* This paper first appeared in a somewhat different form in the book Population Dynamics, Impacts, and Integrated Management of Forest Defoliating Insects edited by M. L. McManus and A. M. Liebhold and published on pages 252-260 in USDA Forest Service General Technical Report NE-247 (1998).

Using new methods of time series analysis I show that population fluctuations of three forest caterpillar species seem to be strongly influenced, if not dominated, by interactions with insect parasitoids, and conclude that parasitoids may play a more significant role in the dynamics of forest caterpillars than is generally recognized.

Some forest moths (Lepidoptera) exhibit remarkable variations in abundance, sometimes going through 10,000-fold changes in density during population increases and decreases; e.g., the larch budmoth, Zeiraphera diniana (Baltensweiler and Fischlin 1988, Berryman 1996). Many other forest caterpillars fluctuate with much less variability, remaining at sparse densities for indefinite periods of time.

Foliage-feeding caterpillars are known to be attacked by numerous insect parasitoids in the families Ichneumonidae, Braconidae, Eulophidae and Chalcidae (Hymenoptera), as well as Tachinidae and Sarcophagidae (Diptera). The larch budmoth, for example, is attacked by 94 species of parasitoids (Baltensweiler and Fischlin 1988). The question I wish to address in this paper is; what role do parasitoids play in the fluctuations, or lack thereof, of forest caterpillar populations? I will approach this question by reference to studies on three forest defoliators.

Morris (1959) analyzed 11 years of data on the density of blackheaded budworm caterpillars and their larval parasitoids (Fig. 1), and concluded that the key factor in the population dynamics of this insect was a suite of insect parasitoids attacking the larval stage. Although key factor analysis has been discredited recently (Royama 1996), and although McNamee (1979) has proposed an alternative hypothesis for blackheaded budworm dynamics, I was forced to agree with Morris (Berryman 1986, 1991a). My conclusions are based on a reanalysis of the budworm-parasitoid data using some new methods of time series analysis (Royama 1977, 1992, Berryman 1991a, 1992, 1994, Berryman and Millstein 1994, Turchin 1990).

Time series analysis of population counts over a number of years looks for correlations between the rate of increase of the average individual, , and population density. In other words we perform a simple regression on the model (known as the R-function)

(1)

where d is the dominant lag in the density dependent feedback response (Berryman 1992), or on the multiple regression on the model

(2)

where d is now the maximum dimension of the feedback structure (Turchin 1990). Some like to transform the independent variables to natural logarithms (Royama 1977, 1992). The dimension is rarely greater than 2 in biological data (for more on model fitting see here)

In the case of the blackheaded budworm, the dynamics are strongly affected by "second order" feedback (d=2), or delayed density dependence (Turchin 1990, Berryman 1986, 1991a, 1992, Berryman and Millstein 1994). What this means is that the survival and/or reproduction of the budworm in one year is dependent on larval density in the previous year. To obtain such an effect, one needs to have a negative feedback mechanism that operates with a delay of the same relative time scale as the budworm. There seem to be two plausible explanations for this apparent second order feedback effect:

1. A foliage effect. Second order feedback can be created if the quality of foliage is affected by defoliation in the previous year (the "delayed induced defense" hypothesis [Haukioja et al. 1988, Baltensweiler and Fischlin 1988]), or if high caterpillar densities and/or food shortages in one year affect the survival and/or fecundity of the next generation via physiological (the "maternal effect" hypothesis [Rossiter 1994, Ginzburg and Taneyhill 1994] or genetical (the "genetic polymorphism" hypothesis [Chitty 1967]) mechanisms. However, blackheaded budworm populations decline before the host plant (balsam fir) is seriously defoliated and food shortage becomes an important limiting factor (Morris 1959, Miller 1966). Hence, it seems unlikely that the second order feedback is due to foliage effects.

2. A parasitoid effect. Many parasitoids, especially those which are relatively specific, have generation spans similar to those of their lepidopteran hosts. This, together with the fact that parasitoids often exhibit strong numerical responses to host density, can give rise to delayed negative feedback. The numerical response of parasitoids can be measured by fitting the equation (Berryman 1991a, 1994)

(3)

to time series data, where is the realized per-capita rate of change of the parasitoid population from one generation to the next, is the density of the parasitoid population, is the density of the host population, is the maximum rate of change of the parasitoid when host density is infinitely large, and is the impact of the parasitoid on its host. Fitting this model to data on the density of budworms and larval parasitoids explains 91% of the variation in , demonstrating that the parasitoids have a very strong numerical response (see here for details of two-species models).

We can also estimate the effect of the parasitoid on the rate of change of the budworm by fitting the equation (Berryman 1992, 1994)

(4)

in which the parameters and have similar meaning as for the parasitoids and reflects the effects of first order feedback due to competition for food, functional responses of predators, and so on. Equation (4) explains 85% of the budworm population changes and, of this, 76% is explained by parasitism alone (partial correlation 82%). Equations (3) and (4) can now be used together to simulate budworm-parasitoid dynamics, and we see that the model predicts the 6-8 year cycles of abundance seen in the data (Fig. 2). These results, together with the analyses of Morris (1959), Berryman (1986, 1991a, 1992) and Turchin (1990), strongly suggest that parasitoids are largely responsible for density fluctuations in budworm populations.

Munster-Swendsen (1991) analyzed 20 years of data on the spruce needleminer inhabiting a Danish spruce plantation (Fig. 3), and used these data to construct a detailed simulation model of the interactions between needleminer, host-tree, parasitoids, predators, diseases and weather (Munster-Swendsen 1985). The model faithfully recreated the dynamics observed in this and other plantations. By deleting variables from his model, Munster-Swendsen found that parasitoids were the major factors regulating populations of this caterpillar. This conclusion is further supported by the fact that strong second order effects are observed in spruce needleminer data, and parasitoids have a strong numerical response, with equation (3) explaining 81% of the variation in parasitoid rates of change (Berryman and Munster-Swendsen 1994).

Like the blackheaded budworm, spruce needleminers rarely cause severe defoliation to their host trees. Parasitoid density also has a strong negative effect on needleminer rates of change, explaining 76% of the variation. Simulation experiments with equations (3) and (4) fit to Munster-Swendsen's data also recreate the 9-10 year oscillations seen in needleminer populations.

One of the interesting things that emerged from needleminer population studies was the phenomenon called pseudoparasitism (Munster-Swendsen 1994). Munster-Swendsen found that "reduction in fecundity" was a key factor in needleminer population fluctuations, and that direct mortality caused by parasitoids was insufficient to explain the decline of needleminer outbreaks. This lead him to discover that parasitoids often sting, but fail to oviposite in their hosts, particularly when parasitoid densities were high (possibly due to interference between parasitoids). Needleminers that were pseudoparasitized developed to adults but were infertile (Brown and Kainoh 1992), thereby explaining, simultaneously, the "reduction in fecundity" effect and the strong suppressive effect of parasitoids. These results may cause us to reconsider the role that parasitoids play in the population dynamics of other forest defoliators.

Sisojevic (1979) collected 26 years of data on the density of gypsy moths and their tachinid parasitoids in the former Yugoslavia (Fig. 4). The data show a strong second order effect (Montgomery and Wallner 1988, Turchin 1990, Berryman 1991b), but in this case defoliation of the host plant sometimes occurs. However, experimental additions of gypsy moth larvae during the low density phase prevented defoliation, suggesting that some other factor, probably parasitoids, were able to respond and suppress the prey population before defoliation could occur (Maksimovic et al. 1970).

On the other hand, gypsy moth dynamics are not quite as simple as the first two species. Berryman (1991b) found that second order effects dominated the time series for the first 16 years but that first order feedback became prevalent in the final 10 years. In addition, multivoltine generalist parasitoids were observed to be more common during this time, while univoltine specialists were most abundant during the first period (Fig. 4). This suggests that the dynamics of gypsy moth populations in southern Europe are largely determined by the relative dominance of tachinid generalists, which generate first order dynamics, and tachinid specialists which generate second order dynamics.

Berryman (1991b) also found strong second order effects in the North American gypsy moth time series following its collapse from very high densities, and concluded that gypsy moth populations had been controlled by introduced parasitoids, an idea that has generated some controversy (Liebhold and Elkington 1991, Berryman 1991c). However, stocking experiments by Gould et al. (1990) strongly suggest that generalist tachinid parasitoids can suppress incipient gypsy moth outbreaks by rapid (first order) spatial density dependent responses. These results suggest that North American gypsy moth populations are being regulated by similar mechanisms as European populations.

I have discussed three cases where parasitoids seem to be a major force in the observed population fluctuations of foliage-feeding forest caterpillars. I could have included several other examples and cited cases where forest caterpillars had been controlled by introduced parasitoids (see, e.g., Berryman 1996). My general conclusion is that parasitoids frequently play a more significant role in the dynamics of forest Lepidoptera than they are often given credit for. Of particular importance is the recent discovery of pseudoparasitism (Brown and Kainoh 1992, Munster-Swendsen 1994) which suggests that the effect of parasites on the dynamics of their hosts may be greater than is generally believed (particularly in Tortricids), and may also explain the reduction in fecundity often observed during the decline of caterpillar outbreaks. This should not be taken to mean that I believe other factors (e.g., food quantity/quality and virus epizootics) are not important in specific cases or at certain times. Parasitoids, however, seem to be a more consistent and persistent force in the dynamics of many defoliator populations, regardless of the other forces that may be involved.

BALTENSWEILER, W. and FISCHLIN, A. 1988. The larch budmoth in the Alps. In Dynamics of Forest Insect Populations: Patterns, Causes, Implications (Berryman, A. A., ed.), pp. 331-351, Plenum Press

BERRYMAN, A.A. 1986. On the dynamics of blackheaded budworm populations. Canadian Entomologist 118: 775-779.

BERRYMAN, A.A. 1991a. Population theory: an essential ingredient in pest prediction, management, and policy-making. American Entomologist 37: 138-142.

BERRYMAN, A.A. 1991b.The gypsy moth in North America: a case of successful biological control? Trends in Ecology and Evolution 6:110-111

BERRYMAN, A.A. 1991c. A reply from Alan Berryman. Trends in Ecology and Evolution 6: 264

BERRYMAN, A.A. 1992. On choosing models for describing and analyzing ecological time series. Ecology 73: 694-698.

BERRYMAN, A.A. 1994. Population analysis system: Two-species time series analysis (Version 4.0). Ecological Systems Analysis, Pullman.

BERRYMAN, A.A. 1996. What causes population cycles in forest Lepidoptera? Trends in Ecology and Evolution 11: 28-32.

BERRYMAN, A.A. and MILLSTEIN, J. A. 1994. Population analysis system: One-species time series analysis (Version 4.0). Ecological Systems Analysis, Pullman.

BERRYMAN, A.A. and MUNSTER-SWENDSEN, M. 1994. Simple theoretical models and population predictions. In Predictability and Nonlinear Modeling in Natural Sciences and Economics (Grasman, J. and van Straten, G., eds.), pp. 228-231, Kluwer Academic

BROWN, J. J. and Y. KAINOH. 1992. Host castration by Ascogaster spp. (Hymenopetra: Braconidae). Annals of the Entomological Society of America 85: 67-71.

CHITTY, D. 1967. The natural selection of self-regulatory behaviour in animal populations. Proceedings of the Ecology Society of Australia 2: 51-78.

LIEBHOLD, A. M. and ELKINTON, J. S. 1991. Gypsy moth dynamics. Trends in Ecology and Evolution 6: 262-263.

GINZBURG, L.R. and TANEYHILL, D.E. 1994. Population cycles of forest Lepidoptera: a maternal effect hypothesis. Journal of Animal Ecology 63: 79-92.

GOULD, J.R., ELKINTON, J.S. and WALLNER, W.E. 1990. Density-dependent suppression of experimentally created gypsy moth, Lymantria dispar (Lepidoptera: Lymantriidae), populations by natural enemies. Journal of Animal Ecology 59: 213-233

HAUKIOJA, E., NEUVONEN, S., HANHIMAKI, S. and NIEMELA, P. 1988. The autumnal moth in Fennoscandia}. In Dynamics of Forest Insect Populations: Patterns, Causes, Implications (Berryman, A. A., ed.), pp. 163-178, Plenum Press

MAKSIMOVIC, M., BJEGOVIC, P.L. and VASILJEVIC, L. 1970. Maintaining the density of gypsy moth enemies as a method of biological control. Zastita Bilja 107: 3-15

MCNAMEE, P.J. 1979.A process model for Eastern blackheaded budworm (Lepidoptera: Tortricidae). Canadian Entomologist 111: 55-66

MILLER, C.A. 1966. The black-headed budworm in eastern Canada. Canadian Entomologist 98: 592-613.

MONTGOMERY, M.E. and WALLNER, W.E. 1988. The gypsy moth, a westward migrant. In Dynamics of Forest Insect Populations: Patterns, Causes, Implications (Berryman, A.A., ed.), pp. 353-376, Plenum Press.

MORRIS, R.F. 1959. Single factor analysis in population dynamics. Ecology 40: 580-588

MUNSTER-SWENDSEN, M. 1985. A simulation study of primary-, clepto- and hyperparasitism in Epinotia tedella (Lepidoptera: Tortricidae). Journal of Animal Ecolology 54: 683-695.

MUNSTER-SWENDSEN, M. 1991. The effect of sublethal neogregarine infections in the spruce needleminer, Epinotia tedella (Lepidoptera: Tortricidae). Ecological Entomology 16: 211-219.

MUNSTER-SWENDSEN, M. 1994. Pseudoparasitism: detection and ecological significance in Epinotia tedella (Cl.) (Tortricidae). Norwegian Journal of Agricultural Science, Supplement 16: 329-335.

ROSSITER, M. 1994. Maternal effects hypothesis of herbivore outbreak. BioScience 44: 752-763.

ROYAMA, T. 1977. Population persistence and density-dependence. Ecological Monographs 47: 1-35.

ROYAMA, T. 1992. Analytical population dynamics. Chapman and Hall.

ROYAMA, T. 1996. A fundamental problem in key factor analysis. Ecology 77: 87-93.

SISOJEVIC, P. 1979. Interactions in the host-parasite system, with special reference to the gypsy moth - tachinids (Lymantria dispar L. - Tachinidae). Papers of the 6^th Interbalcanic Plant protection Conference, Izmir, Turkey, pp. 108-116.

TURCHIN, P. 1990. Rarity of density dependence or population regulation with lags? Nature 344: 660-663.