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Density Dependence and the Stabilization of Animal

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Density Dependence and the Stabilization of Animal DENSITYDEPENDENCE AND THE STABILIZATION OFANIMAL NUMBERS 2.THE PINE LOOPER* by P.J. DENBOER (BiologicalStationof the Agricultural University, Kampsweg 27,9418 PD Wijster, The Netherlands) SUMMARY Totest the hypothesis thatthe density-dependent mortalityof advanced larvae ofthe pinelooper kept density within limits (i.e. "regulated"), thefluctuations of numbers inthe field population studied byKlomp arecompared withthose inthe null model inwhich, onaverage, thismortality ofolder larvae iskept at the field level, but the densitydependence isremoved. Itis concluded thatthe density-dependent mortality ofadvanced larvae, whether ornot in concert with the following density-dependent reductionoffecundity, didnot regulate density, butrather had asomewhat destabiliz- inginfluence byincreasing thechance that very low densities arereached. Inan earlierpaper the same effect was shown tooccur in the winter moth population studiedbyVarley and Gradwell. Itis suggested thatthis destabilizing tendency may resultfrom the fact that the action ofa significantlydensity-dependent factorcan be frustratedbycorrelations withother, more independent andmutually non-randomly interrelated,mortality factors, bywhich thepotentially stabilizing effectcan get lost, andmay even turn into the reverse. INTRODUCTION Thisarticle is published inmemory of HermanKlomp with whom in thecourse of abouttwenty years, I frequentlyand thoroughly dis- cussedproblems concerning the persistence ofpopulations. We were bothconvinced that significantevolution results from continuing selectionprocesses, which we agreed will occur only in long-persisting populations.Klomp thought that populations could only persist long enoughfor this to happen, ifdensity was kept-` `regulated"-within safelimits by powerful density-dependent processes. Otherwise, den- sity wouldrapidly "random-walk", either to extinctionor to catastrophicallyhighvalues (KLOMP, 1962). In particular,I did not agreewith the latter statement. In myopinion, the trend of density willdepend on theparameters of thefrequency distribution of the multiplicationfactors (R = netreproduction), which determine the *Communication no.315 of the Biological Station. 221 randomwalk of densities. Also, I couldimagine random walks that wouldlet density fluctuate within restricted bounds, for hundreds of years.Such favourable distributions of R-values might result, for instance,from a largenumber of factors, each independently affecting density,because there is, then, a goodchance that the influence ofone factorwill be levelled, or evennullified, by the effects of others (DEN BOER,1966). Klomp, however, objected that it can hardly be expected thatthe effectsof such"non-reactive" factors would balance one another,so that meanlnR wouldbe keptvery close to zero,a necessarycondition to avoida significanttrend of numbers.My answerwas that populationswhich do not conformto this condition-whichin my opinion is lesscritical than supposed by Klomp-wouldhave a lowchance of beingobserved (especially if meanIn R < 0),because they would rapidly become extinct. In other words,the populations westudy form a biasedsample with respect to distributionsofR-values. Thiscontroversy dominated the meetings ofthe "Discussion group forpopulation dynamics" (founded in 1962by Klomp and Kluyver) forsome years, and led me to formulate the concept of "spreadingof risk"(DEN BOER, 1968). Although it could be shown (REDDINGIUS & DENBOER, 1970) that spreading ofrisk may significantly contribute to thestabilization ofanimal numbers, and thus could be an alternative to regulationofnumbers, it was not possible to provewhich of these two(or possibly other) principles was generally responsible for the supposedpersistence ofnatural populations. REDDINGIUS (1971),who thoroughlyexamined this question, concluded that the regulation hypothesisloses much of its deterministic rigidity, and probably also muchof its appealto manypopulation ecologists, when it is generalizedtoa morerealistic, i. e. probabilistic, model. On the other hand,however, "spreading of risk"is modelledin probabilistic terms,quite naturally. Therefore, he advisedthat population hypothesesshould be formulated inprobabilistic terms, and he recog- nizedthe potential role of spreadingof riskin thestabilization of numbers.However, this is not to say that regulation ofnumbers may notplay a partin thepersistence ofnatural populations. Therefore, Klomphad good reasons to continuehis search for the "regulating mechanism"ofthe pine looper (Bupalus piniarius) population, which hestudied for many years. Inthe following I will try to evaluate the stabilizing influence ofthe density-dependentprocesses found by Klomp, and which he expected tomake some contribution tothe "regulation ofnumbers" ofthis pine looperpopulation. 222 THEPINE I,OOPER In hismonograph on thedynamics ofthe pine looper population of "HogeVeluwe" (near Otterlo, The Netherlands)KLOMP (1966) carefullydiscussed all aspects of hisinvestigation. We will only be engagedhere with his key-factor analysis, as describedby VARLEY & GRADWELL(1960), which he adoptedto evaluatethe influenceof density-dependentfactors on the pattern of density fluctuations. The relevantdata on densitiesin successivestages of thelife cycle are broughttogether in tableI. I coulduse only the data from 1953 onwards,because only in thatyear did Klomp discriminate between themortality of olderlarvae in Septemberand October (k4 and k5 respectively),which appears to bedistinctly density-dependent, and the mortalityof nymphsin November(k6), which is notdensity- dependent.In table II thedensities offour stages, viz. pupae in April, reproducingfemales, eggs, and olderlarvae in September,are presentedasloglo-values, together with the values (k) of the different mortalityfactors, which are the differences between the loglo-values oftwo succeeding stages in table I (e.g.k8 + k9 in 1956= log 10(2.58) - logI0(1.52)= 0.4116 -0.1818 = 0.230). Todiscover the key factor (MORRIS, 1963), i.e. the mortality factor withthe greatest variation in effectbetween years, and which there- foreis expectedto governthe pattern of densityfluctuations, the changesintime of each mortality factor, distinguished byKlomp, are comparedwith changes in thetotal generation mortality (K): fig. 1. It willbe obvious that eggmortality + juvenilemortality of larvaeI (k2) and of larvae II/III (k3), can be considered the key fac- tor, becausethe variationin total generationmortality (K = ki +k2 + .....+ kf2) mainly results from that in kl_3 (correlation(Pear- son)K/kf-3: r = + 0.78,P =0.006); compare table III, fromwhich willbe clear that also k, +k2 can be considered the key factor. Figure 1 nextshows that k4 + k5 has some tendency (though not significantly so:r = +0.13) to be low when the values of Kare highest. This results fromthe density-dependent relationship between the magnitude of thismortality and the density of the larvae in September,onwhich it acts:p (Spearman) + = 0.77 (P0.01). = Curiously enough, high den- sitiesof larvae in Septembernot only coincide with a highmortality ofthese larvae (k4 + k5), but also with a relativelyhigh reduction of fecundity(kI2) of the moths that develop from the surviving larvae: p = + 0. 76(P =0.016). See also table III. Onaverage k4 + k5 + kl2 isresponsible for18.3% of generation mortality (K), but the variation in thismortality from year to year is high (table IV: between 1.4 and 34.0 %The ). correlation oflarvae Sept. to k4 + k5 +is kI2p = + 0.78 223 224 225 ofthe at Veluwe" Fig. 1.Key-factor Modifiedanalysisfrom KLOMP pinelooper Forpopulationfurther "Hoge see the tables (TheI Netherlands). (1966).andII. expanation (P =0.014). No other k-factors showed significant correlations with thedensities on which they act. Weare thusleft with two interesting questions concerning the regulationofthe numbers of the pine looper: (1)What are the causes of the density-dependent relationship between larvalmortality in September(k4 + k5) and the subsequent fecundity (kl2)? (2)Can the population be "regulated"by only18% of generation mortality,in spiteof the fact that the variance of k4+ k5 (table II: 0.0325)is smallerthan that of the key factor (table II: 0.071)? 226 TABLEIII Product-moment(Pearson)correlations (r)between totalmortality (K)and compos- ingmortality factors (k), as well as between thedifferent mortality factors mutually; 100r29lo ? variation "explained" bythat variable. Note:Correlations between mortality factors aretaken inthe normal time order only, e.g.k¡ + k2 with the k8 + kg-values following intime (next year). IfI r I >0.602 the correlationissignificant at5 % . TABLEIV Proportionalshare( % of )the different mortality factors intotal mortality (K)in dif- ferentyears. Note:K= = k¡ + k2 + k'$ + k4of' year(t) + k5 + k6 + k7 of ycar(t). + 1). + ks + kg + klO + k¡t + k12 227 Thefirst question was studied by GRUYS (1970, 1971). He found that advancedlarvae which make contact during the nightwill regurgitategut fluid, and transmit it to eachother. Because of this, growthis reduced,and this results in smallermoths with lowered fecundity.However, larval and pupal mortality, longevity of the adults,and viability ofthe progeny are all unaffected bythese noctur- nalencounters ofolder larvae. It hadalready been shown by KLOMP (1958)that the density-related reduction of fecundity(k12) cannot regulatepopulation density. He rightly concluded that the range of reductionismuch too small for that (KLOMP, 1966); see also table II (Var =0.0018) and table IV. This is confirmedby fig.2: overthe entirerange
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