OIKOS 108: 495/502, 2005

Detecting the causes of population cycles by analysis of R-functions: the spruce needle-miner, tedella, and its parasitoids in Danish spruce plantations

Mikael Mu¨nster-Swendsen$ and Alan Berryman

Mu¨nster-Swendsen, M. and Berryman, A. 2005. Detecting the causes of population cycles by analysis of R-functions: the spruce needle-miner, Epinotia tedella, and its parasitoids in Danish spruce plantations. / Oikos 108: 495/502.

Explaining the causes of regular multi annual oscillations (cycles) in populations has been a major problem for ecology, partly due to a lack of methodological rigor. In this paper we show how the analysis of R-functions, the functional relationship between the per capita rate of change of a species and components of its environment, can be used to detect the causes of population cycles. Analysis of the R-functions enables one to separate cycles due to negative feedback between species (endogenous causes) from those forced by one-way effects (exogenous causes). We illustrate the approach by reference to the spruce needle-miner inhabiting Danish spruce plantations, and conclude that population cycles in this are probably caused by interactions with two species of parasitic hymenoptera.

$ M. Mu¨ nster-Swendsen / A. Berryman, Dept of Entomology, Washington State Univ., 921 W Main St., Pullman, WA 99164, USA ([email protected]).

Mikael Mu¨nster-Swendsen and I were working on this tables, including all suspected mortality factors, for 9 paper at the time of his untimely death in 2003. The of those years. Finally, he repeated the sampling for purpose of the paper was to show how my approach to various shorter periods of time at 10 additional loca- population analysis (Berryman 1990, 1999, 2001) could tions. Others may have longer time series, more detailed be used to detect the causes of population cycles in his life tables, or more spatial replication, but none to my data on the spruce needle-miner, Epinotia tedella (Cl.) knowledge have more of all three. Mikael recently (Mu¨nster-Swendsen 1979, 1982, 1985). I should point reviewed his analysis in chapter 2 of a book that I edited out here that, at the time we first met, Mikael was not (Mu¨nster-Swendsen 2002), so there is no need for me to too impressed with my approach, being a proponent repeat it here. Suffice to say that the needle-miner of the life table/key factor approach (Varley et al. 1975). population was found to exhibit spatially synchronous

In time, however, he was to change his mind, and 6/7 year cycles of abundance, and that the key factor the reason for that is one of the lessons of this paper. affecting the population change was reduced fecundity. I, on the other hand, was very impressed with his He also briefly mentions how my approach led to a data. For 19 years he measured, with considerable different conclusion, that insect parasitoids were mainly precision (Mu¨nster-Swendsen 1985), the density of responsible for the cyclic dynamics, and that the spruce needle-miners and their primary insect parasi- discovery of pseudoparasitism reconciled this conflict. toids emerging annually from the litter of a Danish However, he did not cover details of our analysis, spruce plantation. He then constructed detailed life referring instead to the present paper, which was

Accepted 10 August 2004 Copyright # OIKOS 2005 ISSN 0030-1299

OIKOS 108:3 (2005) 495 interrupted in such an untimely and tragic manner. Thus, the canopy to hibernate in cocoons in the forest floor I am lead to complete this paper, partly to fulfill my in November. Pupation takes place in early May. Young obligation to Mikael, and partly as a tribute to my friend needle-miner larvae are attacked by a complex and colleague and a great Danish entomologist. of univoltine, well synchronised, endoparasitic wasps (Hymenoptera). In November, parasitised larvae des- cend from the canopy with their healthy cohorts. The The problem parasitoids eventually take over and kill their hosts in late April of the following year. Adult parasitoids emerge Many animal populations exhibit spectacular fluctua- from the forest floor a week or so after the needle-miner tions in abundance that reoccur with almost clockwork . regularity (Elton 1942, Keith 1963), but explaining the The density of mature needle-miner larvae was cause of these periodic oscillations has not been an easy estimated for 19 years in a particular Norway spruce problem for ecology. Many hypotheses have been plantation by placing funnels to intercept larvae as proposed and argued about / e.g. climatic and sunspot they descended from the canopy in November cycles, predator/prey interactions, plant/herbivore in- (Table 1). All larvae were dissected to determine if they teractions, maternal effects, genetic feedback (reviewed contained parasitoids. The number of primary parasi- by Krebs and Myers 1974, Finerty 1980, Myers 1988, toids, Apanteles tedellae Nix. and Pimplopterus dubius Berryman 1996) / but no clear picture has emerged. Part (Hgn.), were identified for all years, and the secondary of this problem may be a lack of methodological rigor parasitoids Campoplex cursitans and Mesochorus and consistency. Here we propose a general methodology silvarum were recorded for nine years (Table 1). The for attacking the problem of population cycles. time series suggest that spruce needle-miners and their In a general sense, there are only two ways by which two primary parasitoids exhibit more or less synchro- regular cycles can be induced in a dynamic system. The nous cycles of abundance (Fig. 1). The question is: is one first and most obvious is that they are driven by, or population merely tracking the abundance of the other follow after, some independent external variable that (exogenous cause) or are cycles the result of feedback cycles with the same frequency as the variable of interest between the parasitoids and their host (endogenous (e.g. sunspot cycles). In this case the cycles are said to cause)? result from exogenous forcing. The second way involves the idea of circular causality (Hutchinson 1948). It is well known that cycles can be caused by time-delays in the operation of negative feedback loops, and that the The analysis length of the time delay is proportional to the number of A common way to search for causes to population cycles variables involved in the loop (Milsum 1966). In this case is to look for correlation between variables. For example, the dynamics are the result of the internal structure of we could calculate the correlation between the spruce the system and are, therefore, due to an endogenous needle-miner and parasitoid time series shown in Fig. 1. process. Thus, the first question that needs to be When we do this we obtain large coefficients, suggesting answered when confronting cyclical population data is that all populations are closely related; i.e. r/0.92 whether the cycles are the result of exogenous or between E. tedella and A. tedellae, 0.81 between endogenous processes. Given an answer to this general E. tedella and P. dubius, 0.70 between A. tedellae and question, then the next problem is to identify the specific P. dubius, and 0.95 between E. tedella and the total mechanism(s) involved. For example, specific exogenous number of primary parasitoids. However, the correlation mechanisms may involve cyclical weather effects on per coefficients alone provide little information about capita birth and/or death rates, while specific endo- the causal structure since they cannot tell us whether genous mechanisms may involve genetic or phenotypic the populations are tracking an exogenous cycle or are feedback or interactions between trophic levels. driven by feedback between parasitoid and host popula- tions. Answering this question requires a different approach. The data We illustrate a solution to this problem by reference Detecting feedback between variables to data on the spruce needle-miner (Epinotia tedella Changes in populations of living organisms are caused (Cl.); : ) inhabiting Danish by factors that affect the birth and death rates of spruce plantations (Mu¨nster-Swendsen 1985, 2002). individual organisms. In other words, it is individuals The needle-miner is a univoltine insect whose adults that are born and die, and it is these individual processes emerge in June to lay eggs on the old needles of Norway that cause changes in population density. From this spruce trees ( Karst.). Larvae mine the perspective, it makes sense to look for associations needles from July through October and descend from between the per capita birth and death rates and the

496 OIKOS 108:3 (2005) Table 1. Data for the spruce needle-miner and its insect parasitoids converted to numbers per 100 m2 of forest soil (Mu¨nster- Swendsen 1985 for details on sampling procedures). Data in parentheses indicate Mesochorus found in Apanteles (including Campoplex) and Pimplopterus, respectively.

Year Epinotia tedella Apanteles tedellae Pimplopterus dubius Campoplex cursitans Mesochorus silvarum

1970 5708 233 2369 1971 21197 1130 7709 178 1051 (134, 917) 1972 33654 3924 13788 327 1393 (308, 1085) 1973 10064 2290 2884 193 560 (248, 312) 1974 2557 312 743 14 42 (12, 30) 1975 6957 1100 952 59 93 (50, 43) 1976 10554 2795 1754 223 116 (71, 45) 1977 24200 8785 3165 466 274 (201, 73) 1978 21525 11578 5196 802 1000 (690, 310) 1979 773 346 255 21 26 (15, 11) 1980 134 30 45 1981 105 2 30 1982 1324 241 15 1983 3550 196 313 1984 19352 2227 1986 1985 69864 22901 7706 1986 55947 22877 17170 1987 7679 2596 1524 1988 1278 322 509

suspected causal variable(s) (Royama 1977, 1992, Berry- parasitoid A. tedellae was found to be r/ /0.46. An man 1999, 2001). Even though these rates may not be almost identical effect was found with the other primary directly measured, we can estimate their net effect by parasitoid, P. dubius. Using the natural logarithm of calculating the realized per capita rate of change from a parasitoid density improved the correlation to r/ /0.61 time series (Berryman 1999) and /0.47, respectively. Using the sum of parasitoids as the independent variable, or entering them separately in N Rt ln (1BD)ln Nt ln Nt1 (1) multiple regression, produced little improvement. Para- sitism, it seems, resolves no more than 40% of the where Nt is the density of population N (say spruce variation in needle-miner rates of change. However, part needle-miners) at time t, B and D are per capita birth of the reason for this poor determination may be that the N and death rates, respectively, and Rt is the realized wrong model is being used for the parasitoid/prey logarithmic per capita rate of change of the population interaction (Berryman 1992). N over the time interval. Natural logarithms are used for The model implied by linear regression of Rt on the biological and statistical reasons (Royama 1992, Berry- density of A. tedellae is man and Turchin 2001, Berryman 2003). The correlation N N N N Rt a b At1 (2) between Rt and the value of another variable (say a population of parasitoids) provides an estimate of the with a and b the parameters estimated by regression (r/ effect of that variable on the per capita rate of change of /0.46), and At1 the density of A. tedellae at the individual needle-miners. For example, the correlation beginning of the period over which the rate of change between needle-miner R-values and the density of the was measured (in our case a year). Since the needle- miner may be influenced by the density of its own 100000 population, the model

N N N N 10000 Rt a b Nt1 c At1 (3) may be more appropriate. Once again the constants a, b, 1000 and c are estimated by multiple linear regression, but the coefficient of multiple correlation (rm /0.50) indicates 100 little improvement over (2). We could also add the other primary parasitoid, P. dubius

Number per 100 sq m sq 100 per Number 10 N N N N N Rt a b Nt1 c At1 d Bt1 (4) 1 improving things slightly (r /0.62). Finally, we can use 1970 1975 1980 1985 1990 m the sum of the parasitoids as the independent variable Fig. 1. Observed population cycles of the spruce needle-miner N N N N (/m) and its primary parasitoids, Apanteles tedellae (/j) and Rt a b Nt1 c (At1 Bt1)(5) Pimplopterus dubius (/'), in a Danish spruce plantation (data collection described by Mu¨nster-Swendsen 1985 and 2002). to much the same effect (rm /0.62).

OIKOS 108:3 (2005) 497 The relationship between the per capita rate of change A A A A At1 Bt1 Rt a b At1 c (9) of a particular species and the variables that affect it Nt1 has been called the R-function (Huffaker et al. 1999, Berryman 1999). R-functions defined by Eq. 3 and 4 are a coefficient of multiple correlation of rm /0.78 is obtained. [Note that the ratio term here comes from of the Lotka/Volterra type because the parasitoid effect is independent and additive. When the independent the logistic relationship N/K with N the density of variables are transformed to natural logarithm, they consumers (in this case parasitoids) and K propor- tional to the supply of food (in this case needle-miner become Gompertz modifications of the Lotka/Volterra model. larvae); Berryman 2004 for an empirical example]. An alternative approach to modeling trophic interac- Entering the parasitoid species separately increases the tions is to use a logistic R-function, in which case the coefficient to rm /0.84. Repeating the analysis with rate of change is related to the ratio of consumers to P. dubius yields coefficients of rm /0.51 and 0.67 for their resources (Berryman 1990, 1999, 2004, Berryman the Lotka/Volterra model, rm /0.68 and 0.84 for the et al. 1995a, Berryman and Gutierrez 1999). The logistic Gompertz variant, and rm /0.86 and 0.87 for the R-function for a host attacked by 2 parasitoids in the logistic R-function. absence of alternative prey is Effects of each species (or combination of species) on the rate of change of the other is summarized in

A B Fig. 2 for the Lotka/Volterra and logistic R-functions. RN aN bNN cN t1 t1 (6) t t1 It is clear that the logistic form provides the best fit to Nt1 the data. Also apparent is the strong and more or less (Note that this is an approximation since P. dubius symmetrical reciprocal interaction (feedback) between attacks other hosts.) When this model is fit to the data, the needle-miner and its primary parasitoids, support- the coefficient of multiple correlation increases to rm / ing the hypothesis that the observed population cycles 0.86, which is a considerable improvement. Omitting the are due to an endogenous mechanism resulting from intra-specific effect (the second term) from the regression the feedback between parasitoid and host populations. gives a simple correlation r/ /0.85 between Epinotia Before accepting this result, however, we need to make R-values and the parasitoid/host ratio (or the proportion sure that the detected interactions make biological of larvae parasitized), suggesting that this variable sense. explains almost all the variation in the multiple regres- The first requirement for biological consistency in a sion. Entering the parasitoid species separately parasitoid/host model is that parasitoids have a negative effect on the per capita rate of change of A B N N N N t1 N t1 their prey (i.e. parasitoids should harm their hosts) Rt a b Nt1 c d (7) Nt1 Nt1 (Royama 1992, Berryman et al. 1995b). Thus, the interspecific interaction coefficient in the prey equation marginally improves the coefficient of multiple correla- should be negative in both Lotka/Volterra and logistic tion to rm /0.90. It is worth noting that the logistic N N models; i.e. c B/0 and d B/0 in Eq. 3/7. The second R-function arises from Thompson’s (1924) model for the requirement is that parasitoid rates of change be probability of host survival from parasitoid attack and, positively related to the density of their prey (i.e. therefore, it has a logical basis for describing parasitoid/ hosts should benefit parasitoids). This means that the host interactions (Berryman and Gutierrez 1999). interspecific interaction coefficients in the parasitoid Although the logistic model indicates a strong impact equation should be positive in the Lotka/Volterra of parasitoids on the realized per capita rate of change of A model and negative in the logistic; e.g. c /0 in Eq. 8 the spruce needle-miner, it still does not tell us whether A and c B/0 in Eq. 9. In addition, we would normally the cycles could have resulted from the endogenous expect the intraspecific coefficient to be negative or interaction between the populations. To do this requires N A zero in all models; e.g. b 5/0 and b 5/0. examination of the reverse relationship, the effect of Figure 2 indicates that the conditions for biological needle-miner density on the parasitoid R-function, plausibility are met in both Lotka/Volterra and logistic thereby closing the feedback loop. The Lotka/Volterra spruce needle-miner R-functions (i.e. negative slopes), R-function for A. tedellae is but that the former is not consistent in the parasitoid RA aA bAA cAN (8) R-functions (i.e. negative slopes when they should be t t1 t1 positive). This inconsistency holds for both simple and which yields a very modest coefficient of multiple multiple regression and for the Gompertz form. Hence, correlation (rm /0.44). Using the Gompertz form the logistic R-function appears to be the superior model improves the fit considerably (rm /0.83). Including for describing parasitoid/host dynamics, not really a P. dubius in the model as a competitor does little to surprising conclusion since it was derived from a analysis improve it. Alternatively, if we use the logistic R- of parasitoid searching (Thompson 1924, Berryman and function for A. tedellae Gutierrez 1999).

498 OIKOS 108:3 (2005) 3 a a' 2 3 Fig. 2. Interactions between r2= 0.211 (0.295) Epinotia tedella and its primary 1 2 parasitoids under the Lotka/ 2 0 1 Volterra (left; r for the Gompertz R N form given in parentheses) and –1 0 logistic assumptions (right). Top: –2 –1 effect of total parasitism on the –3 –2 per-capita rate of change of E. r 2 = 0.726 –4 –3 tedella (/m). Middle: effect of E. 0 5000 10000 15000 20000 tedella on the per-capita rate of –4 change of Apanteles tedellae (/j). At –1 + E t –1 Bottom: effect of E. tedella on the 6 per-capita rate of change of b 6 ' 5 b' Pimplopterus dubius ( ). 5 4 r 2 = 0.037 (0.033) 4 3 2 3 R A 1 2 0 1 –1 0 –2 –1 –3 –2 r 2 = 0.608 –4 –3 –4

4 4 c' c 3 3 2 r = 0.049 (0.012) 2 2 1 1 0 R B 0 –1 –1 –2 –2 r 2 = 0.734 –3 –3 –4 –4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 20000 40000 60000 80000 (At–1 + Bt–1) /Et–1 Et–1

Feedback within the parasitoid complex than that found in the longer (19 year) time series. When In the above analysis we used the 19 year time series the two primary parasitoids are separated, however, A. (Table 1) consisting of data for the needle-miner and its tedellae explains a much higher percentage of the two primary parasitoids, A. tedellae and P. dubius. variability than P. dubius (Table 2; row 6 and 7 under N However, for nine years of this study (1971/1979), R ). Notice that the best multiple regression model Mu¨nster-Swendsen (1985) recorded all species in the explains no more of the variability in the needle-miner parasitoid complex (Table 1), enabling us to examine the R-function than total primary parasitism alone, again separate and combined effects of the different species on implying that total parasitism is the most important each other’s R-functions. In addition to the two primary causal variable in needle-miner dynamics (c.f. row 8 parasitoids (above), the complex contained the clepto- and 13). parasitoid, Campoplex cursitans (Hgn), that only attacks Turning our attention to the R-function for A. E. tedella larvae that have previously been parasitized by tedellae (Table 2 under RA), we see that the largest A. tedellae, and the hyper-parasitoid, Mesochorus effect again comes from the ratio of total parasitoids to silvarum Curt, that attacks all the other parasitoid host numbers (row 8). There is also a fairly strong species. Although these time series are rather short, association between A. tedellae and its own rate of they still offer a chance to extend our analysis. For change (row 2), suggesting that interference competition reasons discussed above, the logistic model was used to may be important in this species (something that we will determine the relative contribution of each species to the encounter again). Note that the proportion of hosts four species-specific R-functions. The results are sum- parasitized by P. dubius contributes little by itself to marized in Table 2. The first thing to notice is that 81% Apanteles rates of change but improves the combined of the variation in needle-miner per capita rates of effect (row 7 and 8), suggesting that competition between change can be explained by total primary parasitism parasitoid species may be important. It is rather inter- (row 8 under RN in Table 2), a value somewhat higher esting that the clepto- and hyper-parasitoids had little

OIKOS 108:3 (2005) 499 Table 2. Simple coefficients of determination (100 r2) for needle-miner and parasitoid R-values regressed against selected independent variables and the best, biologically consistent, multiple regression (* marks variables used in the multiple regression and i blanks cells indicate biologically inconsistent coefficients). R /R-function for the ith species: N/Epinotia tedella,A/Apanteles tedellae,B/Pimplopterus dubius,C/Campoplex cursitans,M/Mesochorus silvarum. Analyses of the 9 year time series (1971/ 1979) for all species and (in parentheses) the 19 year time series for N, A and B.

Row Variable RN RA RB RC RM

1 N 22* (12*) 2 A 54 (21) 47* (11*) 35 (11) 3 B 14 (21) 5 (8) 18* (20) 4 C 57 50* 5 M 22 39 27 28* 6 A/N 45 (68*) 49 (62*) 30 (34*) 7 B/N 4 (6*) 2 (4*) 13 (32*) 8(A/B)/N 81* (74) 77* (61) 78* (73) 9 C/A 1* 0* 10 M/A 4 0 0* 11 M/B 52* 80* 12 M/(A/B) 6* 9 12* 22 13 Multiple 81 (81) 93 (71) 85 (75) 86 92 direct effect on the dynamics of their hosts (row 9 and by the interaction between the needle-miner and its 10) but contributed to the multiple regression (omitting primary parasitoids (i.e. they are exogenous cycles). these variables reduced the coefficient of multiple determination by 15%). The R-function for P. dubius (Table 2 under RB) was again most strongly affected by the total proportion Discussion of host larvae parasitized (row 8), suggesting that Questions about the causes of regular cycles in animal interspecific competition with A. tedellae may be populations have plagued and confused ecologists for quite important. Notice that the hyper-parasitoid, decades. Particularly prevalent has been the search for a M. silvarium, has an important direct effect on P. dubius universal mechanism, and the endless arguments that (row 11) and also contributes significantly to multiple this has precipitated. The approach advocated in this determination (row 13). paper is relatively objective, in the sense that no a priori The R-function for the clepto-parasitoid C. cursitans assumptions are made concerning the causal process, (Table 2 under RC) was most strongly affected by its own and plausible explanations are only hypothesized after density (row 4), suggesting that interference between data analysis. It is very important to realize that the data searching parasitoids may be important. It is surprising needed for this kind of analysis require long-term that, as a specialist on A. tedella, the clepto-parasitoid commitments to monitoring biological populations, was so little affected by the abundance of its host, or the and that short term approaches, no matter how detailed, parasitoid/host ratio (row 2 and 9). In fact the former cannot expose the dynamic relationships between causal relationship was negative and, therefore, deemed im- variables. plausible for biological reasons. On the other hand, A crucial part of this approach is the choice of a the hyper-parasitoid, M. silvarium, seems to have a theoretical model to describe the interaction between detectable effect on the clepto-parasitoid R-function, dynamic variables. Because of the nature of biological systems we, like others (Royama 1977, Turchin and particularly in the multiple regression, where the inclu- Taylor 1992), think that the model should be based on sion of the proportion of total primary parasitoids the R-function. However, the explicit form of this R- attacked by the hyper-parasitoid improved the coeffi- function is open to debate (Berryman 1992). Models can cient of determination by 20%. be chosen on the basis of their goodness-of-fit (coeffi- Finally, the R-function for the hyper-parasitoid M cient of multiple determination), their ability to describe M. silvarium (Table 2 under R ) was very strongly the correct feedback structure, or their appropriateness. affected by the proportion of P. dubius it had parasitized For example, the logistic food web model (Berryman (row 11), suggesting that interference between searching et al. 1995a) may be more appropriate for analyzing hyper-parasitoids may be important. parasitoid/host interactions because it is explicitly Because of these weak bottom-up effects we would not derived from this type of interaction (Thompson 1924, expect strong negative feedback between these secondary Berryman and Gutierrez 1999). Once a model has been species and their hosts, and it seems unlikely that the chosen and fit to the data, the relative importance of cyclic dynamics in the system could be generated by their the independent variables can be assessed by comparing interactions. It seems more plausible that the secondary their coefficients of determination, alone and in combi- parasitoids merely follow the cyclic dynamics generated nation. The detection of strongly symmetrical interac-

500 OIKOS 108:3 (2005) tions (feedback) between species supports an endogen- closing that it was the success of R-function analysis ous explanation for the cyclical population dynamics, and the failure of traditional life table analysis that while strongly asymmetrical interactions (little feedback) finally convinced Mikael of the utility of my approach. support an exogenous explanation. As a result of this In general, life tables are not suited to detecting the total process, it may be possible to build a plausible interac- effect of environmental factors on individual perfor- tion structure for the system under investigation, and to mance, since they focus attention on individual rather make an informed interpretation of the possible causes than combined effects, and on mortality rather than of the cyclic population dynamics (Berryman 2001). In fecundity. According to Price (2003), they would better the case of the spruce needle-miner system, it is difficult be called ‘‘death tables’’. to avoid the conclusion that population cycles are the result of interactions between the needle-miner popula- Note: Mikael Mu¨nster-Swendsen and his contributions to tion and its guild of primary parasitoids. As clepto- and Nordic science hyper-parasitoids seem to have little or no effect on these With the untimely death of Associate Professor Mikael dynamics, we have to conclude that the cycles observed Mu¨ nster-Swendsen on 28 August 2003, at the age of 62 in these top predators are driven from below (exogen- years, Nordic ecology lost one of its most prominent ously) by the interaction between the needle-miner and profiles. From 1974 until a malign cancer forced him to its primary parasitoids. However, although the clepto- retire in 2001, he was employed at the Zoological Institute, and hyper-parasitoids seem to have negligible effect on University of Copenhagen, where he was much appreciated the dynamics, they may add to the stability of the system, by his colleagues and the numerous students he supervised. as suggested by Mu¨nster-Swendsen (1985). Most of Mikael’s research was dedicated to forest entomol- Our analysis indicates that A. tedellae is the domi- ogy, in particular to studies of the biology of the spruce nant, host-specific, parasitoid in this system. This needle-miner (Epinotia tedella) and its complex of natural conclusion is in perfect agreement with Capec (1969), enemies. His research resulted in more than 50 publications. who stated that A. tedellae was the only absolutely host Mikael held several honorary positions, including service specific parasitoid, and with Mu¨nster-Swendsen (1979, on the board of the Danish Ecological Society (OIKOS) 1982), who demonstrated that A. tedellae was the and Danish representative to the board of The Nordic obligate winner in interference competition, and that Ecological Society from 1983/1991. He is sorely missed its searching behavior was better adapted to this host. by his friends and colleagues around the world. A summary Recent studies indicate that the effects of parasitoids of Mikael’s life and work, including details of the data used on spruce needle-miner dynamics are manifested, not in this paper, can be found at http://www.bi.ku.dk/ only through direct mortality caused by successful mmswendsen larval parasitism, but also through sterilization of needle-miners following unsuccessful parasitism, or what is called pseudoparasitism (Mu¨nster-Swendsen 1994, 2002). Sterilization occurs when parasitoids are References disturbed (say by interference competition) before de- Berryman, A. A. 1990. Population analysis system. Two species positing an egg but after sterilizing agents have been analysis and modeling. / Ecological systems analysis, http:// injected into the host (Brown and Reed 1997). It is the classes.entom.wsu.edu/pas. Berryman, A. A. 1992. On choosing models for describing and total combined impact of parasitism on mortality and analyzing ecological time series. / Ecology 73: 694/698. fecundity that apparently provides the strong negative Berryman, A. A. 1996. What causes population cycles of forest feedback needed to drive population cycles in all species Lepidoptera? / Trends Ecol. Evol. 11: 28/32. Berryman, A. A. 1999. Principles of population dynamics and of this community. This example illustrates one of the their application. / Stanley Thornes (Publishers) Ltd., advantages of the approach advocated in this paper, for Cheltenham, United Kingdom. it captures the total impact of a factor or factors on the Berryman, A. A. 2001. Functional web analysis: detecting the per capita rate of change (R-function) of the subject structure of population dynamics from multi-species time series. / Basic Appl. Ecol. 2: 311/321. population, including unknown effects. In fact, our Berryman, A. A. 2003. On principles, laws and theories in analysis captured the total effect of parasitoids on the population ecology. / Oikos 103: 695/701. needle-miner before their effect on fecundity (pseudo- Berryman, A. A. 2004. Limiting factors and population regulation. / Oikos 105: 667/670. parasitism) was discovered. Previous life table analysis Berryman, A. A. and Gutierrez, A. P. 1999. Dynamics of insect had found reduction in fecundity to be the key factor in predator/prey interactions. / In: Huffaker, C. B. and spruce needle-miner population fluctuations (Mu¨nster- Gutierrez, A. P. (eds), Ecological entomology. John Wiley, pp. 389/423. Swendsen 1985), while our R-function analysis sug- Berryman, A. and Turchin, P. 2001. Identifying the density- gested that parasitoids were responsible. These conflict- dependent structure underlying ecological time series. ing results stimulated the search for an explanation, and / Oikos 92: 265/270. Berryman, A. A., Michalsky, J., Gutierrez, A. P. et al. 1995a. the eventual discovery of pseudoparasitism in this Logistic theory of food web dynamics. / Ecology 76: species (Mu¨nster-Swendsen 1994). I should note in 333/343.

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