Download POTENTIAL APPLICATIONS OF BIOME MODELLING

POTENTIAL APPLICATIONS OF BIOME MODELLING
*
by David W. GoonALL
Ecology Center, Utah State University, Logan,
Utah 84321
USA
One of the achievements of the International Biological Pro­
gramme which seems likely to have a lasting impact is the concen­
tration of attention and effort by the ecological community, in a
very broad sense, on ecosystem problems. The ecosystem concept,
corresponding closely with the « biogeocoenosis » of the Russians,
has been in the ecological literature for nearly forty years ; but
it is only during the last ten or fifteen years, and particularly
during the duration of the IBP, that the idea of an integrated
system involving plants, animais, microorganisms, soil and micro­
climate in an interlocking set of processes has really penetrated
deeply into ecological thought.
More recently still has the idea of ecosystem modelling corne
to the fore, and this has become closely associated with a number
of the ecosystem studies under the IBP.
Mathematical representation of ecological processes is not
new. Simple representations of particular processes (predation,
competition, etc.) were being put forward during the 1930's ; but
the simplifications necessary made them unrealistic. Ecosystems
are, except in trivial cases, extremely complicated, with dozens or
hundreds of populations of organisms differing in genetic consti­
tution and consequently in their responses to other factors in the
system, and an environment which is often spatially heterogeneous
on several superimposed scales, all relevant to the functioning of
the system as a whole. It is consequently almost hopeless to try
to express the dynamics of such a system in terms of relatively
simple mathematical expressions capable of analytic treatment.
The availability of digital computers has changed the picture here,
as in so many other fields. No longer is it necessary to limit the
outlook to mathematical treatments which can be handled analy­
ticaly. The sets of non-linear differential equations with disconti­
nuities and subject to constraints which are required for any
•
Based on paper read to
the First
General
Assembly
of
SCOPE
(Scientific
Committee on Problems of the Environment) in Canberra, Anstralia, Sep t. 1, 1971.
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tolerably realistic representation of ecological processes can be
solved digitally without difficulty, though the full complexity of
an entire ecosystem may still be beyond the capacity of the current
generation of computers.
Even so, the way has been opened to
a mathematical representation of ecosystem dynamics which can
be cast into a form suitable for digital solution, and thus enable
the ecosystem to be simulated in the computer.
A number of the ecosystem projects under the IBP - com­
monly known as « Biome » studies, because investigation of eco­
systems have usually been grouped to cover the broad groups of
ecosystems, similar in physiognomy and climatic requirements,
known as « Biomes » - seized on the possibilities afforded by the
newly developing work in ecosystem simulation, and saw that it
would afford them the opportunity of effective integration of the
varied ecological studies which were being initiated under the IBP.
In this, they were encouraged by the closer contacts which deve­
loped, under IBP stimulation, with physical scientists in such fields
as meteorology, soil physics, hydrology and oceanography ; contact
and interchange with these fields were necessary for the deve­
lopment of the programme, and at the same time the concepts of
mathematical modelling and computer simulations were much
more familiar in them than in biology.
In England and Ireland, in Canada and the United States, in
Israel and Australia, considerable progress has been made in this
field, and models have been constructed in greater or lesser detail
covering tundra ecosystems, moorland, temperate and tropical
forests, grasslands, arid lands, lakes, rivers, and marine ecosys­
tems. The principles underlying these models are straightforward
enough. The initial state of the ecosystem at a fixed point in time
is described in terms of a large number of variables, mostly quan­
titative, expressing the numbers, weights, age and sex distribution,
and composition of each of the major groups of organisms, and
similar values specifying their abiolic environment.
All these
values may be subject to spatial heterogeneity relevant to the func­
tioning of the system (the rabbits in warrens in the southeast
corner of a plot may eat the ground bare for a radius of 50 metres,
but have no effect on the vegetation of the northwest corner
200 metres away), and consequently the state variables need to
describe this heterogeneity adequately. The model incorporates
mathematical specifications of the rates of change of each of these
state variables in tenns of the various factors influencing them.
These factors may be other state variables, or may be variables
whose values are not defined within the model.
For the latter
(exogenous variables, or « forcing functions » ) , which normally
include the meteorological conditions, values must be supplied for
the period to be simulated - perhaps as constants, perhaps as
tables with rules for interpolation, perhaps as time-dependent
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functions, perhaps as stochastic functions, but in any case inde­
pendent of events within the system.
Given the initial values of the state variables, functional
expressions for their rates of change, and values for the exoge­
nous variables required, the computer simulation programme pro­
ceeds to solve the set of differential equations, and reports the
values of the state variables at the end of the simulation period,
thus specifying the new state of the system.
I. THE PROCESS OF ECOSYSTEM MODELLING
Let us consider a simplified ecosystem, and the steps neces­
sary in order to produce a computer simulation model of it - a
system such as is represented in Fig. 1, with one primary pro­
ducer, one herbivore and one carnivore, together with decompo­
sers. Sorne of the processes taking place in the system (an arbi­
trary selection) are represented by arrows, and may constitute
causal and dynamic relationships between the components of the
system.
°'
\:::=
�' ===
.,v
Ll
.,..
�.,
HERBIVORY
�'!=-======
Dl PODOMYS
PREDATION
MICROPS
o..,
"'
""
...
�
.._'!:
>:
��
.._
...
"'
�
,,,,..
�
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!!;
MICRO
ORGANISMS
Fig. 1. -- Sub-systems within
a
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simple ecosystem.
The modelling process is often facilitated by dividing the sys­
tem into sub-systems. Each of the « boxes » in Fig. 1 could be
regarded as such a sub-system, with is own inputs and outputs
(including the processes represented by arrows entering or leaving
the box). These interactions between sub-systems sometimcs (as
in Fig. 1) consist in the actual transfer of material ; in other cases
they may rather be an influence exerted by one sub-system or the
other (as, for instance, if a carnivore modifies herbivore behaviour
through proximity, without engaging in actual predation ; or in
the soil changes caused by burrowing animais).
One sub-system within the simple ecosystem of Fig. 1 is illus­
trated in Fig. 2 - the shrub A triplex conf ertifolia. This sub-system
should not be thought of as a single shrub, but as the whole popu­
lation of this species within the boundaries of the ecosystem.
i
a\�o.�
� �. ·
A
0:'o
'.9o....-;
�(
..
1700
..
)
REPRODUCTION
·
�
Fig. 2.
-
�
Processcs in the Atrip/ex confertifolia sub-system.
A number of processes involving this sub-system are shown, some
internai, some linking it with other parts of the ecosystem or with
the exterior.
The rate of each of these processes is dependcnt
upon the current values of a number of factors, and some of these
influences are indicated as dotted lines.
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The model of the sub-system needs to incorporate a mathema­
tical representation of the way in which the rate of each process
is affected by the various factors influencing it.
Fig. 3 isolates
SOIL
CONFERTI FOLIA
"'
<;:;
"-'
"'
....
"""
,__
"'
Cl
....
Cl
"'
�
INTERNAL
CARBOHYDRATE
CONCENTRATION
CURVE
A
HIGH
CURVE
B
LOW
....
"-'
"""
,k2j
�
�
MOISTURE
HIGH
MEDIUM
o
LOW
o
RADIATION
Fig. 3.
-
The photosynthesis process in the
Atriplex confertifolia sub-system.
the process of photosynthesis in this sub-system, and illustrates
graphically the way in which its rate is related to the three factors
(among others) indicated as influencing it in Fig. 2.
For each
process included in the model, an expression like that graphed
in Fig. 3 is needed. The computer simulation, from these expres­
sions, can then determine the rate of change for each of the state
variables in the system, using outputs from one sub-system as the
required inputs to another, and can thus movc the whole system
through successive time steps.
II. APPLICATIONS OF ECOSYSTEM MODELLING
Ecosystem models are of great value in guiding integrated
research programmes, in painting to gaps in knowledge, in correc­
ting conceptual schemes which contain internal inconsistencies or
do not match the real world.
But for the present 1 intend to
concentrate on their potential praclical value.
It is more and more coming to be realized that environmental
changes affecting man are changes in the biosphere - that tenuous
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skin surrounding Space-Ship Earth within which all life is suppor­
ted, and which is only « ecosystem » writ large. The biosphere
is a mosaic of ecosystems, each following its own dynamic course,
but interacting at its borders with other ecosystems through
exchange of material, energy and biota. A full understanding of
processes in the biosphere presupposes an understanding of pro­
cesses in the ecosystems which make it up.
Modifications to ecosystems have often led to unexpected and
unwelcome consequences.
One may instance the effects of chlo­
rinated hydrocarbon insecticides, on the one hand in increasing
to pest proportions the populations of red spider mites, and on
the other in greatly reducing the populations of birds of prey.
The introduction - inadvertent or deliberate - of exotic biota has
had drastic effects - as with the European species of deer in New
Zealand.
Deforestation, over-cropping and over-grazing have in
many parts of the world led to soil erosion of such seriousness
that human depopulation followed. All of these effects could be
attrilmted to lack of foresight. But adequate foresight would have
depended on adequate understanding of the ecosystems in ques­
tion.
And even a sound understanding might not generate ade­
quate foresight in systems as complex, as replete with feedback
mechanisms, as ecosystems are. They have been called counter­
intuitive - the effects of a manipulation may often be the reverse
of those which unsophisticated intuition would suggest.
Conse­
quently, intuition needs aid and guidance in order to make reliable
predictions, however good the understanding, and this aid and
guidance can be provided by modelling.
By changing the input
of the computer model in accordance with the proposed manipu­
lation of the ecosystem, the changed output at different intervals
thereafter can be used as a guide to action ; the cost-benefit
balance of different types of management or modification can be
worked out, and hence the pattern of action can be optimized.
Let us look at some of the types of practical problems in which
such a prediction facility might be valuable.
Modelling has
already been used as a means of studying the movement through
the ecosystem of contaminants such as insecticides, heavy metals,
and radioisotopes (Kaye & Ball, 1969 ; Olson, 1963 ; Raines et al.,
1969). The locations and degree of accumulation of these mate­
rials can point to hazards to Man, or to ecosystem stability.
Attempts to control animal populations can also be guided by
ecosystem modelling - where, for instance, interactions between
predator and prey are involved, or where modifications of the
environment are proposed which will perhaps affect only certain
parts of the life cycle of a pest organism. Organization of grazing
systems, by distribution of grazing intensity in space and time,
and in its qualitative aspects by use of different herbivore species,
is another type of practical problem to which ecosystem modelling
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can contribute.
The practical use of models implies, however,
that a biologically sound conceptual framework has been deve­
loped for the model, and that the necessary data are available.
Too often, the latter is not yet true ; and, unless the former
becomes true, the latter often never will be.
The collection of
ecological data without such an integrating framework as can
be provided by a model may meet ad hoc purposes, but is unlikely
to serve effectively for prediction.
The predominant role in ecosystems of biological organisms,
with infinite possibilities of genetical variation in their responses
to different sets of environmental factors, means that the data on
which an ecosystem model may need to call are far more varied
and numerous than are required for a model of a purely abiotic
system. Even for the abiotic components of ecosystems (soil, for
instance), the complexity of data required is likely to be conside­
rably increased by the importance of their interactions with the
biota.
In general, one must expect every species to behave diffe­
rently, at least in some part of its functioning. Since an ecosystem
commonly includes hundreds - perhaps thousands - of different
species, this might be thought to impose an intolerable compJexity
on the modelling task.
Luckily, however, the distribution of
species abundance is extremely skew, so that in many ecosystems
the bulk of the biomass in any trophic category is composed of
five or ten species only, and in consequence the problem of model­
ling can often be greatly simplified with little loss.
If all the
less important species within a trophic level are pooled, and only
the few dominant ones are treated in individual detail, the
approximation may be satisfactory. Sorne models have even gone
further and pooled the whole of each trophic level ; for certain
purposes this may be satisfactory, but species individuality (as
exemplified by Gause's principle of competitive exclusion, unduly
formalistic though this may be) is so important in ecosystem func­
tioning that to ignore it is dangerous.
Luckily, however, species differentiation does not usually go
so far that models of different structure are required for each
species. Usually, a model of a given structure can be adapted to
apply to a wide range of species. If it reflects faithfully the basic
mechanisms operating, a modification of the parameters involved
will generally suffice to make it apply satisfactorily to a new
species.
As in other fields, the modelling of ecosystems is a balance
between precision and practicality - one must compromise with
known inaccuracies for the sake of simplification.
Pooling of
species is one such simplification.
A different type of simplifi­
cation concerns the processes modelled.
In general, they cannot
be represented in the full complexity with which their mechanisms
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are understood. Vve may perhaps go from the ecosystem level one
or two steps down the scale of integration to that of the organism
or the organ, particularly in parts of the model which are crucial
for the immediate purpose ; but to go below these to the cell, the
organelle or the molecule would be out of place. Thus we must
again compromise and accept a model which, though consistent
with, does not make full use of present-day knowledge.
By limiting the level of integration to be considered in the
biota, we can also limit the degree of resolulion in the time scale
that may be required for the model. If the phenomena in which
we are interested as output are on the scale of years or months,
then it is fruitless to consider mechanisms that operate on the
scale of minutes or seconds.
By not considering processes on a
time scale less than, say, a day, an adequate simulation of the
spatial and qualitative complexities inseparable from ecosystem
dynamics becomes possible.
vVe will now consider one or two specific examples of models
developed to deal with particular questions of environmental
management, and based on simulation of ecosystem behaviour.
Ali have progressed to the point of computer implementation,
though the firmness of the data on which they are based varies,
and in no case has their performance been quantitatively com­
parcd with that of real-life systems.
The type of simplifying
assumptions that may be made in ecosystem models will become
evident in these specific instances, and it should be understood
that simplifying assumptions are an inseparable part of the model­
ling process.
a.
A
MODEL FOR GRAZING MANAGEMENT.
The first of these models concerns grazing management. In
arid or semi-arid vegetation, what population of herbivores could
maintain a steady state ? By shifting the grazing flocks from one
area to another, can the overall productivity be increased ? What
is the effect of changing the number or distribution of watering
points ? How much damage to the vegetation can be permitted
during a season of exceptionally low rainfall, without preventing
recovery when seasons improve ?
This particular model (Goodall, 1967, 1969, 1970 a, b, 1971) is
based on grazing conditions in inland Australia, where livestock
move freely within a large fenced area. Plant growth is treated
simply, animal behaviour in a more detailed fashion. It is assu­
med that ail forage is of perennial plants, and that their repro­
duction can be ignored ; it is further assumed that growth can be
expressed in terms of relative growth rate of the forage portion
of the plant, and that regrowth from organs not eaten by the
herbivores can be ignored. The relative growth rate is treated as
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a function of mean monthly temperature, and of available soil
moisture. The function used - which can serve as an example
of the way the model is constructed - is
R
=
max [O, (a +
b
w + c
)]
(1 +
d + fT)T
where R is the relative growth rate (daily increase in dry matter,
as a proportion of existing dry matter), T is the mean monthly
temperature in °F, and W is the available soil moisture, as a pro­
portion of capacity. (i.e., water in the rooting zone in excess of the
wilting coefficent, expressed as a proportion of the range between
wilting coefficient and field capacity). The values a, b, c, d, and
f are constants characteristic of the species ; representative values
are
.0001, .4, .06 and - .003 respectively. Changes in avai­
lable soil moisture (W in the expression above) are calculated as
a balance between rainfall, evapotranspiration, and run-off (or
run-on) - i.e., possible loss to the sub-soil is ignored.
It is assumed that the area may be divided into compartments
differing in vegetation and in other factors determining herbivore
behaviour, but that the herbivore behaves as if each compartment
is internally homogeneous. The attractiveness of each compart­
ment to the herbivore depends on the quantity of forage of high
and low palatability present, and on its proximity to the fenceline
and to a watering point. The number of animal-days of consum­
ption per day in each compartment is then proportional to its
4000
0.2
3000
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.,.
e
.2
0 2000
"
.2
ü
"
.,,
e
o.
.?::- 1000
8
0.4
0.2
0
Fig. 4.
-
5
10
15
20
25
30
Simulated rainfall and forage production in summer (January)
and winter (July).
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attractiveness.
The amount of forage consumed per animal-day,
and its distribution by species, depends on the amount of the
various species present, weighted by palatability.
The animals gain weight or lose weight according to their
current weight-for-age, and the amount and nutritional quality
of the food they are consuming. No predators are incorporated in
the model, but natural mortality is a fonction of weight-for-age.
Reproduction (varying from month to month) is also a fonction
of the mean adult body weight.
Meteorological conditions are specified in the form of mean
monthly temperatures, together with records of the frequency with
which different daily totals of precipitation have occurred in each
month.
Random samples are then taken from this frequency
distribution.
Examples of the resulting rainfall sequences, and
their effects on total vegetational productivity under grazing, are
shown in Fig. 4.
An obvious way in which such a model could be applied to
practical purposes is in the determination of « safe » stocking
rates - the herbivore population density which, taking good sea­
sons with bad, could be maintained indefinitely.
An example is
given in Table 1 for a short period, using flocks of mature wethers,
and not replacing lasses of animals occurring during the trial. It
is clear that the equilibrium stocking rate for that season and for
the particular conditions envisaged was about 1140.
The wide
variation in rainfall conditions from season to season would make
it preferable, however, to base a management decision on several
repetitions of the simulation, with different random samples of
rainfall.
TABLE 1
Eff ect of stocking rate on results after 4 months.
Stocking
Forage
production
Change
in
Wool
Mean
Mortality
standing crop
production
(metric tons)
(%)
(kg)
(kg)
1,000
168
+ 12.9
1,643
51.5
3.5
rate
live
weight
(%)
1,200
148
- 5.1
1,969
51.2
3.6
2,000
82
-63.3
3,263
47.8
3.8
2,500
59
-80.6
4,035
43.7
4.2
3,000
44
-88.1
4,744
40.0
5.0
4,000
27
-96.l
5,918
34.9
7 .0
Another practical application of the model would be to deter­
mine whether the improved distribution of grazing through pro-
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Figure 5a. Paddock with Water
Supply in one Corner.
Figure 5b. Paddock with Water
Supply in Two Opposite
Corners.
Grozing Pressure
L.owest
Upper
Slope
Lower
SI ope
Flat
Medium
Highest
m .:EJ]]: .i·
��­
��·
:i ii [ [� : j j
1
Km
Figure 5c. A:lddock with Central
Water
Fig. 5.
-
Supply.
Distribution of grazing intensity, as affected by location
of water supply.
vision of extra watering points would be worth the expense invol­
ved. Fig. 511 shows the distribution of grazing pressure in a pad­
dock when water is supplied at one corner, with substantial under­
utilization of forage at a distance from the water supply. Figs. 5b
and 5c show the same paddock with water supplied at two opposite
TABLE
2
Effect of position o/ watering point on rewlts a/ter 6 months
(1,200 sheep, continuous grazing).
Wa t erin g
point(s)
Forage
production
(m ctric ton s)
Mean
Change in
;landing crop
p ro d u ction
(%)
(kg)
(kg)
Wool
]ÏYC
wcight
Mortality
O ne corn er
204
-14.2
2,791
51.fi
5.0
Two corners
221
- 6.!J
2,810
51.!J
4.!J
Centre
218
-
7.8
2,807
51.9
5.0
corners, or in the centre. Table 2 shows the forage production in
this paddock predicted by the computer simulation over a period
of six months with a moderate stocking rate, under the three
It will be
alternative water-supply arrangements postulated.
noted that Fig. 5b represents an appreciable improvement over
Fig. 511, but that a central water supply (Fig. 5c) gives no further
increase in productivity.
Another version of the same model takes account of several
species of herbivores simultaneously. It is assumed here that the
diff erent species act on one another only through their forage
consumption. Some results given by this model arc illustrated in
Fig. 6, for a situation in which rabbits and a breeding flock of
sheep are in competition. The rapid build-up of the rabbit popu­
lation, in response to abundant forage, causes severe depletion of
the vegetation to a point where neither the rabbit population itself
nor the sheep flock (despite its different forage prcferences) can be
supported, and their numbers decline catastrophically to a point
where the trend starts to reverse and the vegetation can bcgin to
recover.
Clearly a model like this would be a valuable aid in making
a cost-benefit judgement on the potential value of a rabbit control
programme. It woul<l also enable questions to be answercd about
whether a mixture of grazing animais with different forage prefe­
rcnces woul<l enable the vegctation to be used more efficiently
and to be kcpt more easily in a stable con di lion lhan single-species
- 129 9
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5000
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NUMBERS
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lt
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JAN
Fig.
G. -
FES MAR APR MAY JUNE JULY AUG SEPT OCT NOV
DEC
Simulated changes in population and 1nean adult weight
population
of sheep and rabbits.
in
a
mixed
utilization - as has often been suggested.
Such a model could
also help decisions regarding the pros and cons of introducing
exotic herbivores.
b. A GRASSHOPPER POPULATION MODEL.
Quite a different type of herbivore problem - so different as
to call for a different modelling approach - is posed by locusts.
Since Biblical times and before, locusts have been feared as a
menace to agriculture in northern Africa and the Middle East, and
in the past two or three decades great progress has been made in
controlling their worst effects, largely through careful study of
population build-up in the areas from which they migrate.
To
take it further and perhaps interfere with the build-up at a still
earlier stage might be even more satisfactory, if suitable means of
predicting the build-up were available.
This prediction could
appropriately be carried out by a computer simulation model ; to
prepare such a model might be a relatively small step, considering
the amount of information already accumulated.
So far as I know, this has not yet been done. But a model is
available covering the interaction between grasshoppers and vege-
Cl
IMMIGRATION
PREDATION
1
11
AIR TEMPERATURE
GRASS HOPPER
SPECI ES COMPOS.
8
DENSITIES
1
PREFERENCE ..
IMMIGRATION
S OIL SURF
PHYSICS
FORAGE AVAi LA BLE
FOR LI V ESTOCK
,..
FORAGE
SPECIES COMPOS.
8 BIOMASS
_____________
...
1
1
..
SOIL
WATER
Fig. 7. - Model to show changes in grasshopper populations and their food plants.
-
131
-
tation in the western United States (1).
Grasshoppers are only
a step away from the migratory locust, and to modify this model
for the latter might not require a great effort.
The logical structure of the model is illustrated in Fig. 7. It
is primarily directed to the effects of a mixed population of
grasshoppers on the composition and productivity of vegetation
including bath annual and perennial species.
Each grasshopper
species has a favoured food plant, and remains in the area only
if that type of food is present. Hatching of each grasshopper spe­
cies depends on accumulation of day-degrees in the spring, and
on adequate soil moisture. The insects are assumed to progress
from one instar to the next after a fixed interval, so that all indi­
viduals of a species are in the same instar at any given time.
Mortality is caused by a predation rate constant for each species ;
by cold ; and by additional causes assmned random. Egg produc­
tion per adult is proportional to the amount eaten during deve­
lopment, and to a soil-surface factor determining whether condi­
tions are suitable for oviposition.
The food consumption per insect is calculated on the basis of
This is distri­
a calorie demand constant for species and instar.
buted among plant species in proportion to the amount in which
they are present, and to a preference factor constant for each
combination of plant and grasshopper species.
Germination of annuals is triggered by accumulated tempe­
rature and soil moisture, regrowth of perennials by photoperiod.
Relative growth rate for each plant species is a constant multi­
plied by a factor varying with the season and inversely with
the total above-ground biomass present. Reproduction by peren­
nials is not provided for.
C.
A MODEL OF MOSQUITO POPULATIONS.
W e turn now to quite a different type of model likely to have
application in quite a different field.
Mosquitoes are important
disease vectors in many parts of the world, and great efforts have
been expended to reduce their populations, with varying success.
Such efforts could be greatly facilitated by a model to predict
the effects of environmental manipulation on their abundance.
A model has been developed to describe the development of
mosquito larvae in cattle tanks in New Mexico, and will serve to
illustrate the potentialities of the modelling approach to this type
(1) This model was developed by Dr. Kent Bridges and his colleagues in the
course of their work in the Desert Biome programme of the US/IBP. A booklet
descrihing
the
model
in
detail has been prepared,
and
rnay
be
obtained
Dr. Bridges, in the Ecology Center, Utah State University, Logan, Utah.
- 132 -
from
----- ..
•
1
•
1
1
1
1
1
1
1
1
Fig. 8.
-
Mode! to show changes in rnosquito populations.
of public-health problem (1). The logical structure of the model
is illustratcd in Fig. 8.
The mosquitoes overwinter as adult
females, which lay eggs as soon as the tcmperature exceeds a
specified minimum.
The number of eggs laid is proportional to
the number of females overwintering and to their probability
of obtaining a blood meal.
Each successive batch of eggs laid
initiates a new cohort, and each cohort is followed separately
through the developmental process. Passage from one instar to
the next depends on the accumulated tempcrature sum for that
cohort. Adults die when the accumulated tcmperature sum after
their emergence excceds a certain limit (different for males and
femalcs), and males also die if the temperature falls below a
A weekly mean temperature below another minimum
mininmm.
causes the females to go into hibernation.
For newly-emerged females, a blood meal (assumed to occur
aftcr a fixed temperature sum) is required for ovary development
to bcgin, and another fixed tempcrature sum is needcd beforc the
female i s ready to mate. Eggs are laid if water is available, the
number depending on the current temperature, and the female
reverts to a hungry state waiting for another blood meal.
(1) Like the grasshopper mode! described in the previous
section,
modcl
was
dcveloped
by
Dr.
Bridges
and his
collcagues
in
the
programme. Booklcts describing the mode! are availablc on request.
- 133 -
this mosquito
Desert Biome
The water content of the tank is a balance betwecn inflow,
withdrawal, and evaporation. If it dries out, all eggs, Iarvae and
pupae die.
WATER DEPTH AND TEMPERATURE
-
-
-
Î
WATER ADCITION
--
--
-
-
-
-
-
- ..........
..
... .........
Î WATER Î WATER
ADDITION
WITHDRAWAL
ADULTS
AQUATIC STAGES
t
APRIL
Fig.
H.
--
1
MAY
t
JUNE
t
JULY
1'
AUGUST
Simulated changes in mosquito populations in relation to water supply
and temperature.
Sorne results produced by the computer simulation pro­
The
gramme implcmenting this mode! are illustrated in Fig. 9.
upper diagram shows the repeated filling of the tank (by rainfall,
or artificially), and a sudden emptying, with the seasonal course
of temperature, while the Iower diagrams show the changes in
population of adults and immatures stages.
Though the prime
purpose of the mode! was to find whether manipulation of the
water Ievel in the tank could effectively control the insects, it
could clearly also serve as part of a larger model used to simulate
other methods of control.
Similar models could be developed to aid in the planning of
control campaigns against diseases dependent on aquatic vectors,
such as bilharziasis and other snail-borne helminth infections.
- 134 -
III. MODELLING,
PREDICTION AND ENVIRONMENTAL MONITORING
It is clear that the building of realistic ecosystem models
demands not only a thorough understanding of the biological
relationships involved, but also a body of detailed data.
Each
of the mathematical fonctions incorporated in the model will
include a number of constants, and estimates of these constants
will be required. The form of the fonctions will often be quite
uncertain.
And it may not be known which factors influence the
rate of each process sufficiently to be worth incorporating in the
model. Answers to all these questions will often not be available
beforehand, and will need ad hoc observations in field or labo­
ratory. And, be it noted, the model itself can play a most impor­
tant part in guiding these observations.
Until at least a provi­
sional version of the model is available, it will not be known which
of these data are required, or what their relative importance
may be. The provisional version can be based on general back­
ground knowledge rather than ad hoc experimentation ; but
without it one is unlikely to make further progress.
There is currently much talk of the need for environmental
monitoring, in order to check possible deterioration of the envi­
ronment through human activity. Monitoring is indeed necessary
and valuable, but it is not enough. Monitoring is concerned with
the present ; we need to look to the future. If we postpone action
until our monitored variables show an undesirable change, we
may have left it too late - we may be locking the stable door after
the horse has been stolen.
To vary the metaphor, we must nip
these changes in the bud - before they reach the stage when they
are detectable by our monitoring devices, and while they are
perhaps at an earlier and qualitatively distinct stage.
Such
qualitative shifts in the type of change in a dynamic system can
be predicted by models, but not by simple monitoring of the
variables directly of interest. Monitoring guided by models, indi­
cating variables which, though not of direct interest, are sensitive
to the early stages of changes, would be more promising. But still
more valuable would be the use of models as a tool for managing
the environment, by predicting the consequences of different
courses of action (including, of course, no action), and hence
making possible the optimization of management towards a set of
accepted goals.
Let us not run before we can walk, though. Modellers are
proceeding beyond the ecosystem or the landscape unit to the
region, or even the world - the biosphere as a whole. W e are
probably not yet ready for this ; and at this scale our models
cannot be tested or validated.
At the ecosystem scale we can
test the accuracy with which our models make predictions, and
- 135 -
improve them whenever they need it.
I f eel that we should make
good use of this feedback possibility in model building before we
extend work to a scale where feedback is impossible, and where
the consequences of decisions based on false predictions may be
much more serious.
I would therefore argue that we should
develop our knowledge of ecosystems and incorporate our know­
ledge into models which can be tested ; when we are satisfied
that, at this scale, we can make reliable predictions, we can feel
reasonably confident that, in moving to the larger scale, our
mistakes will not be too serious.
READING LIST
A
-
Monog
. raphs and Symposizzm Volzzmes on Systems Ecology.
(1970). - Modelling and systems analysis in range
Range Sei. Dept., Colo St. Univ., Sei. Ser., 5 : pp. 134.
JAMESON, D.A. (Ed.)
JONES, J .G.W.
(Ed.) (1970). - The zzse of models in agricullzzral
Range Sei. Dept., Colo. St. Univ., Sei. Ser., 5 : pp. 134.
MARGALEF, R. (1968). - Perspectives in ecological theory.
Chicago & London, pp. viii + 111.
and
science.
biological
Univ. Chicago
Press
:
PATTEN, B.C. (Ed.) (1971). - Systems analysis aT,d simzzlation in ecology. Academic
Press : New York
&
London, pp. 610 (vol. 1).
VAN DYNE, G.M. (1969). - The ecosystem concept in natzzral resozzrce management.
Academic Press
WATT,
: New York
&
London. Pp. xiv + 383.
(Ed.) (1966). - Systems analysis
New York & London, pp. xiv + 276.
KE.F.
WATT, K.E.F. (1968).
-
in
ecology.
Aeademie
Press
:
Ecolog
. y and resoiirce management. A quantitative approach.
McGraw-Hill : New York, pp. xii + 450.
WRIGHT, R.G.
- Simzzlation and analysis of dyna­
Range Sei. Dept., Colo. St. Univ., Sei.
VAN DYNE, G . M . (Ed.) (1970).
&
mics of a semi-desert grassland.
Ser. 6, pp. iv + 218 + 70 + 19.
B - Other Papers.
BocHE, R.E. (1968).
1968
A simulation in plant eeology. Spring. Joint Comput. Conf.,
-
: 67-71.
BRENNAN, R.D., WIT, D.T. de, WILLIAMS, W .A. & QuATI'RIN, E.V . (1970). - The utility
of a digital simulation language for eeologieal modeling. Œcologia, 4 :
113-132.
- Digital computer simulation of ecologieal systems. Nature,
: 856-857.
GARFINKEL, D. (1962).
Lond., 194
(1964). - Digital computer simulation of an eeologieal
based on a modified mass action law. Ecology, 45 : 502-507.
GARFINKEL, D.
GAnFINIŒL, D.
(1965).
system,
Computer simulation in biochemistry and ecology.
Mathematical
Biology
(ed.
T.H.
Waterman
H.J. Morowitz). Blaisdell : New York, pp. 292-310.
-
Theoretical
and
In
&
GARFINimL, D. (1965). - Simulation of ecologieal systems. In Compzzters in Biome­
dical Research (ed. R.W. Staeh & B.D. Waxman)
Academic Press :
New York
&
London. Vol 2, pp. 205-216.
& S A CK, R . (1964). - Computer simulation and
analysis of simple ecologieal systems. Ann. N. Y. Acad. Sei., 115 : 943-951.
GAHFINKEL, D., MAcAnTHUR, R.H.
- Computer simulation of changes in vegetation sub j ect
to grazing. J. lnd. bot. Soc., 46 : 356-362.
GoonALL, D.\V. (1967).
- 136
GooDALL,
D.\V.
(1969).
-
Simulating
Methods of Biomathematics
:
the
grazing
Simulation
situation.
Techniques
In
Concepts
and Methods
and
(ed.
F. Heinmets). Marcel Dekker : New York, pp. 211-236.
GoODALL, D.\V. (1970 a). - Use of computer in the grazing management of semi­
arid lands. XI !nt. Grass/. Congr. Proc., 917-922.
GoooALL, D.\V. (1970 b). - Studing the efîects of environmental factors on eco­
systems. In Analysis of
Springer
:
Tempcrate Forest Ecosystems (ed. D.E. Reichle)
Berlin, pp. 19-26.
GooDALL, D.\V. (1971). - Extensive grazing systems. In Systems Analysis in Agri­
cultural Management
pp. 173-187.
(ed.
J.B. Dent
J.R.
&
Anderson) Wiley
:
Sydney,
HOLLING, C.S. (1965). - The functional response of predators to prey density and
ils role in mimicry and population regulation. Mem. Entom. Soc. Canada,
45 : 1-60.
HOLLING, C.S. (1966). - The functional response of invertebrate predators to prey
density. Mem. Entom. Soc. Canada, 48
HOLLING,
: 1-86.
C.S. (1969). - Stability in ecological
Brookhaven nat. Lab., 22 : 128-140.
and
social
systems.
Symp.
&
BALL, S.J. (1969). - Systems analysis of a coupled compartment
mode! for radionuclide transfer in a tropical environment. Proc. 2nd
Symp. Radioecol. : 731-739.
RAYE, S.V.
KEHSHAW, K.A.
& HARRIS, G.P. (1971). - Simulation studies and ecology : a simple
defined system mode!. In Statistical Ecology (ed. '6.P. Patil, E.C. Pielou
& "\V.E. Waters) Penn. St. Univ. Press : University Park & London. Vol. 3,
pp. l-19.
I{ERSHAW,
ICA. & HARRIS, G.P. (1971). - Simulation studies and ecology : use
of the model. In Statistical Ecology (ed. G.P. Patil, E.C. Pielou et W.E.
\Vaters). Penn. St. Univ. Press : University Park & London. Vol. 3,
pp. 23-39.
N1vEN,
B.S. (1967). - The stochastic
Physiol. Zoo/., 40 : 67-82.
simulation
of
Tribolium
populations.
N1vEN, B.S. (1969). - Simulation of two interacting species of Tribolium. Physiol.
Zoo/., 42
N1vEN,
B.S.
: 248-255.
(1970). - Mathematics
brachyurus
of
populations
of
the
quokka,
Setonix
(Maeropodidae). I. A simple deterministic model for quokka
populations. Aust. J. Zoo/., 18 : 209-214.
O'CONNOR, J.S.
&
PA T TEN , B.C. (1968). - Mathematical rnodels of plankton produc­
tivity. Reservoir Fishery Resources Symp., Athens Ga., April 5-7, 1967
:
207-226.
0LSON, J.S. (1963). - Analog computer models for movement of nuclides through
ecosystems. In Radioecology (ed. B. Schultz
&
A.K. Klement) Rheinhold
:
New York, pp. 121-125.
0LSON, J.S. (1964). - Gross and net production of terrestri:il vegetation. J. Ecol.,
52 (Surpl.) : 99-118.
O'NEILL, R.V. (1969). - Indirect estimation of energy fluxes in animal food webs.
J. theoret. Biol., 22 : 284-290.
PAnKEH, B.A. (1968). - Simulation of an aquatic ecosystem. Biometrics, 24 : 803821.
PATTEN, B.C. (1966). - Systems ecology : a course sequence in mathematical
ecology. BioScience, 16 : 593-598.
PATTEN, B.C. (1968). - l\fathematical models of plankton proLluction. Int. Rev. ges.
Hydrobiol., 53 : 357-408.
PATTEN, B.C. (1969). - Ecological systems analysis and fisheries science. Trans.
Amer. Fish. Soc., 98 : 570-581.
RADFORD, P.J. (1968). - Systems, models and simulation. Ann. Rep. Grass[. Res.
lnsl., for 1967 : 77-85.
RAINES, G.E., BLoOM, S.G. & LEVIN, A.A. (1969). - Ecological models applied to
radionuclide transfer in tropical ecosystems. BioScience, 19 : 1086-1091.
- 137 -
VAN
DYNE,
G.M.,
FRAYER,
W.E.
BLEDSOE,
&
L.J.
-
(1969).
Sorne
optimization
techniques and problems in the natural resource sciences. Stud.
Optim.,
1 : 95-124.
\VAGGONER, P.E.
&
HoRSFALL, J.G. (1969). - EPIDEM. A simulation of plant disease
written for a computer. Bull.
WATT,
K.E.F.
Conn. agric. Exp. Sta., 698
(1956). - The choice and solution of
predicting and maximizing
Canada, 13 : 613-645.
the
yield
of
a
: 1-80.
mathematical
fishery.
J.
models
Fish.
Res.
for
Bd.
WATT,
K.E.F. (1958). - Studies on population productivity 1. Three approaches
to the optimum yield problem in populations of Tribolium confusum.
WATT,
K.E.F.
Gen. Systems, 3
(1959).
: 122-14 7.
A
�
mathematical
model
for
the
effect
of
attacked and attacking species on the number attacked.
densities
Canad.
of
Entom.,
91 : 129-144.
WATT, K.E.F. (1961). - Mathematical models for use in pest control. Canad. Entom.
Suppl., 19 : 1-62.
\VATT,
K.E.F. (1962). -
The conceptnal
formulation
of practical problems in population
and
rnathematical
input-output
dynamics.
tation of Natural Animal Populations (ed. E.D. Le Cren
Blackwell : Oxford, pp. 191-203.
\VATT, K.E.F. (1963). - Dynamic prograrnming,
«
&
ln
solution
Exploi­
M .W. Holdgate)
look ahead programming
the strategy of insect pest control. Canad. Entom., 95
»
and
: 525-536.
(1964). - Compnters and the evolntion of resonrce management
: 408-418.
\VATT, K.E.F. (1964). - The use of mathematics and computers to determine
\VATT,
K.E.F.
strategies. Amer. Sei., 52
optimal strategy and tactics for a given insect pest control problem. Canad.
Entom., 96
WATTS,
D. G.
&
: 202-220.
LoucKs,
O.L. (1969). -
Models
for
describing
exchanges
within
ecosystems. Inst. Envir. Stud., Univ. \Vise. : Madison, pp. 18.
W1T,
C.T. de (1965). - Photosynthesis of leaf canopies.
663 : 1-5 7.
- 138 -
Vers/.
Landbk.
Onderz.,