The use of mathematical modelling as a tool for investigating selected topics in conservation bio... more The use of mathematical modelling as a tool for investigating selected topics in conservation biology is the focus of this thesis. A continuous system of partial and ordinary differential equations model the age structured population dynamics of a cohort of endemic, threatened New Zealand North Island brown kiwi, Apteryx mantelli. Critical predation and recruitment rates of immature birds are estimated. Stoats, Mustela erminea, are the main predator of immature kiwi. A refinement to the model allows the calculation of acceptable stoat densities. In order to reduce stoats to this critical density, a linear system of ordinary differential equations, representing an acute secondary poisoning regime, is solved. An optimal secondary poisoning scheme, which minimises the number of prey poisoned and the amount of poison used, is found. The minimum area required for pest control is estimated by simulating the dispersal of sub-adult kiwi using a discrete random walk approach. Simulations and...
Three hypotheses — demographic and competitive ascendancy, genetic assimilation, and habitat dest... more Three hypotheses — demographic and competitive ascendancy, genetic assimilation, and habitat destruction and disturbance — have been advanced to explain the demise of the gray duck and rise of the mallard in New Zealand subsequent to the introduction of the mallard a century ago. We modelled relative population change over the past 50-60 years, based on hunter kills, and evaluated the competing hypotheses. We conclude that capacity for survival, greater fecundity and productivity, physical domination of gray duck, and willingness to exploit novel feeding opportunities in man-disturbed environments, have contributed most to the present numerical dominance of the mallard. An apparently extensive hybrid swarm may be dominated by a mallard phenotype, but evaluation of genetic exchange based on phenotype alone remains problematic. Gray ducks and the gray duck phenotype may soon disappear from New Zealand.
Proceedings of International Structural Engineering and Construction, 2020
There has been much publicity about New Zealand houses having indoor temperatures below World Hea... more There has been much publicity about New Zealand houses having indoor temperatures below World Health Organization standards and how insulation can benefit the health and comfort of the occupants. Landlords are required to install underfloor and ceiling insulation. In Christchurch, in some council flats, it has been suggested that commercial insulation is not practical and too expensive to retrofit, and tenants have been asked to use bubble wrap on windows. So, does bubble wrap actually improve interior comfort? In this study, air temperatures were measured in a typical New Zealand, three bedrooms, 100 m2, 1960s house. A heat-pump in the living room was set to heat to 18 °C. Bubble wrap was applied to bedroom windows during the winter and spring of 2019. Temperatures were compared to 2016 data, which was prior to the installation of the bubble wrap. Regression analysis was employed to determine if the bubble-wrap had any effect on air temperature by either reducing variability or imp...
Sitona obsoletus is a serious pasture pest in New Zealand where its rootfeeding larvae reduce whi... more Sitona obsoletus is a serious pasture pest in New Zealand where its rootfeeding larvae reduce white clover cover and nitrogen fixation To maintain production farmers may compensate by increasing inputs The parasitic wasp Microctonus aethiopoides Loan was introduced for biological control of S obsoletus and achieved parasitism rates exceeding 70 In Southland where S obsoletus was first detected in 2010 unusually severe and prolonged infestations during 2013 and 2014 prompted intensive biological control releases in 2014 and 2015 This study evaluated if they were cost effective in 2015 On dairy farms biological control returned 1478/ha/year or 23 million over the 158017 ha On sheep and beef farms the estimated return was 686/ha/year or 47 million over 719854 ha Monte Carlo simulations were used to estimate returns (/ha/year) using plausible ranges of model parameter values and returns were positive in at least 975 of simulations Biological control of S obsoletus has returned a net ben...
Journal of Information Technology Education: Innovations in Practice, 2018
Aim/Purpose: To identify positive and negative aspects for learning of interactive tablet technol... more Aim/Purpose: To identify positive and negative aspects for learning of interactive tablet technology learning activities that promote student engagement and learning. Background: Engaging students in mathematics classes is an on-going challenge for teachers. In 2008 we were offered the opportunity to run interactive activities with a class set of tablet PCs that had just been released on to the market. Since then, we have run these interactive activities continuously with mathematics classes for computing students, albeit with two changes in hardware. Methodology: In the interactive activities, students submit full worked solutions to various problem types (classified as table, text, open or multi-choice) which can then be displayed to the class anonymously, discussed and annotated by the teacher. We surveyed student and staff perceptions and monitored academic performance. Contribution: We have over 10 years of results, observations, and experience from 2008, when tablet technologi...
Defoliation has frequently been proposed as a means of controlling Cirsium arvense (L.) Scop. (Ca... more Defoliation has frequently been proposed as a means of controlling Cirsium arvense (L.) Scop. (Californian thistle, Canada thistle, creeping thistle, perennial thistle), an economically damaging pastoral weed in temperate regions of the world, but its optimization has remained obscure. We developed a matrix model for the population dynamics of C. arvense in sheep-grazed pasture in New Zealand that accounts for the effects of aerial shoot defoliation on a population's photosynthetic opportunity and consequential overwintered root biomass, enabling mowing regimes varying in the seasonal timing and frequency of defoliation to be compared. The model showed that the long-term population dynamics of the weed is influenced by both the timing and frequency of mowing; a single-yearly mowing, regardless of time of year, resulted in stasis or population growth, while in contrast, 14 of 21 possible twice-yearly monthly mowing regimes, mainly those with mowing in late spring, summer, and ear...
SummaryThe weedy grass Nassella trichotoma (nassella tussock), historically an economically damag... more SummaryThe weedy grass Nassella trichotoma (nassella tussock), historically an economically damaging invader of modified tussock grasslands in New Zealand, currently causes little if any reduction in farm production. This is a result of successful historical regional management programmes in which plants have been removed manually (by grubbing) each year before they seed. To inform a debate about the need for ongoing regional management, we developed a stage‐structured spatially explicit integrodifference equation population model and linked this to a cost analysis. We used the model to compare the weed's future population trajectories and related regional control costs over 50 years under three alternative management scenarios. The total discounted (3% p.a.) costs of no management, three‐yearly grubbing and continued annual grubbing were NZ $417 million, $736 million and $131 million respectively. These analyses indicate that annual grubbing of N. trichotoma returns a net benef...
In this paper we present an overview of the work undertaken to model a population of cells and th... more In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis ...
An age-structured population analysis is used to determine recruitment levels and a condition for... more An age-structured population analysis is used to determine recruitment levels and a condition for survival which can assist management decisions and hence improve the viability of populations of northern brown kiwi, Apteryx mantelli, in forests on the New Zealand mainland. Currently, in the absence of predator control, recruitment rates are less than 5% due to high levels of stoat, Mustela erminea, predation on juvenile kiwi. Predation levels on adult kiwi are very low. The analysis predicts that a recruitment rate of 19% is required to maintain population stability. To achieve this target, stoat populations have to be reduced by about 80% in some years, and maintained at a critical residual density estimated to be a value less than two animals per square kilometre for up to nine months until immature kiwi reach a safe size of about 1200 g (50% of their adult weight). Recent predator-control initiatives indicate that stoat numbers can be reduced and maintained at low levels in relat...
IMA Journal of Mathematics Applied in Medicine & Biology (1997) 14, 241-250 Preda... more IMA Journal of Mathematics Applied in Medicine & Biology (1997) 14, 241-250 Predation thresholds for survival of endangered species B. BASSE AND GC WAKE! Mathematics Department, University of Auckland-Tamaki Campus, Private Bag 92019, Auckland, New Zealand ...
There is increasing evidence that the growth of human tumours is driven by a small proportion of ... more 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.
The use of mathematical modelling as a tool for investigating selected topics in conservation bio... more The use of mathematical modelling as a tool for investigating selected topics in conservation biology is the focus of this thesis. A continuous system of partial and ordinary differential equations model the age structured population dynamics of a cohort of endemic, threatened New Zealand North Island brown kiwi, Apteryx mantelli. Critical predation and recruitment rates of immature birds are estimated. Stoats, Mustela erminea, are the main predator of immature kiwi. A refinement to the model allows the calculation of acceptable stoat densities. In order to reduce stoats to this critical density, a linear system of ordinary differential equations, representing an acute secondary poisoning regime, is solved. An optimal secondary poisoning scheme, which minimises the number of prey poisoned and the amount of poison used, is found. The minimum area required for pest control is estimated by simulating the dispersal of sub-adult kiwi using a discrete random walk approach. Simulations and...
Three hypotheses — demographic and competitive ascendancy, genetic assimilation, and habitat dest... more Three hypotheses — demographic and competitive ascendancy, genetic assimilation, and habitat destruction and disturbance — have been advanced to explain the demise of the gray duck and rise of the mallard in New Zealand subsequent to the introduction of the mallard a century ago. We modelled relative population change over the past 50-60 years, based on hunter kills, and evaluated the competing hypotheses. We conclude that capacity for survival, greater fecundity and productivity, physical domination of gray duck, and willingness to exploit novel feeding opportunities in man-disturbed environments, have contributed most to the present numerical dominance of the mallard. An apparently extensive hybrid swarm may be dominated by a mallard phenotype, but evaluation of genetic exchange based on phenotype alone remains problematic. Gray ducks and the gray duck phenotype may soon disappear from New Zealand.
Proceedings of International Structural Engineering and Construction, 2020
There has been much publicity about New Zealand houses having indoor temperatures below World Hea... more There has been much publicity about New Zealand houses having indoor temperatures below World Health Organization standards and how insulation can benefit the health and comfort of the occupants. Landlords are required to install underfloor and ceiling insulation. In Christchurch, in some council flats, it has been suggested that commercial insulation is not practical and too expensive to retrofit, and tenants have been asked to use bubble wrap on windows. So, does bubble wrap actually improve interior comfort? In this study, air temperatures were measured in a typical New Zealand, three bedrooms, 100 m2, 1960s house. A heat-pump in the living room was set to heat to 18 °C. Bubble wrap was applied to bedroom windows during the winter and spring of 2019. Temperatures were compared to 2016 data, which was prior to the installation of the bubble wrap. Regression analysis was employed to determine if the bubble-wrap had any effect on air temperature by either reducing variability or imp...
Sitona obsoletus is a serious pasture pest in New Zealand where its rootfeeding larvae reduce whi... more Sitona obsoletus is a serious pasture pest in New Zealand where its rootfeeding larvae reduce white clover cover and nitrogen fixation To maintain production farmers may compensate by increasing inputs The parasitic wasp Microctonus aethiopoides Loan was introduced for biological control of S obsoletus and achieved parasitism rates exceeding 70 In Southland where S obsoletus was first detected in 2010 unusually severe and prolonged infestations during 2013 and 2014 prompted intensive biological control releases in 2014 and 2015 This study evaluated if they were cost effective in 2015 On dairy farms biological control returned 1478/ha/year or 23 million over the 158017 ha On sheep and beef farms the estimated return was 686/ha/year or 47 million over 719854 ha Monte Carlo simulations were used to estimate returns (/ha/year) using plausible ranges of model parameter values and returns were positive in at least 975 of simulations Biological control of S obsoletus has returned a net ben...
Journal of Information Technology Education: Innovations in Practice, 2018
Aim/Purpose: To identify positive and negative aspects for learning of interactive tablet technol... more Aim/Purpose: To identify positive and negative aspects for learning of interactive tablet technology learning activities that promote student engagement and learning. Background: Engaging students in mathematics classes is an on-going challenge for teachers. In 2008 we were offered the opportunity to run interactive activities with a class set of tablet PCs that had just been released on to the market. Since then, we have run these interactive activities continuously with mathematics classes for computing students, albeit with two changes in hardware. Methodology: In the interactive activities, students submit full worked solutions to various problem types (classified as table, text, open or multi-choice) which can then be displayed to the class anonymously, discussed and annotated by the teacher. We surveyed student and staff perceptions and monitored academic performance. Contribution: We have over 10 years of results, observations, and experience from 2008, when tablet technologi...
Defoliation has frequently been proposed as a means of controlling Cirsium arvense (L.) Scop. (Ca... more Defoliation has frequently been proposed as a means of controlling Cirsium arvense (L.) Scop. (Californian thistle, Canada thistle, creeping thistle, perennial thistle), an economically damaging pastoral weed in temperate regions of the world, but its optimization has remained obscure. We developed a matrix model for the population dynamics of C. arvense in sheep-grazed pasture in New Zealand that accounts for the effects of aerial shoot defoliation on a population's photosynthetic opportunity and consequential overwintered root biomass, enabling mowing regimes varying in the seasonal timing and frequency of defoliation to be compared. The model showed that the long-term population dynamics of the weed is influenced by both the timing and frequency of mowing; a single-yearly mowing, regardless of time of year, resulted in stasis or population growth, while in contrast, 14 of 21 possible twice-yearly monthly mowing regimes, mainly those with mowing in late spring, summer, and ear...
SummaryThe weedy grass Nassella trichotoma (nassella tussock), historically an economically damag... more SummaryThe weedy grass Nassella trichotoma (nassella tussock), historically an economically damaging invader of modified tussock grasslands in New Zealand, currently causes little if any reduction in farm production. This is a result of successful historical regional management programmes in which plants have been removed manually (by grubbing) each year before they seed. To inform a debate about the need for ongoing regional management, we developed a stage‐structured spatially explicit integrodifference equation population model and linked this to a cost analysis. We used the model to compare the weed's future population trajectories and related regional control costs over 50 years under three alternative management scenarios. The total discounted (3% p.a.) costs of no management, three‐yearly grubbing and continued annual grubbing were NZ $417 million, $736 million and $131 million respectively. These analyses indicate that annual grubbing of N. trichotoma returns a net benef...
In this paper we present an overview of the work undertaken to model a population of cells and th... more In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis ...
An age-structured population analysis is used to determine recruitment levels and a condition for... more An age-structured population analysis is used to determine recruitment levels and a condition for survival which can assist management decisions and hence improve the viability of populations of northern brown kiwi, Apteryx mantelli, in forests on the New Zealand mainland. Currently, in the absence of predator control, recruitment rates are less than 5% due to high levels of stoat, Mustela erminea, predation on juvenile kiwi. Predation levels on adult kiwi are very low. The analysis predicts that a recruitment rate of 19% is required to maintain population stability. To achieve this target, stoat populations have to be reduced by about 80% in some years, and maintained at a critical residual density estimated to be a value less than two animals per square kilometre for up to nine months until immature kiwi reach a safe size of about 1200 g (50% of their adult weight). Recent predator-control initiatives indicate that stoat numbers can be reduced and maintained at low levels in relat...
IMA Journal of Mathematics Applied in Medicine & Biology (1997) 14, 241-250 Preda... more IMA Journal of Mathematics Applied in Medicine & Biology (1997) 14, 241-250 Predation thresholds for survival of endangered species B. BASSE AND GC WAKE! Mathematics Department, University of Auckland-Tamaki Campus, Private Bag 92019, Auckland, New Zealand ...
There is increasing evidence that the growth of human tumours is driven by a small proportion of ... more 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.
Uploads
Papers by Britta Basse