Mechanistic description of population dynamics using dynamic energy budget theory incorporated into integral projection models

Abstract

Summary1. Integral projection models (IPMs) provide a powerful approach to investigate ecological and rapid evolutionary change in quantitative life-history characteristics and population dynamics. IPMs are constructed from functions that describe the demographic rates -survival, growth and reproduction -in relation to the characteristics of individuals and their environment. Currently, however, demographic rates are estimated using phenomenological regression models that lack a mechanistic representation of the biological processes that give rise to observed demographic variation. This lack of mechanistic underpinning limits the ability of the model to predict future dynamics under novel environmental conditions because the model ingredients pertain to current environmental conditions only. 2. Here, we use dynamic energy budget (DEB) theory to construct DEB-IPMs based on a mechanistic representation of individual life-history trajectories. We derive the demographic functions describing growth and reproduction from a simple DEB growth model. The functions describing mortality and the association between parent and offspring characteristics do not follow DEB theory and hence are estimated from individual-level observations. 3. We apply the DEB-IPM to two contrasting systems: the small, fast-reproducing bulb mite Rhizoglyphus robini and the large, slow-reproducing reef manta ray Manta alfredi. In both cases, predictions of population growth rate, lifetime reproductive success and generation time agree with empirical observations. In case of the bulb mite, predictions and observations even agree across different feeding conditions. 4. If the DEB energetics model is accepted as describing growth and reproduction, DEB-IPMs can be parameterised using easy-to-collect life cycle information (growth rate, length at birth, maturation and old age) making them suitable for data-deficient species. Because species differ only in these DEB parameters, comparative studies of character and population dynamics between species are straightforward, particularly since DEB-IPMs can be extended to include population feedback on resources, of which we give an example. Most crucially, because DEB theory specifies growth and reproduction rates as explicitly dependent on environmental conditions such as food availability or temperature, DEB-IPMs provide a mechanistic platform to investigate the biological processes that determine joint change in phenotypic characters, life-history traits, population size and community structure.

Trait‐based predictions and responses from laboratory mite populations to harvesting in stochastic environments

“…Predictions from the DEB‐IPM matched this overall population response, from which we infer that our cross‐level test on overall population performance was satisfactory. The model therefore likely captures the overall effect of density dependence through food exploitation very well, as population equilibrium is reached across the combinations of expected feeding levels of which we know are close to levels for which we observe population equilibrium in our experimental populations (Smallegange et al., : Appendix S1). In addition, the more general analysis of population performance across a wide range of stochastic environments showed that the pattern of a small reduction in average fitness under large‐adult harvesting persisted across different noise colours and frequencies of good environments.…”

“…For example, tools like bifurcation analysis can now be used to study model dynamics as a function of the values of these life‐history traits (e.g. Smallegange et al., : Appendix S1) so that one could e.g. ask “at what maximum length or mortality rate do abrupt changes, like from population stability to extinction, occur?” Such analyses could be particularly insightful when investigating the intricacies of life‐history effects on population dynamics.…”

“…We parameterised the DEB‐IPM using the same values as previously described (Smallegange et al., ) (Table ): we set L b = 0.166 mm, L m = 1.008 mm, κ = 0.083 and μ = 0.03 d −1 . Bulb mites are very plastic in their size at maturity in response to food conditions, so, as before, we related L p to L ∞ using the linear relationship L p = 0.539 · L ∞ , where the ultimate length L ∞ is the asymptote of the von Bertalanffy growth curve in length and represents the largest length an individual can achieve at a particular feeding level.…”

“…Because we did not know the exact feeding levels experienced by individuals in the experimental populations, we calculated the latter response variables for all pairwise combinations of low and high feeding levels where was within the range and was within the range . These values were chosen because our previous work revealed that bulb mite populations are constant and stable at a feeding level of E ( Y ) = 0.36 (Figure S5 in Smallegange et al., ). Therefore, values always elicit population growth, whereas values elicit population decline.…”

“…We harvested large adults to accurately reflect the common practice of large‐adult harvesting in hunted and commercially harvested populations (Fenberg & Roy, ; Shelton & Mangel, ). Using the parameterised DEB‐IPM (Smallegange et al., ), we simulated the experiment and projected a population forward over the same blue, red and white stochastic time series in order to predict how selectively harvesting large adults affects population structure and growth. We did not compare predictions from the DEB‐IPM with those from a standard IPM as we cannot track the fate of individual mites within populations, which is required to estimate the strength of density dependence in the statistical functions describing survival, growth and reproduction.…”