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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. -118- 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 -119- 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.., "' "" ... � .._'!: >: �� .._ ... "' � ,,,,.. � "' !!; MICRO ORGANISMS Fig. 1. -- Sub-systems within a -120- 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. - 121 - 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 -122- 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 - 123 - 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 - 124 - 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 - 125 - 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 .. .,. 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). - 126 - 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- - 127 - 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 7000 6000 Cj'J a:: w Cil :i;; :::> z 5000 4000 / / / / 1- 3000 <l a:: 2000 / __ , .- ' ' / ' ' / 1.5 iÏi Cil 1.4 1.3 NUMBERS ' ., � RABBITS ' 1.2 ',WEIGHT '·, ' ' ' ' 1.1 ' ' ' .... :I: C) ... �. � :::> 0 4 z 4 ... 2 '·- 1000 -·- - - 1.0 -·- 0 0 /"'--.... 1600 SHEEP -�/ 1400 Cj'J a:: w ID :i;; :::> z <i. w w :r Cj'J 1200 ' NUMBERS ' ' 50 .... ' :I: C) ' ·, ' 1000 ' '· - ... ' � ' '·- BOO - - 40 '·--- � EIGHT - 600 ' - -·- - 400 - ' -., � :::> 0 <l z 4 ... ' 30 ' ..... , ...... 2 '·, 200 "' :.:: ' ' ' '· . 0 0 u; z 300 g w ...J Cil � � � FORAGE 200 w f2 100 � .... fd lt w 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.,