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Estimates of tree heartwood and sapwood profiles are important in the pulp industry and for dynamic vegetation models in which they determine tree biomechanical stability and hydraulic conductivity. Several phenomenological models of stem profiles have been developed for this purpose, based on assumptions on how tree crown and foliage distributions change over time. Here, we derive estimates of tree profiles by synthesizing simple pipe model theory of plant form with a recently developed theory of branch thinning that from simple assumptions quantify discarded branches and leaves. This allows us to develop a new trunk model of tree profiles from breast height up to the top of the tree. We postulate that leaves which are currently on the tree are connected by sapwood pipes while pipes that previously connected discarded leaves or branches form the heartwood. By assuming that a fixed fraction of all pipes remains on the trunk after a branching event, as the trunk is traversed from the root system to the tips, this allows us to quantify trunk heartwood and sapwood profiles. We test the trunk model performance on empirical data from five tree species across three continents. We find that the trunk model accurately describes heartwood and sapwood profiles of all tested tree species (calibration; $R2$: 84–99%). Furthermore, once calibrated to a tree species, the trunk model predicts heartwood and sapwood profiles of conspecific trees in similar growing environments based only on the age and height of a tree (cross-validation/prediction; $R2$: 68–98%). The fewer and often contrasting parameters needed for the trunk model, makes it a potential useful complementary tool for biologists and the foresters.

Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.

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