10. Empirically based modelling approach linking food abundance, breeding performance and population status

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10. Empirically based modelling approach linking food abundance, breeding performance and population status

    1. Introduction

Changes in agricultural practice have been implicated in the declines of many farmland bird species through the effects they may have on food availability (Campbell et al. 1997; Wilson et al. 1999; Burn 2000). The grey partridge (Perdix perdix) provides the best documented case study of such effects (Potts 1986). This species has experienced large and long-term declines throughout its British range (Potts 1986). Detailed studies and modelling of its population dynamics have identified declining chick survival as one of the key elements driving these declines (Potts and Aebischer 1991). Detailed autecological studies have determined the effects of invertebrate food abundance in cereal fields on rates of chick survival (Southwood & Cross 1969; Green 1984). Further studies have identified the effects of changing farming practice, in particular increased pesticide use, on the abundance of these invertebrates (Aebischer 1990; Sotherton and Self 2000). Lastly, large scale field experiments have manipulated pesticide use on cereal field boundaries to increase invertebrate food availability and, as a consequence, chick survival rates (Rands 1985).

Experimental studies to document the responses of farmland birds to changing agricultural practice are by necessity long-term, suffer from scale effect problems, given the mobile nature of many farmland bird populations, experience difficulties in experimental design as treatment and control sites can rarely be randomly allocated, and such experiments can only examine a small number of changes in a given experiment.
From these observations there emerges a need to determine more rapid methods of assessing the likely consequences of agricultural change on farmland bird populations and to model the possible consequences of different scenarios to restore their numbers (Burn 2000). To this end we present an example based on the grey partridge. In this we use the existing knowledge of this species to identify the key relationships required to predict the effects of changing agricultural practice on population status. It is not our intention to build a complete model of grey partridge population dynamics or their likely responses to a wide range of factors, such models are already in existence (Potts 1986; Potts & Aebischer 1991), rather to produce the simplest structure required to link food abundance, breeding performance and population status to allow comparisons of the value of different agricultural strategies to this species.

10.2 Methods

10.2.1 data sources

Invertebrate abundance data were obtained from long-term monitoring of cereal fields in Sussex (Aebischer 1991) and from other Game Conservancy studies of cereal ecosystems. Invertebrate samples were collected from cereal fields using a D-vac vacuum insect sampler (Dietrick 1961); these consisted typically of five sub samples, each of 0.092m2, taken at 5m intervals along a diagonal transect into the field. The invertebrates in the samples were subsequently sorted into taxonomic groups in the laboratory. Further details are provided in Potts &Vickerman (1974) and Aebischer (1991).

Chick survival data from the same areas sampled for invertebrates in Sussex were obtained from annual counts of partridge broods conducted on five farms covering 29km2. The methods and study area are described by Potts & Vickerman (1974) and Potts (1986). An assessment of the accuracy of the data obtained from this study is presented by Aebischer and Potts (1990). In particular, as the number of partridge within the area has declined, so too has the confidence of the estimated chick survival rate. As a consequence only data for the period 1970-1987 is used for analysis.
National annual chick survival figures were obtained for the period 1962-1993 from the Partridge Count Scheme of the National Game Census (Tapper 1992). These figures have previously been presented as an appendix of Potts & Aebischer (1995). They derive from annual field based counts of grey partridge broods from between 30 and 100 sites, concentrated in the south and east of England.
National annual estimates of breeding partridge abundance were obtained from the British Trust for Ornithology’s published Common Bird Census estimates for the period 1962-1993. These estimates are of relative abundance, not density.

10.2.2 THE MODEL

A generalised stochastic difference equation model was constructed in Excel, using Crystal Ball to execute the randomisation procedures. The model was constructed to evaluate changes in the use of pesticides on the survival of the grey partridge. Grey partridge chicks rely on insects for food during the first six weeks. If the amount of pesticide used is changed, we would expect to see a change in the number of available insects, and thus chick survival may change according to the relationship described by Potts & Aebischer (1991). The model runs on one-year time steps, with an arbitrary initial population of 100 adult birds. Values for the model were taken from the literature (Potts & Aebischer, 1995; Potts, 1986; Potts& Aebischer, 1991), then adjusted to give a mean annual growth rate of 0.00. This was to permit interpretation of the output values, as being the change in chick survival rate, or population growth rate.

From the initial 100 birds the number of chicks hatched is calculated, followed by their survival to 6 weeks of age. This was the only stochastic element of the model, so that the overall variation in the final result was not influenced by the stochasticity of parameters that were not subject to adjustment. To introduce the stochasticity the 42 values of insect abundance given in Figure 18.1 of Potts & Aebischer (1991) were used as input values. It is therefore assumed that each of these values is equally likely to occur, and that when it does the chick survival rate will be as given in the figure. This will allow the true variation in chick survival rates to occur in each year, although there is no temporal correlation of survival rates. Insect abundance was then adjusted (increased) in line with field measurements for unsprayed areas (or areas with modified spray regimes according to the “conservation headland” prescription; Sotherton, 1991)). This was modelled by increasing the annual chick survival in line with the regression equation given in Figure 18.1 of Potts (1991) (Aebischer, pers. comm.):
Chick survival (probit) = Insect abundance – 0.665 * 0.399 + 0.889 eqn. 10.1
Actual survival probability was calculated from the probit survival rate. The number of chicks surviving to 12 months of age, and the adult survival rate were then applied to calculate the next year’s adult population size. The model was run for 25 years and the mean chick survival rate (s) and population growth rate (r) calculated over this time interval.


The effect of a reduction in pesticides was calculated by a number of means. The index of insect abundance was calculated using equation 10.2 (reproduced from Potts & Aebischer, 1991) for sprayed and unsprayed or conservation headlands from a number of sources (see table 10.1). Although the method of collection was different between the different studies, and in some cases not all insect orders included in equation 10.2 were recorded, the relative difference between the sprayed and unsprayed areas would be a confident measure of the effect of reducing pesticide spray on chick survival.

Chick food index = 0.141x1 + 0.120x2 + 0.083x3 + 0.006x4 + 0.0004 x5 eqn. 10.2
Where: x1 = density of ground beetles (Carabidae)

x2 = density of caterpillars (Lepidoptera) and sawfly larvae (Symphyta)

x3 = density of leaf beetles (Chrysomelidae) and weevils (Curculionidae)

x4 = density of plant bugs (Heteroptera) and leaf hoppers (Cicadellidae)

x5 = density of aphids (Aphididae)

Table 10.1. The relative change in insect abundance for sprayed and unsprayed fields. The insect abundance indices are calculated from different methods (number per x sweeps, or density per 0.5m2).


Collection method

Year data collected

Sprayed insect index

Unsprayed insect index

Relative change

J. Holland

(pers. comm.)
















Rands (1985)

Sweep net





Sotherton (1989)


Sweep net










Sotherton & Robertson (1990)




(21 June)

1988 (7 July)





Chiverton & Sotherton (1991), Sotherton & Robertson (1990)


1988 (mean of 5 dates)




Overall Mean


10.2.4 relationship between chick survival and change in population size

The above model predicts population growth rate, but in reality this will be limited by density dependent factors including, for the grey partridge, predation, shooting and overwinter losses (Potts, 1986; Potts & Aebischer, 1991). In order to predict the impact on population change, values for the various forms of mortality need to be known for the population being studied. However, in this case, we are interested in the potential effects of pesticides on the national population, independent (or averaged over) the effects of other factors. Furthermore, the intention is to create a simple framework which could also be applied to other species. An empirical relationship was therefore derived between the change in population size (from the Common Bird Census) from one year to the next, and chick survival rate (CSR) (from the Game Conservancy Trust Partridge Count Scheme) as follows (Figure 10.1; Aebischer, pers. comm.):

Nt+1/Nt = 0.301 + 1.995 CSR (r=0.826, 30 d.f.) eqn. 10.3
where Nt = population in the first year and Nt+1 = population in the second year.
This was used to obtain an independent estimate of the impact of changing chick survival rate on population change.

10.3 Results

10.3.1 model output

Two parameters are given for each model simulation; the mean population growth rate (r) and the mean chick survival rate to six weeks of age (s). Sufficient simulations were run to ensure that the results were precise to two decimal places, i.e. further simulation would not change the values given. For the standard model with normal use of pesticides, the population growth rate was (by definition) 0.00 and the chick survival was 0.26 (Table 10.2).

Table 10.2. The mean chick survival probability to six weeks, and population growth rate from 3,000 model simulations, and estimated population change from one year to the next using national data.


Chick survival (s)

Population growth rate (r)

Estimated population change

Basic model (standard spray regime)




J. Holland (pers. comm.)




Mean 0.35




Mean 0.16





Rands (1985)




Sotherton (1989)



Mean 0.44



Mean 0.34




Sotherton & Robertson (1990)



Mean 0.36



Mean 0.18




Chiverton & Sotherton (1991); Sotherton & Robertson (1990)




Overall Mean




It can be seen that increases in insect abundance of the order recorded in studies where pesticide input was reduced can produce substantial changes in the population growth rate.

10.3.2 relationship between chick survival and change in population size

In order to estimate the effect of changing chick survival on population trend, outputs from the model were substituted into equation 10.3 (above). The resulting predicted values are shown in the third column of Table 10.2. It can be seen that for the majority of examples given, numbers increased in the following year when reduced spraying regimes were implemented on cereal headlands. Numbers remain static at a chick survival rate value of 0.35.

10.4 Discussion

10.4.1 the grey partridge model

Quantification of the effects of food abundance on partridge chick survival, together with the effects of chick survival rate on trends in partridge abundance allow food abundance to be related to population status. The examples given are derived from studies of the effects of conservation headland management on partridge chick survival, where no insecticides were applied in summer and herbicide use was modified to remove only yield damaging species (mainly grass weeds), leaving the species which are most important as chick-food host plants. The use of national monitoring data enables the potential implications of such changes on a national scale for partridge populations to be assessed.

The model presented here incorporates variability in the relationship between chick food index and partridge chick survival, derived from the Game Conservancy Trust’s Sussex study, but does not include variability in the relationship between chick survival and population change, though the model could be developed to include this. Similarly, it only accounts for changes in partridge numbers between two years. Longer term population changes are influenced by a wider range of density dependent and independent factors.
Models based upon the grey partridge have the advantage of a considerable supporting literature compared to many other declining farmland birds. As a consequence it is possible to examine selective models for the grey partridge where comparable data would not be available for other species. In this way the grey partridge can be used as an example to demonstrate the minimum data requirements needed to build similar models for other species. For some species, relationships between food abundance and breeding performance or between breeding performance and population change have been determined, though only for the grey partridge have both been defined. The availability of datasets for other species is reviewed in the following chapter.
Grey partridges rear only one brood per year, but a number of farmland bird species have multiple broods. In order to obtain a measure of breeding productivity for these species, it is necessary to evaluate the number of young produced per adult pair. This requires studies with marked birds which are monitored throughout the season. Such studies are very labour-intensive and are have rarely been carried out.
The potential application of this modelling approach to other parts of the life cycle is limited by the availability of data and the difficulties in collecting it. Adult mortality is very difficult to measure for most species, and data indicating direct relationships with food availability are virtually non-existent. For most of the species considered in this report, collection of such data would be difficult because of the wide range of most species in the winter period.

10.4.2 application to other species

In principle, the model devised for the grey partridge may be applied to other farmland species with some modifications. The first stage of a model for farmland passerines differs from that in the grey partridge model because annual breeding output is monitored differently in the two groups of birds. As grey partridge broods leave the nest soon after hatching, their survival is usually assessed from annual field-by-field counts of broods at c. 6 weeks after hatching (Potts & Aebischer, 1991). In the case of passerines, survival of young is generally estimated from the number of nestlings that fledge from each nesting attempt (e.g. Siriwardena et al., 2000). The first stage of the model for a given farmland passerine, therefore, describes the survival of dependent young in the nest to fledging and its relationship with the abundance of arthropod prey.

In the grey partridge model, the measure of food availability is the Chick Food Index, which is derived from field-by-field samples of surface and crop-dwelling arthropods (Potts, 1986). However, this approach is not appropriate for passerines because they are central place foragers (Stephens & Krebs, 1986) during the nestling period. As arthropod density varies spatially in arable fields (e.g. Holland et al., 2002), it is essential that estimates of the abundance of arthropod prey are matched to the foraging ranges of adult birds provisioning their young. A practical approach is to estimate arthropod abundance within a set distance of a given nest while the young are being provisioned. An example is provided in a study carried out by Brickle et al. (2000) on the corn bunting (Miliaria calandra). They took arthropod samples within 115 m radius of each of a sample of nests from the South Downs in Sussex, and calculated a food index for each nest. Arthropod abundances for each taxon were weighted to reflect dietary preferences of corn buntings.

10.4.3 case study: the corn bunting

Elements of a model for corn bunting have been prepared as an example of what might be practicable. The relationship between the probability of a corn bunting brood surviving to fledging and the corn bunting food index was modelled using data from the Sussex corn bunting study (Brickle, pers. comm.) and a binary logistic regression procedure in GLIM4 (Francis et al., 1993).

The initial model contained only one variable, the food index. Predicted values of the probability of brood survival to fledging varied from c. 0.5 to > 0.9 over the range of food abundance values measured, suggesting that arthropod abundance in the vicinity of the nest had a significant effect on the survival of broods. (Fig. 10.1).
A follow-up model included a year factor and indicated that the relationship between brood survival and food abundance varied between the two years when the data were collected. However, the interaction term between year and food was not significant, i.e. the slopes of the relationships in the two years were similar, but the intercepts were different.
The population mode outlined above for the grey partridge, requires a value for the number of young fledged per breeding adult. A comparative estimate for corn bunting might be derived from the predicted probability values from the logistic regression model and average brood size at fledging. Corn buntings are now largely single-brooded (Brickle & Harper, 2002).
This example shows how the grey partridge model of the relationship between invertebrate chick food abundance and chick survival could be adapted for a passerine species. To predict the impact of factors affecting chick food on population size, the relationship between chick survival and population change needs to be established. This can be done in two ways. Firstly, average values for first year survival to the next breeding season and adult survival can be applied in the population model to calculate the size of the adult breeding population in the following year. This approach was adopted by Brickle (1999), who concluded that the corn bunting population on his study site in the south of England was in decline as a result of low productivity. However, he did not investigate the effect of food abundance on in his model. Secondly, an empirical relationship can be established, provided that sufficient annual population count data and estimates of annual breeding output are available over a number of years. Siriwardena et al. (2000) used the British Trust for Ornithology’s nest records scheme database to investigate changes in population in relation to annual breeding performance for several species, including corn bunting. For corn bunting, breeding performance per attempt was higher during the population decline; however, the analyses did not include density dependence, nor did they take account of possible variations in numbers of breeding attempts, so do not preclude the possibility of breeding output being a factor in population decline. These aspects are further discussed in chapter 11. In the context of this study however, we are concerned with predicting the potential impact of changes in management factors, rather than in elucidating the causes of past declines.

Figure 10.1 Fitted curve for binary logistic regression model relating probability of fledging to chick food index for corn bunting. See Brickle et al. (2000) for method of calculation of chick food index. Data from Brickle (pers.comm..)

10.5 Conclusion

In this section we have shown how the impact of changes in pesticide use (or any other management factor) can be related to annual population change through effects on breeding performance by using simple empirically-based models. The approach has been demonstrated for grey partridge, and elements of a similar model for corn bunting constructed to illustrate how it could be applied to passerines. In the following section, we review the availability of datasets for other species which might be used in such models, and discuss further the issues involved in their application.

10.6 References:

Aebischer, N.J. (1990) Assessing pesticide effects on non-target invertebrates using long-term monitoring and time-series modelling. Functional Ecology, 4, 369-373.

Aebischer, N.J. (1991) Twenty years of monitoring invertebrates and weeds in cereal fields in Sussex. The Ecology of Temperate Cereal Fields (eds. L.G. Firbank, N.Carter, J.F.Darbyshire & G.R.Potts), pp. 305-331. Blackwell Scientific, Oxford.

Aebischer, N.J. & Potts, G.R. (1990) Sample size and area: implications based on long-term monitoring of partridges. Pesticide Effects on Terrestrial Wildlife (eds. L. Somerville & C.H. Walker), pp 257-270. Taylor & Francis, London.

Brickle, N.W. (1999) The effect of agricultural intensification on the decline of the corn bunting, Miliaria calandra. Unpublished DPhil thesis, University of Sussex.

Brickle, N.W., & Harper, D.G.C. (2002) Agricultural intensification and the timing of breeding Corn Buntings Miliaria calandra. Bird Study, 49, 219-228.

Brickle, N.W., Harper, D. G. C., Aebischer, N. J., & Cockayne, S. H. (2000) Effects of agricultural intensification on the breeding success of corn buntings Miliaria calandra. Journal of Applied Ecology, 37, 742-755.

Burn, A.J. (2000) Pesticides and their effects on lowland farmland birds. Ecology and Conservation of Lowland Farmland Birds. (eds. N.J. Aebischer, A.D. Evans, P.V. Grice & J.A. Vickery), pp. 89-104. British Ornithologists’ Union, Tring.

Campbell, L.H., Avery, M.I., Donald, P., Evans, A.D. Green, R.E. & Wilson, J.D. (1997) A review of the indirect effects of pesticides on birds. Report No. 227. Peterborough: Joint Nature Conservation Committee.

Chiverton, P.A. & Sotherton, N.W. (1991) The effects on beneficial arthropods of the exclusion of herbicides from cereal crop edges. Journal of Applied Ecology, 28, 1027-1039.

Dietrick E.J. (1961). An improved back-pack motorised fan for suction sampling of insects. Journal of Economic Entomology, 54, 394-395.

Francis, B., Green, M. & Payne, C. (1993) The GLIM system. Release 4 Manual. Clarendon Press, Oxford.

Green, R.E. (1984) The feeding ecology and survival of partridge chicks (Alectoris rufa and Perdix perdix) on arable farmland in East Anglia. Journal of Applied Ecology, 21, 810-830.

Holland, J.M., Southway, S., Ewald, J.A., Birkett, T. Begbie, M., Hart, J., Parrott, D. & Allcock, J. (2002) Invertebrate chick food for farmland birds: spatial and temporal variation in different crops. Aspects of Applied Biology, 67, 27-34.

Potts, G.R. (1986) The partridge: pesticides, predation and conservation. Collins, London.

Potts, G.R. & Aebischer, N.J. (1991). Modelling the population dynamics of the grey partridge: conservation and management. In Bird population studies: relevance to conservation and management (eds C.M. Perrins, J.D. Lebreton & G.J.M. Hirons), pp. 372-390. Oxford Universtiy Press, Oxford.

Potts, G.R. & Aebischer, N.J. (1995) Population dynamics of the grey partridge Perdix perdix 1793-1993: monitoring, modelling and management. Ibis, 137, S29-S37.

Potts, G.R. & Vickerman, G.P. (1974) Studies of the cereal ecosystem. Advances in Ecological Research, 8, 107-197.

Rands, M.R.W. (1985) Pesticide use on cereals and the survival of grey partridge chicks - a field experiment. Journal of Applied Ecology, 22, 49-54.

Siriwardena, G. M., Baillie, S.R., Crick, H.Q.P., Wilson, J.D. (2000) The importance of variation in the breeding performance of seed-eating birds in determining their population trends on farmland. Journal of Applied Ecology, 37, 128-148.

Sotherton, N.W. (1989) Farming Practices to Reduce the Exposure of Non-target Invertebrates to Pesticides. Pesticides and non-target invertebrates (ed. P.C. Jepson) Intercept, Wimbourne, Dorset.

Sotherton, N.W. & Robertson, P.A. (1990) Indirect impacts of pesticides on the production of wild gamebirds in Britain. Perdix V: Gray partridge and ring-necked pheasant workshop. (eds. K.E. Church, R.E. Warner & S.J. Brady), pp.84-102. Department of Wildlife & Parks, Emporia, USA.

Sotherton, N.W. & Self, M.J. (2000) Changes in plant and arthropod diversity on lowland farmland: an overview. Ecology and Conservation of Lowland Farmland Birds. (eds. N.J. Aebischer, A.D. Evans, P.V. Grice & J.A. Vickery), pp. 26-35. British Ornithologists’ Union, Tring.

Southwood, T.R.E & Cross, D.J. (1969) The Ecology of the Partridge III. Breeding success and the abundance of insects in natural habitats. Journal of Animal Ecology, 38, 497-509.

Stephens, D.W. & Krebs, J.R. (1986) Foraging Theory. Monographs in Behavior and Ecology. Princeton University Press, Princeton, USA.

Tapper , S.C. (1992) Game Heritage: an ecological review from shooting and gamekeeping records. Game Conservancy Ltd, Fordingbridge, Hants.

Wilson, J.D., Morris, A. J., Arroyo, B. E., Clark, S. C., & Bradbury, R. B. (1999) A review of the abundance and diversity of invertebrate and plant foods of granivorous birds in northern Europe in relation to agricultural change. Agriculture, Ecosystems & Environment, 75, 13-30.

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