Abstract: Controlling weed populations requires an understanding of their underlying population dynamics which can be achieved through a combination of model development and long-term studies. In this paper, we develop models based on long-term data from experimental populations of the weedy annual plant Cardamine pensylvanica. Four replicate populations of C. pensylvanica were grown in growth chambers under three different nutrient levels but with all other environmental conditions held constant. We analyze the resulting time series using generalized additive models and perform stability analyses using Lyapunov exponents. Further, we test whether the proposed mechanism, delayed density dependence caused by maternal effects, is operating in our system by experimentally manipulating maternal density and assessing the resulting offspring quality. Our results show that that increasing the frequency of nutrients causes plant population dynamics to shift from stable to damped 2-point oscillations to longer cycles. This shift in population dynamics is due to a shift at high nutrients from populations being regulated by first order density feedbacks to being regulated by both first order and second order density feedbacks. A consequence of these first order and second order feedbacks was an increase in cycle lengths as demonstrated by the presence of complex eigenvalues. A short-term experiment confirmed that when grown under high nutrients, the density of maternal plants strongly affected offspring size, providing a mechanism whereby these second order density feedbacks could operate. Our results demonstrate that increasing nutrient frequency results in a qualitative shift in dynamics from stable to longer cycles.
Abstract: The detrimental effects of invasive plant species on ecosystems are well documented. While much research has focused on discovering ecological inﬂuences associated with invasiveness, it remains unclear how these inﬂuences interact, causing some introduced exotic species to become invasive threats. Here we develop a framework that incorporates the inﬂuences of propagule pressure, frequency independent growth rates, feedback relationships, resource competition and spatial scale of interactions. Our results show that these ecological inﬂuences interact in complex ways, resulting in expected outcomes ranging from inability to establish, to naturalization, to conditional invasion dependent on quantity and spatial distribution of propagules, to unconditional takeover. We propose a way to predict the likelihood of these four possible outcomes, for a species recently introduced into a given target community. Such information could enable conservation biologists to craft strategies and target remediation efforts more efﬁciently and effectively in order to help maintain biodiversity in ecological communities.
Abstract: A mathematical model incorporating the effects of possibly asymmetric frequency dependent interactions is proposed. Model predictions for an idealized two-species annual plant community with asymmetric linear frequency dependence are explored using (i) analytic mean field equilibrium predictions, (ii) deterministic, discrete-time, finite-population, mean field predictions, and (iii) stochastic, discrete-time, cellular automata predictions for a variety of sizes of the spatial interaction and dispersal neighborhoods. We define species interaction factors, ranging from 0 to 1, which incorporate both frequency independent and frequency dependent terms. The maximum competitive ability of a species is reduced unless species frequency is optimal based on species-specific frequency dependence coefficients, ranging from −1 to 1. Assuming that maximum competitive ability is identical for two species, they can coexist indefinitely when they have equal absolute magnitude or both have sufficiently negative frequency dependence. Although smaller scales of spatial interactions reduce the region of the parameter space in which stable coexistence is pre- dicted, the time to extinction of one species can be significantly increased or decreased by the locality of interactions, depending on whether the losing species has positive or negative frequency dependence, respectively. The sensitivity to initial conditions in the community at large is dramatically reduced as the spatial scale of interactions is decreased. As a consequence, smaller spatial interaction neighborhoods increase the ability of introduced species to invade established communities in regions of the parameter space not predicted by mean field approximations. In the 'loser positive, winner positive' regions, smaller scales of interaction dramatically increased invasiveness. In the 'loser positive, winner negative' regions of the parameter space, invasion success decreases, but time to extinction of the resident species during successful invasions increases, with an increase in the spatial scale of interactions. The 'loser negative, winner positive' regions were relatively insensitive to initial conditions, so invasion success was relatively high at a variety of spatial scales. Surprisingly, invasions in parts of this region are most often successful with intermediate neighborhood sizes, although the maximum time that the losing species could persist before being driven to extinction increases with an increase in the spatial scale of interactions. These results are explained by understanding cluster formation and density and the relative local interspecific dynamics in cluster interiors, exteriors, and boundaries. In summary, frequency dependent interactions, and the spatial scale on which these interactions occur, can have a big impact on spatio-temporal community dynamics, with implications regarding species coexistence and invasiveness. The model proposed herein provides a theoretical frame- work for studying frequency dependent interactions that may shed light on spatio-temporal dynamics in real ecological communities.