On mutualism, models, and masting: The effects of seed‐dispersing animals on the plants they disperse

Species interactions are context dependent, in that their direction and magnitude can vary across ecological conditions. For seed dispersal interactions—especially interactions between plants and seed‐caching animals—the direction of the interactions is often obscured because of seed mortality inherent in seed handling and the delayed effects of fitness benefits received by plants. It is, therefore, an open question in ecology to understand the ecological contexts under which seed dispersal interactions are facilitative, antagonistic or null. We review the fitness benefits of animal‐mediated seed dispersal, extend a recently published model to include negative density‐dependent effects, and review the feedback between seed production (with a focus on masting) and seed‐caching animal populations. Negative density‐dependent effects are pervasive and strongly affect the direction of plant‐seed‐disperser interactions, and including them into models will give a more accurate understanding of the direction of the interaction. Including negative density‐dependent effects also makes the interpretation of interaction more mutualistic since seed dispersers decrease seed densities. Additionally, there is substantial interannual variability in seed production in most nut‐producing plant species, and the lags between seed production and seed‐disperser population sizes complicate and limit inferences made about the direction of interactions in any given short‐term study. Synthesis. If we wish to know the direction of species interactions in real ecological communities, we need models that contain a minimum level of biological realism. For complex and long‐term phenomena such as context‐dependent species interactions we should embrace a multifaceted approach of short‐term field research, long‐term field research, simple models, and complex models to form a more robust understanding of the ecological problem of context dependency.

To identify the direction of pairwise species interactions as facilitative, antagonistic, or null, we must reduce the complex interactions within communities into pairwise parts and study interactions across different contexts. One common type of species interaction whose direction is seemingly not entirely clear to many ecologists is seed dispersal mutualism between plants and animals. Animals and plants on both sides of the seed dispersal mutualism respectively benefit from a nutriment reward and a dispersal service. Two of the main reasons that the direction of this interaction is not fully clear is because (a) the dispersal service is often difficult to quantify and (b) the reward for animals often includes consuming the embryo of the plant, which is ultimately a mortality event. A recent paper in Journal of Ecology by Bogdziewicz, Crone, and Zwolak (2020) aimed to identify the direction of a particular type of plant-seed-disperser interaction that is often presumed to be mutualistic, synzoochory, which is the dispersal of seeds by seed-caching animals (sensu Gómez, Schupp, & Jordano, 2019). Bogdziewicz et al. (2020) used a combination of modelling and empirical approaches to conclude that synzoochory does not always benefit plant recruitment and that the interaction should be tested rather than be presumed. This work inspired us to write this forum piece, where our intention is to use Bogdziewicz et al.'s (2020) study as the groundwork to more accurately understand the positive and negative effects that seed-caching animals have on plants. We provide some background on dispersal in plants, followed by building negative density-dependent effects into the model from Bogdziewicz et al. (2020), a section on how interannual variability obscures our understanding of this interaction, and ending with some remarks on future directions of modelling synzoochorous interactions. Our main arguments are largely twofold.
First, negative density-dependent effects cannot be overlooked when trying to understand the direction of animal-seed-dispersal interactions, and we show how incorporating them into a model of seed survival makes the interpretation of the interaction more mutualistic and therefore in agreement with our observations in nature. Second, interannual variability in seed production obscures inferences made on short-term empirical studies about the direction of the interaction and conclusions drawn from such studies should be interpreted with caution.

| S EED D IS PER SAL IN CRE A S E S PL ANT FITNE SS IN THREE MAIN WAYS
Animal-mediated seed dispersal may be the most common mode of seed dispersal in the world (Jordano, 2000;Moles et al., 2007), has evolved independently many dozens of times across all major vascular plant taxa (Dunn, Gove, Barraclough, Givnish, & Majer, 2007;Herrera, 2002), and has been shown to influence rates of speciation in plants (Lengyel, Gove, Latimer, Majer, & Dunn, 2010;Onstein et al., 2017). In other words, animal-mediated seed dispersal is an interaction that, at sufficiently large scales, persists as mutualistic through space and time. To be mutualistic, seed-dispersing animals and the plants whose seeds they disperse share an increase in fitness in each other's presence (Bronstein, 2015). Within these interactions there is often a clear increase in fitness of the animal dispersing seeds, often through a resource reward such as fruit pulp or nut endosperm. The increase in plant fitness, however, is less apparent and less feasible to study because the vast majority of plants species engaged in this mutualism are woody and thus longer lived where measuring effects on fitness would take years to decades.
Notwithstanding the empirical obstacles of measuring fitness in plants, conceptual and theoretical developments have identified mechanistically how dispersal increases plant fitness (Howe & Smallwood, 1982): 1. Escape from negative density-dependent effects at the seed and seedling stages. Animals disperse seeds away from parent plants, which increases fitness relative to seeds remaining under the parent plant by reducing negative density-dependent effects of enemies on seeds (Connell, 1971;Janzen, 1970).

Colonization of new sites.
Animals deliver seeds to new sites, which increases fitness relative to remaining under parent plants because spatial spread makes populations more robust to disturbance (which tends to be strongly spatially correlated) and, because conditions and resources vary across space and time, spatial spread allows populations to be more robust to changing conditions (e.g. Comins, Hamilton, & May, 1980;Gadgil, 1971;Grinnell, 1936).
Most bodies of thought and studies on animal-mediated seed dispersal begin and end at the seed or seedling stage, but survival of seeds and seedlings have relatively small effects on fitness. In structured populations-like woody plants that do not reproduce during early life stages, have low survival rates during early life stages and are highly fecund during later life stages-contributions to fitness (population persistence) are strongest in the latest life stages (Caswell, 2006). These later stages of the seed dispersal loop (sensu Wang & Smith, 2002) are influenced by the seed dispersal process, but are not often considered conceptually and are not often measured empirically-the latter being especially true for plants that are dispersed by animals because they tend to be long lived. Beyond plant fitness being increased by seeds and seedlings escaping negative density-dependent effects at the seed and seedling stages (e.g. escaping pathogenic, parasitic, and frugivorous and granivorous enemies), an additional way that dispersal increases plant fitness is through: 3. Reduction in intraspecific competition at later stages. Animals disperse seeds away from parent plants, which increases fitness relative to remaining under the parent plant by reducing intraspecific competition that generally becomes more important to plant fitness at later stages (e.g. sapling and adult stages).
These are the three categorical ways in which animals can increase plant fitness through dispersal. Like all species interactions, however, there are fitness-decreasing and -increasing behaviours that ultimately result in a net fitness effect. Predators bear costs and benefits of attacking prey, but predator-prey interactions are generally understood as being net positive and negative, respectively, for predators and prey; competitive interactions bear costs to both species, but are generally understood as being net negative for both species involved unless one is driven to extinction; and mutualistic interactions include both species bearing costs and receiving benefits, but are generally understood as being net positive for both species involved. Nevertheless, given that the net effect of costs and benefits of mutualistic seed dispersal interactions can have a degree of context dependency like all other species interactions (Chamberlain et al., 2014), it is important to understand the conditions under which we expect the interactions to have a net increase or decrease in fitness. To that end, a mathematical model with parameters that can be measured by empirical ecologists can reveal non-intuitive or counter-intuitive interpretations of what we observe-this is the underlying beauty and power of mathematical models in ecology.

| MODELLING THE NE T EFFEC T OF ANIMAL S ON PL ANT FITNE SS
For models examining the effects of seed-caching animals (hereafter, 'animals') on the plants whose seeds they disperse (hereafter, 'plants') to be accurate, they must include the three ways that animals increase plant fitness through dispersal: (a) seed and seedling escape from negative density-dependent effects, (b) colonization benefit, and (c) reduction in intraspecific competition.
In a recent paper, Bogdziewicz et al. (2020) used a mathematical model developed by Zwolak and Crone (2012) as a basis to empirically determine the direction of the effects of seed-caching animals on the plants whose seeds they disperse (specifically synzoochorous animals sensu Gómez et al., 2019 and nut-bearing plants). Broadly, the model is an inequality relating the proportion of seeds that germinate in the absence of animals (left-hand side) to the proportion of seeds that germinate in the presence of animals (right-hand side). If the proportion of seeds that germinate in the absence of animals is less than the proportion of seeds that germinate in the presence of animals, then the animals could be considered mutualistic dispersers; if not, they could be considered antagonistic predators.
The left-hand side of the equation is the proportion of seeds that emerge (i.e. germinate) in the absence of animals from the surface of the soil, e S . The right-hand side of the equation is, in the presence of animals, the proportion of seeds that germinate, which is comprised of the proportion of seeds that emerge after being handled by animals and the proportion of seeds that emerge that are not handled by animals. The proportion of seeds handled by animals is composed of three factors: the proportion of seeds harvested by animals, p H ; the proportion of those seeds cached by animals and unrecovered, p C ; and the proportion of those that emerge from animal caches e C .
The second term on the right-hand side is the proportion of seeds that are not handled by animals, (1 − p C ) multiplied by the proportion of the seeds that emerge from the surface of the soil, e S . Together, the equation is: Algebraic rearrangement reveals a simple representation to determine if the animals are mutualists or antagonists: That is, if the ratio of the proportions of seeds that emerge from the surface to seeds emerging from caches is less than the proportion of unrecovered cached seeds following removal, then the interaction is mutualistic; if not, it is antagonistic. This threshold of the isolated variable on the right-hand side of the equation is the fixed value against which e S and e C are evaluated, and designated as p C . The outcome of this simple inequality is that empirical ecologists could hypothetically measure these three variables and determine the effect of animals on plant populations. Implicit in Equation 1 is that there is only a single benefit conferred by animals: the benefit of burial. Although seed burial generally confers a large germination benefit, Bogdziewicz et al. (2020) and Zwolak and Crone (2012) argue that it must be placed in the context of the proportion of seeds that animals harvest and consume to understand if the interaction is net mutualistic or antagonistic. We strongly agree with this argument, but contend that it needs to be further extended to more realistically and generally understand the net effect of seed-dispersing animals on the plants whose seeds they disperse. More specifically, the fitness benefits described in Section 2 must be considered to make ecologically meaningful inferences about the direction of the interaction. Of the three benefits conferred by animals described in Section 2, two are not able to be tested with the Bogdziewicz et al. (2020) and Zwolak and Crone (2012) frameworks. Specifically, despite the importance of the benefits of colonization (Section 2, benefit 2) (2) e S e C < p C .
and reducing intraspecific competition (Section 2, benefit 3), they cannot be applied within this framework because it was created for empirical ecologists to collect data on short spatial and temporal scales to approximate if animals are mutualists or antagonists.
Nevertheless, the benefit that animals provide plants by reducing negative density-dependent effects (Section 2, benefit 1) needs to and can be incorporated into this framework. Burying seeds is one benefit conferred by animals, but reducing seed densities around the parent plant reduces mortality imposed by seed predators may be at least, if not more, beneficial to seeds than the benefit of burial itself. The evidence for this claim being that in the vast majority of communities where negative density-dependent effects on seed has been studied (including tropical and temperate ecosystems), they have been found to strongly influence seed, seedling and sapling survival (e.g. Connell, 1971;Harms, Wright, Calderón, Hernandez, & Herre, 2000;Hirsch, Kays, Pereira, & Jansen, 2012;Janzen, 1970;Packer & Clay, 2000;Peters, 2003;Terborgh, 2012).
Therefore, negative density-dependent effects should be a part of any seed or seedling survival model.
We propose two ways to incorporate negative densitydependent effects into the Bogdziewicz et al. (2020) and Zwolak and Crone (2012) frameworks: 1. Whether or not animals are present, seedling emergence from the surface is reduced from negative density-dependent effects.
2. Where animals are absent, seedling emergence from the surface is reduced from negative density-dependent effects.
The first scenario is somewhat trivial, but illuminating. Here, seedling emergence is reduced implicitly as part of Equation 1. But to make it explicit, we can multiply the terms for germination from the surface, e S , by a negative density-dependent term, which we will call δ 1 , with 1 corresponding to the first scenario. As δ 1 approaches 1, survival on the surface is high; as δ 1 approaches 0, survival on the surface is low. Adding it to Equation 1 gives us Algebraic rearrangement yields a simple representation to determine if the animals are mutualists or antagonists: This shows that any increased mortality of the seeds on the surface will result in a smaller value on the left-hand side; thus setting the threshold for the interaction to be mutualistic, p C , lower.
The second scenario is both more substantive and realistic.
Because animals reduce the density of seeds on the surface, in the absence of animals, predators, pathogens and other enemies inflict greater mortality on the undispersed seeds because they are accessible on the surface and are in higher densities. If we add the negative density-dependent effect, δ 2 , with 2 corresponding to the second scenario, in the absence of animals on the left-hand side of the equation, it would be:

Rearrangement yields:
Let us make the biologically reasonable assumption that p H is high (near 1) because most seeds are dispersed and forest floors are not saturated with the accumulation of hundreds to hundreds of thousands of seeds produced per plant per year. Because δ 2 is bound between 0 and 1, we can see that when negative density-dependent effects are weak, as δ 2 → 1, the parenthetical factor is slightly <1, which will slightly lower the threshold for the interaction to be mutualistic, p C . If negative density-dependent effects are strong, as δ 2 → 0, the parenthetical factor is considerably <1, which will considerably lower p C . Figure 1 shows the relationship between 2 , p H , and the parenthetical factor on the lefthand side of Equation 6, further demonstrating that a combination of strong negative density-dependence effects and a low proportion of seeds harvested by animals considerably lowers the threshold for the interaction to be mutualistic (p C ). In sum, any incorporation of the omnipresent and, in many cases of paramount importance, negative density-dependent effects will lower the threshold to make the interaction more mutualistic. Lowering the mutualism threshold is a consequence (3) e S 1 < p H p C e C + 1 − p H e S 1 .
(5) e S 2 < p H p C e C + 1 − p H e S .

F I G U R E 1 Surface (red)
showing how the proportion of seeds handled by animals (p H ) and the strength of negative densitydependent effects (δ 2 ) affect the parenthetical factor on the lefthand side of the inequality in Equation 6; specifically, the vertical axis shows z = ((δ 2 − 1)/(p H ) + 1). When negative density-dependent effects are considered, the threshold for plant-animal interactions to be mutualistic is lowered. Interestingly, when negative densitydependent effects are strong, animals dispersing a small proportion of seeds could be highly beneficial to plants. Contour  is not important to lower the threshold per se, but for a model to be empirically accurate for determining the direction of the plant-animal interaction, it must also include all substantive and realistic aspects of the system's ecology.

| MA S TING AND INFEREN CE S ABOUT S EED DIS PER SAL MUTUALIS MS
Masting, from the seed perspective, is the intermittent synchronous production of large seed crops typically followed by a period of below-average seed crop production. Ultimately, the reasons why plants mast is still not fully understood (Burns, 2012;Kelly & Sork, 2002;Pearse, Koenig, & Kelly, 2016). Regardless of the evolutionary processes that led to masting, we know that masting has strong effects on seed-consuming populations, especially highly specialized guilds like granivorous rodents (McShea, 2000;Ostfeld & Keesing, 2000).
Rodent populations largely track seed production with an increase in populations occurring shortly after (1-2 years) mast events (Clotfelter et al., 2007;Elias, Witham, & Hunter, 2004;Li & Zhang, 2007;Schnurr, Ostfeld, & Canham, 2002;Selås, Framstad, & Spidsø, 2002). The opposite is true during non-mast years, oftentimes creating a significant drop in the populations of rodents that rely on the seed crop as a primary food source (Clotfelter et al., 2007;Wolff, 1996). The variation in the ratio of rodents to seeds is likely an important factor in determining the direction and strength of the interaction, as discussed in the subsequent two paragraphs, and is particularly true where predator satiation is presumed to be the primary driver of masting.
Scatter-hoarding rodents continue to cache seeds in preparation for food scarcity, even if they are currently satiated and have enough food to survive the period of food scarcity (Vander Wall, 2010). We expect p CO (probability that a seed is cached and not retrieved, explicitly accounting for pilferage; Bogdziewicz et al., 2020) to be generally higher during mast years than non-mast years. The opposite would be expected after mast years, when rodent abundances are high and seed production is low, with p CO approaching zero resulting in a strongly antagonistic interaction. As a result, p CO values would tend to be intermittent across a masting plant population based on mast strength and rodent population size.
An increase in seed survival during mast years is often attributed to decreased post-dispersal predation due to a decrease in the number of times a seed is recached and/or pilfered (Perez-Ramos & Maranon, 2008;Vander Wall, 2002). Essentially, more seeds are being cached than rodents need for periods of food scarcity (i.e. p CO increases). Additionally, seed harvest rates increase during mast years (Vander Wall, 2002;Xiao et al., 2005) which means more seeds are being cached in the ground during mast years than non-mast years (i.e. p H p CO increases). This decreases the effects of negative density-dependent factors (δ i ) which we argue are important when looking at the seed dispersal relationship (Section 3).
Not all of the effects of masting may be positive for the plant. Dispersal distance also changes during mast years (Jansen, Bongers, & Hemerik, 2004;Li & Zhang, 2007;Martínez & González-Taboada, 2009;Vander Wall, 2002;Xiao, Zhang, & Krebs, 2013). In cases where dispersal distance decreases, plants may face stronger negative density-dependent effects and experience reduced survival compared to seeds cached at further distances. In another example (Xiao et al., 2013), seed removal rates decreased which also likely increases negative density-dependent effects at least for the short-term. However, despite lower removal rates, overall proportion of seeds removed (ranging from 62% to 96% in Xiao et al., 2013) did not change during masting and non-masting years. Overall, there is evidence that masting has a net positive effect on plant reproduction (Jensen, 1985;Watt, 1923). Jensen (1985) was able to show that despite high seed predation during mast years, sapling age structure showed most individuals germinated the years following a mast year.
This supports the hypothesis that mast years cause plant-animal relationships to surpass p CO by either decreasing surface survival (e S δ i ), increasing the number of seeds cached and not retrieved or pilfered (p H p CO ) or increasing survival in caches (e C ). Thus, we believe that it is incorrect to assume the overall interaction from a temporally limited sample (Bogdziewicz et al., 2020;Hoshizaki & Hulme, 2002;Klinger & Rejmánek, 2010;Theimer, 2005), and would argue masting may in fact be the reason the interaction can be mutualistic.
Masting species may be poor model species when trying to elucidate the generalized or broad relationships animal-dispersed plants have with their dispersers. In a paper on masting and frugivorous birds, Herrera, Jordano, Lopez-Soria, and Amat (1994) eloquently comment on a similar point to ours that '…in recruitment, the whole is not the sum, but the product of parts, and as such, permanently susceptible to the overwhelming influence of some near to zero operand'.
In synzoochory, this is primarily due to the fact that the majority of animal-dispersed masting plants are long-lived shrubs and trees (Kelly & Sork, 2002). For a population of synzoochorous plants to persist the growth rate during any generation only needs to be positive during a single season to make the overall interaction with its disperser mutualistic. That is, p CO > e S /e C (Bogdziewicz et al., 2020). Here in eastern North America, a common seed dispersal mutualism is between the eastern grey squirrels (Sciurus carolinensis) and oaks (Quercus spp.).
One species, the red oak (Q. rubra), can live several centuries and has been recorded in natural populations at over 250 years old (Orwig, Cogbill, Foster, & O'Keefe, 2001;USDA & NRCS, 2019). The average life span of the eastern grey squirrel is 6-12 years (Koprowski, 1994) meaning an individual red oak will experience multiple generations and pines (Pinus spp.) representing a minimum of 1,300+ species (Gómez et al., 2019). Furthermore, not all mast years are equal, varying across time (Clotfelter et al., 2007;Herrera, Jordano, Guitián, & Traveset, 1998;Wolff, 1996), and to a lesser degree spatially (Curran & Leighton, 2000;Lázaro, Traveset, & Méndez, 2006). Masting may in fact only be beneficial under a very specific set of circumstances (e.g. years with relatively low seed predator abundance and relatively high seed production-see years 1992years , 1996years , and 1998years in fig. 2 of Elias et al., 2004 and may be infrequent throughout a plant's life. Lastly, abiotic factors are also an important factor that can influence the interaction between plants and animals. In the western United States many rodent species in arid and semi-arid environments can only detect and pilfer caches (effecting p CO ) under favourable soil moisture conditions (Vander Wall, 1995, 1998. One could imagine a scenario where a community experiences drier fall months during a mast year being very beneficial to a plant population as the caching rodents would be satiated (i.e. do not retrieve all caches) and cache pilferage would be low as seeds would remain mostly undetectable in the dry soils. Thus, in these years p CO would be exceptionally high.
Despite the conditions where mutualism would occur seeming obvious, Price and Jenkins (1986) perspicaciously remark that understanding the overall interaction with and without rodents would be successful in only exceptional circumstances. In The strategy of model building in population biology, Levins (1966) identified three orthogonal axes of models: realism, generality, and precision. He argued that it was impossible for a model to maximally satisfy all three, and observed that, in practise, modelling strategies tend to maximize two but sacrifice one of these axes.

| THE S TR ATEGY OF MODEL BU ILD ING TO UNDER S TAND THE ECOLOGY OF S PECIE S INTER AC TI ON S
Each strategy has its strengths and weaknesses, and ultimately all three collectively contribute to a robust understanding of the biological phenomenon in question, which in this case is the direction of species interactions broadly, and plant-seed-disperser interactions specifically. The models by Bogdziewicz et al. (2020) and Zwolak and Crone (2012) fall into the strategy of sacrificing realism for generality and precision. The models sacrifice realism by excluding many biologically relevant terms that we know affect the direction and strength of these interactions such as negative density-dependent effects (e.g. Sugiyama, Comita, Masaki, Condit, & Hubbell, 2018), animal densities (e.g. Zeng, Swihart, Zhao, Si, & Ding, 2019), interannual variation in seed densities (e.g. Bell & Clark, 2016), seed competitor densities (e.g. Masaki et al., 2019), and densities of alternative seeds (e.g. Fricke & Wright, 2017). Their models maximize generality and precision by including a few, simple, linearly proportional terms that result in a precise quantitative outcome from which a decision about the direction of the interaction could be made.
If we desire to make inferences from real ecological communities about the direction of the interaction between plants and animals that disperse and consume their seeds, then a realistic model is needed. According to Levins (1966), either generality or precision must therefore be sacrificed as a model becomes more realistic. To our knowledge, there is a dearth of realistic models that do this: this is a glaring gap in our knowledge; a gap that can and must be filled.
Precise and realistic models, like those by Price and Jenkins (1986) and Mittler (2003, 2006), are more realistic by having full biologically relevant model terms or parameter values (e.g. 40 parameters in the latter two studies), but, despite having relevant terms for determining the direction of plant-animal interactions, are focused on seed fates and animal population persistence and not the effects on plant fitness. General and realistic models focused on the qualitative outcomes of plant-seed-disperser interactions are rare.
The work by Lichti, Steele, Zhang, and Swihart (2014) is a step in this direction, as they include meaningful nonlinear terms and most of the biologically relevant terms. They do not, however, extrapolate over time to determine how their short-term data would affect plant fitness over longer periods of time. Ultimately, we must see the value in all three strategies to form a robust understanding of seed dispersal and other species interactions. Indeed, because no single strategy or model can give full insight alone, as stated by Levins (1966), '… our truth is the intersection of independent lies'.

DATA AVA I L A B I L I T Y S TAT E M E N T
No data were used in this manuscript.