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Table of Contents
A Model to Understand Population Decline of the Devil’s Hole
Pupfish (Cyprinodon diabolis) and Support Habitat Management
Decisions
Yuri V. Graves and Krystyna A. Stave
Graduate Student and Associate Professor, respectively.
Department of Environmental Studies, University of Nevada Las Vegas,
4505 Maryland Parkway, Las Vegas Nevada 89154-4030
(702) 450-8833, (702) 895-4833
(E-mail for corresponding author Graves: Y URGGIE@aol.com)
Abstract
This paper describes a system dynamics simulation model created to help the Devil's
Hole Pupfish Recovery Team understand reasons for population decline since the mid-1990s and
to evaluate potential interventions to reverse the population decline. After intensive efforts in the
1970s to stabilize the water levd in Devil's Hole, the population of the Devil's Hole Pupfish
showed slight but steady increase from the 1970s until the mid-1990s. The Teamis seeking ways
to reverse the recent population decline in the native habitat, but has limited information about
the system as well as limited resources for data collection. The focus of this study is the
development of a system dynamics model that can help the Team understand the reasons for the
population decline, identify critical parameters that should be monitored to anticipate future
population changes, and help find habitat management levers that can reverse the population
decline.
Keywords: Devil’s Hole Pupfish, Devil’s Hole, population, Cyprinodon diabolis, habitat
management
Introduction
Approximately 100 miles northwest of Las Vegas, Nevada, exists “the smallest vertebrate
habitat known to contain the entire population of a species” (Riggs and Deacon 2003). Devil's
Hole, a water- filled cavem forming a skylight into the regional aquifer is a “disjunct part of the
Death Valley National Park” in Ash Meadows, NV. The Hole was created about 60,000 years
ago when the roof of an underground fissure collapsed, creating an opening to the surface (Riggs
and Deacon 2003). The opening is approximately 15 feet wide and 40 feet long and the water
depth is unknown, but greater than 400 feet. It is the only natural habitat for the Devil’s Hole
Pupfish (Cyprinodon diabolis).
Devil's Hole was designated as part of the Death Valley National Monument in 1952.
Large-scale land development and aquifer pumping in the area surrounding Devil's Hole in the
1950s and 60s led to declining water levels in Devil’s Hole and a dramatic decrease in the
pupfish population. In 1970, a Pupfish Task Force and the Desert Fishes Council were
established to address issues related to the endangerment of the Devil’s Hole Pupfish. Successive
decisions from the U.S. Supreme Court and District Court resulted in the designation of a
minimum water level in Devil's Hole. These efforts not only stabilized the population of the
Devil’s Hole Pupfish, but also helped build support for the Endangered Species Act of 1973. The
Devil’s Hole Pupfish was one of the first fishes to be listed as an endangered species (Anderson
& Deacon, 2001). Based on these early and intensive habitat protection efforts, the pupfish
population showed a slight but steady increase from the 1970s until the mid- 1990s (Figure 1).
The Devil’s Hole Pupfish has again become a focal point for policy managers, however.
Since 1994, the population has seen a sharp and sustained decline. While the risk of extinction
has been lowered by a successful refugium program, the protection of the native population in its
native habitat is essential to long-term survival, since the long-term effects of refugium
environment on the evolutionary trajectory of the species is not entirely understood (Baugh and
Deacon, 1988). The U.S. Fish and Wildlife Service, under provisions of the Endangered Species
Act, has appointed a Recovery Team consisting of federal, state and educational agency
representatives charged with formulating management recommendations likely to reverse the
downward trend in the population. The group has limited information about the system as well as
limited resources for data collection. Their monitoring and management efforts must be carefully
targeted. The focus of this study is the development of a system dynamics model that can help
the group understand the reasons for the population decline, identify critical parameters that
should be monitored to anticipate future population changes, and help find habitat management
levers that can reverse the population decline. Figure 2, illustrating annual maximum and
minimum population sizes recorded in Devil’s Hole since 1972, represents the reference mode
for the model. This paper describes the first four steps of a system dynamics approach to
understanding this problem: problem definition, system description, model development,
building confidence in the model, using the model and initial conclusions.
Problem Definition
The behavior over time graph (Figures 1 and 2) depicts the annual maximum (summer)
and minimum (winter) population sizes of mature Devil’s Hole pupfish from 1972 to the present.
The result of intensive habitat management can be seen on the graph as the population increases
in the first few years after implementation of legally imposed controls on groundwater pumping.
The population then levels off at a slight growth rate for nearly 20 years. The decline that
inspired this analysis appears to have started about 1994.
System Description
The system generating the Devils Hole Pupfish population pattem of change has its basis
in a generic population model. The model is dominated by one positive and one negative loop
(Figure 3). The positive loop portrays the reproductive and maturation process, ultimately
‘producing’ more mature pupfish. Absent any stabilizing forces, this loop would result in
exponential growth of the pupfish population. As in other population models, the negative loop
causes the stabilization of the population as mature fish expire.
This typical population model was a starting point for explaining what was causing the
number of mature pupfish to expire at higher than normal rates. Through discussions with
pupfish experts, it became apparent that the cause of the decline was not likely related to a higher
mortality rate of mature fish. Rather, it was the hypothesis of the experts that the population was
declining because of a greater mortality rate d eggs and larvae. Accordingly, the focus tumed in
the direction of understanding what variables affected the hatch and survival rates. | Some of the
variables to be defined further are the effects of filamentous algal growth (cyanobacteria and
green algae) on larvae and eggs, the effect of seismic activity and sedimentation on available
interstitial space in the substrate of the spawning shelf, and the effects of predation and possibly
cannibalism on larvae and eggs. All of these variables would directly impact the existing
variable, Hatch Rate Modifier due to Habitat Change, on all three areas of the spawning shelf.
Model Development
The stock and flow diagram (Figure 4), represents a simple aging chain, in which pupfish
begin as eggs, eggs hatch to produce larvae, larvae mature to become juveniles and finally, adult
pupfish. Flows representing the rate at which eggs become larvae, and the rate at which larvae
become mature pupfish were added. The number of mature pupfish multiplied by the egg
production rate determines the rate of egg production. This stock and flow structure forms the
backbone of the model. Once the relationships comprising the reproductive cycle of mature
pupfish were established, the relationships that are affecting the population negatively were
explored and added to the model structure.
Subsequent iterations of this process and consultation with a newly established Pupfish
Modeling Group, a sub-group of the Pupfish Recovery Team, have produced a more detailed
model (Figure 5) that represents more variables and processes within the system. The
importance of spatial distributions in the critical habitat known as the “spawning shelf’ was
introduced into the model. These divisions were based upon substrate characteristics and
potential productivity established by Gustafson et al, (1998) and the consultations mentioned
above. The stock for Juvenile pupfish was added because it is an established stage of life for the
pupfish that represents the ability of the pupfish to become mobile for the first time and,
therefore, avoid most of the losses that occur during earlier life stages. It is also an important
part of the model because it represents a convergence of the three separate areas of the spawning
shelf into one single stock variable derived from larval maturation rate. Variables for initial
numbers of eggs, larvae, juveniles and adults also had to be added to account for initial
populations in each stage of life.
The original variables for Pupfish eggs and larvae were divided into three paths in the
model each representing areas of the spawning shelf with different habitat characteristics. The
Eggs stock became Eggs on outer shelf, Eggs on middle shelf and Eggs on inner shelf. Until
further defined, each area of the shelf is assumed to have 1/3 of the canying capacity of the total
shelf. A new variable, Total Number of Eggs, linked the Egg Production on each part of the
shelf to the actual determinant variables for production including Egg Production LOOKUP,
Normal Production Rate Month Number and Percent Female. The Egg Production LOOKUP
variable is based upon a 12-month measurement of the number of eggs produced per female
(Chemoff, 1985). This distribution may reflect the relationship between food availability and
diel variability of water temperature, as related to time of year, and egg production. Fluctuations
in egg production on the spawning shelf throughout the year result in the highest rates occurring
in the spring and summer and the lowest rates occuring in the fall and winter. This variable is
critical to the overall hypothesis that the recent decline in population is due to reduced egg and
larval survival rates. Percent Fennle is also a sensitive variable that will significantly skew the
population even with the slightest increase or decrease in percentage. Percent Female is
presently set at 50%.
Egg losses on each part of the shelf are affected by a number of variables. The Normal
Hatch Rate that varies from a high of 7% on the inner shelf to a low of 5.5% on the outer shelf
(Deacon, 2003). Egg Loss is modified due to habitat changes and the timing of this change.
They are presently assumed to be a default value of 1. The (inner, middle, outer shelf) Hatch
rate modifier due to habitat change is critical to understanding the recent decline in the adult
pupfish population and evaluating any causes related to a reduction in eggs or larvae.
Larvae loss on each part of the shelf is a function of Normal Larvae loss. This value is
assumed to be equal for each part of the shelf and formulated using 33.3% for each. The
variables Time to Incubate Time to Mature Larvae to Juvenile and Time to Mature Juvenile to
Adult are representative of scientific data gathered in these areas. The Time to Incubate is
consistent on all areas of the shelf and is expressed as 1 week (.25 months) (Gustafson et al,
1998). The Time to Mature Larvae to Juvenile is also consistent on all areas of the shelf and is
expressed as 1 month (Deacon et al, 2003). The Time to Mature Juvenile to Adult is expressed as
2 months (James, 1969). The Average Lifespan is 10 months (Chemoff, 1985) but is expressed
as 8 months when time spent in previous life stages are accounted for.
Building C onfidence in the Model
In order to gain confidence in the results, the model must be shown to replicate the
reference mode. Figure 6 shows that the model output does replicate the population trend
witnessed by actual adult population counts from 1972-1994 (Figures 1 and 2). This is
represented by the “base” run of the model. Figure 6 also shows that a 10% increase in egg loss
replicates the decline in population from 1994-2002. This indicates that the model does replicate
the overall trend shown in figure 6 and supports the hypothesis that egg loss, and possibly larvae
loss, are significant contributors to the declining population trend. _—‘ Figure 7 represents the next
iteration of the causal loop diagram. It builds upon the initial diagram and builds into the model
factors such as predation, cannibalism, effects of water level and substrate porosity. All of these
factors need to be defined in order to understand their potential relationship to reduced egg and
larvae populations that may have contributed to the recent decline in the adult pupfish
population.
Using the Model
Intensive group modeling sessions were held with members of the Pupfish Recovery
Team between January and May 2003. Modeling group members have specified model
parameters, helped to refine the model, and use the model to design monitoring and management
strategies. In February, Pupfish populations fell to their lowest recorded level. This has
intensified the group's use of the model. The group is aiming to have another revised version of
the model completed by August 2003, but to use preliminary versions of the model in March,
April and May to test potential emergency management options in the meantime.
The Pupfish Modeling Group has made several recent runs on the model to determine
areas of emphasis for research and management strategies. One of the early runs (Figure 8)
represented an attempt to understand how all the stages of life of a pupfish are related
temporally. It showed the expected lag time between maximum population types. A maximum
in adult pupfish followed by a maximum in eggs, then larvae and juveniles.
Modeling Group members had thought that human intervention in the hatch rate, perhaps
through temperature modification through shading or substrate porosity changes could
significantly increase the adult population. Subsequent runs (Figure 9) showed that an increase
of 8% to the middle shelf hatch rate raised the overall adult population when compared to the
base run, but did not warrant a management action at this point. Another run (Figure 9) showed
that adding to the number of initial adults did not have a significant impact on the long-term
population. This run was actually very similar to a decline in the initial adult population (Figure
9) thereby disproving a theory that initial populations could play an important role in overall
model effectiveness.
Another critical factor that was determined by model development and use was the
determination of gaps in existing data. Seismic activity, flushing events and algal growth may
play critical roles in the overall success or failure of eggs and larvae. Seismic activity may cause
the porosity of the substrate on the spawning shelf to be minimized resulting in less space for
eggs and larvae to safely grow. Flushing events may wash some a all of the existing substrate
from the shelf, while also depositing a new substrate on the shelf. Algal growth, depending on
the species, may become so extreme as to form “shrink wrap” on top of the substrate. This
coverage produces an anoxic environment in the substrate that could be fatal to both eggs and
larvae. Predation of eggs and larvae by flatwoms (Dugesia dorotocephala) and other
invertebrates is known to occur but the rate at which this occurs is unknown and difficult to
quantify. Cannibalism of eggs and larvae is thought to occur but, again, is difficult to quantify
and include in the model until further research is conducted.
The development of the model has also caused members of the Pupfish Recovery Team
and the Modeling Group on variables included in the model and the assumptions that have been
made. The Percent Female is assumed to be 50% but we do not know if this is consistent
throughout the year. This may be a variable better represented by a LOOKUP table to show the
distribution of females throughout the year when this can be quantified. The hatch rates on all
three areas of the shelf are estimates based upon results from one experiment (Deacon et al,
1995) conducted under laboratory conditions. Members of the Modeling Group then
incorporated the results into the model. Initial values for all stocks are established from several
previous works and then extrapolated by members of the Modeling Group.
Further monitoring efforts, some of which may be implemented in a new long-tem
monitoring plan, would increase the effectiveness of the model to replicate the behavior of the
actual pupfish ecosystem. For example, there are no counts currently being conducted of eggs
and larvae. This information could prove useful in validating whether a reduction in eggs and
larvae has caused the adult population decline. These counts would help determine whether the
pupfish had reached a critical population point in regards to potential extinction as the number of
larvae are thought to represent the overall success of the population. Monitoring of water
temperature, water chemistry and available pore space in the substrate of the spawning shelf
would help discem whether these have a significant impact on eggs and larvae. Flatworm or
algal coverage estimates and spreading rates would assist in determining potential effects
through predation and “shrink wrap.” The effect of seismic activity on substrate porosity needs
to be understood to establish potential relationships between available pore space, which serves
as protection against predation, and egg and larvae survivability. The presence of sediments that
could potentially reduce substrate porosity need to be examined further.
Initial C onclusions
The model has proven useful to the Pupfish Recovery Group. Initial runs have provided
insight into potential leverage points within the system. Some variables, such as initial
populations, which were thought to be sensitive leverage points, have been reevaluated as to
overall significance. Other variables, such as hatch rate modifier due to habitat change, are now
known to be potential leverage points in the system and require more research to define their
role. The model will continue to be modified as research and professional consultation provide
more information about this tiny, yet complex, ecosystem and it unusually “charismatic mini-
fauna” (Deacon, 2003).
Acknowledgments
We thank Dennis Bechtel, Amanda Brandt, Mike Dwyer, and Josh Hoines for
patticipating in the initial stages of this project. We also thank Dr. James Deacon and members
of the Pupfish Recovery Group and Modeling Group for their expert insight into the complexities
related to the Devil’s Hole Pupfish and active participation in the modeling effort.
References
Anderson, M. and Deason, J. 2001, Population Size of Devils Hole Pupfish
(Cyprinodon diabolis) Correlates with Water Level. Copeia, 2001, No. 1
Baugh, T. M. and Deacon, J. E. 1988. Evaluation of the Role of Refugia in
Conservation Efforts for the Devil’s Hole Pupfish, (Cyprinodon diabolis)
Wales. Zoo Biology, 7:351-358.
Baugh, T. M. and Deacon, J. E. 1983. Daily and Yearly Movement of The Devil’s
Hole Pupfish Cyprinodon Diabolis Wales in Devil’s Hole, Nevada. Great Basin
Naturalist, vol. 43, no.4.
Chemoff, Barry. 1985. Population Dynamics of the Devil’s Hole Pupfish,
Environmental Biology of Fishes, vol. 13, no.2.
Deacon, J. E. and Deacon M. S. 1979. Research on Endangered Fishes in
the National Parks with Special Emphasis on the Devils Hole Pupfish, pp. 9-19 In: R.
Linn (ed.). Proceedings of the first conference on scientific research in the National
Parks. U.S. National Park Service Transactions and Proceedings, No. 5.
Deacon, J. E., Taylor, F. R., Pedretti, J. W. 1995. Egg Viability and Ecology of Devil’s
Hole Pupfish: Insight From Captive Propogation, The Southwestem
Naturalist, vol. 40, no.2.
Deacon, J.E., Goodchild, S., Manning, L. and Parker, M. 2003. Minutes of
the Devil’s Hole Pupfish Modeling Group meetings. Unpublished document.
Ford, A. 1999. Modeling the Environment: An Introduction to System Dynamics
Modeling of Environmental Systems. Washington, DC: Island Press. 401
pages.
Gustafson, E. S. and DeaconJ.E. 1998. Distribution of Larval Devils Hole Pupfish,
Cyprinodon diabolis Wales, in Relation to Dissolved Oxygen C oncentration in
Devil’s Hole, Final Report to the National Park Service, Death Valley National
Park.
James, C.J. 1969. Aspects of the Ecology of the Devil’s Hole Pupfish, Cyprinodon
diabolis Wales, Unpubished Master's Thesis, University of Nevada Las Vegas.
Minckley, C. and Deacon, J. 1975. Foods of the Devil’s Hole Pupfish, Cyprinodon
Diabolis (Cyprinodontidae). The Southwestem Naturalist. 20(1):105-111.
Minckley, C. and Deacon, J. 1973. Observations on the Reproductive Cycle of ,
Cyprinodon Diabolis Copeia, Number 3, pp. 610-613.
Riggs, A.C. and Deacon, J.E., 2003. Devil’s Hole: This Magical Place, Unpublished
Manuscript.
Wilson, K., Blinn, D., and Herbst, D. 2001 Two Year Progress Report: Devils Hole
Energetics/C ommunity Relationships: Death Valley National Park,
California. Unpublished Manuscript.
Figure Captions
Figure 1: Reference mode for Devil’s Hole Pupfish population 1972-2002.
Figure 2: Reference mode including trend line.
Figure 3: Initial Causal Loop Diagram.
Figure 4: Original Stock and Flow Diagram.
Figure 5: Updated Stock and Flow Diagram
Figure 6: Model output showing replication of reference mode and the results of a
10% increase in egg loss and trend lines.
Figure 7: Second iteration of Causal Loop Diagram.
Figure 8: Comparison of Life Stages
Figure 9: Results of various runs as compared to base run.
Figures
SY STEM BEHAVIOR
Devil's Hole Pupfish
Eo
A A_KA. RAR
§ a W ah =
ers a
a ] -H— Winte
100 ~
¥ 0
vr OB oD PAK EHP SH HP HS O
Year
Figure 1.
SY STEM BEHAVIOR
Devil's Hole Pupfish
—+— Summer
|= Winter
Vie © oP HF SHS P Hp HP Hw O
Year
Figure 2.
CAUSAL LOOP DIAGRAM
Egg Production
Rate
oO Loss
+ a
)) Rate
Deaths ‘—) f+. a
+ ae
by |)
Xe & Larvae Loss
Maturation Rate
Figure 3.
ORIGINAL STOCK and FLOW MODEL
Egg Production
Time to Incubate
Normal
Production Rate ‘Novia Hiatt Rats
Average Lifespan
Time to Mature
St - Eggs Larvae >) Pupfish anit)
Egg Production x a ee i
Percent Femal
Normal Egg Loss Egg Loss fsarvel
Additional Egg Loss
due to Habitat
Conditions
Time of Habitat
Change
Normal Larvae Loss
Figure 4.
UPDATED STOCK
inital eggs on
outer shalt
‘Time to Incubste intial Larvae ot
‘outer shelf
A
a
ND
‘Time to Mature
Lange t Juvenile
‘on outer self
sie A Hpouter belt
Noma Hach Rao, ad
Larvae maturation
outer shelf
FLOW MODEL
outer shelf hatch rate Larvae loss on
EggProduction ‘modifier due to habitat sha
LOOKUP. « <n change
Nonna Eag Lost
sii on outer shal
‘ time of habitat change
Number ‘ ‘on outer shelf foal Larvae Loss ‘Time ty Mature
ss time onouter shelf Juvenile to Adit Keanilgm:
© Time to Mature
ops inital eggs on <Time to initial lavae on Larvge to Juvenil initia adits
middle shalt Tncuba mide shelf
Juveniles Pupfish >
Total Number of ‘Egg Production on ‘Hatch middle shelf middle shelf Larvae maturation Juvenile maturation Deaths
mide shelf middle shelf
‘ nomna juveile
qq os on f| Noma Hatch Rate | mide sha hatch rete loss
ree ertA onmiddesbelf J | modifier due to habitat hs
Parent Peale change
Nonmal Egg Loss on time>
ote middle shelf
oan time of habitat change Normal Larvae Loss
con middle shalt on middle shelf
<Time to Mature
Time t 26 to Juvenile total larvae
Inqubats initial larvae on
Tavae on avae on inner <Lavae on l
tale eee Larvae maturation shel helf>
inner shelf hatch rate cael
‘modifier due habitat er total eggs.
( -%
time of habitat change = Jo <Edysonoute
eae ggson inner <Eqgs on mid oe
Figure
MODEL OUTPUT
Graph for Pupfish
600
nd
itp,
y val 7m
awl
a ty ,
ARVANA
300
0
0 32 64 96 128 160 192 224 256 288
Time (Month)
Pupfish : addl egg loss 10% pupfish
Pupfish : base: pupfish
Figure 6.
Water Level
Predation Rate +
wv of Shelf
Egg Production
We ;
Rate Egg Loss Habitat er
(Index)
ae Hatch Rate ) *
mae >) ) Larvae Loss
Mature Pupfish
aw, ee: Pop ian Laver ’ Substrate
4 +
CA i Cannibalism Rate )
os
Flushing Events
Maturation Rate
Figure 7.
life stages compared
800
total larvae : base
Juveniles : base
Z
Time (Month)
226
Pupfish : base
total eggs : base
Figure 8.
pupfish
pupfish
pupfish
pupfish
Pupfish
Time (Month)
Pupfish : decline 100
Pupfish : add adults
Pupfish : incr hatch on middle
Pupfish : base
Figure 9.
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pupfish
pupfish
pupfish
pupfish
