Ilkka Hanski, the “Compleat Ecologist”: an Homage to His Contributions to the Spatial Dimension of Food Web Interactions

Ann. Zool. Fennici 54: 51–70 ISSN 0003-455X (print), ISSN 1797-2450 (online) Helsinki 15 May 2017 © Finnish Zoological and Botanical Publishing Board 2017

Ilkka Hanski: The legacy of a multifaceted ecologist

Ilkka Hanski, The “Compleat Ecologist”: an homage to his contributions to the spatial dimension of food web interactions

Robert D. Holt

Department of Biology, University of Florida, Gainesville, FL 32611, USA

Received 31 Jan. 2017, final version received 21 Apr. 2017, accepted 21 Apr. 2017

Holt, R. D. 2017: Ilkka Hanski, The “Compleat Ecologist”: an homage to his contributions to the spatial dimension of food web interactions. — Ann. Zool. Fennici 54: 51–70.

Ilkka Hanski is most widely known for his seminal contributions to metapopulation ecology, both theoretical and empirical. But he also made many important and wide-ranging contributions to other arenas of ecological inquiry, including in particular predator–prey, host–parasitoid, and host–pathogen interactions. This paper pro- vides an overview of his work in trophic ecology, ranging from individual behavior of foraging predators and fleeing prey, up to effects of spatial patchiness on the persistence of specialist natural enemies, and even the determinants of food chain length. In recent years, his work on food web interactions took on an increasingly genetic and evolutionary slant. In this paper, I also return to two theoretical models that I discussed over the years with Ilkka, where we contemplated carrying out collaborative work, but never managed to do so. The first of these models involves how habitat patchiness might moderate apparent competition between prey species. The second of these has to do with splicing evolutionary dynamics into metapopulation models, so as to craft hypotheses about how food chain length might be influenced by the coevolutionary struggle between predators and their prey. I developed simple models of the sort we should have explored together, in the style we would have used at the time of our conversations on these themes, in homage to my memory of our interactions.

Introduction missive to the world, Messages from Islands: A Global Biodiversity Tour (Hanski 2016), he Ilkka Hanski to many scientists was “Dr. Meta- recounts how his love of biodiversity began with population.” In his long and highly distinguished moth and butterfly chasing at the age of eight, career, Ilkka championed the critical role of and was sustained in particular by his capture spatial structure and dynamics for understanding in 1964 of a dusky meadow brown butterfly population dynamics and persistence, not least (Hyponephele lycaon), which had been thought in the context of landscapes radically altered by to be extinct in Finland for some decades at the human activities, and with a particular focus on time. He never lost his interest in issues such as insect populations, such as the famed Glanville population rarity and extinction, and his profes- fritillary. Indeed, in the preface to his valedictory sional career in some ways was an unfolding of 52 Holt • ANN. ZOOL. FENNICI Vol. 54 a chrysalis of sustained intellectual orientations, trophic interactions, namely consumption of a developing out of his youthful enthusiasm for shared, depletable resource base. Moreover, the understanding diversity. patchiness and ephemeral nature of the resource I suggest that we should also applaud Ilkka base for these guilds, along with the intertwined Hanski for his contributions well beyond meta- vicissitudes of colonization, extinction, and local population biology, for he was in many ways dynamics, could at times help facilitate competi- “The Compleat Ecologist” (with due acknowl- tive coexistence (Hanski 1983a). Understanding edgement to Izaak Walton 1653). Ilkka made competitive coexistence is essential to eluci- significant contributions across all levels of eco- dating controls on diversity on the “horizontal” logical inquiry, ranging from early work on dimension of communities. But communities ecosystem processes in bogs (Silvola & Hanski also have a “vertical” structure of interlocked 1979), through addressing broad-scale questions feeding interactions and other dependencies, in biodiversity science (Hanski 1982, Rybicki & sometimes expressed as simple food chains, and Hanski 2013), down to scrutinizing the level of more often as complex webs of trophic interac- behavioral ecology (e.g., Niitepõld et al. 2011) tions. Many horizontal interactions emerge from and even the microbiome of individual organ- vertical interactions (as clearly recognized by isms (Hanski et al. 2012, Hanski 2014). His Robert MacArthur in the early 1970s, in papers central abiding focus, however, was surely pop- and monographs published about the time Ilkka ulation biology, largely though not entirely in Hanski was a student). a spatial context, with an increasing emphasis My paper is intended to pay homage to the on genetics and evolution in the latter part of many contributions that Ilkka Hanski made to his life (e.g., Fountain et al. 2016). In addition our understanding of the vertical structure of to hundreds of papers on population biology, ecological communities, ranging from the details Ilkka wrote or edited major books with a strong of the trophic ecology of individual organisms, population focus (Gilpin & Hanski 1991, Hanski to predator–prey dynamics (and in particular & Gilpin 1997, Hanski 1999, Hanski & Gag- the potential role of predation in driving rodent giotti 2004). It is hard to imagine any corner of population cycles), to the consequences of tro- population and spatial ecology and conservation phic interactions for broader patterns of com- biology today that has not been influenced by his munity structure and dynamics, to eco-evolu- profound insights into how populations respond tionary dynamics. In scanning his bibliography, to spatial heterogeneity and patchiness in the I identified a substantial array of papers on these environment. themes. By my count, Ilkka published 46 papers Yet, throughout his career, Ilkka never lost on trophic ecology, broadly conceived (and I sight of the importance of embedding an under- have doubtless missed a few). This is a fine standing of the population and evolutionary corpus of work, all on its own. Many of these dynamics of each individual species into the contributions of course interdigitate with Ilkka’s broader context of the web of species in which interest in spatial ecology, but not all. it occurred. Many of his early papers focused on Starting in the early 1980s, my path and competitive interactions among species occu- Ilkka’s intersected frequently, both in Finland pying naturally patchy environments, such as and other venues, such as Imperial College at guilds of carrion flies (Hanski & Kuusela 1977) Silwood Park, and NCEAS in Santa Barbara. and dung beetles (Koskela & Hanski 1977, He kindly invited me to participate in a number Hanski & Koskela 1979). These are all groups of workshops in Finland, and to visit his lab at of species that can be viewed as classic compet- the University of Helsinki. We talked on many itors, in that they are similar species contending occasions about potential collaborations, and it for similar resources, leading to the expectation is one of the great regrets of my life that we did of competitive interactions due to scramble com- not push these thoughts through to fruition. One petition and interference while contending for thing I have done in thinking about what I might limited resources. But as Ilkka recognized, such do in this homage to Ilkka is to go back through competitive interactions emerge in part from my notes and correspondence, and rummage in ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 53 my memory, so as to allow some ideas to resur- of past locations of cocoon groups for a while, face. So I will attempt in this paper to provide a leading to spatially dependent predation. The personal overview of some of the contributions paper ends by suggesting that these results may Ilkka Hanski made over his life to the study of help explain the fact that sawfly outbreaks often trophic interactions and food web ecology, and start on barren soils, which have fewer general- also to return to two specific thematic areas ist mammalian predators, permitting the inverse where he and I had thought to collaborate, but density dependence due to saturating functional did not. I present some simple models illustrat- responses by specialist predators to be particu- ing — in a counterfactual world — what we larly important in these populations. might (and should) have done together, using the There are several things that strike me about modeling approaches that would have occurred this paper. First, there is a concern with the to us at the time we had those conversations. spatial attributes of ecological systems. Second, One of these has to do with how patchiness can there is a grounding of the population analyses modulate apparent competition, and the other in the details of organismal biology (how long with how evolutionary dynamics might influence can shrews and voles remember where they food chain length. My intent for both of these is last encountered sawfly cocoons?). Finally, the not to provide a comprehensive review of all the authors aim to use local analyses to explain work that has subsequently emerged on these broader spatial patterns, such as the initial loca- themes (though I will touch on that), but instead tions of sawfly outbreaks in heterogeneous land- to provide homage to my friendship with Ilkka scapes. I think these themes resonate throughout by developing thoughts that we never quite got a broad swathe of Ilkka’s career. around to publishing, using approaches that we Let me mention a couple of other contribu- would have used at the time. tions Ilkka made to individual trophic ecology. In Sundell et al. (2000), he reported experiments in which least weasels were given the opportunity The trophic ecology of individual to predate radio-collared Microtus voles, released organisms into enclosures at different densities. Poor voles, they did not have a chance; over three days, a At the most basic level, trophic ecology has to very large fraction of these prey were killed by do with the struggle between consumers, trying the weasels. The weasels had a classic saturating, to acquire resources, and their living resources, type II functional response, but with a killing rate attempting to escape consumption. Until prepar- greater than might be expected based just on the ing this paper, I was unaware of (or had forgot- daily energetic demands of weasels. The bottom ten) several interesting empirical contributions line of the study is that for Microtus, per capita Ilkka had made at this most basic level of trophic mortality, though overall quite high, is reduced ecology. at higher conspecific densities. This basic rela- For instance, he reported experiments tionship underlies many important ecological and (Hanski & Parviainen 1985) in which groups of evolutionary phenomena, ranging from explana- pine sawfly cocoons (of the species Nodiprion tions for population cycles, to the evolution of sertifer) were placed at sites across a wide range synchronized breeding, to group formation, and of forest types, then monitored. These exper- it is believed this contributes to the celebrated iments showed that very rapid destruction of rodent outbreaks of Fennoscandian ecosystems cocoons by small mammals occurred, suggesting (see below). A related paper (Hellstedt et al. that mammal predation could be a major driver 2002) showed that field vole movements, rate of sawfly dynamics. The masked shrew was of maturation, and breeding success were not particularly effective in attacking spatially scat- measurably altered by the simple presence of a tered cocoons, whereas the bank vole differen- key predator, the least weasel. This eliminates tially hammered clumped cocoons. An intriguing one potential source of complexity in population detail parenthetically remarked on in the paper models of field voles impacted by predation. is that individual predators can retain memory Peter Abrams (1984, 1995) among others (e.g., 54 Holt • ANN. ZOOL. FENNICI Vol. 54

Kotler & Holt 1989) has long emphasized the into a sustained and influential set of studies of particular importance of shifts in behavior and microtine rodent dynamics. A landmark paper other traits as modulators of trophic interactions in 1991 (Hanski et al. 1991, cited according (what are now called “trait-mediated interac- to Google Scholar over 600 times) argued that tions,” a growing field of interest in community the relative importance of specialist and gen- ecology, Ohgushi et al. 2012). Peter gave a sem- eralist predators varied systematically along a inar in Helsinki in the early 1990s, visited with latitudinal gradient in Finland. Ilkka in this paper Ilkka (P. Abrams pers. comm.), and doubtless extended a predator–prey model explored by prompted Ilkka to think more carefully about the May (1973) (which in turn was based on Leslie behavioral dimensions of trophic ecology. Stud- 1948, and Leslie & Gower 1960) to examine the ies such as Hellstedt et al. (2002) are important combined impacts of specialist and generalist because they indicate that sometimes these poten- predators on rodent cycles. The model is as fol- tially important complications may not be present lows: in particular systems. This concern with the details of the organis- dN/dt = rN(1 – N/K) – cPN/(N + D) – Gf(N), mal dimension of trophic interactions continued dP/dt = sP[1 – P/(qN)]. in Ilkka’s research right up to the present. For example, Duplouy et al. (2015) reported the Here N, P, and G are respectively the abun- impact of Wolbachia infection on a parasitoid dances of a focal prey population, a specialist (Hyposoter horticola, a specialist on the Glan- predator upon it, and a generalist predator. The ville fritillary butterfly), and in particular on par- prey grows logistically on its own, but suffers asitoid fecundity and other direct fitness traits. mortality from both specialist and generalist pre- The infection did not seem to affect these fitness dation. The specialist has a type II (saturating) traits of the host, but there did appear to be an functional response to the prey (which is key influence on rates of hyperparasitism. This paper to facilitating outbreaks, and such a functional raises the fascinating possibility that infection response indeed typifies the specialist mamma- by Wohlbachia could lead to a “bottom-up” tro- lian predators of rodents, as shown in Sundell phic cascade, altering parasitoid-hyperparasitoid et al. 2000); the generalist was assumed to have dynamics, thus in turn modulating impacts of the an accelerating functional response to the focal parasitoid on its butterfly host. prey, at least at low prey densities. The specialist predator dynamics phenomenologically follow a logistic growth equation, where predator car- Predation and small mammal rying capacity is directly proportional to prey population dynamics abundance. The number of generalist predators, G, is assumed fixed. A more sustained dimension of Ilkka’s research The model can produce predator and prey in trophic ecology was the population-level cycles, and it predicts that as generalist preda- consequences of trophic interactions. In par- tor abundance increases, the magnitude of the ticular, he played a major role in championing oscillation decreases, as does the length of the the importance of predation for understanding prey cycle. At some point cycling entirely dis- rodent population dynamics in Fennoscandia, appears, and a limit cycle is converted into a and by extension, elsewhere in the world. Ecol- stable equilibrium. Both these predictions do ogists have been intrigued by the causes of the match patterns observed in Fennoscandia, where oft-dramatic fluctuations in rodent population cycle amplitude and period decline from north size since at least the 1920s (Elton 1924, Krebs to south, and indeed cycling is not observed in 2013). Ilkka’s initial interest in small mammal southern latitudes. ecology was in shrew population dynamics (e.g., These basic ideas were extended in a string Kaikusalo & Hanski 1985), but in collaboration of papers, impressive enough to be summarized in particular with Lennart Hansson, Heikki Hent- in a separate paragraph in a Proceedings of tonen, and Peter Turchin, this shifted over time the National Academy of Sciences of the USA ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 55 encomium (Trivedi 2011). Hanski et al. (1994) et al. 2003) for the specialist predator than did responded to criticism by noting that compara- earlier contributions by Ilkka on rodent dynam- ble patterns emerge for other taxa (e.g., grouse) ics, namely that stoat dynamics reflect a kind which are also affected by generalist predators, of classical Lotka-Volterra assumption, in that whose abundance and impacts vary systemati- numerical responses of the specialist predator cally with latitude. Heikkilä et al. (1994) argued are related directly (albeit in a complicated way) that regional synchrony of microtine rodent pop- to the abundance of its preferred prey, rather ulation dynamics was consistent with the role of than following the logistic formulation of May a mobile, specialist predator, the stoat (Mustela (1973). erminea). With Peter Turchin, Ilkka (Turchin This is an impressive body of results. How- & Hanski 1997) showed that this model made ever, one potential weak link is that the popu- quantitatively sensible predictions about latitu- lation model explored in most of these papers dinal patterns in the amplitude and periodic- assumes the Leslie-Gower predation model, in ity of population fluctuations. Follow-up papers which the predator growth rate depends on the (Turchin & Hanski 2001, Hanski et al. 2001) ratio of predator to prey abundances, rather than contrasted several alternative explanations, and the rate of consumption of prey by predators. concluded that the hypothesis of latitudinal shifts As has been noted (and questioned) by many in the relative importance of specialist and gen- authors (e.g., Arditi & Ginzburg 2012: 30; also eralist predators best fit the available evidence, P. Abrams pers. comm.), this assumption about compared to other plausible alternatives. Much logistic predator growth seems drawn from a of this work is synthesized in Turchin’s mono- hat, and may embody internal inconsistencies. graph (Turchin 2003: 317–325). Sundell et al. The model is still being used at a fair clip by (2004) reported that vole-eating avian predators mathematical biologists doing purely theoreti- have cyclic breeding success correlated with cal studies (e.g., Gonzalez-Olivares et al. 2011, cyclic vole abundances, with latitudinal shifts in Gupta & Chandra 2013, Yue 2016), but the Les- breeding success paralleling that of their rodent lie-Gower model has not been recently applied prey; they also show that vole cycles are spa- to empirical predator–prey systems, as best as tially synchronized, in a way that matches dis- I can tell. The main biological difficulty posed persal abilities of their avian predators. by the model formulation is that the numerical Ilkka also examined predation and rodent response of the predator does not really depend dynamics in another high latitude ecosystem on the rate at which it is consuming the prey; if — the high Arctic of Greenland. Gilg et al. one fixes the predator/prey ratio, predator growth (2003) examined in detail the collared lem- rate is fixed, even if the prey population goes ming, and showed that the 40-year periodicity to very low abundances where the functional in lemming abundance observed in Greenland response of the predator approaches zero. Gilg emerges robustly from time-lagged responses et al. (2003, 2009) abandoned this particular for- by a specialist predator (again the stoat), sta- mulation, but still make assumptions about the bilized by direct density-dependent predation coupling of numerical responses to functional from several generalist predators (in this case, responses that warrant more scrutiny. Future the arctic fox, the snowy owl, and the long-tailed work on latitudinal gradients should explore jaeger). Gilg et al. (2009) revisited the theme of different methods of linking predator functional predator–prey cycles, in the context of climate and numerical responses by specialists and gen- change in the high Arctic. They conclude that eralists as potential explanations for the latitu- climate change will likely reduce the reproduc- dinal gradient in rodent oscillations. Traditional tive success of predators, and might even lead to predator–prey models often neglect interference local extinctions. The model results match with among predators that enters into the functional the observed disappearance of lemming cycles response, but such interference could well affect in eastern Greenland in recent years. From the the magnitude of predator–prey cycles (and there point of view of ecological theory, this paper uti- is increasing evidence for interference among lized a different model formulation (as did Gilg predators in functional responses, Abrams 2015). 56 Holt • ANN. ZOOL. FENNICI Vol. 54

To me, a major contribution of this body of (van Nouhuys & Hanski 2005). As van Nouhuys work has been to emphasize the potential impor- and Hanski noted in their 2005 review (see also tance of the interplay of generalist and specialist van Nouhuys & Hanski 2004), the Glanville predation in driving population fluctuations at fritillary in the Åland Islands is embedded in high latitudes. Moreover, as noted by Krebs complex, multispecies assemblages that include: (2013), although these studies “do not suffice to several plant host species, polyphagous herbi- conclusively demonstrate the validity of the pre- vores that are potential competitors, primary par- dation hypothesis [for rodent population oscil- asitoids that attack the butterfly, hyperparasitoids lations], the breadth of observations that can be that in turn attack them, a diffuse and shifting resolved under it is impressive.” The basic idea ensemble of infectious diseases (e.g., Laine & explored by Ilkka over several decades of think- Hanski 2006), and generalist arthropod and ver- ing about small mammal population dynamics tebrate predators. The metapopulation dynamics was that classic problems in population ecology of the Glanville fritillary butterfly leads naturally might be best understood in the context of mul- to metapopulation dynamics in the specialist tispecies interactions in communities. This is a parasitoids it supports (e.g., Lei & Hanski 1997). general insight that resonates well beyond the Ilkka and his lab used the Glanville fritillary but- rodents of Fennoscandia, as well as beyond the terfly system to show that such spatial dynamics limitations in the specific models explored by could facilitate the coexistence of two competing Ilkka and his colleagues. specialist parasitoids, both sustained by their fritillary host (Lei & Hanski 1998, van Nouhuys & Hanski 2002, van Nouhuys & Punju 2010), Interspecific interactions in patchy due to a trade-off between competition and dis- and heterogeneous landscapes persal ability. The host butterfly in turn utilizes two host plant species which differ in quality, Many of Ilkka’s earliest scientific contribu- with emergent effects on butterfly colonization tions were indeed in community ecology, for and hence its colonization–extinction dynamics instance analyzing succession and niche rela- (Hanski & Singer 2001). One important issue tions in dung beetles (Koskela & Hanski 1977, alluded to in the 2005 contribution is the poten- Hanski & Koskela 1977). Ilkka’s interest in tial role of evolutionary dynamics in governing community ecology continued throughout his metacommunity dynamics (see also below). career, with many intersecting research angles crucially involving spatial population dynamics. As one mark of this sustained interest, in each Apparent competition in patchy of the monographs and edited volumes noted environments above, there are one or more chapters dealing with multispecies interactions. In Hanski (1999), When I first met Ilkka, some decades past, one for example, chapter 7 deals with the interface theme we discussed (but never followed up on) between metapopulation and metacommunity at the interface of metapopulation dynamics and theory. This included pairwise competition in a community ecology was the interplay of direct patchy environment, coexistence of predators competition and apparent competition in spa- and prey due to spatial dynamics surmounting tially heterogeneous environments. One of the local instability and predator-driven extinctions, very first theoretical papers Ilkka wrote (Hanski and complex spatial patterns emerging in spa- 1981) had to do with how predation influenced tially explicit predator–prey and host–parasitoid coexistence between species. Back in the 1960s interactions. Ilkka kindly invited me to con- and early 1970s, many ecologists uncritically tribute a chapter on fusing metapopulation and assumed that predation in some sense generi- metacommunity perspectives in his 1997 edited cally boosted the number of species that could volume (Holt 1997), and he later reciprocated coexist in a local community. But in the 1970s by providing a lovely synthetic chapter in my it was recognized that the relationship of species own edited volume on metacommunity ecology coexistence to predation was more complex; in ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 57 some situations, predation had no effect on coex- ent. These authors also observed that at broad istence, whereas in others, it hampered coexis- spatial scales, the presence of the second host tence. Leigh Van Valen (1974: 18) had earlier could boost the occupancy and abundance of argued that “Equivalent predation on all species the shared parasitoid, and thus lead to apparent cannot plausibly increase the number of species competition at large (but not small) scales. There of prey,” and Abrams (1977) noted that indis- thus can be a scale dependency in the qualitative criminate predation could increase the amount of nature of interactions among species (as noted niche differentiation required for resource com- on purely theoretical grounds in Holt 1987). petitors to coexist. Chase et al. (2002) provided What Ilkka pointed out in Hanski (1981) an overview of how predation could modulate was that the theoretical literature on compe- competitive interactions. tition, predation, and species coexistence had Moreover, if predators can respond numer- largely assumed spatially homogeneous envi- ically or in activity levels to their prey, shared ronments, where both predators and their prey predation could lead to an emergent competitive were in a certain sense “well-mixed.” He then interaction (apparent competition) between alter- developed a model in which there is a patchy native prey (Holt 1977, Holt & Kotler 1987), habitat structure, and local density dependence which could lead to exclusion among prey spe- occurs at the patch scale. Within-patch compe- cies that would otherwise not interact. In later tition was assumed to be linear (on a per capita years, a really nice experimental study in the basis), so in each patch a Lotka-Volterra compe- Åland Islands (van Nouhuys & Hanski 2000) tition model holds. If densities are homogeneous demonstrated apparent competition: a primary across space, then the existence of patchiness specialist parasitoid (Cotesia melitaearum) of is irrelevant to competitive coexistence, if local the Glanville fritillary butterfly declined when interaction coefficients are spatially invariant. a second primary parasitoid (C. glomerata) was But as Ilkka noted, there is almost always spa- added to the system, not because of competition tial variance in abundance, even if the envi- for resources (C. glomerata attacks a different ronment is physically homogeneous. So in the butterfly family), but because of a boost in 1981 model he assumed that there is variability attacks by a shared hyperparasitoid, Gelis agilis. in local density within each prey species, across But this tendency towards exclusion could patches, and a well-known empirical relation- be mitigated if predators ignored prey that were ship between average local abundance and vari- rare (Holt 1977: 215–216), or if prey were spa- ance in such abundance was assumed to operate tially segregated and predators either moved within each species. The two prey species were at low rates among patches, or adjusted their assumed to be both patchily and independently foraging so as to lead to an approximately “ideal distributed in space (i.e., their spatial covariance free” distribution of predators across space (Holt in abundances was approximately zero, as often 1984) (one way this pattern could emerge is if observed in nature), and to experience com- predators tended to spend more time in patches parable per capita predation rates within each with more prey). Moreover, theoretical work patch. Ilkka defined “equivalent predation” as (e.g., Holt & Kotler 1987) suggested that shared resulting from a “process of similarly searching predation could in some circumstances lead to for prey individuals regardless of species, both indirect commensalism and even apparent mutu- at the within-patch and between-patch level.” alism, because of weak aggregative or repro- This was not the same as random foraging — ductive numerical responses, prey refuges, and predators were assumed to forage non-randomly saturating functional responses. Again, an ele- and adaptively among patches, focusing their gant field experiment in Ilkka’s lab in the Åland attention on whichever patches had the greatest Islands (van Nouhuys & Kraft 2011) revealed total prey abundance. He showed that with these this effect; there is an indirect commensalism assumptions, equivalent predation could at times between Melitaea cinxia and M. athalia, in that actually facilitate coexistence. (This meaning at a fine spatial scale, the former enjoyed reduced of “equivalent predation” may not match usage parasitism when the second species was pres- of the term in other papers, in that predators in 58 Holt • ANN. ZOOL. FENNICI Vol. 54

Hanski’s 1981 model would focus attacks on So in honor of the memory of those conver- whichever patches had the higher summed abun- sations, I decided to go back to the model of dance, which could be dominated by the prey Hanski (1981), add a predator with a numerical species with higher overall abundance; however, response (in the simplest manner), and now the assumption is that within patches, predators to assume that the prey do not directly com- do not discriminate between prey species). pete between species, but instead experience One thing that strikes me in reading this direct intraspecific density dependence, and also paper again is how many of its themes reso- apparent competition via the numerical response nated through Ilkka’s career. There is of course of their shared natural enemy (as Ilkka and I an emphasis on the consequences of spatial intended to do back then). The basic approach is patchiness for population processes. Beyond what we would have done at that time, and the that, however (as in the rodent cycle work sum- derivation of the model follows that of Hanski marized above), there is an interest in placing (1981). Using the same assumptions as presented population dynamics in the broader context of there, we have for local interactions between community interactions (here, both competition species n and m in patch i (i = 1, S): and predation), and paying attention to sensible assumptions about organismal biology (e.g., foraging by adaptive predators). Moreover, Ilkka , (1) had an abiding interest in the persistent coexistence of similar, competing species, and in how resource patchiness and spatial processes leading to aggregation could facilitate coexistence (i.e., where the quantities ni, mi, pi are respectively the Kuusela & Hanski 1982, Kouki & Hanski 1995). densities of two prey species, and their shared Indeed, one of his last publications (Ruokolainen predator, in patch i. The parameters r and k are & Hanski 2016) developed a novel mechanism intrinsic growth rates and carrying capacities, whereby reproductive interference among spe- indexed for each prey species; the quantity c cies could reduce their spatial correlation, per- is the per capita attack rate by the predator, mitting the coexistence of ecologically identical assumed equal for the two prey. competing species. Finally, as in so very many of We now follow Ilkka’s derivation. Let his papers, there is a conceptual elegance, and a willingness to take simplifying (but reasonable) , assumptions that lead to biologically interpreta- ble results. and assume that for each prey species, the vari- Returning to the 1981 piece, Ilkka assumed ance in abundance among patches increases with that predator numbers were fixed, which allowed mean abundance according to him to portray the impact of predation upon the competitive interaction as a shift in isoclines in , a two-dimensional phase space. He does note (p. 310) that “Obviously, a model including a where the overbar denotes average local den- dynamic equation for the predator population sity. So more abundant species are also more would be preferable.” Ilkka and I talked when aggregated. Also, we assume that the covari- we first met in person (I think it was around ance in abundance between the two prey species 1990, at Silwood Park in the UK) about com- is approximately zero. Both these assumptions bining our interests in patchiness, predation, and about spatial variances and covariances seemed species coexistence, starting with the ideas of his to match much empirical data (Hanski 1980, 1981 paper broadened to include numerically 1981). It would be valuable to explore the current responsive predators, and including ideas from state of these relationships. Peter Abrams (pers. a couple of my own papers (Holt 1984, 1987) comm.) suggests that in the limit of very low prey and his own (Hanski 1983b), but we never got density, this empirical relationship might change around to doing so. (between mean and variance of abundance), ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 59 because all individuals of a species should tend Prey species m can invade when rare (so that to be found in the best patch, if they have adap- one can neglect its own direct density depen- tive behavior; he also suggests that there might be dence), if and only if positive covariance between species that are similar enough to be consumed by the same predator. . (3) However, for our present purposes, we will retain the assumption made in Hanski (1981). The fraction in brackets on the right-hand side Because we are interested in apparent com- describes how much lower the intrinsic growth petition, we set the competition coefficients to rate can be for prey species m, than species n, zero, and add an equation for the numerical and still permit coexistence of the two prey response of the predator. We contrast two kinds species. Patchiness and increased aggregation of predators, each with a simple local linear in the resident prey species (increasing a) inten- functional response to each prey species. sifies intraspecific density dependence. This in The first predator moves rapidly and indis- effect reduces the productivity that can flow criminately among patches, so its density is through to the predator, sustaining its abundance. approximately the same everywhere. After some Reducing predator abundance weakens apparent manipulations, we arrive at: competition. So patchiness and prey aggregation relax constraints on coexistence that arise from apparent competition, even if a predator moves indiscriminately across space. . (2) Ilkka in his 1981 paper made a different and clever assumption about predator behavior. Rather than moving indiscriminately, he argued that one should expect predators to tend to aggregate where they have greater rewards, which with The first term in each of the two prey equations the assumptions of the model (equal attack rates corresponds to eq. 11 in Hanski (1981), with and predator mortality across space), implies they interspecific competition turned off, and a sim- tend to aggregate where total prey abundance is plified predation term. Because the predator is greatest. One of the models in Holt (1984) also uniformly distributed across patches, the mor- assumed such adaptive predator behaviors, but tality it inflicts on each prey fits a mean-field allowed predators to be ideal-free in their habitat assumption. The predator has a linear numerical use. Ilkka by contrast reasonably assumed that response to the average density of prey across predators move adaptively, but are not necessarily the landscape, and has a constant per capita perfectly optimal in their habitat choice. In partic- mortality rate of µ. Finally, each consumed prey ular, he assumed that local predator abundances produces e predators. approximately match local prey abundances, so

We assume that prey species n has the higher that pi ≈ q(ni + mi). This assumption implies a spa- intrinsic growth rate. In general, this gives an tial covariance between local predator abundance advantage to a species in apparent competition and local prey abundance. This affects both the (Holt & Lawton 1994), both because a species growth dynamics of the prey, and of the predator, can thereby better withstand predation pressure, as follows (the quantity q drops out of the model): and also because it can thereby sustain high predator numbers (productivity at lower levels flows through to upper levels). We assume that the predator and prey species n are present and at equilibrium, so the average local abundance of . (4) the predator is

60 Holt • ANN. ZOOL. FENNICI Vol. 54

0.8

0.6 for m invasion n 0.4 µ/(cek ) = 1/3

/ r n m r

Minimum 0.2

µ/(cekn) = 2/3

0 0 0.5 1.0 1.5 2.0 a Fig. 1. The condition for invasion of species m when it is rare and species n is at equilibrium with the predator for the model of Eqs. 2 and 4. Species m can invade when rm /rn is above each curve. Solid lines are for a randomly attacking predator, while dashed lines are for a predator whose density is proportional to the local total prey density

(as in Hanski 1981). For a high value of µ/(cekn), invasion is always easier with the random predator, while for small

µ/(cekn) and low a, invasion is easier for the aggregating predator (thick dashed line below the thick solid lines), while for higher a, invasion is easier with the random predator.

As before, we assume that prey species m is The parameter “bandwidth” (sensu Armstrong rare and attempting to invade, and prey species n 1976) permitting prey coexistence differs between and the predator are at equilibrium. the predator movement scenarios (see Fig. 1). At Predator density is now low values of the prey aggregation parameter a, in some cases adaptive foraging by the predator facilitates prey coexistence, compared to a uni- form predator distribution. But at higher values and so the criterion for prey species m to invade of a, density dependence in the resident prey becomes strengthens, which for an indiscriminate predator eventually precludes its own persistence. In this . (5) case, exclusion due to apparent competition will not occur for such a predator, when it still con- Once again, aggregation in the resident prey ceivably could (for prey with quite low r’s) for the makes it easier for a prey species with a lower adaptively foraging predator. intrinsic growth rate to invade; the right-hand One way to characterize the equilibrium is sides of Eqs. 3 and 5 decrease with increasing a. to examine the shape of the predator isocline, However, the reason is different than with a uni- which defines the possible combinations of prey formly distributed predator. Because predators densities at which the system equilibrates. As differentially attack high-density prey patches, noted in Holt (1977), if the predator isocline has density dependence in the resident prey is weak- a negative slope, there is necessarily an apparent ened, which boosts predator numbers. However, competition relationship between the two prey there is a countervailing effect, which is a reduc- species in their equilibrial abundances. However, tion in the maximal number of predators that can some multi-prey–predator models can lead to be sustained, when predation is intense (e.g., isoclines that bulge away from the origin, or high c), in effect because of an increase in the even have positive slopes, if predators have sub- average attack rate. optimal foraging strategies (Holt 1983). Figure ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 61

1.0

0.8 Fig. 2. Predator isocline for the Hanski (1981) model with a dynamic aggregating predator (Eq. 4) with 0.6 c = 1 and µ = 1. (The straight line with a = b = 0 m a = b = 0.5 also describes the predator 0.4 a = b = 0 isocline for the indiscriminately foraging predator, Eq. 2 in text.) The predator increases for 0.2 a = 0.5, b = 2 above the isocline. It is easier for the predator to increase with higher prey aggregation (higher a and 0 b), which pushes the iso- 0 0.2 0.4 0.6 0.8 1.0 cline closer to the origin. n

2 shows the isocline shapes for the two predator erning predator movement behavior, the dynamic scenarios of models of Eqs. 2 and 4. For the case rules governing the generation of prey aggre- of a predator moving indiscriminately across gation in the first place, the relative values of the landscape, if both prey can coexist, the equi- the two prey to the predators, and other factors. librium will lie along the predator isocline, and For instance, Abrams (1999) explored a model each prey species will have a lower abundance, where predators adaptively moved between two than it would enjoy, were it alone with the pred- patches, each with a distinct prey species. Adap- ator. In other words, apparent competition still tive predator switching was shown to poten- exists, even though the prey coexist. A com- tially lead to strong apparent competition, when parable predator which responds to total prey the prey exhibited asynchronous dynamics. One numbers by aggregation has an isocline shifted assumption made in the above model (building towards the origin, so overall, prey densities at on that in Hanski 1981) is that there is a partic- equilibrium will be reduced. However, the iso- ular relationship between mean prey abundance cline can now bow outwards for some parameter and variance among patches in prey abundance, values. This implies the potential not just for and zero covariance between alternative prey a weakening of apparent competition, but the species’ abundances. But these attributes of prey potential for (+,–) interactions (as assessed by abundance themselves are likely to be altered by say removal experiments) (Holt 1983). the pattern of predator movements and attacks. The bottom line is that in a patchy envi- Kilpatrick and Ives (2003) even argue that Tay- ronment, this phenomenological model suggests lor’s law (a power-law relation between the that prey aggregation tends to weaken appar- variance and mean of a species’ abundance) may ent competition between prey species, and thus emerge from interspecific interactions. In future facilitates coexistence, and can even lead to studies, it would be valuable to explicitly link emergent alternative modalities of indirect inter- dynamical models of interacting predators and actions, depending on how predators respond to prey moving in a patchy environment to emer- prey aggregation. However, other analyses of gent statistical properties of the patch ensemble, the interaction between aggregation and prey such as analogs of Taylor’s law, and the temporal coexistence in more recent years suggest that and spatial correlation structure of across-spe- this conclusion should be viewed cautiously, as it cies abundances. These issues are also ripe for depends on the details of the explicit rules gov- focused empirical study. 62 Holt • ANN. ZOOL. FENNICI Vol. 54

Eco-evolutionary dynamics and cialized parasitoids, which are already known food chain length to be influenced by host diet (van Nouhuys & Hanski 1999). A lovely empirical study (Farkas Ilkka had a long-standing interest in the genetic et al. 2013) demonstrated that maladaptation in and evolutionary dimensions of ecological pro- stick insects due to gene flow in a mosaic land- cesses, an interest which grew and transformed scape permitted greater visitation by birds onto over time. His 1998 paper in Nature on inbreed- particular local habitats, which then inflicted ing and extinction risk (Saccheri et al. 1998) higher mortality on other resident species of highlighted how inbreeding by depressing local insects in those habitats — an example of appar- fitness could exacerbate extinction (see also ent competition facilitated by gene flow. So the Nieminen et al. 2001). This interest developed interplay of evolutionary dynamics and spatial in many directions in the last decades of his processes could lead to novel community-level life, for instance with analyses of the evolution consequences in food webs. of dispersal (Heino & Hanski 2001, Singer & A classic problem in community ecology is Hanski 2004, Hanski et al. 2006, Hanski & to understand the factors governing the length Mononen 2011), elucidation of the genetic bases of food chains (Hutchinson 1959, McGarvey et and environmental influences for variation in al. 2016). In several publications, I have argued dispersal (Haag et al. 2005, Hanski et al. 2006, that for specialist consumers, spatial dynamics Zheng et al. 2009, Mattila & Hanski 2014, Wong could be important in constraining food chain et al. 2016), and examination of the interplay of length (e.g., Holt 1997, 2010), and some empir- local adaptation and metapopulation processes ical systems provide suggestive evidence that (Hanski & Heino 2003, Hanski et al. 2011). such effects indeed matter (e.g., Komonen et al. Again, Ilkka and I often talked about how 2000, Roslin et al. 2014). One idea Ilkka and the interplay of genetics, evolution, and ecology I played with (but never got around to pulling could bear on a wide range of topics, such as together) was that evolutionary dynamics (e.g., patterns in community structure at broad spatial local adaptation) in predator–prey interactions scales. The basic idea was that local evolu- could influence colonization and extinction rates tionary dynamics should influence colonization in ensembles of trophically interacting species, and extinction rates (as seems to hold in the and thus influence food chain length (and other Glanville fritillary), and thus patterns of species food web metrics). We talked about extending a occupancies in metacommunities. Interactions specific model presented in a chapter in a book between species could be a prime driver of local Ilkka edited (Holt 1997). A simplified version of selection, and if such selection corresponded eq. 8 in that publication is as follows: to shifts in population abundance or stability, this could translate into altered colonization and dH/dt = cH(1 – H – P) – cpHP – eH, (6) extinction rates across a food web. In turn, how dP/dt = cpHP – epP. (7) interacting species were co-distributed across space would influence spatial variation in selec- Here, H is the fraction of patches that only have tion, and shifting patterns in abundance could prey, and P is the fraction of patches with both likewise modulate the availability of genetic the predator and its prey. Prey colonize empty variation in traits governing fitness, as well as patches at a rate defined by c, and go extinct at the magnitude of nonselective forces such as rate e. Predators colonize prey patches at rate cp, gene flow, inbreeding and drift on local adapta- and go extinct at rate ep; such extinctions could tion and thus population sizes. occur because the predators over-exploit prey, so All these effects could have community-level that both go extinct, or because prey go extinct consequences. The Glanville fritillary utilizes for other reasons, and the predators are dragged different host plants, and selection on host plant to their doom with them. use alters its extinction–colonization dynamics. For the prey to persist on its own requires This could have consequences for the coloni- that 1 > e/c. Given that the prey is present at its zation-extinction dynamics of dependent, spe- equilibrial occupancy of H* = 1 – e/c , the preda-

ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 63 tor can persist if and only if by Abrams and Matsuda (1997) (among others, e.g., Jones et al. 2009) can be embedded in a

1 > e/c + ep/cp. (8) spatial context, and have implications for both extinction and colonization dynamics. Popula- Comparing these inequalities shows that there tions that cycle spend periods at low densities, could well be metapopulations that sustain the with elevated extinction risks. And changes in prey species, but not the specialist predator local abundance due to evolutionary dynamics which depends upon it. There are some excellent can alter the number of propagules available for examples matching this prediction in the Glan- colonizing empty patches from occupied patches. ville fritillary (van Nouhuys & Hanski 2005). I will make some specific assumptions. As So in honor of past conversations with Ilkka in Eqs. 6–7, a patch that is empty can be colo- about extending such models to incorporate nized by a prey species, but not the predator. A eco-evolutionary dynamics, in the next several patch occupied by a prey species may experience paragraphs I will present a simple model in extinction, persist unchanged, or be colonized by which local adaptation by a prey/host species a predator. Once the predator is present, however, to a predator/pathogen can influence occupancy the prey can then adapt to its presence. If the prey of the latter (in the simplest possible “food adapts sufficiently so as to avoid predation, the chain,” namely a bitrophic interaction). As Ilkka predator on that patch may end up at such low often emphasized, the intellectual roots of meta- abundance that it rapidly goes extinct (e.g., at the population ecology are in island biogeography low trough in abundances in the predator–prey (Hanski 2004). In classic metapopulation and cycles of the Abrams-Matsuda 1997 model). Or, metacommunity models, rather than track indi- the prey may adapt, and the predator still persists vidual populations sizes, genotype frequencies, for a while, albeit at such low densities that it ends and the like, one imagines that each site in up going extinct. One question that immediately a metacommunity can be characterized by a arises in either case is: what is the relationship “state” defined by the presence/absence of dif- between adaptation by prey to avoid predation, ferent combinations of species (as in Eqs. 6–7 and the realized length of food chains across all above). Transitions among these states of course patches (in comparison say to the expectations include colonization, extinction — and now, we from the non-evolutionary model above)? will assume, local, within-patch, adaptation by We assume that there is an exponentially the victim species to its natural enemy, as well. distributed “waiting time” for a prey population In homogeneous systems, it is becoming exposed to predation to adapt to the predator. increasingly appreciated that there can be a wide Prey populations can fall into several states: the range of potential consequences of local evolu- prey can be present alone on a patch, but not tion on population dynamics of interacting preda- adapted to the predator; or, the predator can be tors and prey (Hairston et al. 2005). For instance, present, with the prey in a non-adapted state; evolution can lead to longer periods in predator– or, the prey can have adapted to the predator. prey cycles, thus increasing the length of time Adapted patches with predators can lose those species are at low densities. Abrams and Matsuda predators, and the prey population there can (1997) explored a predator–prey model in which then revert to a non-adapted state (viz., because prey adapted to predation, at a cost to their intrin- anti-predator adaptations are costly). sic growth rate. In the absence of such evolution A metapopulation model incorporating adap- (in the example shown in Hairston et al. 2005), tation by prey to shake off the predator is as the populations settle to a stable equilibrium. follows: With evolution in the prey, pronounced population cycles arise, so that periodically predators dH/dt = cH(1 – H – P – H´) – cpHP + rH´ – eH collapse to low density because the prey have dP/dt = cpHP + epP – aP. (9) evolved to escape predation; when predation is dH´/dt = aP – rH´ – e´H´ low, prey defense wanes, allowing predators to eventually rebound. The local dynamics explored The quantity H´ is the fraction of patches with 64 Holt • ANN. ZOOL. FENNICI Vol. 54 prey that have adapted to the predator, which damped oscillations, settles into a system where happens at rate a. We assume that the number of most occupied patches have both predator and colonizing individuals moving among patches prey. At t = 100, we allow adaptation to begin, is always small, relative to local average abun- but adapted patches neither recover, nor colo- dances, post-colonization (this way we can to a nize other patches. There is a transient phase of first approximation neglect complications due to increase in adapted patches, which leads to a gene flow swamping local selection), and also rapid decline in occupancy by the predator. In that if predators happen to persist on patches some cases (Fig. 3), the predator persists, as does with adapted prey, these predators are scarce a mix of patches, some with maladapted prey, and so negligible as sources of colonists into and some with adapted prey. In this case, we available patches with non-adapted prey. (Such then allow adapted hosts to lose their adaptation patches would have an effective food chain (starting at t = 200), which leads to an equilib- length of unity.) Predator colonization thus only rium with fewer adapted patches and the same occurs from patches where prey are still not number of adapted patches. The number of pred- adapted to predation. Likewise, we assume that ator patches increases to a level slightly higher in patches in which prey have adapted to predators overall occupancy of the landscape than before are not able to directly send prey colonists to adaptation started, basically because allowing the empty patches. This could occur if for instance prey to adapt to the predator, and also to lose that there were a strong trade-off between dispersal adaptation once the predators are gone, permits ability, and ability to escape predators within a replenishment of susceptible prey patches the patches. Eventually, we assume that predators predator can colonize. So prey adaptation can disappear from these adapted-prey patches. After boost food chain length a bit, in this example. the predators are gone, the selective costs of In other cases (Fig. 4), rapid adaptation by anti-predator adaptations are not matched by the prey leads to a sharp decline in preda- any benefits, and over time (again, exponen- tor occupancy, and ultimately predator extinc- tially distributed), these patches lose anti-pred- tion. Predator exclusion occurs not because prey ator adaptations, re-enter the pool of vulnerable are persistently adapted to avoid predation, but prey patches (at rate r) and again can contribute because they can quickly, locally adapt to preda- colonists to the metapopulation. tion, reducing the predator’s ability to colonize With these assumptions, the condition for the other patches. Rapid prey evolution can thus lead predator to invade when rare, and the prey is at to a kind of dynamic, transient exclusion of a equilibrium, becomes specialist predator. The basic conclusion of these simple models . (10) is that prey adaptation to withstand predation should be able to influence food chain length on Reversing this inequality characterizes meta- islands, but that whether or not it is expected to populations where the predator cannot increase shorten or lengthen food chain length depends when rare. Permitting prey to adapt to the on how such adaptation translates into impacts predator removes (by our assumptions) those on extinction and colonization rates. Moreover, patches from the dynamically relevant part of the potential for prey adaptation may permit the predator metapopulation, and hence makes predators to be excluded from a metapopulation, it harder for the predator to persist. Comparing even if a snapshot assessment of prey traits in the expressions for predator invasion shows that the predator-free landscape (where the prey is prey adaptation makes it harder for the predator expected not to be adapted to avoid this specific metapopulation to persist. predator) might suggest that the predator could Numerical examples are presented in Figs. 3 successfully establish. and 4. We start with a prey metapopulation occu- This metapopulation model is akin to models pying most of the landscape, and assume that in epidemiology, where hosts are classified into the prey is for a while not able to adapt to preda- discrete states, such as susceptible, infected, and tion. The predator invades, and after a period of resistant (SIR models). In a sense, the evolu- ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 65

1.0 H P H' 0.8

0.6

0.4 Fraction of patches

0.2

0 0 50 100 150 200 250 300 Time Fig. 3. Fraction of patches occupied by the original host (H ), this host and the predator (P ) or the adapted host (H´) for the metapopulation model of Eq. 9. Initially, the host is at its equilibrium if alone (H = 0.9), the predator fraction is P = 0.001 and there are no adapted hosts (H´ = 0). For t < 100, the parameters are c = 1, cp = 2, e = 0.1, ep = 0.2, e´ = 0.1, a = 0 (so there is no host adaptation) and r = 0. At t = 100, the hosts become able to become adapted, so a = 0.3 thereafter. At t = 200, adapted hosts become able to lose adaptation, so r goes to 1. Adaptation causes the predator fraction to decline, which allows the non-adapted host patches to increase along with the adapted host patches. Loss of adaptation causes the adapted patches to drop and the predator patches to increase (with no effect on non-adapted host patches).

1.0 H P H' 0.8

0.6

0.4 Fraction of patches

0.2

0 0 50 100 150 200 Time Fig. 4. Fraction of patches occupied by the original host (H ), this host and the predator (P ) or the adapted host (H´) for the metapopulation model. Initially, the host is at its equilibrium if alone (H = 0.9), the predator fraction is P =

0.001 and there are no adapted hosts (H´ = 0). For t < 100, the parameters are c = 1, cp = 2, e = 0.1, ep = 0.2, e´ = 0.1, a = 0 (so there is no host adaptation) and r = 0. At t = 100, the hosts become able to become adapted, so a = 1.6 thereafter. In this case, the adaptation rate is high enough to cause loss of the predator (and adapted patches). tion of anti-predator adaptations embodied in number of secondary infections spawned by a the model above is akin to the development of primary infection) is pushed below one, which resistance in an infected host. If such resistance prevents the spread of the infection. In like rapidly develops, the R0 of the infection (viz., the manner, the rapid evolution of resistance by prey 66 Holt • ANN. ZOOL. FENNICI Vol. 54 to predation can lower the ability of the predator by say a modest reduction in attack rates. If to increase when rare in a metapopulation, thus predators thereby are less able to overexploit the leading to the exclusion of predators from a prey, extinction rates could be lowered by prey patchy landscape. evolution, and predator numbers even enhanced. There are many ways in which these occu- In this case, prey evolution could sustain longer pancy models could be elaborated to include food chains across the metapopulation. other evolutionary and ecological scenarios. All such model extensions rely upon the Predator–prey interactions are prone to sustained simplifying assumption that one can characterize instability, and even asymptotically stable sys- patches into discrete states (e.g., non-adapted tems can show pronounced oscillations follow- prey, vs. adapted prey). This may be a gross and ing environmental perturbations, so examining at times misleading oversimplification of sys- how these issues play out in the context of tems with complex eco-evolutionary dynamics, non-equilibrial dynamics could be of particular for which an explicit accounting of within-patch importance (P. Abrams pers. comm.). As noted processes might be needed. For instance, if gene in Holt (1997), at times predators can moderate flow among patches can perturb local popula- instability in their prey, and even increase prey tions away from their local selective equilibria, abundance (e.g., by preventing overexploitation much more complex models would be required by the prey of its own resource, a phenom- that pay specific attention to the microevolution- enon related to the “hydra effect” identified ary mechanics of selection, gene flow, and drift by Abrams 2009). Adding evolution can alter in determining local adaptation of prey to pred- these ecological effects, or lead to more com- ators (and vice versa), with emergent impacts plex dynamical behaviors (e.g., Cortez & Ellner on colonization and extinction processes in a 2010, Yamamichi et al. 2011). For instance, one metacommunity. might envisage that prey populations that have adapted to the predator could themselves send out colonists into empty patches. (As with our Discussion and conclusions above results, we can assume to a first approximation that immigration into occupied patches is The basic conclusion I draw from my overview negligible, so can ignore the complications of the of Ilkka Hanski’s contributions to trophic ecol- interaction of gene flow and selection.) In this ogy is that they are intellectually expansive and case, we could replace the last sub-equation in of enduring value. The issue of understanding Eq. 9 with say the contribution of predation as drivers of dramatic oscillations in the abundance of small dH´/dt = aP – rH´ – e´H´ + c´H´(1 – H – P – H´). mammals has not been resolved by his work (Krebs 2013), but to my eyes there is a much In a sense, adapted and non-adapted prey stronger case than was available thirty years populations “compete” for empty patches. It can ago that the interplay of generalist and specialist be shown that if, with no predator and r = 0, H predators has a special role in observed patterns. eliminates H´, then this will also obtain if r > 0. In terms of the specific themes that I wish I Such elimination requires c/e > c´/e´; in other had followed in collaboration with Ilkka, there words, if there is demographic cost of adaptation are of course many directions in which both to the predator at the metapopulation scale, one could be pushed. My extension of Hanski (1981) expects the predator-free landscape to have prey presented above made a number of simplifying vulnerable to predation. assumptions, matching those that he made in The specific conclusions drawn from the that paper. Space is implicit. Stochasticity must model assume in particular that prey so effec- underlie spatial variation in prey abundance, but tively adapt to predators that if they continue to such stochastic sources of variation are likewise co-occur, the predators cannot send colonists to implicit. The predator functional and numeri- predator-free patches. An alternative scenario cal responses within patches are linear. All of would be that prey weakly adapt to predators these should be relaxed in future analyses of ANN. ZOOL. FENNICI Vol. 54 • Hanski’s contribution to the spatial dimension of food web interactions 67 this problem. A contemporary approach to this patches. Islands or patches might be represented issue might for instance use individual-based as a continuum of evolutionary states, rather analytic or simulation models, which allow one than as simply “adapted” or “not adapted,” and to include realistic assumptions about predator moreover, all interacting species (not just the movement and foraging across explicit land- prey in the pairwise predator–prey interactions I scapes. These models could include heterogene- assumed above) should be allowed to co-evolve ity in the model parameters themselves, and also in tandem. And dispersal does not merely colo- incorporate impacts of demographic stochastic- nize empty patches, it also couples over evolu- ity and the details of life histories (e.g., Detto & tionary time scales occupied patches, infusing Muller-Landau 2016, who conjecture that time genetic variation and at the same time pulling lags in natural enemy effects could influence local populations away from local optima. It is the buildup and decay of spatial correlation a very large challenge, splicing together all the structures in shared predation systems). Another separate pieces that are at play in metacommuni- analytic approach might be to use moment-clo- ties — the direct and indirect interactions among sure techniques (e.g., Bolker et al. 2003) to look a multiplicity of species, the playing out of inter- explicitly at the dynamics of spatial variances actions via dispersal over large landscapes, the and covariances for each species and set of inter- reciprocal impacts of these ecological processes acting species. In Holt (1987) I surmised that the on evolutionary dynamics, and the resultant shift sign of indirect interactions between alternative in ecological processes because of evolved trait prey species could shift with the spatial scale of differences — but as we address this challenge investigation. It would be useful to examine this over the years to come, I have no doubt that the conjecture more forcefully in models with realis- wonderful foundational work of Professor Ilkka tic assumptions about predator–prey interactions Hanski will continue to resonate. and spatial dynamics playing out across complex landscapes. One could also add additional species (e.g., a mix of specialist and generalist pred- Acknowledgements ators), and examine how this alters expectations about coexistence. The food web dimension of I thank the organizers for their invitation. I thank my asso- ciate Mike Barfield for help with model analyses and figure coexistence theory is receiving increasing atten- preparation, and my lab manager Vitrell McNair with manu- tion (e.g., Chesson & Kuang 2008), and placing script preparation. I thank very much Peter Abrams for a very this issue in a spatial context would likely open perceptive review of the manuscript, and the editors for their up new avenues for both coexistence and exclu- patience. And finally, most of all, I thank Ilkka Hanski for sion in metacommunities. many years of friendship, inspiring science, and professional and personal camaraderie. Metapopulation approaches to understanding food chain length and other attributes of food webs are receiving increasing attention. Gravel et al. (2011) provide a valuable way forward References in trophic island biogeography by permitting Abrams, P. A. 1977: Density-independent mortality and inter- colonization and extinction rates to be defined specific competition: a test of Pianka’s niche overlap by whether or not generalist consumers have hypothesis. — The American Naturalist 111: 539–552. at least one requisite prey species present on Abrams, P. A. 1984: Foraging time optimization and inter- an island. Carrying out comparable analyses in actions in food webs. — The American Naturalist 124: 80–96. metacommunities, rather than islands, is inher- Abrams, P. A. 1995: Implications of dynamically variable ently a more complex problem, in part because traits for identifying, classifying, and measuring direct of the multiple potential sources of colonization and indirect effects in ecological communities. — The for any particular species. The way in which American Naturalist 146: 112–134. evolution was represented in the above models is Abrams, P. A. 1999: The adaptive dynamics of consumer choice. — The American Naturalist 153: 83–97. really a cartoon; ideally, one would track explicit Abrams, P. A. 2009: When does greater mortality increase gene frequencies of particular loci, or assume population size? The long history and diverse mecha- quantitative genetics, in each of a number of nisms underlying the hydra effect. — Ecology Letters 68 Holt • ANN. ZOOL. FENNICI Vol. 54

12: 462–474. Gravel, D., Massol, F., Canard, E., Mouillot, D. & Mouquet, Abrams, P. A. 2015: Why ratio dependence is (still) a bad N. 2011: Trophic theory of island biogeography. — model of predation. — Biological Reviews 90: 794–814. Ecology Letters 14: 1010–1016. Abrams, P. A. & Matsuda, H. 1997: Prey evolution as a cause Gupta, R. P. & Chandra, P. 2013: Bifurcation analysis of predator–prey cycles. — Evolution 51: 1740–1748. of modified Leslie-Gower predator–prey model with Arditi, R. & Ginzburg, L. R. 2012: How species interact: Michaelis-Menten type prey harvesting. — Journal of altering the standard view on trophic ecology. — Oxford Mathematical Analysis and Applications 398: 278–295. University Press, Oxford, UK. Haag, C. R., Saastamoinen, M., Marden, J. H. & Hanski, I. 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