Transient Top‐Down and Bottom‐Up Effects of Resources Pulsed To

Transient top-down and bottom-up effects of resources pulsed to multiple trophic levels

1,3,5 2,4 2 2 MATTHEW A. MCCARY , JOSEPH S. PHILLIPS , TANJONA RAMIADANTSOA , LUCAS A. NELL , 2 2 AMANDA R. MCCORMICK , AND JAMIESON C. BOTSCH 1Department of Entomology, University of Wisconsin, Madison, Wisconsin 53706 USA 2Department of Integrative Biology, University of Wisconsin, Madison, Wisconsin 53706 USA

Citation: McCary, M. A., J. S. Phillips, T. Ramiadantsoa, L. A. Nell, A. R. McCormick, and J. C. Botsch. 2020. Transient top-down and bottom-up effects of resources pulsed to multiple trophic levels. Ecology 00 (00):e03197. 10.1002/ecy.3197

Abstract. Pulsed fluxes of organisms across ecosystem boundaries can exert top-down and bottom-up effects in recipient food webs, through both direct effects on the subsidized trophic levels and indirect effects on other components of the system. While previous theoretical and empirical studies demonstrate the influence of allochthonous subsidies on bottom-up and top- down processes, understanding how these forces act in conjunction is still limited, particularly when an allochthonous resource can simultaneously subsidize multiple trophic levels. Using the Lake Myvatn´ region in Iceland as an example system of allochthony and its potential effects on multiple trophic levels, we analyzed a mathematical model to evaluate how pulsed subsidies of aquatic insects affect the dynamics of a soil–plant–arthropod food web. We found that the relative balance of top-down and bottom-up effects on a given food web compartment was determined by trophic position, subsidy magnitude, and top predators’ ability to exploit the subsidy. For intermediate trophic levels (e.g., detritivores and herbivores), we found that the subsidy could either alleviate or intensify top-down pressure from the predator. For some parameter combinations, alleviation and intensification occurred sequentially during and after the resource pulse. The total effect of the subsidy on detritivores and herbivores, including top- down and bottom-up processes, was determined by the rate at which predator consumption saturated with increasing size of the allochthonous subsidy, with greater saturation leading to increased bottom-up effects. Our findings illustrate how resource pulses to multiple trophic levels can influence food web dynamics by changing the relative strength of bottom-up and top-down effects, with bottom-up predominating top-down effects in most scenarios in this subarctic system. Key words: allochthonous inputs; bottom-up; food webs; resource pulses; subsidy; top-down.

by plants, which in turn leads to elevated biomass and INTRODUCTION diversity at higher trophic levels (Sanchez-Pinero and Temporal variation in the availability of either inter- Polis 2000). They can also affect top-down control on nally (autochthonous) or externally (allochthonous) lower trophic levels by increasing predator populations derived resources can alter the dynamics of ecological (Henschel et al. 2001, Luskin et al. 2017). For example, systems (Anderson et al. 2008, Yang et al. 2010, Hast- aquatic insects moving from water to land can subsidize ings 2012). Resource pulses are episodic, short-duration diverse communities of terrestrial predators such as spi- events of enhanced resource availability that can exert ders (Power et al. 2004) and birds (Nakano and Mura- both direct and indirect bottom-up effects on recipient kami 2001), enhancing top-down control on local ecosystems (Yang et al. 2008). Pulsed allochthonous herbivores and thereby increasing plant productivity. resources to terrestrial ecosystems (e.g., seabird guano Resource pulses potentially exert multiple direct and on subarctic islands) can increase primary production indirect effects on recipient systems, making them a valu- able context in which to study temporal variation in the strength of bottom-up and top-down control, a topic of Manuscript received 1 March 2020; revised 20 July 2020; accepted 7 August 2020. Corresponding Editor: Evan L. Preis- recent and general ecological interest (Meserve et al. ser. 2003, Fath et al. 2004, Polishchuk et al. 2013, Leroux 3School of the Environment, Yale University, New Haven, and Loreau 2015, Vidal and Murphy 2018, Piovia-Scott Connecticut, USA et al. 2019). 4Department of Aquaculture and Fish Biology, Holar´ University, Skagafjor¨ ður, Iceland The influence of resource pulses on bottom-up and 5 E-mail: [email protected] top-down effects depends on a variety of factors,

Article e03197; page 1 Article e03197; page 2 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx including the magnitude of the pulse, the trophic Midge position of recipient populations, the structure of the Midges inputs (M ) recipient food web, and the relative propensity of the (iM ) recipient population to exploit the allochthonous resource (Huxel and McCann 1998, Leroux and Lor- eau 2012, Miller et al. 2019). Theoretical models show that allochthonous subsidies can increase the strength Predators of trophic cascades in simple food webs, with the (X ) strength of the cascade being mediated by consumers with an intermediate preference for allochthonous vs. + + autochthonous resources (Leroux and Loreau 2008). Temporal shifts in the strength of top-down and bottom-up effects due to subsidies have also been Detritivores Herbivores observed empirically. For example, island lizards tem- (V ) (H ) porarily reduced predation on local herbivores when pulsed seaweed subsidies increased detritivorous prey, + + but after the pulse-associated period of enhanced resource availability, top-down pressure on herbivores strengthened due to elevated lizard abundance (Pio- Detritus Plants via-Scott et al. 2019). (D ) (P ) While previous theoretical (Huxel and McCann 1998, Leroux and Loreau 2012, Miller et al. 2019) and empir- + + ical (Nowlin et al. 2007, Hoekman et al. 2011, Yee and Juliano 2012) studies demonstrate the influence of External allochthonous subsidies on bottom-up and top-down Soil inputs (I ) processes, our understanding of how allochthony influ- (iI ) ences these forces in conjunction is still poor. Moreover, an allochthonous resource may also simultaneously subsidize multiple trophic levels, a research topic that has also received limited attention. To address these FIG. 1. Conceptual diagram showing how midge pulses are incorporated into the Myvatn´ terrestrial food web for our issues, we developed a mathematical model that reflects model, with arrows showing the flow of N. Black arrows illus- the terrestrial food web adjacent to Lake Myvatn´ in trate the movement of N (i.e., consumption, remineralization, northeastern Iceland (Fig. 1). Myvatn´ is naturally and uptake) through the food web. Solid gray arrows indicate eutrophic and sustains large populations of midges the loss of N via mortality; the gray dotted arrow denotes N loss from the system from the soil compartment. Other model (Diptera: Chironomidae), which emerge as adults for parameters are omitted for simplicity. several weeks each year and form mating swarms over the surrounding heathland landscape. When not swarm- ing, the adult midges settle in the vegetation where they become an abundant food resource for predatory Liebhold 2005); however, most cicadas escape predation arthropods (Dreyer et al. 2016, Sanchez-Ruiz et al. and become deposited as detritus following death (Yang 2018). In addition, when the midges die uneaten, their 2004, Nowlin et al. 2007). carcasses enter the detrital food web and subsidize the We analyzed a mathematical model of a soil–plant–- soil biota (Hoekman et al. 2011), ultimately leading to arthropod food web receiving an allochthonous resource the remineralization of nitrogen (N) and other nutrients that directly subsidizes both predators (as live prey) and that affect plant productivity and community composi- detritus (as carcasses). We asked three questions: (1) tion (Gratton et al. 2017). Because midges subsidize How do allochthonous pulses entering multiple com- both upper (as prey) and lower (as detritus) trophic partments affect transient top-down and bottom-up levels (Fig. 1), this resource pulse potentially exerts effects on recipient food webs? (2) Does the relative both bottom-up and top-down effects on the intermedi- strength of top-down and bottom-up effects induced by ate trophic levels, such as detritivorous and herbivorous resource pulses differ between intermediate trophic levels arthropods. While Myvatn´ has particularly large aqua- (i.e., detritivores and herbivores)? (3) Under what condi- tic insect emergences, the general phenomenon of tions do bottom-up vs. top-down effects dominate when allochthony having an effect as both a prey item and as an allochthonous pulse enters multiple entry points? To a detrital input is not unique. For example, the 13- or address these questions, we examined the responses of 17-yr periodical cicada (Magicicada spp.) can fall prey intermediate trophic levels that are not directly subsi- to many terrestrial predators (e.g., birds, reptiles, and dized by the allochthonous resource, which allowed us rodents) during emergences in North American forests to examine the indirect effects of subsidies that propa- (Karban 1982, Williams et al. 1993, Koenig and gate throughout the food web. Xxxxx 2020 TRANSIENT EFFECTS OF PULSED RESOURCES Article e03197; page 3

Each living pool experiences density-dependent losses METHODS due to processes such as mortality, excretion, and shed- ding of tissue (e.g., leaves). Model structure Plant uptake of N from the soil-nutrient pool, detriti- We analyzed a model informed by the terrestrial food vore consumption of detritus, and herbivore consump- web surrounding Lake Myvatn´ where midges are tion of plants are all modeled as type-II functional allochthonous inputs to multiple trophic levels. We for- responses (Holling 1959), whereby uptake saturates with mulated the model in terms of nitrogen (N) to provide a increasing resource availability. Predator consumption “common currency” among the inorganic, dead, and liv- of herbivores, detritivores, and midges is modeled as a ing pools. We chose N as our common currency because multispecies type-II functional response (Murdoch it is one the most limiting elements in arctic ecosystems 1969), whereby consumption of each of the pools satu- (Chapin III et al. 1986, Manzoni et al. 2010), biological rates with the total availability of all three pools. For processes are intimately involved in its circulation both single and multispecies functional responses, the through terrestrial systems (Bosatta and Agren˚ 1996), saturation is influenced by both the uptake or “attack” and it is a common tracer used in other food web studies rate (the rate at which uptake increases when resources (Liu et al. 2005, Zelenev et al. 2006, Manzoni and Por- are sparse) and the “handling time” (the inverse maxi- porato 2009). mum uptake rate when resources are abundant). For We analyzed a hybrid community–ecosystem model as simplicity, we use the same predator handling time for a system of ordinary differential equations (ODEs) com- detritivores and herbivores; however, we use a separate bining classical consumer–resource dynamics (e.g., Rosen- handling time for midges and explore how variation in zweig and MacArthur 1963) with nutrient cycling via this value affects the dynamics. The midge handling time inorganic soil and detrital N pools (DeAngelis 1992, Lor- likely varies depending on the size and composition of eau 2010). The model contains seven N pools: midges the midge subsidy; at Myvatn,´ the individuals within (M), inorganic soil N (I), detritus (D), plants (P), detritiv- midge swarms vary in size. orous arthropods (V), herbivorous arthropods (H), and Together, these assumptions translate into the follow- predatory arthropods (X; Fig. 1). While the model does ing system of ODEs: not explicitly include microbial pools, it does include microbially mediated processes such as decomposition dI μ aI IP μ ¼ iI þ ðÞ1 l DD I I and remineralization; this is equivalent to assuming that dt 1 þ aI hI I these processes are proportional to the substrate availability but not microbial biomass. We perturbed the model dD μ ∑ with pulsed inputs to the midge pool, which in turn ¼ ðÞ1 l M M þ ðÞ1 l dt j ∈fgP,V,H,X directly subsidized the detritus and predatory arthropods; therefore, effects of the midge pulse on the other trophic μ aDDV μ j þ mjj j DD levels arise through bottom-up and top-down processes 1 þ aDhDD propagating from predators and detritus. The model was formulated such that equilibria were locally stable (Hast- dP aI IP aPPH μ ings 2013; Appendix S1: Section S1 and Appendix S2: ¼ ðÞP þ mPP P dt 1 þ aI hI I 1 þ aPhPP Fig. S1) in the absence of allochthonous pulses, which allowed us to track the temporal variation in bottom-up dV aDDV aX VX and top-down effects during and after the pulse as the ¼ dt 1 þ aDhDD 1 þ aX hX H þ aX hX V þqaX hM M system returned to equilibrium. ðÞμ þ m V V In the model, soil nutrients increase from a fixed exter- V V nal input rate and remineralization of detritus, while the dH a PH a HX detritus pool increases through losses from the living ¼ P X dt 1 a h P 1 a h H a h V qa h M pools (i.e., non-consumptive mortality) and midges. The þ P P þ X X þ X X þ X M μ transfer of N to both the soil and detritus pools is ðÞH þ mH H H assumed to occur with some inefficiency (the terms “1 – l” in Eq. 1), reflecting inefficient transfer of nutrients dX ðÞaX V þ aX H þ qaX M X μ ¼ ðÞX þ mX X X between trophic levels and facilitating the stability of the dt 1 þ aX hX H þ aX hX V þ qaX hM M model in the absence of the midge pulse (Leroux and Loreau 2008, Loreau 2010). The living pools increase dM qaX MX μ ¼ iMtðÞ M M through N uptake from the inorganic pool or consump- dt 1 þ aX hX H þ aX hX V þ qaX hM M tion from either the detritus or living pools (Fig. 1), an (1) approach similar to models presented in Loreau (2010). Gains to the living pools are in terms of N, and therefore with state variables and parameters defined in Table 1. are not only due to the reproduction of individuals, but The input of midges to the system is characterized as also to increases in individual N content (i.e., biomass). a step-function Article e03197; page 4 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx

TABLE 1. Food web model parameter definitions.

Pool Description Units Baseline value I inorganic soil nitrogen (N) g N/m2 250† D detritus g N/m2 15† P plants g N/m2 40† V detritivores g N/m2 1† H herbivores g N/m2 1† X predators g N/m2 0.5† M midges g N/m2 NA −2 −1 iI inorganic nutrient input rate g Nm d 10‡ −1 μI density-independent loss of soil nutrients d 0.01‡ −1 μD density-independent loss of detritus d 0.1‡ −1 μP density-independent loss of plants d 0.01‡ −1 μV density-independent loss of detritivores d 0.1‡ −1 μΗ density-independent loss of herbivores d 0.1‡ −1 μX density-independent loss of predators d 0.1‡ −1 μΜ density-independent loss of midges d 0.5‡ 2 −1 −1 mP density-dependent loss of plants m gN d 0.024§ 2 −1 −1 mV density-dependent loss of detritivores m gN d 2.36§ 2 −1 −1 mH density-dependent loss of herbivores m gN d 0.1‡ 2 −1 −1 mX density-dependent loss of predators m gN d 0.1‡ lx proportion mortality of x lost from system dimensionless 0.1‡ 2 −1 −1 aI uptake rate of soil nutrients by plants m gN d 0.0078§ 2 −1 −1 aD uptake rate of detritus by detritivores m gN d 0.032§ 2 −1 −1 aP uptake rate of plants by herbivores m gN d 0.012§ 2 −1 −1 aX uptake rate of detritivores, herbivores, and midges by predators m gN d 0.125§ q predator exploitation of midges dimensionless 8 × 10−3 to 8‡ hI handling time of soil nutrients by plants d 0.51‡ hD handling time of detritus by detritivores d 2.1‡ hP handling time of plants by herbivores d 2.1‡ hX handling time of herbivores and detritivores by predators d 2.7‡ hM handling time of midges by predators d 1.3 to 5.3‡ Notes: Density-dependent and density-independent losses are the “natural” values (i.e., the values for those pools at equilibrium). The x in lx represents all pools, as they have the same value. †Value is based on empirical approximation from the literature. ‡Values on a comparable scale to the other parameters. §Value was solved from the equilibrium of the ODEs. For more details, see the Parameter values subsection in the methods.

< ≤ b fort0 t t0 þ w whereas reduced plant structure favors ground-hunting iMtðÞ¼ (2) 0 spiders with much faster handling times. where t0 is the time at which the pulse begins, w is the width or duration of the pulse, and b is the rate of midge Parameter values input during the pulse. The total midge input over the duration of pulse equals b × w. Once in the midge pool, While we present our model in the context of Myvatn´ the midge N either enters the detritus pool via decay of to make the analysis more concrete, our objective is to carcasses or the predator pool via consumption. “Preda- use the model to provide broader insights into transient tor exploitation” (q) is the predator attack rate on food web responses to pulses with multiple entry points. midges relative to that on herbivores and detritivores, Nonetheless, to numerically explore the dynamics of the and it partly controls the number of midges captured model, it was necessary to select parameter values. and consumed by predators. At Myvatn,´ various factors Rather than conducting an exhaustive exploration of the may affect how effectively arthropod predators can pas- dynamics across the full parameter space, we defined a sively exploit midges, including the vegetation structure. “baseline” parameter set partially informed by data from Grasslands have more structure in which midges can Myvatn´ or similar systems. We then explored the become trapped, thereby increasing predators’ abilities dynamics across a range of values for a select set of to exploit midges and decreasing the direct input into parameters that governed the intensity (and conse- the detrital pool. Furthermore, increased plant structure quently, total magnitude) of midge pulse (b), and direct favors web-building spiders with slower handling times, responses to the pulse (e.g., predator exploitation of Xxxxx 2020 TRANSIENT EFFECTS OF PULSED RESOURCES Article e03197; page 5 midges, q, and the predator handling time on midges, values in the absence of midges, such that they would hM). remain fixed through time in the absence of perturba- To define the baseline parameters, we first specified tions from the midge pulse. We ran the models for 500 equilibrium sizes of the N pools in the absence of midge time steps to ensure that they all returned to equilibrium subsidies based on empirical estimates. Pool sizes were (defined as being within 1% of the equilibrium pool − − based on biomass estimates (g Nm 2yr 1) within a size). We present the timescale in terms of days to help range of values from studies in similar habitats (midges constrain the range of midge pulse durations we from Dreyer et al. [2015]; soil and plants from Marion explored; specifically, we constrained the midge pulse et al. [1982]; detritus from Shaver et al. [1992]; herbi- duration (w) to 20 d, which is approximately twice the vores, detritivores, and predators from Hoekman et al. duration of an average single midge emergence at [2011] and Dreyer et al. [2012]). Next, we fixed values for Myvatn.´ However, we note that the timescale is relative parameters that could be intuitively related to the equi- to the internal rates of the model, many of which are not librium pool sizes. For example, we selected the handling well constrained. Therefore, the timescales in the model times for the type-II functional responses (e.g., hP) such should be interpreted loosely. that the resource level at which the uptake reached one- We focused our analysis on the dynamics of herbi- half its maximum (i.e., the half-saturation value) vores and detritivores because neither of these two pools occurred at the equilibrium density for that pool. The is directly influenced by midges but are indirectly exception to this was the predator handling time (hX), affected through both top-down and bottom-up forces. which was selected so that the half-saturation value was The top-down effects of midges on herbivores and detri- 50% of the combined equilibrium densities of the detriti- tivores manifest through consumption by the predators vores and herbivores; this allowed the predators to and are identical on a per capita basis for the two pools exploit the midge subsidy when all pools were at their (because they are modeled symmetrically). In contrast, equilibria. Other parameters were given arbitrary values the bottom-up effects differ because of their different based on comparable scales to the other parameters trophic positions and proximity to the subsidy entry until enough were specified so that the remaining values point: decaying midges directly enter the detritus pool could be determined by solving the system of equations and are then available to the detritivores, while the midge set to their equilibria (with the midge pool set to 0; N must additionally enter the soil pool from the detritus Table 1). This approach ensured that the relative equilib- and then be taken up by plants before becoming avail- rium pool sizes resulting from the combinations of able to the herbivores. Therefore, detritivores receive an parameters were empirically plausible and ensured that immediate benefit from allochthonous resources enter- the corresponding equilibria were locally stable (Appen- ing the detrital pool, whereas herbivores are several steps dix S1: Section S1 and Appendix S2: Fig. S1). There- removed, leading to a slower response to midge pulses. fore, we had a clear baseline against which we could To measure the proximate mechanisms through which explore the transient dynamics of the system in response bottom-up and top-down fluxes affect target pools, we to resource pulses. quantified the effect of the midge pulse on detritivores Although we focus our analysis on the baseline and herbivores as the difference between either the N parameter set, to assess the generality of the results we gain due to consumption (bottom-up) or loss due to pre- also analyzed the model for alternative parameter sets dation (top-down) in response to a midge pulse (both for different combinations of herbivore/detritivore during and after the pulse) and the corresponding gain uptake rates (Appendix S2: Fig. S2) and inorganic nutri- or loss given the equilibrium pool sizes in the absence of ent input and outflow rates (Appendix S2: Figs. S3–S4). the pulse (i.e., in an unperturbed system). Specifically, These combinations were selected based on how relevant the effect of midges on the bottom-up flux of N to detri- they were to the main questions of our research. The tivores at time t was defined as qualitative dynamics for these alternative parameteriza- ∗ ∗ tions were similar to the baseline set; therefore, all the aDDtðÞVtðÞ aDD V results refer to the baseline parameter set unless noted BUV ðÞ¼t ∗ (3) 1 þ aDhDDtðÞ 1 þ aDhDD otherwise.

where D(t) and V(t) are the pool sizes at time t obtained Analysis from the numerical solution of the system of ODEs To explore the effects of midge pulse intensity and when perturbed with the midge pulse, while D* and V* multitrophic entry points, we numerically solved the sys- are the equilibrium pool sizes in the absence of the tem of ODEs for different combinations of parameters midge pulse. This expression gives the difference between that governed the total magnitude of the midge pulse (b, the bottom-up gain to the detritivore pool at a given keeping pulse duration w fixed) and direct responses to point in time and what that gain would be in the absence the pulse, such as predator exploitation (q) and the of the midge pulse, per unit of N in the detritivore pool. predator handling time on midges (hM). For each run of The bottom-up effect of midges on the herbivores was the model, the pools were initialized at their equilibrium defined analogously Article e03197; page 6 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx

∗ ∗ aPPtðÞHtðÞ aPP H manipulating the way in which midges enter the food BUH ðÞ¼t ∗ (4) 1 þ aPhPPtðÞ 1 þ aPhPP web and quantifying fluxes to and from each pool, we were able to provide a comprehensive assessment of bot- where P(t) and H(t) are the pool sizes at time t obtained tom-up and top-down effects. Furthermore, our scenar- from the numerical solution of the system of ODEs ios parallel how bottom-up or top-down effects are when forced with the midge pulse, while P* and H* are studied empirically (e.g., Marczak and Richardson 2007, the equilibrium pool sizes in the absence of the midge Hoekman et al. 2011, Dreyer et al. 2016), while our met- pulse. The effects of the midge pool manifest through rics based on proximate fluxes (i.e., BUH,BUV, and TD) the solution to the system of ODEs, and these effects capture mechanisms that are difficult to directly observe can persist beyond the end of the midge pulse. and so take advantage of the theoretical setting. We note The effect of midges on top-down pressure on detriti- that other metrics that have been developed for quantify- vores at time t was defined as ing transient responses to pulses in theoretical (Neubert and Caswell 1997) and empirical (Yang et al. 2010) set-

aX VtðÞXtðÞ tings. We opted for our approach because it allowed us TDV ðÞ¼t to separate transient responses of certain trophic levels 1 þ aX hX HtðÞþaX hX VtðÞþaX hM qMðÞ t a V ∗X ∗ to the pulse into bottom-up and top-down components. X The analyses above demonstrate how the transient 1 þ a h H∗ þ a h V ∗ X X X X responses of detritivore and herbivore pools to midge (5) subsidies vary across different scenarios of midge entry to the food web. To provide a more comprehensive where V(t), H(t), M(t), and X(t) are the pool sizes at time exploration of these processes, we also calculated the t obtained from the numerical solution of the system of cumulative effect of midges on bottom-up and top-down ODEs when forced with the midge pulse, while V*, H*, processes over the entire period during and after a midge and X* are the equilibrium pool sizes in the absence of pulse until the return to equilibrium. We focused on the the midge pulse. Analogous to the top-down effects case where midges subsidize both the detrital and preda- (Eqs. 3 and 4), Eq. 5 gives the difference between the tor pools across different levels of cumulative midge top-down loss from the detritivore pool due to predation input, the predator exploitation (q), and handling times at a given point in time and what that loss would be in on midges (h ). the absence of the midge pulse, per unit of N in the detri- M The effect of midges on bottom-up N gains to detriti- tivore pool. Because the per capita multispecies func- vores (BU (t)) and herbivores (BU (t)) was nonnegative tional response was the same for both detritivores and V H across the full range of explored parameters. Therefore, herbivores, they experienced identical top-down effects we defined the cumulative bottom-up effect of midges to per unit N, such that TDV(t) = TDH(t) ≡ TD(t). detritivores as Ztend In addition to top-down losses of N due to predation, the midge pulse also affects the loss of N from detritivore BUV,total ¼ BUV ðÞt dt (6) and herbivore pools through density-dependent mortality. t0 On a per capita basis, the density-dependent mortality for where t0 = 0 and tend = 500, by which point all pools a given pool directly follows changes in the size of the cor- were within 1% of their equilibrium abundance in the responding pool, and so does not provide much addi- absence of midges. The total bottom-up effect of midges tional information about the factors driving the dynamics. on herbivores was defined analogously. This stands in contrast to the effects of the midge pulse We observed both positive and negative effects of the on bottom-up and top-down processes, which involve the midge pulse of the strength of top-down pressure interactions between multiple pools and so drive the [TDV(t)]; thus, we defined the cumulative intensification dynamics. Therefore, while it is worth noting that the total of top-down pressure during and after a midge pulse effect of the midge pulse includes its effects on density-de- Ztend pendent mortality, we focus our analysis of the impacts of midges on bottom-up and top-down processes. TDintensification ¼ minðÞ 0, TDðÞt dt (7)

Our metrics of top-down and bottom-up effects of t0 midges are proximate, in the sense that their directional- and the cumulative alleviation as ity (i.e., bottom vs. top) is defined with respect to the tar- Ztend get pool. However, an alternative approach is to define : the directionality relative to the entry point of the midges TDAlleviation ¼ maxðÞ 0, TDðÞt dt (8) to the food web (i.e., low vs. high trophic levels). To t0 explore this, we analyzed scenarios with different entry The net top-down effect of midges was therefore points for midges into the food web: (1) midges to detritus only, (2) midges to predators only, and (3) midges to TDnet ¼ TDintensification TDalleviation: (9) both detritus and predators (see Appendix S1: Section S2 All analyses were performed in R v4.0.0 (R Develop- for corresponding modifications to Eq. 1). By both ment Core Team 2020). Numerical solutions to ODEs Xxxxx 2020 TRANSIENT EFFECTS OF PULSED RESOURCES Article e03197; page 7 were obtained using the ode function from the deSolve a Upper trophic levels package (Soetaert et al. 2010). 4

Predator RESULTS 2 Detritivore Our analysis was designed to illustrate how a resource pulse that simultaneously enters multiple trophic levels Herbivore 0 affects the transient dynamics of a recipient food web, Pulse with a focus on how the bottom-up and top-down consequences of resource pulses vary through time. We begin b Lower trophic levels by presenting the transient dynamics of the model given some example parameter combinations to illustrate its 4 key behaviors, followed by an exploration of the dynam- Proportional change in N Detritus ics across a wider range of parameter values that influ- 2 Soil ence the capacity of different predators to exploit the resource pulse (e.g., predator exploitation of the resource Plant pulse and handling time). Rather than attempting to 0 Pulse provide a comprehensive assessment of the model 0 25 50 75 100 dynamics across the full parameter space, our analysis Time (d) instead provides a more focused examination of the qualitative behaviors that can arise in a system with FIG. 2. Time series of proportional changes in N content resource pulses to multiple trophic levels (see Appendix among (a) upper trophic level (herbivore, detritivore, predator) S2: Figs. S2–S4 for results of alternative parameteriza- and (b) lower trophic level (detritus, soil, plant) pools. Lines indi- − tions). cate the N content at time t relative to that at time 0 (i.e., (Nt N0)/N0). The lower black bar represents the duration of the midge N pulse. Parameter values are as in Table 1, with predator exploitation q = 3, pulse duration w = 20, and pulse rate b = 50. Responses of lower and upper trophic levels to midge pulse We first show the time series for the N content of each trophic level in response to a single resource pulse using the baseline parameter set (Fig. 2); the values are relative gradual and monotonic decay toward their equilibrium to the equilibrium (see Appendix S2: Fig. S5 for abso- pool sizes following the end of the midge pulse. This was lute values). An unrealistically large pulse (i.e., accompanied by a modest increase in the abundance of 1000 g N/m2,10–100× higher than empirical estimates predators, which was stimulated by the increased abun- in Dreyer et al. 2015) was used to better illustrate the dance of herbivores and detritivores. When midges only qualitative behavior of the system under extreme condi- entered via predators (Fig. 3c), there was an increase in tions. All trophic levels increased in response to the the abundance of herbivores and detritivores during the pulse, followed by a gradual decline from their peaks pulse followed by a steep decline immediately following towards their respective equilibria in the absence of ele- the pulse to sub-equilibrium levels, followed by a gradual vated resources. However, the timing and relative magni- increase to equilibrium. This was accompanied by a tude of each peak’s response varied depending on the steep increase in the size of the predator pool. The trophic position of the recipient pool. For example, the responses of herbivores and detritivores were nearly detritus pool is directly subsidized by decay from the identical as the consumption of herbivores/detritivores midge pool and therefore has a rapid response to the by predators was identical on a per capita basis due to midge pulse. In contrast, for N from midges to enter the the use of the same uptake rates and handling times. soil and plant pools, it must first be remineralized from When both predators and detritivores received the sub- the detritus pool into the inorganic N pool before then sidy (Fig. 3b), the qualitative dynamics were generally being taken up by the plants. This introduces lags to the similar to the case when only predators were the recipi- responses of the soil and plant pools, which manifest as ents. However, both the increase in herbivore/detritivore a delay in their peak responses relative to the detritus abundance during the pulse and the decline in abun- pool. dance following the pulse were more dramatic in the presence of midge subsidies to both detritus and predators; this was especially true for detritivores. Transient responses of detritivores and herbivores To explore the mechanisms responsible for transient There were qualitatively different responses of detriti- dynamics exhibited by herbivores and detritivores, we vores and herbivores that arose through changes in the examined the proximate bottom-up and top-down pulse entry point of the midges (Fig. 3). When midges effects of midges through time (Eqs. 3–5). Overall, the only entered via detritus (Fig. 3a), detritivore and herbi- bottom-up effect of midges was greater for detritivores vore pools increased during the midge pulse, showing a than for herbivores when midges entered the detrital Article e03197; page 8 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx pool (Fig. 4a,b), which is expected given that herbivores detritivores than for the herbivores (Appendix S2: were further removed from the entry point of the midges Fig. S2). Therefore, their relative trophic positions with into the food web. For the baseline parameter set, the respect to the pulse entry point caused the difference in uptake rate of detritus by detritivores was higher than the bottom-up effects on these two pools. When preda- the uptake rate of plants by herbivores (Table 1), which tors were the only recipients of the pulse (Fig. 4c), the also contributed to the larger bottom-up effect of midges bottom-up effects were negligible, reflecting the limited on detritivores. However, even when switching the contribution of N passing through predators to the uptake rates for detritivores and herbivores, the bottom- detrital and soil N pools. up effect of the midge pulse was always greater for the The per capita top-down effects of the midge pulse on detritivores and herbivores were identical (Fig. 4a–c), due to the predator attack rates and handling times on a) Midges to detritus only those pools being set to the same values. When midges only entered via the detrital pool, there was a modest 4 increase in top-down pressure (Fig. 4a), due to the 1.0 a) Midges to detritus only 0.5 2 0.10

0.0 0 BU detritivore 0.05 BU herbivore Proportional change in N (predator) 0.00 b) Midges to detritus and predators TD both

predator 4 1.0 b) Midges to detritus and predators 0.5 2 )

detritivore 1 − 0.10

0.0 0 herbivore pulse 0.05 Proportional change in N 0.00 c) Midges to predators only

4 Effect on pool (day 1.0 c) Midges to predators only 0.5 2 0.10 0.0 0

0.05 TDintensification 0 25 50 75 100 Time (d) 0.00

FIG. 3. Time series of proportional changes in N content TDalleviation for detritivore and herbivore pools (indicated by the left y-axis). This is shown for when (a) midges only enter the detritus pool, 0255075100 (b) midges enter both detritus and predator pools, and (c) Time (d) midges only enter the predator pool. The blue-shaded regions represent the proportional change in N for predators, which is FIG. 4. Time series of the top-down (TD) and bottom-up indicated by the right y-axis. Different y-axis scales are used to (BU) effects on detritivore and herbivore pools. This is shown for aid visualization of the transient dynamics of the herbivores when (a) midges only enter the detritus pool, (b) midges enter and detritivores, which had a weaker response to the pulse than both detritus and predator pools, and (c) midges only enter the predators for the selected parameter values. The lower black predator pool. The gray line indicates the top-down effects on bar represents the duration of the midge N pulse. Parameter both detritivore and herbivore pools, as they are identical in the values are as in Table 1, with predator exploitation q = 3, pulse model. Parameter values are as in Table 1, with predator duration w = 20, and pulse rate b = 20. exploitation q = 3, pulse duration w = 20, and pulse rate b = 20. Xxxxx 2020 TRANSIENT EFFECTS OF PULSED RESOURCES Article e03197; page 9

elevated predator abundance sustained by the increased TDintensification at high midge inputs, whether approached herbivore and detritivore pools. In contrast, when monotonically or following a peak, is the result of the midges entered via the predator pool (regardless of saturation of the multispecies functional response that whether they also enter the detrital pool), there was a limits the ability of the predator to exploit high midge steep reduction in top-down pressure during the pulse inputs. The level of this saturation is determined by both followed by a steep increase after the pulse (Fig. 4b,c). the midge handling time and predator exploitation, with The reduction in top-down pressure during the pulse low predator exploitation and handling times yielding occurred because predator consumption of all prey types the largest TDintensification (Fig. 5a). It may seem counter- saturated according to the multispecies functional intuitive that low predator exploitation yielded greater response. This is an example of “apparent mutualism” intensification of top-down effects at high midge inputs; between the midge pool and the herbivore/detritivore however, this is because predator exploitation scales the pools (Abrams and Matsuda 1996). Following the end “effective” size of the midge pool available to predators, of the midge pulse, the elevated predator pool size and which in turn contributes to the saturation of per capita the rapid depletion of the midge pool cause a steep predator consumption. This is made clear by the pres- increase in top-down pressure (Fig. 4b,c). This is an ence of the predator exploitation parameter q in the example of “apparent competition” between the midge denominator of the multispecies functional response. pool and the herbivore/detritivore pools (Holt 1977). When midge handling time was low (Fig. 5a,b), total Therefore, when predators are able to exploit the midge alleviation of top-down effects (TDalleviation) was low pool, there is a serial pattern of alleviation (i.e., apparent and varied non-monotonically with total midge input, mutualism) followed by intensification (i.e., apparent with the exact pattern depending on predator exploita- competition) of top-down pressure (Fig. 4c). tion. When handling time was high (Fig. 5c,d), In addition to apparent mutualism and competition TDalleviation was much higher and increased monotoni- between midges and herbivores/detritivores, there is also cally with total midge input. Across the range of total potential for apparent mutualism and competition midge inputs and handling times, TDalleviation was between herbivores and detritivores themselves that slightly higher when predator exploitation was high than could change in response to the midge pulse. To explore when it was low. The saturation of TDalleviation at high this, we performed numerical experiments with midge midge inputs occurred for the same reason as for pulses to both detritus and predators and then removed TDintensification: alleviation of top-down pressure was a either herbivores or detritivores from the model (recalcu- direct result of the saturation of the multispecies func- lating the equilibrium pool sizes for each case). This tional response, and so could only increase over the analysis shows that apparent mutualism between herbi- range of midge inputs where the predator consumption vores and detritivores predominates (Appendix S2: was not completely saturated. Figs. S6–S7). The net midge effect on top-down pressure (TDnet) was determined by the balance between TDintensification and TD (Eq. 9). Over the range of parameters Cumulative responses of detritivores and herbivores alleviation examined here, the magnitudes of TDintensification and We show BUV, total,TDalleviation,TDintensification, and TDalleviation at high midge inputs were negatively TDnet for the detritivores across a range of total midge associated across scenarios. Specifically, low handling inputs for different predator exploitations and handling time and predator exploitation yielded the greatest times on midges (Fig. 5). The cases with subsidies going TDintensification and lowest TDalleviation (Fig. 5a), while to either detritivores or predators (but not both) are the reverse was true for high handling time and predator shown in Appendix S2: Fig. S8a,c, and the qualitatively exploitation (Fig. 5d). Consequently, the values of similar results for herbivores are shown in Appendix S2: TDnet varied more widely than either TDintensification and Fig. S8b. Here, we focused on predator exploitation and TDalleviation, with TDnet ranging from strongly positive handling time because they mediate the ability of preda- (i.e., stronger top-down pressure in the presence of tors to prey on the midge pulse, which in turn mediates midges) to weakly negative (i.e., weaker top-down pres- their effects on detritivores. Furthermore, changes to sure in the presence of midges). The negative association predator exploitation represent a continuous analogue between TDintensification and TDalleviation is a direct conse- to inclusion or removal of the midge subsidy to preda- quence of the saturation of the multispecies functional tors, as we do for the “numerical experiments” in Figs. 3 response, in which the basic mechanism for TDalleviation and 4. imposes a constraint on TDintensification. In general, TDintensification increased with total midge The total effect of midges on bottom-up pressure input until plateauing at high values (Fig. 5a,c,d). The (BUV, total) increased monotonically with the total midge exception was when predator exploitation was high and input and did not vary substantially across exploitation handling time was low (Fig. 5b), where TDintensification or handling time; this is expected, since the bottom-up reached a peak at low midge inputs before declining effect of midges was chiefly dictated by processes occur- towards relatively stable values (although with a slight ring at the lower trophic levels. The net effect of the increase at high midge inputs). The saturation of midge pulse on both top-down and bottom-up pressure Article e03197; page 10 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx

BU total TD net

TD intensification TD alleviation

a Low midge b High midge exploitation exploitation

4 handling time handling time Low midge 3 2 1 0

c d

4 High midge

Total midge effect 3 2 1 0

0 100 200 300 400 0 100 200 300 400 Total midge input (g N/m2)

FIG. 5. Cumulative midge effect on total bottom-up control (BUtotal), net top-down control (TDnet), top-down intensification, and top-down alleviation as a function of total midge inputs. The panels show different combinations of high and low predator exploitation and handling times on midges. Data are from detritivores; herbivores gave broadly similar responses to the cumulative midge effects (Appendix S2: Fig. S8b). Parameter values are as in Table 1, with low exploitation q = 0.8, high exploitation q = 8, low midge handling time hM = 1.3, high midge handling time hM = 5.3, pulse duration w = 20, and pulse rate b ranging from 0.1 to 23 to produce different total midge inputs.

DISCUSSION is determined by the balance between BUV, total and TDnet, with points of intersection (i.e., BUV,total = We developed and analyzed a mathematical model of – – TDnet) indicating no net effect of midges, excluding a soil plant arthropod food web to examine how those arising from changes in density-dependent mortal- allochthonous resource pulses affect transient top-down ity. Because BUV, total was relatively stable across differ- and bottom-up dynamics when entering multiple trophic ent scenarios, variation in the net midge effect was levels. We found that all trophic levels increased in bio- primarily determined by changes in TDnet. For low han- mass during an allochthonous pulse, but the magnitude dling times (Fig. 5a,b), TDnet exceeded BUV,total at low and timing of the peaks depended on the trophic posi- total midge inputs. However, the more rapid saturation tion. Inorganic soil N, detritus, and plants were mainly of TDnet with increasing total midge input relative to affected by bottom-up processes, whereas intermediate BUV, total caused them to intersect at intermediate midge trophic levels (detritivores and herbivores) were affected inputs, above which BUV,total exceeded TDnet. This inter- by a combination of top-down and bottom-up forces. section point was affected by predator exploitation, with We also found that midge subsidies could either alleviate lower exploitation resulting in BUV, total exceeding TDnet or intensify top-down effects on intermediate trophic at relatively higher total midge inputs. Under high han- levels; the former resulting from saturation of the preda- dling times (Fig. 5c,d), detritivore (and herbivore) tors’ ability to exploit the allochthonous resource while growth was enhanced by indirect effects of the midge the latter resulting from elevated abundance of preda- subsidies through both enhanced bottom-up and gener- tors. The net cumulative top-down effect on herbivores ally weakened top-down forces. and detritivores was determined by the tendency of the Xxxxx 2020 TRANSIENT EFFECTS OF PULSED RESOURCES Article e03197; page 11 multispecies functional response to saturate, with greater predation pressure on some focal population (e.g., herbi- saturation leading to increased dominance of bottom-up vores) is reduced in the presence of alternative resources. effects. Our findings show how resource pulses to multi- We used parameter values that were informed by the ple trophic levels can influence transient food web Myvatn´ system and selected to have reasonable equilib- dynamics, with bottom-up dominating top-down effects rium pool sizes in the absence of the midge subsidy. under most circumstances. Under these conditions, bottom-up effects always domi- Our results illustrate that bottom-up and top-down nated for the lower trophic levels (inorganic soil N, detri- responses to the midge pulses can alter detritivore and tus, and plants) and often predominated for herbivore dynamics, with the relative balance of top- intermediate trophic levels (detritivores and herbivores), down and bottom-up effect being determined by prox- especially when the magnitude of the subsidy was large. imity to the pulse entry point, pulse size, and ability of Our model results are consistent with empirical assess- predatory arthropods to exploit it. Due to direct access ments of the dynamics observed at Myvatn.´ For exam- to allochthonous N in the form of detritus, detritivores ple, high-midge areas adjacent to Myvatn´ are generally receive an immediate boost from subsidy inputs, buffer- productive grasslands with higher densities of arthro- ing them against top-down effects from predators. In pods compared to nearby heathlands with fewer midge contrast, allochthonous inputs must go through the subsidies (Dreyer et al. 2012, Hoekman et al. 2019). detritus, soil, and plant pools before herbivores are sub- Moreover, adding midge carcasses to heathlands near sidized, leading to increased sensitivity to top-down Myvatn´ increased grass cover, plant biomass, detritivore pressures. However, our model shows that when pulse and herbivore densities, and abundances of several inputs are sufficiently high, the bottom-up pathways for predator groups (e.g., predaceous beetles and para- detritivores and herbivores are enough to overcome top- sitoids) (Hoekman et al. 2011, Gratton et al. 2017). down effects of predators, leading to a dominance of These results are also consistent with how pulsed bottom-up forces. resources influence food webs in other nutrient-poor We also show that predators’ abilities to exploit pulsed ecosystems, which are generally controlled by bottom-up resource subsidies can lead to both intensification and forces (Sanchez-Pinero and Polis 2000, Schwinning and alleviation of top-down pressure on intermediate con- Sala 2004, Stoessel et al. 2019). sumers, akin to apparent competition (Holt 1977) and apparent mutualism (Abrams and Matsuda 1996). When Conclusions predators can exploit midges at a high rate, we found that both top-down intensification and alleviation were Our findings indicate that when an allochthonous possible on intermediate tropic levels, with alleviation resource pulse enters a recipient food web through multi- occurring during the pulse and intensification occurring ple compartments as both live prey and carcasses, bot- after the end of the pulse. Such a shift from apparent tom-up effects prevail in most circumstances, mutualism to apparent competition was shown theoreti- particularly when the pulse magnitude is high. Although cally by Takimoto et al. (2002). Though their model only our model results hold across a range of parameter com- investigated top-down effects, they demonstrated a sea- binations, our food web is a simple caricature of natural sonal switch from predators utilizing prey subsidies early systems. Food webs in nature have multiple predators, in the season to local prey late in the season, leading to each with a distinct preference for herbivores, detriti- stronger top-down effects on local prey when subsidies vores, or allochthonous prey. Thus, future work should were absent. Several examples from natural systems have evaluate transient bottom-up and top-down effects of also observed this seasonal shift in top-down pressure pulsed resources for multiple predators with different on local prey following a resource pulse (Nakano et al. prey preferences. Furthermore, as soil microbial activity 1999, Sabo and Power 2002, Piovia-Scott et al. 2019). likely influences cycling of N via resource subsidies For example, Henschel et al. (2001) found that aquatic (Yang 2004), incorporating soil microbes into future insect subsidies lead to short-term depression of top- models would clarify their role in mediating these down pressure from spiders on terrestrial leafhoppers dynamics. due to diet shifts, followed by enhanced top-down pres- While research on bottom-up vs. top-down control in sure resulting from increased predator abundance. These ecology has a long history of manipulating both basal top-down effects are likely enhanced by aggregative resources and consumers simultaneously (Hillebrand responses of large mobile generalist predators, which are 2002, Gruner et al. 2008), no empirical study has simul- commonly observed in studies of pulsed dynamics (Sch- taneously manipulated allochthonous pulses entering midt and Ostfeld 2008, Yang et al. 2010, Dreyer et al. the food web via multiple pathways (Allen and Wesner 2016). It is important to note that previous theoretical 2016). Empirical research could test our model results studies have often included explicit prey switching or by manipulating a single resource pulse that enters the preference for allochthonous vs. autochthonous food web at multiple trophic levels and then monitoring resources, which is absent from our model. However, the the food web responses through time, especially at peri- saturating functional response has a similar effect to ods during the resource pulse and immediately after. these more explicit mechanisms in that per capita Future research should also evaluate how pulse Article e03197; page 12 MATTHEWA. MCCARY ET AL. Ecology, Vol. xx, No. xx magnitude might influence the net bottom-up vs. top- Henschel, J. R., D. Mahsberg, and H. Stumpf. 2001. Allochtho- down effects on recipient food webs, as our model sug- nous aquatic insects increase predation and decrease her- – gests that the magnitude of the pulse can amplify top- bivory in river shore food webs. Oikos 93:429 438. Hillebrand, H. 2002. Top-down versus bottom-up control of down control under certain conditions. Such empirical autotrophic biomass—a meta-analysis on experiments with work will further improve our mechanistic understand- periphyton. Journal of the North American Benthological ing of the interrelationship between bottom-up and top- Society 21:349–369. down dynamics across time and space (Leroux and Lor- Hoekman, D., J. Dreyer, R. D. Jackson, P. A. Townsend, and C. eau 2015). Gratton. 2011. Lake to land subsidies: experimental addition of aquatic insects increases terrestrial arthropod densities. ACKNOWLEDGMENTS Ecology 92:2063–2072. Hoekman, D., M. A. McCary, J. Dreyer, and C. Gratton. 2019. This research was funded by National Science Foundation Reducing allochthonous resources in a subarctic grassland grants DEB-1556208, DGE-1256259, DGE-1747503, and alters arthropod food webs via predator diet and density. Eco- DEB-1611638. We thank E. J. 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DATA AVAILABILITY STATEMENT All analyses and accompanying scripts are available on Zenodo: https://doi.org/10.5281/zenodo.3981035