Using experiments, demography and population models to estimate interaction strength based on transient and asymptotic dynamics


  • John L. Maron,

    Corresponding author
    1. Division of Biological Sciences, University of Montana, Missoula, MT 59812, USA
      Correspondence author. E-mail: john.maron@mso.umt.eud
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  • Carol C. Horvitz,

    1. Department of Biology, University of Miami, PO Box 249118, Coral Gables, FL 33124, USA
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  • Jennifer L. Williams

    1. National Center for Ecological Analysis and Synthesis, University of California – Santa Barbara, 735 State Street, Suite 300, Santa Barbara, CA 93101, USA
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Correspondence author. E-mail: john.maron@mso.umt.eud


1. Despite a large literature documenting the effects of mutualists and/or antagonists on plant performance, we still have limited insight into the strength of these interactions, as this involves quantifying how one species influences the population dynamics of another.

2. Here, we use data from two example systems, Cynoglossum officinale and Calathea ovandensis, to illustrate how experiments, demographic data and stage-based population models can be combined to estimate interaction strength of insect herbivores on plants. Because many plant populations may not be at equilibrium, we conduct transient analyses and contrast these results to more traditional asymptotic results.

3. We calculate three metrics of interaction strength, Δλasymptotic, the change in asymptotic annual per capita plant population growth rate resulting from herbivore exclusion, Δλ(t), the change in transient λ caused by herbivores at M (where M = the time of their maximum effect during the transient phase) and Δλtransient, a time-averaged effect of consumers on λ across the entire transient phase.

4. Fairly strong impacts of insect consumers on plant fecundity do not translate similarly to Δλasymptotic. Results show that Δλ(t) can be larger (or smaller) than Δλasymptotic but in our examples Δλtransient was similar in magnitude to Δλasymptotic.

5. The transient effects of consumers on λ were driven by changes in the elasticity of fecundity across the transient phase. These effects were dynamic even though consumer impacts on demography and vital rates were held constant. The importance of particular stages and transitions to annual population growth vary during the transient phase.

6.Synthesis. We describe three metrics of interaction strength, Δλasymptotic, Δλ(t) and Δλtransient. These metrics have several advantages over more commonly used trait or performance measures that quantify the outcome of interactions. We illustrate how the transient impacts of consumers on λ are dynamic, with the changing stage distribution of a population and transient elasticities driving these effects. More generally, this study shows that the impacts of animals on plant performance do not translate equivalently to plant population growth, thereby underscoring the importance of using population models to extend the inference of individual-level experiments.