COMPLEX STRUCTURE OF THE INTERREGNUM BETWEEN COMPETITIVE EXCLUSIONS

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Data may be preliminary. 23 June 2025 V1 Latest version Share on COMPLEX STRUCTURE OF THE INTERREGNUM BETWEEN COMPETITIVE EXCLUSIONS Authors : John Vandermeer 0000-0002-3366-4343 [email protected] , zachary Hajian-forooshani , and Ivette Perfecto 0000-0003-1749-7191 Authors Info & Affiliations https://doi.org/10.22541/au.175067545.52757133/v1 199 views 189 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The dichotomy of stable equilibrium versus indeterminate competition is a core principle of ecological theory, as is the effect of a predator in the competitive dynamics. Using a model of invasive ant species that act as pest control agents in Puerto Rican coffee farms we explore the intricate interplay between competition, predation, and species coexistence within ecological systems. Employing concepts from complexity science, including period-doubling bifurcations and chaotic transients, this research examines the dynamics between two invasive ant species, Solenopsis invicta, and Wasmannia auropunctata, and the interaction of S. invicta with phorid fly parasitoids. Empirical data from field and laboratory experiments demonstrate that S. invicta typically dominates W. auropunctata unless phorid flies are present, the latter of which alter the S. invicta behavior and reduce its competitive advantage. Extending the Lotka-Volterra framework, we uncover a parameter-dependent chaotic interregnum where neither species maintains consistent dominance, contrary to traditional models of coexistence. This research revisits the well-known conundrum that ecological outcomes are more intricate than merely dominant-subdominant dynamics, suggesting that biodiversity may thrive within this chaotic interregnum, with implications for the management of the pest control system. COMPLEX STRUCTURE OF THE INTERREGNUM BETWEEN COMPETITIVE EXCLUSIONS ABSTRACT The dichotomy of stable equilibrium versus indeterminate competition is a core principle of ecological theory, as is the effect of a predator in the competitive dynamics. Using a model of invasive ant species that act as pest control agents in Puerto Rican coffee farms we explore the intricate interplay between competition, predation, and species coexistence within ecological systems. Employing concepts from complexity science, including period-doubling bifurcations and chaotic transients, this research examines the dynamics between two invasive ant species, Solenopsis invicta, and Wasmannia auropunctata , and the interaction of S. invicta with phorid fly parasitoids. Empirical data from field and laboratory experiments demonstrate that S. invicta typically dominates W. auropunctata unless phorid flies are present, the latter of which alter the S. invicta behavior and reduce its competitive advantage. Extending the Lotka-Volterra framework, we uncover a parameter-dependent chaotic interregnum where neither species maintains consistent dominance, contrary to traditional models of coexistence. This research revisits the well-known conundrum that ecological outcomes are more intricate than merely dominant-subdominant dynamics, suggesting that biodiversity may thrive within this chaotic interregnum, with implications for the management of the pest control system. math_shortcuts Introduction Two essential theoretical arrangements have long been central in ecology, forming an abstract foundation for more elaborate theorizing (e.g., Hofbaur and Schreiber, 2022): First, if two species compete only weakly, they may coexist in an equilibrium state, whereas if they compete strongly, one of them will disappear; Second, a specialist predator on a dominant competitor can reverse the dominance. With regard to competition, the dichotomy of stable equilibrium versus indeterminate outcome is a core principle – communities either coexist in equilibrium or the seemingly non-equilibrium alternative may be resolved through the extinction of a species. Adding the predator may provide a rescue from the local extinction expected from strong competition, seemingly also rescuing the basic Gausian principle of equilibrium coexistence versus non-equilibrium exclusion. Either the elimination of the competitively subdominant species B, or a predator on the dominant species A weakens it so that the competitively subdominant species B may win in competition. There is, however, a notable and potentially important additional theoretical structure, that of the “interregnum,” a dynamic place in parameter space in which any equilibrium is unstable, yet both competitors coexist in perpetuity. Here we highlight how the interregnum emerges from a series of natural history observations on a system of two ant species in competition, a system that intersects with the practical matter of pest control and, additionally, qualitatively mirrors a structure common to many ecological communities. One ant species is clearly dominant over the other, and a predator of that dominant species reduces its dominance such that the subdominant takes over. The two ant species are Solenopsis invicta (the red imported fire ant), and Wasmannia auropunctata (the electric ant, or “little” fire ant), and the predator is a species complex of the phorid genus Pseudacteon ( P. curvatus, P. tricuspus, and P. obtusus ). There are two evident “regimes”, first S. invicta dominates, and second W. auropunctata dominates, and under some parametric circumstances a shift between these two regimes occurs, observable in both space (Vandermeer and Perfecto, 2020: 2023; 2024) and time (Vandermeer and Perfecto, 2023). Yet that shift theoretically, based on a standard Lotka/Volterra approach, deviates from the standard idea of a regime shift as a critical transition (or tipping point). Rather, there is an interregnum between the two regimes. Furthermore, the behavior of the system within that interregnum is very complicated (albeit recognizable with simple ideas derived from complex systems, as discussed later). Thus, coexistence in this system (and higher biodiversity – two versus one species) exists only within a complex dynamics that is fundamentally chaotic, suggesting a new “mechanism” of biodiversity preservation, complex system behavior within an interregnum. That it may be useful for pest control to have both species simultaneously present is at first seemingly compromized by the competitive dominance of one or the other ant predator, but in the context of a permanent persistence within the interregnum, the same mechanism for biodiversity preservation may translate into a practical mode of ecosystem service. The natural history of the exemplary system The theoretical analysis presented here is inspired by a real-world system of two dominant ant species in a coffee agroecosystem in Puerto Rico. We refer to the two ant species, neither of which is native to Puerto Rico, by their generic names only, Solenopsis and Wasmannia . Both are involved in biological control of at least two of the major pests of coffee (the coffee berry borer, Hypothenemus hampei , and the coffee leaf miner, Leucoptera coffeella ), although the mode of action for each is distinct (Fig 1) and indeed may sometimes be contrary to one another through an indirect interaction (Newson et al., 2021; Perfecto et al., 2021; Rivera-Salinas et al., 2024). Figure 1. Basic natural history of the system. The large ant is Solenopsis , the small ant is Wasmannia . a. The coffee berry borer bores a hole in the coffee fruit, reproduces inside of the fruit, eating the endosperm and causing a great deal of damage. Solenopsis captures the adult beetle before it ever enters the fruit, thus preventing damage. Wasmannia is small enough that it enters the fruit and preys on both adult and larval beetles. b. The coffee leaf miner creates blotches of necrotic tissue on the leaf (resulting from the mine within which the larva is feeding), and surfaces to weave a cocoon on the undersurface of the leaf (looking like parallel strands of threads). Both Solenopsis and Wasmannia prey directly on the larva as it is exposed while weaving its cocoon and chew on the fibers of the cocoon and eventually prey on the enclosed larvae or pupa. Both ant species feed on a wide variety of organic material and are assumed to be in constant competition with one another when together. Solenopsis competitively dominates Wasmannia , all things being equal (Vandermeer and Perfecto, 2020; 2024; Perfecto and Vandermeer, 2020; Nie et al., 2023). The presence of phorid flies, well-known parasitoids of Solenopsis (Gilbert and Morrison, 1997; LeBrun et al, 2008), adds complexity. The phorid flies ( Pseudacteon spp.) mainly affect the dominant competitor through changing its behavior, harassing it so that its foraging effectiveness is reduced, thus reducing its competitive effect (Fig 2). The cycle, Wasmannia predominance, replaced (through competition) by Solenopsi s predominance, which is then replaced by phorid/ Solenopsi s predominance, which then goes back to Wasmannia predominance, forms an indirect intransitive structure (Vandermeer and Perfecto, 2020), obviously emerging from the notion of predator-induced competitive coexistence. That coexistence, however, is dynamically situated between two “regimes,” the predominance of Solenopsis and the predominance of Wasmannia . math_shortcuts Figure 2: The basic dynamic processes: Solenopsis (large ant) and Wasmannia (smaller ant) compete, the phorid fly parasitizes Solenopsis , and the phorid fly lowers the competitive effect of Solenopsis on Wasmannia (circle at end of connector indicates a negative effect; arrowhead indicates a positive effect; solid connector indicates direct effect; dashed connector indicates trait-mediated indirect effect). The indicated parameters those relevant to the model developed. Previous field studies of these two species (Vandermeer and Perfecto, 2020; 2024) have suggested, mainly through interpretation of changing spatial patterns, that Solenopsis has a strong competitive effect on Wasmannia . Additionally, in a brief field study conducted from December 2024 to February 2025, we placed hotdog fragments as bait at 60 different sites on a coffee farm (UTUA 2, as referenced in Perfecto and Vandermeer, 2020). The study took place across four distinct locations over 14 sampling days. We encountered a total of 186 occurrences of either Solenopsis or Wasmannia dominating at the bait 15 minutes after placement. Of 69 instances of Wasmannia being the predominant ant after 15 minutes, in 31 cases Solenopsis completely took over the bait within 1.5 hours. Of 117 instances of Solenopsis being the predominant ant at a bait after 15 minutes, in all cases Solenopsis was still dominant after 1.5 hours (i.e., there was never a case where a bait with Solenopsis predominant at 15 minutes, was taken over by Wasmannia after 1.5 hours). It was also clear in this study that those baits where Wasmannia was able to dominate for the entire 1.5 hours, were far from any Solenopsis nest and probably outside of foraging areas of any Solenopsis . In a supporting laboratory experiment, nests of Solenopsis and Wasmannia (containing brood but no queens) were connected inside of insect enclosures, with or without the addition of phorids. The results are summarized in figure 3. In figure 3b we plot the number of Solenopsis workers found in their own nest box or in the nest box of Wasmannia after 48 hours. In nine of the 15 cases when phorids were present, large numbers of workers were encountered within their original nest box, for both species. In contrast, when phorids were absent, in only two cases were there significant numbers of Solenopsis workers that remained in their own nest box, the vast majority choosing to forage, presumably for Wasmannia brood, in the Wasmannia nest chamber (Fig. 3c). In contrast, there was no difference between phorid presence or absence in the number of Wasmannia active in their own nest box (Fig. 3c). However, the number of Wasmannia workers within the nesting material was dramatically different between presence and absence of phorids – in the absence of phorids, no Wasmannia workers were found in the nesting material (which was dominated by Solenopsis ) (Fig. 3b). Those Wasmannia workers found in the nest box (Fig. 3b) where mainly on the inner sides of the nest box, evidently seeking refuge from the attacks of Solenopsis , unable to remain within their nesting material, but also only rarely able to make it out of their own nest box since the connecting element (a pipe cleaner) was itself dominated by Solenopsis . The presence of Solenopsis restricted Wasmannia movement in both nest boxes. Indeed, it is notable (Fig 3c) that there were frequently Wasmannia workers found in Solenopsis nest boxes, in at least two cases many. These were generally individual foragers that had been displaced from their own next box by Solenopsis , the latter of which had effectively abandoned its own nest box. These results suggest that Solenopsis effectively preys on Wasmannia , even abandoning its own nest box to swarm and prey upon the brood of Wasmannia (to the point of completely relocating its own brood) when phorids are absent. The presence of phorids completely reverses this tendency. Figure 3. Results of laboratory competition experiment (see methods). a. photo of experimental methods. b. Number of Solenopsis (red) and Wasmannia (green) workers found in their own nest box. Solid symbols for Wasmannia indicate workers found in the nest. c. Number of Solenopsis found in Wasmannia nest box (red) and number of Wasmannia workers found in the Solenopsis nest box (orange). Thus, both empirical results (above text and Fig. 3) and knowledge of the basic qualitative nature of the system (Fig. 2), suggest an important contingency arises somewhat cryptically from the most elementary ecological dynamics of the situation. A dominant competitor, all things elsewise constant, will eliminate the subdominant. If the dominant competitor has its dominance reversed for whatever reason, the original subdominant can persist, even dominate. Two regimes exist, 1) the dominant competitor persists alone, or 2) the subdominant competitor persists alone. The region between these two regimes is rarely examined, yet, as we show herein, this is the space that may be the most interesting. While there are two distinct “regimes,” there is a clear “interregnum,” a part of parameter space in which the regime change is never realized. If the interregnum is vanishingly small it is referred to as a “critical transition” (tipping point), a subject currently receiving substantial attention (Scheffer et al., 2012; 2015). Yet, it is possible that there is a significant interregnum, that is, a relatively large parameter space in which it occurs, during which two regimes compete for dominance, as can be detected with a simple model. A theoretical framework We investigate the following “toy” model of the natural system: \(\frac{\text{dS}}{\text{Sdt}}=\ 1-S-\ \alpha_{\text{SW}}W-\ \gamma\phi(S)F\) 1a \(\frac{\text{dW}}{\text{Wdt}}=\ 1-W-\ \alpha_{\text{WS}}\psi(F)S\) 1b \(\frac{\text{dF}}{\text{Fdt}}=\ \phi(S)S-m\) 1c \(\phi\left(S\right)=\frac{1}{1+\zeta S}\) 1d \(\psi\left(F\right)=\frac{1}{1+\theta F}\) 1e where S represents Solenopsis , W represents Wasmannia , F represents the phorid, ζ is the functional response parameter of the predator/prey pair, θ is the indirect nonlinear effect and γ is the direct effect of the phorid on the Solenopsis (the reciprocal γ, the consumption rate of the predator which one might expect to appear in equation 1c, is set = 1.0 for simplicity). φ and Ψ are functions that stipulate how θ and ζ fit into equations 1a, b, and c, formulated this way to reduce clutter in the main model (equations 1a, b, and c). The model is evidently an extension of the Lotka/Volterra framework. If F=0 (parasitoids absent) equations 1a and b become the classic LV competition equations with carrying capacities scaled to 1.0. If W = 0 (subdominant competitor absent) equations 1a and 1c are the classic LV predator/prey equations with type II functional response (with parameter ζ). Because of the qualitative nature of the natural system described above, we stipulate that the competition coefficients, α SW and α WS, are both large and that ζ, the functional response term for the predator/prey formulation, is set such that the predator-prey subsystem, when taken alone, is in a limit cycle. In particular, we set ζ = 0.1. With these parameters set, we study variability in the two parameters involved in the predatory effect on competition, θ, frequently referred to as a trait-mediated indirect interaction, and γ, frequently referred to as a density-mediated interaction (Werner and Peacor, 2003). Exemplary solutions for equation set 1 are presented in figure 4. math_shortcuts Figure 4. Exemplary trajectories of the model system. Parameters are α WS = 2.0; α SW = 1.1, m = 0.2, ζ = 0.1, θ = 0.21 – 0.2* γ . Basic qualitative behavior is a. Wasmannia dominates, b. chaos, c. beginning of period doubling, and d. focal point equilibrium with Wasmannia << Solenopsis . Reduction of γ from d to c to b represents the period-doubling route to chaos (see Fig 1a). These exemplary trajectories (Fig 4) are suggestive of some well-known concepts in complex systems. Indeed, ecology often involves multiple interacting factors, making it an ideal field for interpreting patterns in light of structures known from the science of complexity (Mitchell, 2009; Solé and Levin, 2022). The present communication analyzes a seemingly simple system that is exemplary of such structures, explicitly, period doubling bifurcations (May, 1976; Feigenbaum, 1980), strange attractors with basin-boundary collisions (Grebogi et al., 1982; Vandermeer and Yodzis, 1999), and chaotic transients (Hastings, 2004), as illustrated in figure 5. math_shortcuts Figure 5. Four phenomena associated with complexity science that emerge in the system. a. Periodic bifurcation to chaos, illustrated with the classical logistic map. Cascading bifurcations of population “equilibria” lead to immensely complex trajectories, rendering long-term prediction impossible. b. A strange attractor (a region of state space to which all other points in the space are attracted but within which no point attractor exists) and the boundary thereof (bold dashed curve), illustrated with the Lorenz attractor. Trajectories within that space are chaotic, and every point within the boundary will eventually be visited by all trajectories on that attractor. c. Basin boundary collision occurs when the boundary of a chaotic attractor intersects the edge of a basin of attraction of some other attractor, in this case illustrated with an “attractive equilibrium point.” Note the distinction between the “original boundary of chaos,” which is the same as in part b, and the “expanded boundary of chaos” which, at a critical point intersects with the edge of the basin of attraction surrounding the attractive equilibrium point. d. Chaotic transients, frequently resulting from a basin-boundary collision, in which a trajectory has all the properties of a chaotic attractor, but if enough time passes, the edge of that attractor is reached very close to the basin of another non-chaotic attractor and eventually they collide resulting in the whole system reaching an equilibrium point. These dynamics are sometimes also referred to as chaotic repellors. Expanding on those exemplars (Fig. 5) we set θ = 0.21 - 0.2 γ, to mimic a tradeoff between the two predator effects (the density effect and the trait-mediated effect) and to construct a single parameter for bifurcation analysis. While such an assumption certainly warrants a deeper discussion of its significance biologically, the convenience for bifurcation is our main justification here. Constructing a bifurcation diagram as γ varies, the signature of period doubling chaos is obvious (as γ decreases) (Fig. 6), but at the other extreme, we see a clear indication of a basin boundary collision (illustrated in the inset) and thus a chaotic transient. In Figure 7, we show a qualitative sketch of both regimes along with the chaotic structure of the interregnum. Figure 6. Bifurcation diagram direct effect of parasitoid consumer ( γ ) on Solenopsis (parameters the same as Fig 4). Figure 7. Qualitative sketch of the basic outcomes of the model with the bifurcation diagram of Figure 6 placed in its appropriate position. Upper left (green shading) indicates the regime in which Wasmannia prevails. Lower right (red shading) indicates the regime in which Solenopsis prevails. The area in between is what we refer to as the interregnum, where all three species coexist in a temporary chaotic state – temporary with respect to the defining parameters of γ and θ. In the case of Solenopsis dominant (red color), there are always cases where Wasmannia dominates instead, (e.g., when the initial conditions create initial overwhelming pressure on Solenopsis by a randomly chosen extreme value of the phorid – the phorid drives the Solenopsis to extinction and then dies itself, leaving nothing to control Wasmannia) . Such cases are increasingly rare as γ becomes large and θ becomes small. The interregnum thus has a complicated structure, but can be best characterized qualitatively as chaotic. The part nearest to the dominant competitor regime ( Solenopsis in this case) is either a stable focus with both Wasmannia and Solenopsis quite rare, or a system of periodic cycles, sometimes of large and complicated periods, or a chaotic structure. In contrast, the edge of the interregnum nearest to the regime of the subdominant competitor is sharp with expected chaotic transients and critical transition. Furthermore, as in most cases of period-doubling bifurcations, there are windows of periodic behavior (sometimes very complicated) interspersed in a “sea” of truly chaotic trajectories. It is tempting to suggest that the many empirical cases now understood to be chaotic (Rogers et al., 2022) might be located in an interregnum between two or more (perhaps many more) possible regimes, or even that high-biodiversity situations might be located therein also. Since both ant species are important predators on two critical coffee pests, the interregnum also generates important insights for the ecosystem service of pest control. Discussion The natural system we use as motivation for this work is certainly not unique in its basic structure. Although pairs of competitors can sometimes coexist because competition between them is weak, it is also the case that sometimes they are not able to coexist because competition between them is too strong. Although much of community ecology has been about how species can coexist, the most recent, more sophisticated elaboration of this old idea being modern coexistence theory (Barabás et al, 2018), the simplifying assumption that they do so because of weak competition is frequently asserted or assumed. Yet, the undeniable reality of strong and asymmetrical competition is evident in various contexts, as highlighted, for example, in the literature on invasive species (Koenig, 2020) or the ongoing challenges posed by weeds in agriculture (Sardana et al., 2017). Among the modifiers of this strong and asymmetrical competition is predation (herbivory, parasitism, pathogens). It seems a simple story, that the subdominant species will be excluded until the predator, a specialist on the dominant species, has an effect sufficiently strong to disrupt the competitive process, at which time the competitive outcome may be reversed. The elegant outcomes first suggested by Lotka, Volterra and Gause are thus reconstituted. That simple story of competitive exclusion has long been understood to be an excessively streamlined version of reality (Caswell, 1978 ; Butler and Wolkowicz, 1986; Abrams, 1999). Here, we explore the consequences, suggested by the natural history of the particular system under consideration, of a specialist predator acting against the dominant, strong competitor. The generalized qualitative conclusions of the subdominant competitor being “rescued” by the dominant is unsurprisingly confirmed. Yet there is a complication. As relevant parameters change to provoke that rescue, the regime of dominant versus the regime of subdominant do not switch as a critical transition, or tipping point. Rather, there is an interregnum, a range of parameter values for which complicated, chaotic attractors exist, interspersed with a multitude of simple limit cycle oscillations (witness the periodic windows in the bifurcation – Fig. 6). It is perhaps of interest to interrogate the nature of that interregnum for different theoretical constructs and, especially, search for evidence thereof in natural situations. Indeed, a so-called “leading indicator” of regime change is flickering, one clear consequence of our proposed dynamics of the interregnum (Meunier, et al, 2024), at least at one of its extremes. The literature on trait-mediated versus density-mediated effects (e.g., Křivan and Schmitz, 2004) is reflected in this study. The parameter γ represents the classic case of density mediation, while the parameter θ represents the classic case of trait mediation. The bifurcation diagram (Figs. 5 and 6) is undertaken under the assumption that there is a tradeoff between density and trait-mediated effects (i.e., θ = 0.21 – 0.2* γ) and leads to the pattern as illustrated in Figure 6. If, contrarily, we assert a positive relation between θ and γ (the density and trait-mediated effect are positively correlated), it is obvious that, because of the orientation of the chaotic zone (Fig. 7), increasing the general effects of the predator (simultaneously density and trait-mediated) will not necessarily change the basic outcome – a predator that places the system within the interregnum will likely continuing to do so no matter how much more or less effective it becomes. An issue that emerges immediately upon extrapolation to multiple species cases, is whether the interregnum is actually the place where most species diversity occurs? Contrary to an equilibrium interpretation it could be that species interacting with strong competitive effects, when limited, especially periodically (as in predation), create a permanent or semi-permanent interregnum where they are in a constant state of transient behavior (Hastings, 2004). Indeed, such transient behavior might allow for the insertion, even if temporary, of other species that, under more equilibrium conditions, would be completely excluded from the community. This interregnum hypothesis is perhaps a unique way of examining the question of species diversity maintenance. If alternate regimes consist of subgroups of species each of which could be the final outcome of competition, there is by definition an interregnum between these alternatives, where the dynamic processes are in the process of being worked out. The interregnum is thus likely a region of higher biodiversity, and sustaining it could be crucial for maintaining biodiversity in that region. In the case of only two species, as treated herein, this “biodiversity-preserving” characteristic of the interregnum is trivial (two species in the interregnum versus one in each of the associated regimes), but examining it carefully may provide insights into other, more biodiverse situations. As noted previously, this study is inspired by a particular system that has important implications for pest control, especially since both ant species involved are significant predators of key coffee pests (Fig 2). Emerging from the theoretical results are questions that have evident practical importance in this context. Since one species, Solenopsis , attacks the coffee berry borer (CBB) as an adult before it enters the fruit, the direct damage done to the coffee is curtailed on the plant where the Solenopsis is patrolling. But on that plant, and there inevitably will be one, where Solenopsis is not patrolling, the reproductive potential of the CBB can be fully realized through the completion of the life cycle through larvae, pupa, and adult (since Solenopsis is too big to enter the fruit). However, in areas where Wasmannia is predominant, for whatever reason, predation pressure is brought on all stages of the CBB since the ant enters the fruit through the hole made by the CBB. Thus Solenopsis decreases local damage but allows the more regional CBB population to flourish while Wasmannia is less able to curtail the local damage (since it infrequently is able to stop burrowing into the fruit by the CBB) but reduces the population growth of the CBB at a regional level (through predation on all life stages). It might be postulated that the chaotic behavior within the interregnum represents a sort of balance between the local control over damage and the regional control over pest population density by allowing a local mixture of both species of predators in the same general area. Regarding the other major pest, Solenopsis workers (and perhaps Wasmannia workers too) prey on the larval stage of the coffee leaf miner (CLM) at the time of its emergence from the mine. Both species dismantle the cocoon thread by thread and consume both CLM larvae and pupae. It has been suggested that only Wasmannia has been reported to prey on CLM eggs and that Solenopsis is more efficient in preying on the larva as it is spinning its cocoon. If these effects are strong it could be that the two ant species exhibit synergistic effects when coexisting. Since they strongly compete with one another, the only way such synergism can occur is in the interregnum. Methods: competition experiment: Experiments were performed in standard bug tents (BioQuip, 60x60x60 cm) with ant nests placed in small plastic nest boxes (plastic containers 15x15x10 cm, with constraining fluon) containing nesting material (5-7 leaves of a bromeliad with small amount of soil) placed in the insect tent. Twenty tents were arranged in pairs on laboratory benches and one of the pair was randomly consigned to receive phorids. 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