Evaluating consumptive and nonconsumptive predator effects on prey density using field time‐series data

Abstract

Determining the degree to which predation affects prey abundance in natural communities constitutes a key goal of ecological research. Predators can affect prey through both consumptive effects (CEs) and nonconsumptive effects (NCEs), although the contributions of each mechanism to the density of prey populations remain largely hypothetical in most systems. Common statistical methods applied to time‐series data cannot elucidate the mechanisms responsible for hypothesized predator effects on prey density (e.g., differentiate CEs from NCEs), nor can they provide parameters for predictive models. State‐space models (SSMs) applied to time‐series data offer a way to meet these goals. Here, we employ SSMs to assess effects of an invasive predatory zooplankter, Bythotrephes longimanus, on an important prey species, Daphnia mendotae, in Lake Michigan. We fit mechanistic models in an SSM framework to seasonal time series (1994–2012) using a recently developed, maximum‐likelihood–based optimization method, iterated filtering, which can overcome challenges in ecological data (e.g., nonlinearities, measurement error, and irregular sampling intervals). Our results indicate that B. longimanus strongly influences D. mendotae dynamics, with mean annual peak densities of B. longimanus observed in Lake Michigan estimated to cause a 61% reduction in D. mendotae population growth rate and a 59% reduction in peak biomass density. Further, the observed B. longimanus effect is most consistent with an NCE via reduced birth rates. The SSM approach also provided estimates for key biological parameters (e.g., demographic rates) and the contribution of dynamic stochasticity and measurement error. Our study therefore provides evidence derived directly from survey data that the invasive zooplankter B. longimanus is affecting zooplankton demographics and offer parameter estimates needed to inform predictive models that explore the effect of B. longimanus under different scenarios, such as climate change.

A skewed literature: Few studies evaluate the contribution of predation‐risk effects to natural field patterns

“…Prior to our review we were aware of a few PLP risk‐effect studies, and we use two here to illustrate their implementation (see Discussion for further examples). First, Marino et al (2019) examined a 20‐year time series of Daphnia density in Lake Michigan that was collected as part of a National Oceanic and Atmospheric Administration survey programme. They used state‐space models with predator–prey equations that differentiated the consumptive effects and NCEs of the predatory cladoceran Bythotrephes on Daphnia population growth rate and abundance.…”

Long‐term survey data reveal large predator and temperature effects on population growth of multiple zooplankton species

“…For example, our results do not distinguish between the relative contributions of B. longimanus CEs and NCEs to changes in estimated growth rate, although estimates for both B. longimanus consumption requirements (Pothoven and Vanderploeg ) and reductions in population growth due to NCEs (Pangle et al ) suggest that both mechanisms may contribute. These findings should therefore motivate and inform future work using approaches (e.g., state–space models, Marino et al ) that allow for explicit tests of hypothesized mechanisms (e.g., differential effects of water column temperature structure on CEs and NCEs) underlying effects found here.…”

“…We think this confounding factor is likely responsible for a large part of the negative effect of density, as is highlighted by the fact that an effect of density was observed even for several species that occur at relatively low densities (e.g., S. oregensis ). Other approaches that can explicitly account for the influence of measurement error (e.g., state–space models, Newman et al ; Marino et al ) as well as other factors not considered here (e.g., stage‐structure, water column structure, interspecific competition, predator–prey feedbacks, multiple predators) should be useful to more directly and mechanistically assess the impact of density and other factors on dynamics.…”

Bagged filters for partially observed interacting systems

“…Plug-and-play inference algorithms based on sequential Monte Carlo likelihood evaluation has proved successful for investigating highly nonlinear partially observed dynamic systems of low dimension arising in analysis of epidemiological and ecological time series data Bretó (2018); Pons-Salort and Grassly (2018); de Cellès et al (2018); Marino et al (2018). A benefit of the plug-and-play property is that it facilitates development of broadly applicable software, which in turn promotes creative scientific model development Bretó et al (2009); He et al (2010).…”