Britta Basse

Recovery and maintenance of North Island kokako (Callaeas cinerea wilsoni) populations through pulsed pest control

Abstract Kokako ( Callaeas cinerea wilsoni ) population recovery on the North Island of New Zealand depends primarily on control of key introduced mammal pests, especially ship rats ( Rattus rattus ) and brushtail possums ( Trichosurus vulpecula ). Recovery can still occur if pest control is pulsed (x years ‘on’; y years ‘off’) because kokako sub-adults and adults are generally long-lived, although chick production is high only during ‘on’ years. Pulsing effort means that conservation resources can be extended to other sites or problems during ‘off’ years; that toxin input at any one site is reduced; and that project staff do not burn out by repeatedly working at a site. Mathematical modelling supports empirical evidence that pests need not be controlled every year in order to maintain or greatly increase kokako populations. It predicts that the total number of years during which there is pest control is the main factor determining population size. Three years of pest control in each 10 should be sufficient to at least maintain a population with 20 females when mean parameters apply, but pulsed control should still be effective with very pessimistic parameters. In the safest strategies, control should occur in minimum pulses of 2–3 years to avoid single poor years when few breeding attempts are made. Very small populations should first be increased to at least 20 females by translocation or continuous pest control. This will greatly reduce the probability of chance extinction, and increase the efficiency of subsequent pest control. The model will apply best to closed kokako populations below carrying capacity, in which pests are controlled over the entire block. Empirical data on the effects of habitat carrying capacity on kokako dispersal, and on the importance of stoats as predators of adult females are required to further strengthen the model.

Using a stem cell and progeny model to illustrate the relationship between cell cycle times of in vivo human tumour cell tissue populations, in vitro primary cultures and the cell lines derived from them.

There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1-3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor-product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.

Mathematical Determination of Cell Population Doubling Times for Multiple Cell Lines

Cell cycle times are vital parameters in cancer research, and short cell cycle times are often related to poor survival of cancer patients. A method for experimental estimation of cell cycle times, or doubling times of cultured cancer cell populations, based on addition of paclitaxel (an inhibitor of cell division) has been proposed in literature. We use a mathematical model to investigate relationships between essential parameters of the cell division cycle following inhibition of cell division. The reduction in the number of cells engaged in DNA replication reaches a plateau as the concentration of paclitaxel is increased; this can be determined experimentally. From our model we have derived a plateau log reduction formula for proliferating cells and established that there are linear relationships between the plateau log reduction values and the reciprocal of doubling times (i.e. growth rates of the populations). We have therefore provided theoretical justification of an important experimental technique to determine cell doubling times. Furthermore, we have applied Monte Carlo experiments to justify the suggested linear relationships used to estimate doubling time from 5-day cell culture assays. We show that our results are applicable to cancer cell populations with cell loss present.

A NONLINEAR MODEL OF AGE AND SIZE-STRUCTURED POPULATIONS WITH APPLICATIONS TO CELL CYCLES

The Sharpe�Lotka�McKendrick (or von Foerster) equations for an age-structured population, with a nonlinear term to represent overcrowding or competition for resources, are considered. The model is extended to include a growth term, allowing the population to be structured by size or weight rather than age, and a general solution is presented. Various examples are then considered, including the case of cell growth where cells divide at a given size.

Modelling biological invasions over homogeneous and inhomogeneous landscapes using level set methods

The establishment, spread and subsequent degradation of existing environments by invasive species is a worldwide problem affecting native and agricultural ecosystems. The phenomenal cost to governments as a result of research and eradication or control drives the need to understand invasion characteristics. In this paper we develop a method for modelling the boundary of an invasion over time with model inputs being the initial distribution of the invasion and the speed at which the invasion front moves over time. This speed function can depend on the topography of the ground cover and we consider examples of homogeneous and inhomogeneous spread. The possibility of a long-distance dispersal event occurring is also considered. In particular, examples of the spread of emergent weeds and weeds which favour creeks and river beds in New Zealand are presented.