The results described above show how phenotypic plasticity of a resident species can effectively act as a barrier to invasion. Clearly if phenotypic plasticity increases fitness (including offsetting effects of costs to plasticity), then plasticity will increase an invading species ability to invade [18
] or a resident species ability to retard invasions. This expected result was evident by comparing the NPP-resident/NPP-invader case to the NPP-resident/PP-invader or PP-resident/NPP-invader cases. However, our analysis uncovers an additional and unforeseen effect of plasticity when we compare the case in which both invader and resident were plastic to the case in which both resident and invader were not plastic. When both residents and invaders are plastic, an invader individual may be near
the optimal strategy in regards to trait expression (e.g., probability to eat related to foraging behavior), but because it is not at
the optimal strategy, it will nevertheless be at a large fitness disadvantage due to the steep fitness landscape induced by phenotypic plasticity, and it will therefore die before reproduction. In contrast, when both residents and invaders are not plastic, an invader that is near the optimal behavioral strategy in regards to trait expression is not at a large fitness disadvantage and is much more likely to gain resources, reproduce, and displace the resident. The effect of phenotypic plasticity therefore has a profound effect on invasion through its effect on the fitness surface.
What is the origin of the large difference in the steepness of the fitness surface with, and without, phenotypic plasticity? Without plasticity, an optimal strategy must balance tradeoffs associated with exhibiting the same phenotype as an environmental factor fluctuates, in our case predator density. Deviations from this strategy will necessarily have opposing effects on overall fitness, which will reduce the net effect. Although similar opposing effects may result from deviations from the evolved behavior with phenotypic plasticity, because strategies are optimized to a particular environmental state (rather than balancing contrasting demands of different states), any deviations will generally have a stronger net negative effect on fitness. For example, in our computational model experiments for PP-consumers, eating with a lower probability in predator absence than the optimal (evolved) strategy will negatively affect fitness with no associated benefit. In contrast, for NPP-consumers, eating less than the optimal strategy will lead to less energy gain, but this negative effect will be opposed by lower predator risk associated with the strategy in predator presence.
The key elements of our model are: (1) competition by the two species for a resource, (2) a variable environment, and (3) a plastic trait that is modified in an adaptive manner in response to this variability. Competition between a resident and an invader is to be expected; environmental variability is ubiquitous; and phenotypic plasticity is widespread in nature. Whereas our investigation uses a variable predation risk and the behavior of consumers in response to this particular aspect of environmental fluctuations, we expect similar results can occur in any other system that includes the above three elements. Further, whereas these arguments suggest generality of the patterns revealed by our individual-based modeling approach, other methods amenable to analysis, such as game theory [29
], adaptive dynamics [30
], and incorporation of phenotypic plasticity into traditional differential equation–based food web models [32
], may offer promising approaches to address this problem analytically.
There are several approaches that can be taken to empirically evaluate the theoretical prediction proposed here. First, an experimental design analogous to the model design could be used by comparing dynamics of a plastic resident–invader pair in two experimental arenas: one that allows the plastic behavior, and the second that constrains the resident–invader pair to a non-plastic phenotype, thereby mimicking non-plastic species. Methods used effectively previously could be used to simulate predator-induced phenotypic changes and predation [13
]. One example is provided for a system with zooplankton consumers that respond to predator kairomones (i.e., chemical cues) by migrating deeper at the cost of reduced growth rate due to colder temperatures [35
] (Text S3
). Second, in systems in which it is not possible to constrain plasticity, it may be possible to combine an empirical examination of plasticity's affect on the fitness landscape with a dynamical model. For example, Stinchcombe and Schmitte [28
] (see also [36
]) measured fitness of the herbaceous Impatiens capensis
as a function of hypocotyl length in bare soil and leaf litter. Using these empirically derived data, they constructed a fitness landscape for I. capensis
that experiences variability in leaf litter as a function of encounter frequencies of the two environmental states. This type of derivation could be combined with dynamical models to examine the effect of plasticity on invasion success. Third, invasion properties of species with plastic and fixed (i.e., non-plastic) responses to environmental variation could be compared experimentally. For example, in zooplankton prey communities, some species respond to predator presence through vertical migration, whereas others do not. Lastly, an analysis of invasions by exotic species, in which systems with plastic and non-plastic invader–resident pairs are compared, could yield insight into this prediction. Note that this latter method is distinct from comparing the degree of plasticity of invaders to that of residents or noninvasive exotics [18
Our theoretical results have clear extensions to the stability of species interactions in general, and consequently to species coexistence and biodiversity. The increase in steepness of the fitness surface caused by phenotypic plasticity will have a destabilizing effect on competitor coexistence at a local scale, because small differences in traits will have much larger effects on fitness. Indeed, this predicted effect on competition is evident in the invasion simulations in which coexistence periods were more pronounced with NPP-invader/NPP-resident pairs. When invasion in the PP-invader/PP-resident case occurred, there was an initial period of low invader density, maintained by pressure from introduced individuals, followed by a fast increase in density and exclusion of the resident. In contrast, in cases of similar invasion time with NPP-invader/NPP-residents, density initially increased steadily followed by long periods of intermediate densities of both the invader and resident. Thus, due to fitness landscape steepness differences, coexistence was much less stable with plasticity than without plasticity. Conversely, the model results predict that phenotypic plasticity will have a stabilizing effect at a larger regional scale (i.e., heterogeneous habitats), because phenotypic plasticity of species that respond adaptively to local variable environmental factors will increase resistance to invasion from the larger regional pool. Our results on invasions, and extensions to competition, thus have implications for the relationship between regional and local patterns of species distributions, e.g., metacommunities [6
Our results exemplify how using an individual-based computational approach [19
] can elucidate how individual-level behavior generates macroscopic patterns at the community level. Although very simple in representation, the state dependence of an individual's behavioral strategy had a profound effect on invasion at the community level. Importantly, the stabilizing mechanism involving the fitness surface was unforeseen and discovered as we were exploring the parameter spaces [38
]. Additional research now can be carried out to examine the generality of the mechanism, and whether and how the mechanism extends to higher-dimensional systems, thus influencing patterns of food web structure and biodiversity.
Phenotypic plasticity and evolution operate on different time scales (plasticity within generations and evolution across generations) but are fundamentally similar in the manner that traits change adaptively to environmental change. Therefore some study results based on evolutionary changes can be extended to predict effects of phenotypic plasticity. Evolution of traits is predicted to reduce competition and increase coexistence of competitors [33
]. Generalizing this result to the effect of phenotypic plasticity suggests that phenotypic plasticity could increase the probability of invasion by reorganizing the food web in a way that increases likelihood of survival of a new species. The process responsible for this predicted effect of plasticity is distinct from that involving the fitness landscape steepness examined in the present study.
The search for ecosystem properties that affect invasions is an intensively studied discipline. For example, environmental variability has been argued to increase species invasions because it can provide footholds, or extend niche space [41
]. Further, biodiversity is hypothesized to impede invasions by reducing the niche widths or resource levels available to invaders [43
]. Our study is distinct from these studies by considering the invasion process over longer time periods and adaptation to many cycles of environmental change.
In summary, our results suggest that phenotypically plastic responses to a dynamic environment can strongly impact invasion, coexistence, and therefore biodiversity. Factors that affect species invasions and coexistence are fundamental to ecological communities [46
], in part because such factors underlie the extraordinary biodiversity of natural systems, and have implications for management of ecosystems. Our study provides an additional mechanism based on adaptive responses to environmental variability that can potentially affect species interactions and invasion.