Table of Contents
Theory Building with System Dynamics: Ice A ge Extinctions
Elin Whitney-Smith, Ph.D.
Geobiology, George Washington University
dlin@quatemary net
‘http,//quatemary net
Abstract
Arecently developed system dynamics model specifies a new hypothesis for the extinctions at the
end of the Pleistocene - Second Order Predation - and compares it with the overkill hypothesis
(see http://quaternary.net/extinct2000). It provides a quantitative description of the
interrelationships between four plant stocks, four herbivore stocks, carnivores, and H. sapiens.
Different assumptions regarding H. sapiens in-migration, hunting of prey or predators, can be
simulated. Second Order Predation: i.e. H. Sapiens killing of other carnivores, leads to herbivore
overpopulation, environmental degradation, and differential extinction of herbivores. The paper
suggests thinking about whole system evolution and calls for additional models that will support
comparison of competing hypotheses, allow precision in quantities and timing, and exhibit internal
dynamics. It challenges scientists conversant with models to simplify models to encourage their use
by their colleagues.
Background
Climate change theories put forward to explain the extinctions at the close of the Pleistocene are
unsatisfactory because the animals in question (mammoths, mastodons, horses) survived previous changes
of similar magnitude. The overkill theory is unsatisfactory because predators cannot hunt their prey to
extinction without starving themselves. Combining the theories, without a proposed mechanism, is
incomplete and inadequate. All current models assume animal populations decrease monotonically to
extinction. An altemate scenario and computer simulation characterized by a boomy/bust population pattem
is presented. It suggests that H. sapiens reduced predator populations, causing a herbivore population.
boom, leading to overgrazing of trees and grass, resulting in environmental exhaustion and extinction of
herbivores. If true, bison survival through the Pleistocene may be accounted for thus: herbivore population
explosion created a condition of scarcity in which there was selective pressure favoring animals that could
extract maximum energy from low quality forage to survive and reproduce.
Imagine the following scenario:
Homo sapiens enters the New World. The introduction of a new predator, H. sapiens, reduces the
number of herbivores available to each of the existing predators.
Predators who are unable to find enough to eat and who have no experience with H. sapiens prey on
H. sapiens.
Tn revenge and to cut down on competition, H. sapiens establishes a policy of killing predators.
Through this policy predator populations are reduced below the level where they are able to control
hetbivore populations. Herbivore populations boom.
H. sapiens populations expand, but more slowly than the predators they kill because humans recruit
mare slowly. H. sapiens does not control herbivore populations as well as the now scarce predators
did formerly.
Herbivore populations overgraze the environment. Herbivores are forced to eat their less preferred
foods. Mammoths and mastodons knock over trees, eventually tuming mixed parkland into grassland
(Wing and Buss, 1970).
Without sufficient food, herbivore populations crash (Leader Williams, 1980; May, 1973; Scheffer,
1951).
As H. sapiens populations begin to experience food stress, they strengthen their policy to exterminate
any remaining predators who are now more serious competition.
Tn the denuded environment, herbivores that can get the most nutrition and reproduce soonest from
resourves which recruit quickly are selectively favoured - bison. H. sapiens populations have been
decimated. Relict groups establish new life ways. The new Holocene equilibrium is established
(Whitney-Smith, 1995).
Methods
Three system dynamics computer models were designed as a test of the hypothesis presented above.
Assumptions behind the simulations are: that ecosystems are generally in equilibrium, that vegetation
continues to grow until it fills up the available area, that each sector of the ecosystem (predator, herbivore,
H. sapiens) is dependent upon its food source, and that the food sourve is depleted by the populations
which use it.
The steps in the process of simulation are: 1 - Establish an equilibrating ecosystem with three
sectors; Plants, herbivores, and predators, 2a - Introduce H. sapiens as a second predator, 2b - Link the
H. sapiens sector and the predator sector to simulate H. sapiens killing predators - (Second Order
Overkill), 3 - Build a model with vegetation partitioned into big and small trees, high and low quality grass;
herbivores partitioned into browsers, mixed feeders and grazers, 4 - Build a model with grazers partitioned
into ruminants and non-ruminant herbivores.
Values used in these simulations: Table 1 shows the values used in the simulations based directly on
those used by Whittington and Dyke (1989) .
Table 1- Values based directly on Whittington and Dyke (1989)
Description of Variable Baseline Source
Human population size 200 Budyko 1967, 1974
Human population growth rate 0.0443 Birdsall 1957
Table 2 below shows values used as starting values and modified to fit the modeling paradigm
Table 2 - Whittington and Dyke (1989) values, changed in this model - all based on Mossiman
and Martin (1975)
Desciiption of Variable Basdine Variation
Prey canying capacity au.* 25 Changed to the amount of Plants per square mile.
Prey biomass replacementau* 0.25 Used as base recruitment rate: Birth rate -(average
death through hunting by predators + natural death rate)
=0.25
Animal Units =1K Lb. of herbivore
The hunting rate used in the simulation presented in this paper is based on food needed per pound of
predator per year. Data from extant predators suggests 20 pounds of food per year per pound of predator
(Intemational Wolf Center, 1996; Cat House, 1996; Petersen, 1977; Schaller, 1972). It is assumed that H.
sapiens requires half the amount of meat that an obligate predator needs.
Running the model with approximated values until the model reached equilibrium derived a number of
values. The division between trees and is arbitrary and set at 50%.
Modeling paradigm: Each of the sectors in all of the models take a similar form: The amount of stock in
the sector at any given time is determined by the amount of stock in the sector at the previous time times
some growth rate, discussed above, modified by the limit of that sector and minus the death rate and the
hunting or consumption rate. Available resources modify birth and death rates for the members of the
sector. Thus herbivores are limited by the amount of Plants times the efficiency rate for that animal.
Hunting values are based on density of herbivores. It is assumed that an average predator can cover a
hunting range of 2 miles per day and if prey is sufficiently dense it will kill all the prey it desires within that
radius. If prey is less dense then the predator population is not able to recruit at its biological maximum.
Since populations rarely recruit at their biological maximum this has the effect of reducing the effective
reproduction rate. Hence populations of predators are dependent on a certain density of herbivores. Over
time the system stabilizes where predator, prey and food populations are in balance.
In the Three Herbivore model hunting rates were based on gross density rather than subtracting the actual
density from the preferred density as in the base model. It became apparent in simulations of the base
model that it was possible to base hunting rates directly on density. Since this conceptualization of the
model is simpler it was decided to use it in both the Three and Four Herbivore models.
Results
The first step - Establish a stable ecosystem with three sectors; Plants, herbivores, and predators -
produced the graph shown below (Figure 1). Since the goal of this step is a stable ecosystem, the model
was perturbed and subsequently retumed to normal. This is the base model from which all subsequent
models are derived.
Figure. 1. Graph of the base model
Pulse Reduction in
125 Carnivore Population 0.10
100)
jerbivoresNormalized
PlantsNormalizec
CarnivoresNormalized;
62.5
Population Normalized (Equilibrum:
0
~11600 11350 -11100 10850 -10600
Key
Plants Herbivores (Prey) Carmivores
(Predator)
The second step is a model with a second predator, H. sapiens. It is broken into two parts.
Step 2a is to introduce H. sapiens as a second predator. H. sapiens enters the New World -11500 BP,
100 years after the start of the model. Figure 2 shows the impact of a second predator. It is the position of
the overkill hypothesis.
Fig. 2. Graph of the second predator (overkill) mode.
Hsapiens enters
the New World
125)
=}
S | PlantsNormalized
u
—
5
| | CarnivoresNormalized
& Decor rtteee-
w -
3 . ;
o HerbivoresNormaliz:
N62.5 |
E
8 | ,
c | ‘
a ’
s ’
2 | a ;
e _-77 HsapiensNormalized
| es ics
0
-11600 -11350 -11100 -10850 -10600
Hsapiens normalized to Carnivore equilibrium
Key
Plants Herbivores Carnivores H.sapiens
(Prey) (Predator) (2° Predator)
— er
Herhbivores decreased less than predators, and food for predators increased. At the end of the model
predator populations are 59% of what they were when the model started; Herbivore populations are 63%
and Plants has increased to 103% of the starting value. (There are fewer herbivores therefore there are
more plants) It has been assumed that H. sapiens needs half the food per year per pound (10 Ib.) than
non human predators. H sapiens is considered to be as effective a hunter as are non-human predators.
As in the Whittington and Dyke model H. sapiens is 200 individuals at year-11500 BP. Each person is
100 lb, of biomass.
Step 2b is the position of the scenario presented above. It links the H. sapiens sector and the predator
sector to simulate H. sapiens killing predators - (Second Order Overkill). The graph is presented below.
(Figure 3)
Fig. 3. Graph of the second order predation model Key as in figure 2.
Hsapiens enters Hsapiens reduces
the New World Carnivore Population 0.015
125)
r=) | |
=
3 PlantsNormalized
e
4 <i ee
5
Ea
x |
3
N62.5
ow | HerbivoresNormalized
5 | ‘
z ‘
§ | |
3 | | 0"
8 ae
a ae,
6 ee eel ace
-11600 -11350 -11100 -10850 -10600
Hsapiens normalized to Carnivore equilibrium
In this version of the Base Model, 400 years after H. sapiens enters the New World predator populations
are reduced by 1.5%. This destahilizes the system. Herbivore populations escape from predator control.
This creates a population boom. Herhivores eat the Plants faster than it can be replaced. Ultimately
herbivore populations crash. The crash in herbivore populations allows the Plants to recover. This boom/
bust cycle is repeated with each cycle decreasing in amplitude. After several cycles the system stabilizes.
Duting the boom bust cycles the animals that can survive on the fastest recruiting resource and who can
extract maximum nutrition should be favored over those who cannot.
The task of the next steps in the modeling effort is to examine why some animals are favored over others.
Step 3 is to build a model with vegetation partitioned into hig and small trees, high and low quality grass;
herbivores partitioned into browsers, mixed feeders and grazers. The reduction in camivore populations is
based on camivores killed per H. sapiens per year. The reduction in camivore populations is a factor of
camivore density and kills per H. sapiens. At maximum density a 100 lb H. sapiens kills 2.5 lbs. of
camivore per year. As camivore densities fall off kills per unit of H. sapiens drop off to zero.
The stable ecosystem graph (Figure 4) is like the stable ecosystem in the Base Model (Figure 1) presented
above. The only difference is that the increase in size and stability of a more complex system made it
necessary to perturb the predator sector with a pulse reduction of 3% before any disturbance of the
system was observable.
In the Three Herbivore model the introduction of H. sapiens causes very little disturbance to any of the
sectors. Populations are 90% of starting values. Predator populations are reduced relatively more than
Hexbivores but only a fraction of a percent, and Plants still increase slightly to 101% of its starting value
(Figure 5).
Tn second-order overkill mode, where H. sapiens hunts camivores, results in a major crash of Herbivore
and Camivore populations after which populations level off. It is shown in Figure 6.
Consider the Herbivore sector. The graph below shows the behavior of browser, mixed feeder, and grazer
populations (Figure 7). Browsers and mixed feeders expand and crash. Grazers, initially have a population
slump, as they bear all the pressure of predation by both non-human predators and H. sapiens. As H.
sapiens and predator populations diminish, grazers rebound, and stabilize.
Figure. 4. Equilibrium mode graph. Three herbivore model. Key as in figure 1
Pulse Reduction in
150- Sommer Population 0.10
H HerbivoresNormalized
PlantsNormalized
CarnivoresNormalized
7: |
|
-11600 -11075 -10550 -10025 -9500
Population Normalized (Equilibrum=100)
Fig. 5. - Second predator (overkill) mode, aggregated view. Key as in figure 2.
Hsapiens enters
the New World
|
|
E
PlantsNormalized
¢ “HerbivoresNormalized
eS o CarnivoresNormalized
Population Normalized (Equilibrum=100)
;
-11600 “11075 10550 -10025 -9500
Hsapiens normalized to Carnivore equilibrium
Fig. 6. Second-order predation, aggregated view. Key as in figure 2.
Hsapiens enters
the New World
|
|
PlantsNormalized
HerbivoresNormalized
| ¢
Population Normalized (Equilibrum=100)
, CarnivoresNormalized
+
| “i ¢HsapiensNormalized
oper”
-11600 -11075 -10550 -10025 -9500
Hsapiens normalized to Carnivore equilibrium
Fig. 7. Second-order predation, herbivores
Hsapiens enters
250, the New World
Grazers
| Normalized
Population Normalized (Equilibrum=100)
R
an
°
on Peer ere r errr rere ea
-11600 -11075 -10550 -10025 -9500
Key
Grazers Grazers Mixed
Non-Ruminant Ruminant Browsers: Feeders
— —— ereue
Figure 8 - shows why herhivore populations crashed. We see that the browsers and mixed feeders are
eating trees faster than they can recruit, resulting in a complete crash of small trees, followed by near
extinction of large trees as well. The dip in grazer populations after the extinction of browsers and mixed
feeders allows the two grass sectors to boom until grazer populations equilibrate.
Fig. 8. Second-order predation, plants
Hsapiens enters
250, the New World
8 |
£ | SmaliTrees
& Normalized
5 |
A BigTrees
w | GrasslLow gempeemeeneesen Normalized
3 4 GrassHigh
2 1257 | ? Normalized
5 worse
=
ce
2
5
3
a
°
a
-11600 -11075 -10550 -10025 -9500
Key
GrassLow GrassHigh BigTrees SmallTrees
meee — —
In the Four Herbivore model the Stable Ecosystem mode is the same as is the Stable Ecosystem mode of
the Three Herbivore Model illustrated above. Like the Three Herbivore Model the only difference from.
the Base Model is that the stable ecosystem needed to be perturbed by a 5% pulse reduction before any
difference could be observed.
The Second Predator mode of the Four Herbivore Model is the same as it is in the Three Herbivore
model. There is litle disturbance to either herbivores or predators.
The only difference between the Three Herbivore and Four Herbivore models is in the Second Order
Overkill mode shown in Figure 9,
Fig. 9. Second-order predation, Four-herbivore model Key as in figure 2
Hsapiens enters
the New World
a
oS
CarnivoresNormalized
Population Normalized (Equilibrum=100) _,
~
a
4
| ,’ HsapiensNormalized
poe"
-11600 -11075 -10550 -10025 -9500
°
Hsapiens normalized to Carnivore equilibrium
The graph is very like the graph of the Second Order mode presented for the Three Herbivore Model until
after the crash in all sectors. Then we see a further dip in Herbivores, Predators and H. sapiens
populations. The crash in populations occurs later in the Four Herbivore Model than it does in the Three
Herbivore Model.
In Figure 10 we see the reason for that dip. There are two interesting things about this graph. First,
ruminant population levels impact non-ruminants more than they are by predation. Second, when ruminant
populations fall, after the extinction of browsers and mixed feeders, non-ruminants boom. As ruminant
populations recover, non-ruminant populations fall and eventually go extinct. Just as after the extinction of
browsers and mixed feeders, ruminant populations dip as they are hit with the full weight of predation.
Fig. 10. Second-order predation, herbivores. Key as in figure 7
Hsapiens enters
250, the New World
=100)
GrazersNormalized
Ruminant
is}
ov
*
MixedFeeders*.
Normalized *s, {Browsers
Normalized
Population Normalized (Equilibrum
°
-11600 -11075 -10550 -10025 -9500
The vegetation graph below shows the reason, Figure 11. Browsers and mixed feeders eat trees faster
than trees can recmuit, resulting in a complete crash of small trees, followed by near extinction of large
trees as well. The competition between the two grazer populations keeps grass stable Trees, freed from
yedation by browsers and mixed feeders colonize new tenitory. The loss of grassland to trees coupled
with the decline in predators (human and non-human) sets up a competitive situation between the grazer
populations. Since non-ruminants are less efficient than ruminants the competition drives non-ruminants to
final extinction.
Discussion
The major assumption of this research effort is that North American ecosystems were in equilibrium prior
to the anival of H. sapiens. This modeling paradigm forces an understanding of the web of relationships
that support equilibrium. Only then are we able to come to grips with the perturbations associated with the
migration of H. sapiens.
Fig. 11. Second-order predation, plants. Four-herbivore model
Hsapiens enters
450, the New World
8
i
E | SmallTrees
5 Normalized
3 |
a BigTrees
w | Normalized
3225)
4
5 | en
z a GrassHigh
§ : iv Normalized =
cs '
5 Newee
a
0 al
-11600 -11075 -10550 -10025 -9500
In this modeling effort as the models have become more complex and more like the real world, the intpact
of H. sapiens in the Second Predator - Overkill mode has been less and less severe. In the Second Order
mode, as the models have become more complex, there have been more extinctions and greater overall
change with little additional reduction in predator populations.
Given the assumption of equilibrium, overkill has been shown to be inconsistent with extinction. Second
order predation (H. sapiens reducing predator populations) has been shown to be more consistent with
extinctions in an equilibrium system. The proximate cause of the extinctions is environmental exhaustion
from destabilizing predator control of herbivore populations.
Environmental exhaustion as the proximate cause for extinctions suggests a period of extreme scarcity of
vegetation. During that period ruminant digestors who extract the maximum nutrition and energy from their
food would be selectively favored.
Environmental exhaustion would also acoount for the shift from plaids - patchy mixed woodland - to stripes
- Closed canopy forest near the mountain refugia and unbroken grassland in the center of the country
(Guthtie, 1989). The shift, in tum, suggests why two ecophenotypes or two sub-species of bison emerged -
B. bison bison, grazers of the prairie and B. bison athabascae, mixed feeders of the woodland. B. bison
bison kept the woodland from encroaching on the plains by eating new trees and thus preserved the
Prairie.
Environmental exhaustion accounts for the hias in favor of small size observed in many species including
bison and the extinction of animals that were not hunted by H. sapiens (e.g. ground sloths) and should not
have suffered from climate change (e.g. horses).
Environmental exhaustion explains the data from Hansen's (1978) study of Rampart cave. There was
apparently no evidence of climate change which would have reduced the food available to the Shasta
ground sloth (Nothrotheriops shastensis) but in studying the evidence of diet in its dung Hansen found
more and more Monmon tea (Ephedra navadensis) and less and less of its staple, globemallow
(Sphaeralcea ambigua). Globemallow is used by other extant herbivores whereas Monnon tea is not. If
the Second Order Overkill is correct the ground sloth would have been out- competed by more efficient
herbivores in the time of extinction - the booms and busts.
Significance for evolution
The entire ecosystem evolved through the mechanism of extinctions. The extinctions being the result of an
anthropogenic change in the relationship between camivores and herbivores and thus changing the
relationship between herbivores and plants.
Bison, being ruminant grazers made it through the bottleneck. The new “striped” Holocene environment
gave two possibilities - grazing and mixed browsing. Living in one of the two stripes. Plains hison (B.
bison bison) are obligate grazers whereas woodland bison (B.bison athabascae) are, as their name
implies browsers and grazers. Both are significantly smaller than their Pleistocene forbears. Until they
were hunted to near extinction during the 1880s, plains bison maintained the prairie as a grazing ground.
Once they were removed trees began to encroach upon the long grass prairie. In the absence of farming,
over time the increased number of trees would have changed the relative humidity through transpiration.
This, in tum may have led to a decrease in continentality.
Significance for modellers
This project made a conscious effort to keep the model as simple as possible. Scientists who are not
comfortable with complex models can see the utility of sinaple models that test one hypothesis against
another. This is especially important for paleontologists and archaeologists who have little data and no
other way of testing. Scientists who are conversant with models should make a concerted effort to bring
their colleagues into the modeling community through the use of simple models.
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