Sharp boundary formation and invasion between spatially adjacent periodical cicada broods
Introduction
With increasing interest in the effects of climate change on the geographical distribution of species, as well as the increasing numbers of biological invasions, there is a growing need to improve our knowledge of mechanisms that determine the range boundaries of populations and species. Climate is a well-known driver of species range boundaries and there have been extensive efforts to understand and model the climatic niche of various species (Peterson, 2003, Morin et al., 2007, Thomas, 2010). But climate forms just one part of a species’ ecological niche; species ranges are also affected by biotic interactions such as competition, predation and herbivory (Holt, 2009, Roux et al., 2012). Despite the fact that many theoretical and empirical works have contributed to the understanding of coexistence and geographic overlap of organisms, the biotic mechanisms that form sharp range boundaries are complex and difficult to identify in natural systems.
Periodical cicadas (Magicicada spp.) are ideal model organisms to examine ecological processes that lead to sharp spatial boundaries, due to their long lifespans, exceptionally high densities, unique spatial distributions and developmental synchronization. For more than 350 years (Unnamed Observer, 1667), periodical cicadas have captured the interest of biologists, naturalists, and entomologists. Their life cycles were first outlined in detail in the early 20th century (Marlatt, 1907, Snodgrass, 1919, Marlatt, 1898). After hatching from eggs, which are laid in the twigs of trees, periodical cicada nymphs burrow underground, feeding on xylem fluids from tree roots. At the end of their 13th or 17th year underground (periodical cicadas have a 13 year life span in portions of their range and 17 years in other regions), they emerge en masse and spend about a month as adults, during which time they mate and oviposit. Periodical cicada populations typically exist at exceptionally high densities (as high as 1000/ m2) and their loud buzzing mating calls can be heard from hundreds of meters away.
In any one part of the range of periodical cicadas, annual development of populations is synchronized and these synchronized populations, termed “broods”, extend over several hundred km2 (Fig. 1). Because of the sudden, regular, and periodic emergence and mating patterns, a cicada brood is defined as a population of temporally isolated cicadas: a single-aged cohort of individuals that live together underground and emerge together in the same year. Broods generally consist of 3–4 different sympatric species that are phenotypically very similar. This means that every 13th or 17th year, the entire region experiences a single mass emergence event in the early summer. Studies have theorized that this synchronous emergence of cicadas allows for satiation of predators, giving a sufficient number of adults the chance to survive, mate and reproduce (Karban, 1982). Their disappearance underground also prevents the occurrence of a long-term numerical response in above ground predators (Koenig and Liebhold, 2013), allowing populations to maintain high densities from generation to generation. In addition, the regions that the broods occupy and the boundaries between them appear to be stable over multiple generations (Williams and Simon, 1995), implying some type of synchronous ecological equilibrium.
Given their long lifespans that are spent almost entirely underground, multi-generational time-series data on periodical cicada populations takes decades to procure and reveal little about their lives as nymphs. What is known is that periodical cicada nymphs experience competition-driven mortality over time (although the details of how this competition works are unknown (Karban, 1984, Karban, 1997)) and adults experience predation-driven mortality once they emerge. In addition, periodical cicadas are sometimes observed emerging four years early, one year early, or one year late. This phenomenon is referred to as “stragglers” (regardless of whether emergence is late, as this term would imply, or early) and it provides a mechanism by which individuals effectively leak into another brood. What meditates these leakage events, how large they usually are, or how commonly they occur, however, are all poorly understood (Heath, 1968, Lloyd and White, 1976, White and Lloyd., 1979, White et al., 1979). Taking into account these uncertainties, Blackwood et al. (2018) built a model to capture the effects of competition and leakage that lead to single cicada broods at a single spatial location. Specifically, they considered the cicada population dynamics assuming either a steady annual rate of leakage among nymphs or a single large leakage event and determined the conditions that lead to replacement of the dominant brood. In both of these scenarios, they varied the form of competitive interaction between nymphs to reflect uncertainty in the details of nymphal competition. Assuming a steady leakage rate, under all forms of inter-brood competition, they found that a single brood persists for sufficiently low levels of leakage and over a range of competition intensity. This finding is consistent with the observation that locations typically contain only a single brood (Fig. 1), despite the existence of stragglers. They also discovered that the magnitude of a large leakage event (i.e. the proportion of cicadas in a brood that accelerate or delay development) determines whether and when a leaked brood outcompetes and supplants the parent brood in a single patch.
Previous work thus indicates that the predation on adults creates a strong Allee effect and this play a key role in limiting the presence of only a single brood at most locations (Lehmann-Ziebarth et al., 2005, Tanaka et al., 2009). But why do single broods occupy large, spatially-distinct regions (Cooley et al., 2009) with sharp boundaries between regions with different broods (Williams and Simon, 1995)? To answer this, we build and expand upon the framework presented in Blackwood et al. (2018) by looking at multiple spatial locations (hereafter, “patches”) and introducing dispersal between them. We focus on periodical cicadas that have a 17 year life span and explore the processes that affect interactions between spatially adjacent periodical cicada broods and their spatial dynamics. We examine the conditions that lead to different types of equilibrium, such as the persistence of only the native brood in its original patch, the invasion of one brood into the other’s patch, or coexistence of multiple broods in a single patch. We also consider a two-patch version of Machta et al. (2019) analytical approximation to the Blackwood et al. model, to examine the generality of our results. Our study provides insights into the formation of range boundaries in periodical cicadas as well as other interacting populations.
Section snippets
Growth and reproduction
Our model follows (Blackwood et al., 2018), but with the addition of a second patch and dispersal between patches (as explained below). To model population size in a 17-year cicada population, we let the population density of age i individuals () in patch A and at time t be . We then build a 17-dimensional vector, , that describes the population density of every age group within patch A at time t.
Two types of life history processes occur each year (Fig. 2). First, the nymphs
Types of equilibrium
In their non-spatial model, Blackwood et al. found that without stragglers (), at most one brood could persist in any one patch (Blackwood et al., 2018). However, the identity of this brood may depend on initial conditions. Because we recover Blackwood et al.’s model by setting , this is also the behavior we observe in each patch in the absence of any dispersal. Following the arguments of Karlin and McGregor (1972) – who noted that due to continuity in both the locations of equilibria and
Equilibria in the hybrid model approximation
Machta et al. (2019), derived an approximation to the Blackwood et al. (2018) Leslie matrix model that yields qualitatively similar results and can be solved analytically. The key approximation in this hybrid approximation is to replace the discrete age-structured matrix model by a continuous time differential equation while retaining reproduction as a discrete event. To facilitate an analytic solution we also use a simplified functional response. The phase diagram in the dispersal–competition
Discussion
Understanding the different processes that affect interactions between spatially adjacent periodical cicada populations and their spatial dynamics was the primary goal of this study. These types of interactions between adjacent broods and influences on brood boundaries provides insight into the role of competitive interspecific interactions and their influences on species range boundaries. Boundaries of periodical cicada broods are in some ways analogous to species range boundaries; in some
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
CRediT authorship contribution statement
Geunho Kye: Conceptualization, Formal analysis, Methodology, Writing - original draft. Jonathan Machta: Conceptualization, Writing - review & editing, Analysis in Sec. 4. Karen C. Abbott: Conceptualization, Writing - review & editing. Alan Hastings: Conceptualization, Writing - review & editing. William Huffmyer: Conceptualization, Writing - review & editing. Fang Ji: Conceptualization, Writing - review & editing. Andrew M. Liebhold: Conceptualization, Writing - review & editing. Julie C.
Acknowledgements
AML was funded by grant EVA4.0, No. CZ.02.1.01/0.0/0.0/16_019/0000803 financed by OP RDE. We also thank two anonymous reviewers for their thoughtful comments which have led to an improved manuscript.
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