The Modellers' Halting Foray into Ecological Theory: Or, What is This Thing Called 'Growth Rate'?

This discussion paper describes the attempt of an imagined group of non-ecologists ("Modellers") to determine the population growth rate from field data. The Modellers wrestle with the multiple definitions of the growth rate available in the literature and the fact that, in their modelling, it appears to be drastically model-dependent, which seems to throw into question the very concept itself. Specifically, they observe that six representative models used to capture the data produce growth-rate values, which differ significantly. Almost ready to concede that the problem they set for themselves is ill-posed, they arrive at an alternative point of view that not only preserves the identity of the concept of the growth rate, but also helps discriminate between competing models for capturing the data. This is accomplished by assessing how robustly a given model is able to generate growth-rate values from randomized time-series data. This leads to the proposal of an iterative approach to ecological modelling in which the definition of theoretical concepts (such as the growth rate) and model selection complement each other. The paper is based on high-quality field data of mites on apple trees and may be called a "data-driven opinion piece".

Reproductive value, sensitivity, and nonlinearity: population-management heuristics derived from classical demography.

In classical demographic theory, reproductive value and stable age distribution are proportional to the sensitivities of the asymptotic population size to changes in mortality and maternity, respectively. In this note we point out that analogous relationships hold if the maternity function is allowed to depend on the population density. The relevant formulae can essentially be obtained by replacing the growth rate ("Lotka's r") with zero. These facts may be used to derive heuristics for population management (pest control).

Simulating effects of environmental factors on biological control of Tetranychus urticae by Typhlodromus pyri in apple orchards.

Successful biological control of mites is possible under various conditions, and identifying what are the requirements for robust control poses a challenge because interacting factors are involved. Process-based modeling can help to explore these interactions and identify under which conditions biological control is likely, and when not. Here, we present a process-based model for population interactions between the phytophagous mite, Tetranychus urticae, and its predator, Typhlodromus pyri, on apple trees. Temperature and leaf nitrogen concentration influence T. urticae rates of development and reproduction, while temperature and rate of ingestion of prey and pollen influence T. pyri rates of survival and reproduction. Predator and prey population dynamics are linked through a stage structured functional response model that accounts for spatial heterogeneity in population density throughout the trees. T. urticae biomass-days (BMD's), which account for sizes of larvae, nymphs and adults, indicate level of mite-induced leaf damage. When BMD's exceed 290 per leaf, there are economic losses. When BMD's exceed 350 per leaf, T. urticae population growth is curbed and eventually the population decreases. Simulations were run to determine which conditions would lead to current year economic loss and increased risk of loss in the following year, i.e. where more T. urticae than T. pyri are present at the end of September. Risk was high with one or more of the following initial conditions: a high prey: predator ratio (10:1 or more); a low to intermediate (0.04-0.2 T. urticae per leaf) initial density; T. urticae with a higher initial proportion of adult females than T. pyri; and a delayed first detection of mites, whether in late July, or sometimes in late June, but not in early June. Warm summer weather, higher leaf nitrogen and T. urticae immigration into trees were also risk factors. Causes for these patterns based on biological characteristics of T. urticae and T. pyri are discussed, as are counter measures which can be taken to reduce risk.