Modelling the partitioning of research effort in ecology

J. theor. Biol. (1984) 111, 451-461

Modelling the Partitioning of Research Effort in Ecology

RODERICK HUNT

Unit of Comparative Plant Ecology (Natural Environment Research Council), Department of Botany, The University, Sheffield SI0 2 TN

AND

C. J. DOYLE

Grassland Research Institute, Hurley, Maidenhead, Berkshire SL6 5LR

(Received 19 October 1983, and in revised form 9 April 1984).

Using a simplified model we investigate how the partitioning of research effort between the goals of increased precision, realism and generality might influence the resulting growth in understanding achieved in respect of any particular ecological process. The optimal allocation of research effort is shown to depend upon the weights attached to the different goals. Surprisingly, it appears that where growth in understanding is to be maximized, proportionally more effort should be allocated to goals whose growth is valued less. However, little can be done by way of repartitioning to promote those areas of research where efficiency in terms of returns to effort is low. Somewhat against current practice, it appears from simple and relatively unexceptionable initial assumptions that only a judicious partitioning of research resources between efforts to increase all three goals, precision, realism and generality, is likely to realize great benefit in terms of increasing overall understanding.

1. Introduction

Greater understanding of ecological processes is arguably derived from three things: (i) increased knowledge of the changes occurring in natural systems; (ii) greater ability to predict the course of such changes; (iii) the establishment of scientific relationships which have general ecological applicability. In other words, increases in knowledge come through achieving greater realism, precision and generality (Levins, 1966).

More formally, understanding of ecological processes may be defined as a composite of the quantity and quality of established, reliable correlations or chains of causation achieved by any programme of ecological research. Precision may be defined as a composite of exactitude (reliable and repeat- able measurability within a chosen dimensional scale) and accuracy

451 0022-5193/84/230451 + 11 $03.00/0 © 1984 Academic Press Inc. (London) Ltd.

452 R. H U N T A N D C. J. D O Y L E

(absolute truthfulness of the chosen scale). Realism may be defined as the degree of independence from human interference or management. General- ity may be defined as that fraction of all possible similar systems which is encompased by any particular investigation. The last three variables are quite independent of one another.

Research in plant ecology, for example, often involves compromising between these different aims (Harper, 1982). Several alternative approaches have evolved. First, generality may be sacrificed in the interests of achieving greater realism and precision, as when studying individual plant species in a specific environment (Tamm, 1972; Sarukhan & Harper, 1973). Second, precision and generality may be emphasised at the expense of realism; such an approach is typified by the plant competition models of May (1974) and Newman (1982), which involve the derivation of general equations from which precise results are obtainable, and also by "screening" experiments such as those described by Grime & Hunt (1975). Third, precision may be sacrificed to realism and generality as in surveys encompassing several plant communities (e.g. that of Grime & Lloyd, 1973). The question often facing the researcher is which of these approaches to adopt.

The purpose of the present study is to isolate and investigate the critical factors which can be expected to influence the choice of approach. Using a deliberately simple model we assess how the partitioning of research effort between the three goals of increased precision, realism and generality might influence the resulting growth in scientific understanding. Since the goals themselves are pure abstractions, the exercise constitutes a true "model", in the sense defined by Maynard-Smith (1974) rather than a "simulation" based upon specific observational data and predicting some specific final outcome. So, while this means that the model cannot be used to determine the optimal allocation of research effort in any particular case, it does allow the research worker, in a variety of possible situations, to see in which direction each of a range of design options might influence the net outcome of his work. The variables are defined in broad ecological terms so that the model may remain useful in the widest possible context.

2. The Model

The degree of understanding about a particular ecological process that is achieved by any single research programme (Du) may be assumed to depend upon the degrees of precision (Dp), realism ( D R ) and generality (DG) attained by that programme. Each of these four attainments is expressed as a proportion of the maximum possible attainment; for instance, perfect or complete ecological understanding would be attained at Du = 1.

M O D E L L I N G R E S E A R C H E F F O R T 453

We have considered four possible variants of an objective model:

D u = BoDp+ BIDR+ B2DG

Do = BoDp+ BIDR+ B2DG+ B3DpDRDG

(la)

(lb)

Do = ( BoDp)( BIDR)( B2DG)

FIBoF'jB I F IB Du = ,.,p "JR ,_..~2.

(lc)

(ld)

The parameters Bo. . . B 3 indicate the proportional change in the degree of understanding which arises from a given proportional change in each of the variables or combination of variables. They thus provide a means of examining the outcome of different assumptions concerning the relative contributions of Dp, DR and DG to Du.

Equation (la) is a simple additive model which carries the unlikely implication that the pursuit of one particular goal to the exclusion of all others can nevertheless advance understanding. Even if this goal is easily achieved, the definitions put forward in the introduction make it clear that pursuing, say, realism to the complete exclusion of precision and generality (that is, retrieving no information of any kind from any part of the system under study) will, whatever the degree of realism attained, produce no understanding at all. Equation (lc) returns the same value of D o for given values of Dp, DR and Do, no matter how any single set of weights B0, Bt and B2 is allocated. Thus, the combination Bo = 0-5, BI = 1 and B2 = 1 will return the same value of Du as the combination Bo = 1, BI = 1 and Bz = 0-5. This implies that the choice or relative weights is unimportant as far as the allocation of research effort is concernedqagain an unlikely conclusion. Equation (lb) is a hybrid between equations (la) and (lc). If the weight, B3, o n the multiplicative term is low, the whole equation will behave like equation (a); if the weight is high, the equation will behave like equation (lc). Since neither of these equations is satisfactory, equation (b) is itself unsuitable. Equation (ld) appears to have the most acceptable properties. Though arbitrary, the assumed multiplicative relationship may be satisfactory in so far as (i) no research programme can exist without all three goals being attained to some degree (Dr, DR, D o > 0 ) , and (ii) it is likely that these goals are mutually supportive in their contributions to understanding, at least at low levels of attainment. Further, the weights allocated to Dp, DR and DG may be varied independently of one another. Equation (ld) also encompasses the idea of a "scientific breakthrough", in which a large advance in Do can be achieved through a sudden release of attainment in only one of the independent variables.

454 R. H U N T A N D C . J . D O Y L E

Where equal importance is attached to the degrees of precision, realism and generality attained, then Bo = B~ = B 2. If, on the other hand, Bo = B~ B,, then the relative contributions (W) made to ecological understanding by equivalent degrees of precision and generality are given by

W = X { t~o- 8~-j (2)

where W is the weight attached to Dp relative to De and X is the degree of precision or generality attained. For Bo < B2, precision is valued more than generality; conversely for B0> B2.

E F F O R T A N D A ' I - F A I N M E N T

Attainment of any given degree of precision, realism or generality is obviously not automatic. Degree of achievement, D, will depend in some way upon the effort (E) expended on the part of the research worker towards achieving each goal. For the model, some function, D=f(E) , must thus be chosen for each variable. Linear functions of the form D = k(E), where k is a simple coefficient, have been considered. Although we believe that more is known about the form of these relationships than simple functions such as these can represent, tests of the model using linear functions produced only small differences in the final result. Accordingly, we have proceeded below with the simplest of the functions which also satisfy the beliefs available a priori, knowing that any errors in establishing their true identity would be unlikely to have a marked influence on the final outcome oi ~ the model.

T H E D E G R E E O F P R E C I S I O N A T T A I N E D , Dp

It is assumed that the degree of precision achieved is hyperbolically proportional to the research effort (Ee) directed towards this goal. Specifi- cally,

Dp = Ep/(Ep+ kp) (3)

where Ep equals the effort, measured in man/hours or money, expended on increasing the precision with which ecological change is measured. The parameter kp is a constant. Equation (3) exhibits properties that seem reasonable. For a given kp, little research effort initially brings considerable returns, but increasing levels of effort are required to secure gains in Dp as the latter tends to its maximum value of 1.0.


DEGREE OF REALISM ATTAINED, DR

The degree of realism attained is also assumed to be hyperbolically proportional to its research effort (ER), namely

Dr~ = ER/(ER+ kR) (4)

where k R is a constant. As in equation (3), the supposition is that there are diminishing returns to increasing effort on the premise that moderate realism is easily attained but a high measure of freedom from human interference, including that of the observer, requires the expenditure of disproportionally great effort.

DEGREE OF GENERALITY ATTAINED, D G

The search for generality is likely to lead to an emphasis on large-scale surveys or on screening operations. But since many of the relevant biological phenomena manifest themselves as near-normal or near-lognormal distributions of frequency against value (e.g. Obeid, Machin & Harper, 1967; Hunt, 1984), their frequency distributions often appear bell-shaped. This being so, the form of the relationship between completeness of coverage and sampling effort must be sigmoidal, since it will be determined by the parallel examples of the bell-like probability density function of the normal distribu- tion and its correspondingly sigmoidal cumulative frequency function (e.g. Colquhoun, 1971; pp. 66 and 68 respectively). Hence, low sampling effort may be expected to achieve disproportionally small gains in generality, though high generality may be attained from the expenditure of only moderately high effort. One of the simplest sigmoidal functions is

DG = 1/[l + kG exp (-KGEG)] (5)

where k~ and Ko are constants. As EG tends to infinity, so De tends to its maximum value of i.0. Alternatively, as Eo tends to zero Do tends to 1 / ( l + k o ) ; where ko is large this implies a value for De close to zero. Unlike equations (3) and (4), the maximum response to research effort (dDG/dEG) does not occur at E o = 0 , but at EG=In (k~)/KG (Crowe & Crowe, 1969), producing a sigmoidal curve.

EFFORT CONSTRAINT

The efforts expended on research aimed at securing precision (Ep), realism (ER) and generality (EG) are assumed to be subject to an overall budgetary constraint, such that

Ep+ E R + E G ~ E T (6)


where ET is the total research effort available in respect of the particular programme.

3. Simulated Research Strategies

P A R A M E T E R VALUES

We have explored the properties of this model by investigating the implications of: (i) changes in the relative contributions which Dp, DR and Do make to overall understanding; (ii) changes in the efficiency with which research efforts are translated into increased precision, realism and generality; (iii) changes in the allocation of research efforts between these three goals.

As regards the weights attached to the extents to which increased precision, realism and generality contribute to overall understanding (equation (1)), three different options have been considered. First, there is the "observational" option which discounts generality and places a premium on realism and precision. Second, the "global" option discounts precision in favour of achieving high realism and generality and, third, the "aetiological" option discounts realism and places a premium on precision and generality. The corresponding values for B0, B~ and B2, together with the relative weights at Dp= DR = Do = 0.5, are shown for each of the options in Table 1.

T A B L E 1

The relative weights attached to increasing precision, realism and generality for three different objective functions, together with the implied values of Bo, B~ and B2 in equation ( ld)

Relative weights t a t tached to Values o f Objective funct ion Dp D R D G B o B I B 2

Observat ional op t ion 1 I 0-5 0. I 0.1 I. 1 Global op t ion 0.5 1 I 1.1 0. t 0 o 1 Aetiotogical op t ion 1 0.5 I 0.1 t- 1 0.1

t Est imated at D p = D R = D G = 0 . 5

The comparative efficiencies with which research efforts are translated into increasing precision, realism and generality are also relevant to the allocation of research effort. From equations (3) to (5), at equivalent levels of effort (Ep = ER = Eo = X) the efficiency of each type of research is given

by


D d Ep = l / ( X + kp) (7a)

DR/ER = 1 / (X + k S) (7b)

DG/EG = 1/{X[l + kG exp (-KGX)]}. (7c)

For the present purposes, three combinations of comparative efficiency have been considered:

2 Dp/Ep = DR/ER = DG/EG (8a)

Dp/ Ep = 2DR/ ER = DG/ EG (8b)

Dr,/Ep = DR/ER = 2DG/ EG. (8C)

Arbitrarily fixing the total research budget (ET) at 10 000 units, KG at 0.001 and kG at 50, Table 2 shows the values of kr, and kR at X = 3333 which are required to satisfy equations (8a) to (8c).

TABLE 2

Values of kp, kR and kG under different assumptions about the comparative efficiency of research into increasing precision, realism and generality; KG fixed at 0.001 and X at 3333 units

Comparative efficiencies expressed as a proportion of

D J X See equation Dp/ X DR/ X DG/ X kp kg k G

(8a) 0-5 1.0 1.0 15 227 5 947 50 (8b) t-0 0-5 1.0 5 947 15 227 50 (8c) 2-0 2.0 I-0 1 307 I 307 50

Finally, the effect of altering the partitioning of total research effort between increasing precision, realism and generality has been investigated. For a finite total effort (ET = 10 000), EG has been taken to be 0.1, 0 .2 . . . 0.9 of ET. The remaining effort (ET-EG) has been partitioned in varying proportions between Ep and ER.

RESULTS AND DISCUSSION

The effect of altering the allocation of research effort between the three goals of increasing precision, realism and generality are investigated in Fig. 1. In each case, for a given research effort devoted to attaining greater


DU

// I 0 ~

0'8" ~ ~.~ 0"61 ,~ 04../ f ~.

EI~/(ER + E P) 0

(o)

~9

(b) (c)

FIG. I. The effect of altering the allocation of research effort between increasing precision, realism and generality under three different objective functions for research: (a) an "observational" option, discounting generality; (b) a "global" option discounting precision; (c) an "aetiological" option, discounting realism. See also equation ( ld) and Table I.

generality (EG), the impact of partitioning the remaining available research effort between achieving greater precision (Ep) and greater realism (ER) is illustrated. In estimating Du in Fig. l(a), for example, it is assumed that research directed to increasing the degree of realism is pursued with the same efficiency as that devoted to realizing greater precision; in contrast, research conducted into attaining greater generality is only half as efficient.

Where increasing realism and greater precision are considered to make an equal contribution to greater understanding--the "'observational" option--then it is evident in Fig. l(a) that the degree of understanding is maximized, i.e. (Du)m,x occurs, where Ee = ER, though the curves are very flat-topped and (Du)ma x is little affected by any but extreme imbalances in Ep/ER. In the Ec dimension, (Du)m,x occurs at about Eo = 0.7Er. Hence, for ET = 10 000, approximate co-ordinates for (Du)max lie at (Ep, E•, EG) = (1500, 1500, 7000).

On the other hand, where a given degree of realism is weighted more heavily than an equivalent degree of precision, as in the "global" option, then the optimal allocation of research effort unexpectedly involves Ep > ER (Fig. l(b)). Here, (Du)max always occurs at about 4ER = Ev while, in the EG dimension, the optimum lies near EG = 0"4ET. Approximate co-ordinates for (Du)max thus lie at (Ep, ER, EG)= (4800, 1200, 4000), again for the condition ET = 10 000.


The converse applies where the "aetiological" option is adopted and precision is weighted more heavily than realism (Fig. l(c)). Maximum Do occurs at about ER = 4Ep and, again, near E6 = 0-4ET. Co-ordinates for ( D u ) m a x thus lie near (Ep, ER, EG)= (1200, 4800, 4000) if ET = 10 000.

From Figs l(a-c), we may also deduce that a fourth "neutral" option, with Bo = BI = B2 in equation (1), would predict a (Du)max near Ep= ER = Ec=O.33ET.

Considering only the "observational" option, Fig. 2 shows how the comparative efficiency of research efforts devoted separately to increasing the degrees of precision, realism and generality influences the optimal partitioning of funds between precision- and realism-oriented research.

Du

/

,.o~ / / ~ o8~ V

0.2

o o5~~5 0 9

ER/(ER + EP) I 0 / ~ ' 0 I E6/ET

(o)

o

0 5 0 9

ER/{ER+Ep) I' ET

(b)

o ~9

ER/(ER + Ep)~ C)~O. I EG/ET

(c)

FIG. 2. The effect of changes in the comparative efficiency with which research directed at increasing precision, realism and generality is conducted. In each case the objective function i s D U = D °'t 0.t t.J D R D G , i.e. the "observational" option of equation ( ld) , discounting generality: (a) D e achieved at half the efficiency of either o f the other factors; (b) D R achieved at half the efficiency of either of the other factors; (c) D G achieved at half the efficiency of either of the other factors. See also equations 8(a-c) and Table 2.

It is clear that varying the assumptions concerning the efficiency with which increasing precision, realism or generality is pursued do not affect the position of the optimal allocation of resources. In each case, it is the same as that of the parent option (Fig. 1 (c)) which forms the basis for each of these sets of curves. The absolute value of (Dv)max varies with each efficiency assumption, however: where achieving precision or realism is held to be only half as efficient as achieving realism and generality, or

460 R . H U N T A N D C . J . D O Y L E

precision and generality respectively (equation 8(a, b)) (Du)max lies near 0-64; the corresponding value assuming inetficiently-achieved generality (equation 8(c)) is 0.84.

Finally, increasing the imbalance of efficiency, for example by re-writing equations 8(a-c) as 3Dp/Ep... etc., also has little effect on the values of Du obtained: curves remain of the form depicted in Fig. 2, but somewhat lower values of (Du)max are attained.

More generally, an analysis of Figs 1 and 2 suggests that so long as the three goals of higher precision, increased realism and greater generality are considered to make separate and positive contributions to increased understanding, then research efforts should be channelled simultaneously in all three directions. Only in the extreme case, where Bo, B~ or B2 in equation (1) falls as far as zero, will this conclusion be invalidated. Harper (1982) has argued the case for progress by means of repeated studies of very low generality but high in precision and realism, so that in the context of equation (1) B2 ~ 0. The optimal solution here would involve allocating little or no resources to research specifically oriented towards increasing DG.

4. Conclusions

Clearly, this conceptual model of partitioning of ecological research effort between precision, realism and generality represents a highly abstracted view of the real world. For that reason, its use as a practical aid for the management of scientific research is strictly limited. Nonetheless, some of the broad principles arising from the model may be of value if, when based upon modest assumptions, they robustly predict unusual or little-acknowl- edged consequences.

First, evidence from Fig. 1 indicates that where growth in one objective, say realism, is valued more highly than growth in the other objectives, it is not necessarily correct to conclude that proportionally more resources should be allocated to realism-oriented research. This conclusion would only be appropriate if an additive objective model were admissible and it has been argued that it is not. On the contrary, the evidence is that more areas where a lower value is attached to increments in knowledge if the overall growth in understanding is to be maximized.

Second, Fig. 2 suggests that no special effort should be devoted to those areas of research with a low comparative efficiency in terms of returns to effort expended. The implication here is that where growth in understanding is being constrained by slow advancement in one area, be it Dp, DR or De, this will inevitably result in a lower attainment of understanding which no practicable amount of re-partitioning of effort can alleviate.

M O D E L L I N G RESEARCH EFFORT 461

Th i rd , it a p p e a r s tha t research s t ra tegies which focus on one , o r even two, goa l s to be exc lus ion o f the o ther ( s ) are un l ike ly to be very p roduc t ive , on a c c o u n t o f the mul t ip l i ca t ive s t ruc ture o f the mos t de f e ns ib l e o f the ob jec t ive mode l s . E x c e p t where mos t e x t r e m e va r i an t s o f the la t te r a re he ld to be t rue , on ly j u d i c i o u s pa r t i t i on ing o f effort be tw e e n resea rch a i m e d at i nc reas ing rea l i sm a n d tha t d i r ec t ed at i nc reas ing p rec i s ion a n d genera l i ty is l ike ly to b r ing grea t benefi ts .

We thank Dr J. H. M. Thornley and an anonymous referee for helpful suggestions. This work was supported, in part, by the Natural Environment Research Council.

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Arnold. HARPER, J. L. (1982). In: The Plant Community as a Working Mechanism, p. I I. Oxford:

Blackwell Scientific Publications. HUNT, R. (1984). J. Ecol. 72, 299. LEVlNS, R. (1966). Am. Nat. 54, 421. MAY, R. M. (1974). Stability and Complexity in Model Ecosystems. Princeton: Princeton

University Press. NEWMAN, E. I. (1982). In: The Plant Community as a Working Mechanism, p. 61. Oxford:

Blackwell Scientific Publications. MAYNARD-SMITH, J. (1974). Models in Ecology. Cambridge: University Press. OBEID, M., MACHIN, D. & HARPER, J. L. 0967). Crop Science. 7, 471. SARUKHAN, J. & HARPER, J. L. (1973). J. Ecol. 61, 675. TAMM, C. O. (1972). Oikos 23, 159.

Modelling the partitioning of research effort in ecology

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