detected at site iduring survey replicate
kin year t, but could not be placed into any size or age
class (unk
i,k,t
in Figure 3); (2) “Aged”includes observa-
tions in which the individual was assigned to either the
immature (size class junknown but ≤3; age.im
i,k,t
in
Figure 3) or mature (size class junknown but ≥4; age.
ad
i,k,t
in Figure 3; Table 1) age class; and (3) “Sized”
includes observations in which the individual was
assigned to one of the six size classes (c
j,i,k,t
in Figure 3).
To estimate size class-specific abundance, we created
three submodels in which numbers of alligators detected
at increasingly finer demographic resolution were probabi-
listically linked to numbers (possibly latent) at coarser
resolutions. The Detections level, the coarsest level of reso-
lution, included all three observation types—Unknown,
Aged,andSized. We defined the latent quantity d
j,i,k,t
as
the number of alligators detected at site iduring replicate
kin year tthat belonged to size class j. This quantity is
generally unobservable because not all alligators detected
that belong to size class jcan be assigned to size class j.
We modeled d
j,i,k,t
as the outcome of a binomial process
with success probability p.d
j,i,k,t
and the number of trials
N
j,i,t
, that is, the abundance of alligators in size class jat
site iat time t:
dj,i,k,tbinomial Nj,i,t,p:dj,i,k,t
:ð1Þ
Thus, p.d
j,i,k,t
is the overall detection probability for individ-
uals of size class j, regardless of whether an individual of
that class can be assigned as such. The Aggregate level, the
next finest level of demographic resolution, considers the
Aged and Sized observation types. We defined the latent
quantity a
j,i,k,t
as the number of alligators assigned either to
a size or age class that belonged to size class j. Again, a
j,i,k,t
is generally unobservable because it includes alligators
belonging to size class jthat cannot be determined as such.
We modeled a
j,i,k,t
as the outcome of a binomial process
with success probability p.aand index d
j,i,k,t
:
aj,i,k,tbinomial dj,i,k,t,p:a
:ð2Þ
Parameter p.ais the probability that an individual, condi-
tional on its detection, can be placed into either an aggre-
gated age class (age.im
i,k,t
, age.ad
i,k,t
in Figure 3)ora
specific size class. Lastly, the Classified level, the finest
level of demographic resolution, includes only the Sized
observations. Here, the count of individuals for a particu-
lar size class, site, and occasion, c
j,i,k,t
, is a directly
observable quantity. We modeled c
j,i,k,t
as the outcome of
a binomial process with success probability p.cand
index a
j,i,k,t
:
cj,i,k,tbinomial aj,i,k,t,p:c
:ð3Þ
Parameter p.cis the probability that an individual, condi-
tional on having been identified to at least an age class,
can be placed into a specific size class. Thus, through the
parametric linkages among models, all three observation
types ultimately inform size class-specific population
abundance. We did not consider size, site, survey, or tem-
poral variation for the detection probabilities for the
Aggregate and Count levels; thus, these parameters lack
the size (j), site (i), survey (k), and time (t) indexing.
We used a series of sum constraints within JAGS to
link the raw observations to the quantities in
Equations (1)–(3) above (Plummer, 2017):
unki,k,t¼X
6
j¼1
dj,i,k,tX
6
j¼1
aj,i,k,t,ð4Þ
age:imi,k,t¼X
3
j¼1
aj,i,k,tX
3
j¼1
cj,i,k,t,ð5Þ
age:adi,k,t¼X
6
j¼4
aj,i,k,tX
6
j¼4
cj,i,k,t:ð6Þ
In Equation (4), the number of Unknown observations
(unk
i,k,t
)mustequalthedifferencebetweennumberof
Detection observations, which includes all three data cate-
gories (Unknown, Aged, and Sized), and the number of
Aggregate observations (Aged and Sized only). Equation (5)
constrains the number of age.im
i,k,t
observations, which
must equal the number of Aggregate immatures (j≤3)
minus Classified immatures. Similarly, in Equation (6), the
number of age.ad
i,k,t
observations must equal the number of
Aggregate adults (j≥4) minus Classified adults.
Lastly, while our model accounts for imperfect detec-
tion, it assumes no errors in age- or size-class assignments,
though we note that such errors are likely to influence esti-
mates resulting in imprecision and/or bias (Kellner &
Swihart, 2014). While we cannot verify the absence or com-
position of size classification (over- or underestimation)
errors in our data, observers were not permitted to size alli-
gators until sufficiently trained (see Lawson, 2019 for
details regarding observer training).
10 of 22 LAWSON ET AL.
Abundance state process
For the state process component of our state-space model,
we integrated the likelihoods for abundance (N
j,i,t
)from
the observation component of the state-space model and
apparent survival parameters (φ
j
) from the multistate
mark–recapture–recovery model (Figure 3). To complete
the IPM specification, we parameterized a fecundity for-
mula using mean annual clutch size data from YWC (CL
t
)
and extrinsic reproductive variables (Appendix S2:
Table S1) that were stochastically sampled from beta dis-
tributions in each iteration to incorporate parametric
uncertainty (Appendix S2: Table S1). Within our life cycle
model (Figure 2), only females in size classes 4 and 5 could
contribute to population growth. Though females (F) were
allowed to enter size class 6 (i.e., ψF
5> 0), we never
documented a female with a measurement of SVL that
would place it in size class 6 (Appendix S1: Table S2). As
such, we defined annual fecundity (f
i,t
) for site iin
year tas:
fi,t¼N4,i,tFP4
ðÞþN5,i,tFP5
ðÞ
fg
BR NS CLt
ðÞ,
ð7Þ
in which the number of individuals in each of size
classes 4 and 5 is multiplied by the proportion of females
for that respective size class (FP
j
; Woodward, 1996)to
derive the number of females within the breeding size
classes. The number of females is multiplied by the pro-
portion of breeding females (BR), apparent nest survival
(NS) rate, and average annual clutch size (CL
t
) for the
YWC population. We used the same subcomponents of
fecundity for females in size classes 4 and 5 because our
auxiliary data did not reflect size-related differences
(Appendix S2). Moreover, in a sensitivity analysis of
American crocodile (Crocodylus acutus) life-history
parameters, Briggs-Gonzalez et al. (2017) reported that
age-specific variation in fecundity had minimal impact
on the population growth rate.
We modeled the number of young-of-the-year
hatchlings (YOY; individuals hatched in the current
year) on occasion tat site ias a Poisson outcome, with
fecundity from the current year as the mean and vari-
ance term:
YOYi,tPoisson fi,t
:
Because we completed all nightlight surveys before
hatching in the current nesting season, we never
encountered YOY hatchlings. Therefore, all hatchlings
(j=1) encountered during nightlight surveys in year
twere hatched in year t1 and survived for approxi-
mately six to nine months, and both fand YOY are
modeled as functions of conditions in year t1, not
year t. The number of individuals in the hatchling
size class (N
1
) observed during surveys in year tat
site iis binomially distributed as a function of the
nine-month hatchling survival rate and YOY in
year t1:
N1,i,tbinomial YOYi,t1,φ0:75
1
,
s1,i,tbinomial N1,i,t1,φ1
ðÞ:
We assume that the survival rate of hatchlings to the
juvenile stage, φ
1
, also applies to YOY alligators prorated
over a nine-month timescale.
To model transitions into all other size classes j≥2,
we used a series of binomial distributions to implement
the survival and somatic growth processes. First, we
modeled the number of surviving individuals in year
t(s
j,i,t
) as a stochastic outcome of a binomial draw based
on the size class-specific survival probability (φ
j
) and the
total number of individuals to survive harvest in the pre-
vious year:
sj,i,tbinomialðNj,i,t1hj,i,t1,φjÞ,ð8Þ
in which N
j,i,t1
denotes the number of individuals
alive prior to harvest in year t1 and h
j,i,t1
is the num-
ber of individuals harvested in size class jat site iin t1.
Size classes in our study population were exposed to
different levels of harvest pressure, as public harvest
regulations for alligators in South Carolina prohibit
the take of individuals <120-cm TL. Therefore, we
assumed h
j,i,t
=0 for j≤3 in Equation (8). We note
that Equation (8) assumes an additive harvest mortality
structure, as opposed to compensatory harvest mortality
in which harvested individuals are assumed to represent
a“surplus”of individuals that were likely to die over the
same time period (Williams et al., 2002). We believe the
additive structure used in the model is appropriate because
when given the opportunity, alligator hunters generally
select for relatively larger size classes that have the
highest survival rates, based on the few existing crocodil-
ian demographic studies (Briggs-Gonzalez et al., 2017).
Moreover, multiple historical examples demonstrate
that crocodilian populations are relatively sensitive to
overharvest consistent with additive mortality, particularly
with a fixed-quota harvest strategy as used in South
Carolina (Bradshaw et al., 2006; Marioni et al., 2021;
SCDNR, 2017; U.S. Fish and Wildlife Service, 1967;Webb
et al., 1984).
Next, the number of individuals growing (transitioning)
from size class jto j+1 was distributed binomially:
ECOSPHERE 11 of 22
gj,i,tbinomial sj,i,t,FP
jψF
jþ1FPj
ψM
j
,j≥2,
in which the probability of growth was the sum of
the size- and sex-specific growth probabilities (ψSex
j) mul-
tiplied by their respective sex proportion (FP
j
for females
and 1 FP
j
for males) from the number of surviving indi-
viduals (s
j,i,t
). Because the transition into the juvenile
stage by surviving hatchlings is compulsory, we model
transition probability of hatchlings simply as follows:
g1,i,tbinomial N1,i,t1,φ1
ðÞ:
Finally, the total number of individuals for size class jis
the sum of growing individuals from j1(g
j1,i,t
) and
the total of nongrowing (retained) individuals from size
class j, determined by subtraction of growing individuals
(g
j,i,t
) from the total that survived (s
j,i,t
):
Nj,i,t¼gj1,i,tþsj,i,tgj,i,t
:ð9Þ
Lastly, we were interested in describing general popula-
tion trends within each site. Therefore, we obtained
NTOT
i,t, the sum of all size classes (j=1, …, 6) for site iat
time t, as a derived parameter.
Covariate structures and selection
Our model included the effects of three covariates. First,
we created a covariate for the mark–recapture–recovery
detection probability (p.m
j,t
) to account for temporal vari-
ation in CE, which varied in both duration (i.e., number
of capture days) and intensity (i.e., number of capture
methods used or personnel). Unfortunately, traditional
metrics of CE or trap days were not consistently recorded.
Experiences by the authors and other principal investiga-
tors on the YWC study indicated that at least one alliga-
tor was captured each field day (P. M. Wilkinson &
T. R. Rainwater, personal communications). Therefore,
for each day that an alligator was captured, we assigned a
“1”if only one capture technique was used, or a “2”if
two or more techniques were used. We summed the cap-
ture day scores within each year and z-standardized
(mean: 0.0, SD: 1.0) the scores across years.
Both WL and WT are known to influence detection
probability of alligators in nightlight surveys (Fujisaki
et al., 2011; Waddle et al., 2015); therefore, we modeled
these effects for the count-based detection probability
(p.d
j,i,k,t
). We used the average river gauge height in feet
(0.01) during the survey as a measure of WL. Due to
structural and hydrological differences between the two
survey sites, we z-standardized WL within each river for
a more generalizable interpretation of results. We used
the YSI measurements recorded during each survey to
determine the average WT (0.1C), and we
z-standardized across both routes.
All four detection probabilities (p.m
j,t
,p.d
j,i,k,t
,p.a,
and p.c) were modeled with a logit link, though they dif-
fered in the number of covariates and other constraints:
logit p:mj,t
¼βjþβCE CEt,
βjnormal 0,0:37ðÞ,
where β
j
denotes the baseline mark–recapture detection
probability for each size class, and β
CE
is the effect of the
CE, assumed common across size classes. We held the
p.aand p.cterms constant across size classes, with no
covariate effects:
logit p:aðÞ¼βa,
logit p:cðÞ¼βc,
βa,βcnormal 0,0:37ðÞ:
For the p.dterm, we used a different formula for hatch-
lings compared with the other size classes. Alligator
youngareknowntoremainingroupswiththeirmother
over the first two years of life (McIllhenny, 1935).
Hatchlings occurring in groups could violate the
assumption of independent detections required of
N-mixture models (Royle, 2004), which is known to bias
parameter estimates (Martin et al., 2011). We therefore
modeled hatchling detection (p.d
1,i,k,t
)asa
beta-binomial process:
d
p:di,k,tbeta αi,k,t,βi,k,t
,
αi,k,t¼θp:d1,i,k,t,
βi,k,t¼θ1p:d1,i,k,t
ðÞ,
in which θis the exponentiated form of a normally
distributed variable with a mean of zero and 0.37 SD.
We included a size class trend term for count detection
that was not included in the covariate selection
procedure:
logit p:dj,i,k,t
¼βdþβd:TjþβWL WLi,k,tþβWT WTi,k,t,
βd,βd:Tnormal 0,0:37ðÞ,
12 of 22 LAWSON ET AL.
where β
d
reflects the baseline detection probability, β
d.T
is
the size class (j) trend term, and β
WL
and β
WT
are the
effects of WL and WT, respectively. All terms in the
detection models were given a Jeffreys prior, which is
weakly informative on the logit scale.
We used indicator variable selection with a “slab and
spike prior”to evaluate the potential influence of the CE
covariate on detection probability p.m
j,t
and the WL and
WT covariates on detection probability p.d
j,i,k,t
(Hooten &
Hobbs, 2015; Miller, 2002). Indicator variable selection is
useful for assessing the degree of support for each set of
candidate predictors (Hooten & Hobbs, 2015). Using
this approach, the beta coefficient for covariate i(β
i
)is
defined as the product of a binary indicator variable (w
i
)
and a regression coefficient γ
i
:
βi¼wiγi,
wiBernoulli p:wi
ðÞ
,
p:wiuniform 0, 1ðÞ,
γinormal 0, σγ
:
In each Markov chain Monte Carlo (MCMC) iteration,
the ith covariate enters the model as a predictor when
w
i
=1 and is excluded from the model when w
i
=0.
Thus, the posterior mean of w
i
roughly reflects the proba-
bility of the covariate’s inclusion in the model. As an
additional metric of covariate support, we compared the
relative “model weights,”in which the inclusion or exclu-
sion of covariates in specific combinations induces eight
unique models (2
3
=8 models; m
1–8
in Appendix S4:
Table S1) and the weights reflect the proportion of itera-
tions in which the model (covariate combination) was
selected. A complete list of model parameters, their defi-
nitions, and priors is given in Appendix S4: Table S2,
whereas a summary of extrinsic variables and their sto-
chastic distributions is provided in Appendix S2:
Table S1.
Model fitting
We used Bayesian inference to estimate all IPM
parameters and derived quantities; to calculate their pos-
terior distributions, we used MCMC in JAGS 4.3.0
(Plummer, 2017) run from the jagsUI package
(Kellner, 2021) in program R (R Core Development
Team, 2019). We ran three chains with a 50,000-iteration
adaptive phase, followed by 600,000 iterations with the
first 20,000 discarded as burn-in, and a thinning
rate of 40; this yielded a combined chain of 14,500 MCMC
samples. We used noninformative wide priors for all
parameters and checked for convergence by visually
inspecting the trace plots and confirming that the
Gelman–Rubin diagnostic statistic (b
R; Gelman & Rubin,
1992) satisfied our accepted convergence threshold
(b
R< 1.10). Parameter estimates are presented as the
median of the posterior distribution with their 95% credible
intervals, unless otherwise noted.
RESULTS
Multistate mark–recapture–recovery
Our mark–recapture–recovery dataset was comprised of
557 individuals of known-sex (females: 275; males: 282;
Appendix S1) and 282 unknown-sex individuals that
were randomly assigned to a sex prior to data analysis.
The majority of unknown-sex individuals were hatchlings
captured prior to 1981 (Appendix S1: Tables S1 and S2).
Apparent survival was lowest for the hatchling size class
(0.160; 95% CI 0.093–0.242) and was relatively high and
similar for all other size classes (Figure 4). Among the
nonhatchling size classes, apparent survival was highest
for juveniles (0.981; 0.921–0.999), followed by large adults
(0.977; 0.956–0.992), subadults (0.967; 0.919–0.994),
small adults (0.960; 0.929–0.986), and bulls (0.960;
0.930–0.983). Apparent survival estimates were more pre-
cise for size classes that had more capture observations
(Figure 4; Appendix S1: Table S1).
The size mark–recapture–recovery detection probabil-
ities (p.m
j,t
) at mean CE were highest for large adults
(0.080; 0.063–0.101), followed by small adults (0.074;
0.052–0.103), bulls (0.046; 0.030–0.069), and lowest for
subadults (0.025; 0.008–0.061). The CE covariate had a
high probability of inclusion (ω
CE
=1.00; Appendix S4:
Table S1) and a positive effect on p.m
j,t
(β
CE
=0.870;
0.689–1.054), indicating a 2.39-fold increase in odds of
detection per standard deviation increase in the covari-
ate. Recovery probability for size classes j> 2 was esti-
mated to be 0.160 (0.092–0.260).
Abundance state-space model
The two count detection covariates were WL (WL
i,k,t
in
Figure 3) and WT (WT
i,k,t
). We found a positive trend
across size classes for p.d
j,i,k,t
(β
T
=0.336; 0.185–0.479;
Figure 5) and strong support for the inclusion of both WL
(ω
WL
=0.81; Appendix S4: Table S1) and WT
(ω
WT
=1.0). WL had a negative effect (β
WL
=0.167;
0.218 to 0.115) on p.d
j,i,k,t
, whereas WT was positive
ECOSPHERE 13 of 22
FIGURE 5 Estimated size class-specific (j) American alligator detection probabilities (p.d
j
) during nightlight surveys in coastal South
Carolina from 2011 to 2017. CRI, credible interval.
FIGURE 4 Posterior distributions of American alligator apparent survival probabilities (φ) for six size classes within the protected Tom
Yawkey Wildlife Center in coastal South Carolina, USA, 1979–2017. The solid black circles and error bars indicate the mean and standard
deviation; note the different y-axis scales in each panel (left: hatchlings, right: nonhatchlings).
14 of 22 LAWSON ET AL.
(β
WT
=0.211; 0.152–0.271). Collectively, the model
containing all covariate terms (m
8
; CE, WT, and WL)
received the largest share of model weight (ω: 0.81;
Appendix S4: Table S1). The probability of size class
determination given the ability to distinguish between
immature and adult (p.c: 0.795; 0.762–0.825) was greater
than the probability of being able to discern either age or
size given detection (p.a: 0.379; 0.356–0.403).
Total alligator abundance NTOT
i,t
for each site
showed subtle contrasting patterns (Figure 6). In GPD,
total abundance remained relatively stable, varying
between extremes of 1305 (959–1755; 2016) and 1414
(1108–1815; 2012) alligators, whereas SAN exhibited a
clear peak in 2012 (1965; 1588–2456) followed by a con-
sistent annual decline through 2016 (1493; 1086–2031).
Both the average estimated density and total individuals
(2011–2016) appeared higher across years for SAN (22.28
alligators km
1
;NTOT
i,t:1711; 1331–2211) compared with
GPD (5.89 alligators km
1
;NTOT
i,t:1358; 1037–1781),
despite the latter site containing more habitat
(38.4 vs. 12.8 river km).
At the size class level, temporal patterns differed
between the two sites (Figure 7). Hatchling abundance at
both sites initially increased from 2011 to 2012 and then
continued to increase at a slower rate (GPD; range of
annual means: 167–331) or slowly decline (SAN; range:
158–515). Juveniles showed slightly contrasting, albeit
highly uncertain, abundance patterns, reflected by a
slight decline in GPD (range: 260–341) and a slight
increase in SAN (range: 266–330), whereas subadults
declined at both sites (GPD: 251–448, SAN: 255–462).
All the adult size classes showed contrasting patterns
among sites. On GPD, small adults increased from 2011
to 2014 and then remained stable (range: 192–294),
whereas both large adult (range: 147–161) and bull abun-
dance (range: 56–64) remained relatively flat the entire
study period (Figure 7c). In contrast, all three adult size
classes on SAN initially declined, but appeared to stabilize
around 2014 or 2015, depending on the group (Figure 7d).
Small adults ranged from 322 to 414 individuals, whereas
large adults declined by 35% (range: 193–299) and bulls by
50% over the same period (range: 46–92).
DISCUSSION
We constructed an IPM that synthesized multiple
high-resolution datasets to resolve substantial state
uncertainty in coarse-scale census data to estimate size
class-specific abundance estimates for alligators. Linking
the detection parameters in our observation model
(p.d,p.a, and p.c) through a conditional structure was a
novel development that allowed us to make efficient use
of data collected at different resolutions of observer per-
ception. The parameter estimates produced by the IPM
provided important insights into alligator demography,
FIGURE 6 Posterior distribution of American alligator total abundance (all size classes) on the Great Pee Dee and Waccamaw River
(GPD; left panel) and South Santee River (SAN; right panel) in coastal South Carolina from 2011 to 2016. The dark gray shaded area
represents the 95% Bayesian credible interval (CRI).
ECOSPHERE 15 of 22
FIGURE 7 Size class-specific American alligator abundance posterior means with 95% Bayesian credible intervals (CRIs) from
nightlight survey counts on the Great Pee Dee and Waccamaw Rivers (left column) and the South Santee River (right column) from 2011 to
2016 in coastal South Carolina, USA. The top panels (a, b) show abundance estimates for immature size classes and the bottom panels (c, d)
show adult size classes.
16 of 22 LAWSON ET AL.
the detection process and nightlight survey design con-
siderations, and drivers of site-level alligator abundance,
which we discuss below, in turn.
The IPM we created is the first ever for crocodilians
(to our knowledge) and the survival probability estimates
derived from a multidecadal crocodilian mark–recapture
study are among the most comprehensive for this species.
The general pattern of low survival probability for the
smallest sizes or ages and high survival among larger size
classes has been observed in both American crocodiles
in southern Florida (Briggs-Gonzalez et al., 2017)
and Nile crocodiles (C.niloticus) in the Okavango Delta
(Bourquin & Leslie, 2012). Our estimates of hatchling
survival were markedly lower than those reported from a
mark–recapture study of alligators at an inland freshwa-
ter lake in central Florida (0.41 0.06 SE; Woodward
et al., 1987), which could be attributed to salinity regimes
in the two systems. Salinity, which is higher at YWC due
to its coastal location, adversely affects the physiology of
immature alligators and therefore may reduce survival in
this age class (Faulkner et al., 2018; Laurén, 1985).
While our study presents a large leap forward in under-
standing crocodilian vital rates, future studies are needed
to identify potential environmental or anthropogenic
drivers of variation in these rates, in both protected and
harvested populations.
Our study further elucidates how environmental,
demographic, and study design-related factors may influ-
ence alligator detectability during nightlight surveys, the
primary method used for monitoring crocodilians
(Bayliss, 1987; Fujisaki et al., 2011; Shirley et al., 2012).
The negative relationship between WL and p.d(hereafter
detection) we reported is well documented for nightlight
monitoring of crocodilians (Fujisaki et al., 2011; Waddle
et al., 2015; Woodward & Marion, 1978); as water levels
rise, alligators have more water surface area and depth in
which to submerge and evade detection. Similarly, alliga-
tor activity (i.e., visibility) is positively correlated with
WT (Smith, 1975), which subsequently has a positive
influence on detection, though the relationship may dif-
fer among size classes due to metabolic requirements
(Lang, 1987). The positive trend we detected between alli-
gator size class and detectability was also reported by
Fujisaki et al. (2011) and is also likely driven by visibility,
as the eyeshine of larger alligators is likely more obvious
to observers than those of smaller individuals.
Our detection estimates (range: 0.01–0.07) were similar
to those reported from Florida by Waddle et al. (2015) for
all size classes (0.11) and Fujisaki et al. (2011) for small
(0.03) and large alligators (0.09). However, our detection
probability estimates were substantially lower than
Gardner et al.’s(
2016) 0.5 estimate for all size classes in
coastal North Carolina. Differences in detection
probability among studies could reflect differences in
population structure as well as study design, specifically
the temporal spacing between replicate surveys. Gardner
et al. (2016) conducted three temporally replicated sur-
veys within one week to meet the assumption of geo-
graphic closure. In contrast, the two temporal replicate
surveys used by both Waddle et al. (2015) and Fujisaki
et al. (2011) were spaced at least two weeks apart in
Florida’s Everglades, meaning that the assumption of
geographic closure was likely violated and that their
parameters were reflective of an open “superpopulation”
in which abundance reflects all individuals that could
potentially be encountered by the nightlight surveys
(Royle, 2004). In this study, temporal spacing between
replicate surveys was variable (24 h–14 days) within a
highly connected area, during the alligator’s peak move-
ment period (Nifong & Silliman, 2017; Rosenblatt
et al., 2013), meaning we likely sampled from a geograph-
ically open system. Thus, while both survey design
approaches are valid, comparison and interpretation of
parameters derived from different approaches require
important context.
Despite the connected nature of our study area, we
detected contrasting patterns in total alligator densities
and immature size class-specific abundance temporal
trends between the two sites. Though total abundance esti-
mates were relatively similar between the two sites
(Figure 6), SAN (approximately one third of the route
length of GPD) appeared to have substantially higher alli-
gator densities. We posit that the difference in density is
likely a reflection of habitat, which, in turn, may drive dif-
ferences in hunting pressure (i.e., hunters are attracted to
high-density habitats). Multiple studies indicate that
coastal alligators periodically forage in saline areas to take
advantage of marine prey items (e.g., blue crabs Callinectes
sapidus)(Nifong&Silliman,2017; Rosenblatt &
Heithaus, 2011). As such, alligators within the SAN route
can take advantage of a freshwater–marine gradient with
the South Santee River to balance osmoregulatory and for-
aging needs. In contrast, freshwater marshes such as those
surrounding the GPD are typically nutrient-limited and
host lower alligator densities. Site-specific differences
in habitat are also reflected in the immature size
class-specific abundance patterns. Suitable nesting habitat
is relatively abundant on the Santee River Delta and scarce
along the Great Pee Dee and Waccamaw Rivers within the
GPD route (Wilkinson, 1983). As such, hatchlings were
less abundant than both juveniles and subadults on GPD
for most of the study (Figure 6a), whereas hatchlings were
the most abundant size class on SAN for all years except
2011. We also note that the general deviation from the
expected pattern for long-lived species in which abun-
dance and size class are negatively correlated (Nichols
ECOSPHERE 17 of 22
et al., 1976)(Figure6a,b) is likely a reflection of habitat
differences as well. Breeding females typically construct
nests in highly vegetated habitat and remain close to
the nesting site with their hatchlings and surviving
young from the previous year following nest excavation
(Chabreck, 1965;McIllhenny,1935; Woodward et al.,
1987), meaning that the nightlight surveys conducted in
open-water habitats were less likely to encounter alligators
in the smallest size classes. Adult females with young and
other immature size classes are thought to avoid
open-water habitats, such as large rivers where nightlight
surveys take place, as a way to avoid predators like larger
alligators that cannibalize young (Lawson et al., 2018;
Rootes & Chabreck, 1993b; Somaweera et al., 2013).
In contrast, though the mature size classes followed
the expected composition patterns and those of previous
studies (Nichols et al., 1976), the size class-specific abun-
dance trends differed markedly among sites (Figure 7c,d).
On GPD, small adult abundance appeared to increase dur-
ing the first half of the study and then stabilize, whereas
the abundance of large adults and bulls remained rela-
tively consistent over time (Figure 7c). In contrast, despite
SAN containing better foraging habitat due to access to
marine resources, all adult size classes declined during the
study. The decline was largest for bulls (50%), followed
by large adults (35%) and small adults (18%)
(Figure 7d). Given the low probability that an alligator
lives long enough to reach 3.05-m TL (Wilkinson
et al., 2016), the finding that bulls were least abundant of
the size classes was somewhat expected. However, the
contrasting patterns of decline between the two sites sug-
gest other factors may be differentially affecting the popu-
lation segments, namely, harvest. Over the course of the
study, more than twice as many alligators were removed
from SAN compared with GPD for both the public (500 vs.
196; Appendix S1: Table S3) and private harvests (93 vs.
46; Appendix S1: Table S3). This observation, coupled with
the evidence of decline in all adult size classes in SAN and
the lack of any such evidence for GDP, supports the propo-
sition that the two population segments are experiencing
different levels of harvest pressure and exhibiting different
responses to harvest.
Compared with a conventional approach of synthesiz-
ing results from separate analyses of disparate datasets,
the IPM framework we employed provided advantages for
making inferences on quantities more efficiently
(e.g., survival) and on quantities that were otherwise
unattainable in any dataset individually (e.g., size
class-specific abundances). Despite these advantages, our
approach faced some limitations. However, all the limita-
tions described below would have also impeded the use of
a nonintegrated approach. First, each of our data
sets—mark–recapture–recovery, nightlight survey counts,
clutch sizes, and harvest totals—were sparse and necessi-
tated simplification within the constituent model compo-
nents to facilitate estimation. For example, the assumption
of constant survival over time is not realistic for some of
the age classes, but it was a reasonable concession to the
reality of the data in hand. Second, data provided to us
had known deficiencies that could not be completely
resolved and could have affected our inference. For exam-
ple, the harvest data we incorporated into the model were
based on self-reported alligator TL from hunters and did
not account for missing tails. Thus, it is possible that our
model inappropriately directed too much harvest into
smaller size classes, resulting in positive bias in abundance
of larger size classes. A strength of the IPM comes from
the model of population dynamics that forms the founda-
tion of the framework. Because functional processes link
estimated quantities, the IPM is able to produce estimates
abundance in years when no nightlight surveys were
conducted. However, the ability to impute such quantities
in the face of missing data depends on both the functional
linkages in the model as well as prior distributions pro-
vided to uncertain quantities, such as abundance for the
initial year of the study (2011). Together, these may create
apparent statistical artifacts when data are missing in
some years (and sparse elsewhere), such as the large
one-year increase (2011–2012) in hatchlings in SAN.
Our IPM addresses a widespread, critical challenge in
the conservation of species that are difficult to directly
observe and exhibit complex life-history patterns, in
which the preferred monitoring method produces data
of lower demographic resolution than what is needed
to make effective decisions and reduce uncertainty
(i.e., “demographic resolution mismatch”; Hauser
et al., 2006; Link et al., 2003). Hostetter et al. (2021) dem-
onstrated the potential benefits of avoiding mismatch by
examining the consequences of incorporating age struc-
ture into population models for polar bears (Ursus
maritimus) in Canada. In a simulation study, they
reported that age-structured Jolly Seber models produced
higher precision estimates of survival, abundance, and
recruitment compared with models that lacked age struc-
ture and increased the power to detect changes in abun-
dance (Hostetter et al., 2021). In contrast, the use of
low-resolution monitoring data may leave a population
more vulnerable to perturbations in population structure
(e.g., size-selective harvest) in long-lived species can have
long-lasting impacts on population growth and abundance
that may not be immediately detected (Hoy et al., 2020;
Koons et al., 2006;Regehretal.,2017). Worse, demo-
graphic resolution mismatch could also limit conservation
actions or management interventions that could otherwise
benefit the species. For example, managers may be forced
to rely upon predictive models that make simplifying
18 of 22 LAWSON ET AL.
assumptions about population structure (e.g., stable age or
stage distribution) that are rarely met in practice and may
lead to flawed inference from elasticity or sensitivity ana-
lyses (Koons et al., 2006,2007). The method we describe
here using IPMs to resolve latent population structure and
thereby reduce demographic resolution mismatch could
be extended to applications including uncertainty in age
assignment for long-lived species with variable reproduc-
tive value (e.g., bears), species assignment for closely
related species like mallard (Anas platyrhynchos)and
black ducks (A.rubripes), or sex assignment for species
that lack sexual dimorphism (e.g., raptors). Though some
monitoring programs could be restructured to obtain the
necessary level of resolution, or stopped entirely in favor
of promising alternative methodologies (e.g., unmanned
aerial vehicles), such options severely restrict the use of
existing, long-term datasets.
Despite their potential low resolution, some
long-term datasets may have inherent value for
slow-growing or long-lived species in which the effects of
management or conservation decisions may operate at a
lagged timescale. The IPM described here provides a
promising, flexible approach to merge high-resolution
demographic data with low-resolution, but less costly,
monitoring data to describe and quantify latent popula-
tion structure and abundance trends. The flexible nature
of IPMs offers the ability to synthesize multiple
datastreams to produce more precise demographic
parameter estimates that can be used in other contexts to
guide not only conservation decisions but also improve-
ments to the design of the monitoring program. Hence,
IPMs are a valuable tool in conservation because they
provide a means to both increase the resolution and pre-
cision of existing data, and potentially improve upon how
monitoring data are collected for managed species.
ACKNOWLEDGMENTS
We thank the many technicians and volunteers who
assisted with nightlight surveys and alligator captures, and
the Tom Yawkey Wildlife Center for logistical support. We
specifically acknowledge Brad Taylor, Jamie Dozier, and
Derrell Shipes who were instrumental in the completion
of this study, as well as Allan Woodward, Erin Leone, and
Mark Bara for use of the alligator growth data. We thank
Beth Ross, Robert Baldwin, Anna Tucker, Dave Koons,
and one anonymous reviewer for their helpful comments
on earlier versions of this manuscript, and Nathan
Hostetter for data and software review. This work was
supported by the South Carolina Department of Natural
Resources (grant numbers 2009094 and 20100899).
We acquired all necessary alligator sample collection
permits from the South Carolina Department of
Natural Resources, and the study was approved by the
Institutional Animal Care and Use Committees at
Clemson University (permit numbers 2015007, 2016059;
2015–2017) and the Medical University of South Carolina
(permit number 3069; 2010–2017). This paper represents
Technical Contribution Number 6731 of the Clemson
University Experiment Station. Any use of trade, firm, or
product names is for descriptive purposes only and does
not imply endorsement by the US Government.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
DATA AVAILABILITY STATEMENT
Model code (Lawson, Dunham, & Moore, 2022) is avail-
able from the US Geological Survey Office Source Code
Archive at https://doi.org/10.5066/P92I95YE. Data
(Lawson, Jodice, et al., 2022) are available in the US
Geological Survey Science data catalog at https://doi.org/
10.5066/P9AEXW1Z.
ORCID
Abigail J. Lawson https://orcid.org/0000-0002-2799-
8750
Patrick G. R. Jodice https://orcid.org/0000-0001-8716-
120X
Thomas R. Rainwater https://orcid.org/0000-0003-
4682-7735
Kylee D. Dunham https://orcid.org/0000-0002-9249-
0590
Morgan Hart https://orcid.org/0000-0001-6448-0785
Clinton T. Moore https://orcid.org/0000-0002-6053-
2880
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SUPPORTING INFORMATION
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How to cite this article: Lawson, Abigail J.,
Patrick G. R. Jodice, Thomas R. Rainwater, Kylee
D. Dunham, Morgan Hart, Joseph W. Butfiloski,
Philip M. Wilkinson, K. W. McFadden, and
Clinton T. Moore. 2022. “Hidden in Plain Sight:
Integrated Population Models to Resolve Partially
Observable Latent Population Structure.”
Ecosphere 13(12): e4321. https://doi.org/10.1002/
ecs2.4321
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