Daniel Bearup

The input-output relationship approach to structural identifiability analysis

Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input-output relation of a model summarises the input-output structure of the whole system and as such provides the potential for an alternative approach to this analysis. However for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes.

Synchronized Dynamics of Tipula paludosa Metapopulation in a Southwestern Scotland Agroecosystem: Linking Pattern to Process

Synchronization of population fluctuations at disjoint habitats has been observed in many studies, but its mechanisms often remain obscure. Synchronization may appear as a result of either interhabitat dispersal or regionally correlated environmental stochastic factors, the latter being known as the Moran effect. In this article, we consider the population dynamics of a common agricultural pest insect, Tipula paludosa, on a fragmented habitat by analyzing data derived from a multiannual survey of its abundance in 38 agricultural fields in southwestern Scotland. We use cross-correlation coefficients and show that there is a considerable synchronization between different populations across the whole area. The correlation strength exhibits an intermittent behavior, such that close populations can be virtually uncorrelated, but populations separated by distances up to approximately 150 km can have a cross-correlation coefficient close to one. To distinguish between the effects of stochasticity and dispersal, we then calculate a time-lagged cross-correlation coefficient and show that it possesses considerably different properties to the nonlagged one. In particular, the time-lagged correlation coefficient shows a clear directional dependence. The distribution of the time-lagged correlations with respect to the bearing between the populations has a striking similarity to the distribution of wind velocities, which we regard as evidence of long-distance wind-assisted dispersal.

Indistinguishability and identifiability of kinetic models for the MurC reaction in peptidoglycan biosynthesis

An important question in Systems Biology is the design of experiments that enable discrimination between two (or more) competing chemical pathway models or biological mechanisms. In this paper analysis is performed between two different models describing the kinetic mechanism of a three-substrate three-product reaction, namely the MurC reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable; however, if standard quasi-steady-state assumptions are made distinguishability cannot be determined. Once model structure uniqueness is ensured the experimenter must determine if it is possible to successfully recover rate constant values given the experiment observations, a process known as structural identifiability. Structural identifiability analysis is carried out for both models to determine which of the unknown reaction parameters can be determined uniquely, or otherwise, from the ideal system outputs. This structural analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis.

Food web persistence in fragmented landscapes

Habitat destruction, characterized by patch loss and fragmentation, is a key driver of biodiversity loss. There has been some progress in the theory of spatial food webs; however, to date, practically nothing is known about how patch configurational fragmentation influences multi-trophic food web dynamics. We develop a spatially extended patch-dynamic model for different food webs by linking patch connectivity with trophic-dependent dispersal (i.e. higher trophic levels displaying longer-range dispersal). Using this model, we find that species display different sensitivities to patch loss and fragmentation, depending on their trophic position and the overall food web structure. Relative to other food webs, omnivory structure significantly increases system robustness to habitat destruction, as feeding on different trophic levels increases the omnivores persistence. Additionally, in food webs with a dispersal–competition trade-off between species, intermediate levels of habitat destruction can enhance biodiversity by creating refuges for the weaker competitor. This demonstrates that maximizing patch connectivity is not always effective for biodiversity maintenance, as in food webs containing indirect competition, doing so may lead to further species loss.

Robustness of metacommunities with omnivory to habitat destruction: disentangling patch fragmentation from patch loss

Habitat destruction, characterized by patch loss and fragmentation, is a major driving force of species extinction, and understanding its mechanisms has become a central issue in biodiversity conservation. Numerous studies have explored the effect of patch loss on food web dynamics, but ignored the critical role of patch fragmentation. Here we develop an extended patch-dynamic model for a tri-trophic omnivory system with trophic-dependent dispersal in fragmented landscapes. We found that species display different vulnerabilities to both patch loss and fragmentation, depending on their dispersal range and trophic position. The resulting trophic structure varies depending on the degree of habitat loss and fragmentation, due to a tradeoff between bottom-up control on omnivores (dominated by patch loss) and dispersal limitation on intermediate consumers (dominated by patch fragmentation). Overall, we find that omnivory increases system robustness to habitat destruction relative to a simple food chain.

Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data

1. Characterisation of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions, and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments. 2. Walking beetles (Tenebrio molitor ) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations. 3. We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model. 4. We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context-specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring.

A new dimension: Evolutionary food web dynamics in two dimensional trait space.

Species within a habitat are not uniformly distributed. However this aspect of community structure, which is fundamental to many conservation activities, is neglected in the majority of models of food web assembly. To address this issue, we introduce a model which incorporates a second dimension, which can be interpreted as space, into the trait space used in evolutionary food web models. Our results show that the additional trait axis allows the emergence of communities with a much greater range of network structures, similar to the diversity observed in real ecological communities. Moreover, the network properties of the food webs obtained are in good agreement with those of empirical food webs. Community emergence follows a consistent pattern with spread along the second trait axis occurring before the assembly of higher trophic levels. Communities can reach either a static final structure, or constantly evolve. We observe that the relative importance of competition and predation is a key determinant of the network structure and the evolutionary dynamics. The latter are driven by the interaction-competition and predation-between small groups of species. The model remains sufficiently simple that we are able to identify the factors, and mechanisms, which determine the final community state.

On time scale invariance of random walks in confined space.

Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour.

Multiscale ecology of agroecosystems is an emerging research field that can provide a stronger theoretical background for the integrated pest management. Reply to comments on "Multiscale approach to pest insect monitoring: random walks, pattern formation, synchronization, and networks".

We would like to thank all commentators for their insightful and thought-provoking commentaries [1–4] that also helped to further broaden the scope of our review [5] as well as to extend the list of references. We very much appreciate the positive comments on the relevance, timeliness and comprehensiveness of our work. Meanwhile, we want to emphasize that multiscale pest monitoring is an emerging research theme rather than a well-established one. Indeed, although the existence and importance of multiple scales has long been known in spatial ecology [6,7], their quantitative investigation has not started in full until relatively recently, e.g. see [8,9] and references therein. For this reason, in our review [5], several relevant aspects might have been either just touched briefly or not mentioned at all. In particular, Rebecca Tyson [1] rightfully brought attention to the importance of transient environmental factors, e.g. temperature, that may control the build-up of pest populations. The effects of temperature on the rates of insect development through their life-stages and on insect population growth are well-known [10, 11] and have been utilized in some empirical approaches used in Integrated Pest Management (IPM), e.g. in what is known as degree–day models [12,13]. Models of this type, however, are essentially based on average insect population

Evolutionary food web models: effects of an additional resource

Many empirical food webs contain multiple resources, which can lead to the emergence of sub-communities—partitions—in a food web that are weakly connected with each other. These partitions interact and affect the complete food web. However, the fact that food webs can contain multiple resources is often neglected when describing food web assembly theoretically, by considering only a single resource. We present an allometric, evolutionary food web model and include two resources of different sizes. Simulations show that an additional resource can lead to the emergence of partitions, i.e. groups of species that specialise on different resources. For certain arrangements of these partitions, the interactions between them alter the food web properties. First, these interactions increase the variety of emerging network structures, since hierarchical bodysize relationships are weakened. Therefore, they could play an important role in explaining the variety of food web structures that is observed in empirical data. Second, interacting partitions can destabilise the population dynamics by introducing indirect interactions with a certain strength between predator and prey species, leading to biomass oscillations and evolutionary intermittence.