2013, 10(3): 691-704. doi: 10.3934/mbe.2013.10.691

An example from the world of tsetse flies

1. 

SACEMA, (DST/NRF Centre of Excellence, in Epidemiological Modelling and Analysis), 19 Jonkershoek Road,Stellenbosch 7600, South Africa

Received  October 2012 Revised  January 2013 Published  April 2013

In biomathematics, communication between mathematicians and biologists is crucial. This matter is illustrated using studies aimed at estimating mortality rates of tsetse flies (Glossina spp.). Examples are provided of apparently sound pieces of mathematics which, when applied to real data, provide obviously erroneous results. More serious objections arise when mathematical models make no attempt to address the real world in such a way that they can be tested. Unless models account for the known biology of the problem under investigation, and are challenged with data, the existence and nature of imperfections in the models will likely not be detected.
Citation: John Hargrove. An example from the world of tsetse flies. Mathematical Biosciences & Engineering, 2013, 10 (3) : 691-704. doi: 10.3934/mbe.2013.10.691
References:
[1]

G. Caughley, "Analysis of Vertebrate Populations,", John Wiley & Sons, (1977).

[2]

A. Challier, Amélioration de la méthode de détermination de l'âge physiologique des glossines. Études faites sur Glossina palpalis palpalis Vanderplank, 1949,, Bulletin de la Société de Pathologie Exotique, 58 (1965), 250.

[3]

C. F. Curtis and A. M. Jordan, Calculations on the productivity of Glossina austeni Newst.maintained on goats and on lop-eared rabbits,, Bulletin of Entomological Research, 59 (1968), 651.

[4]

R. D. Dransfield, R. Brightwell, J. Kiilu, M. F. Chaudhury and D. A. Adabie, Size and mortality rates of Glossina pallidipes in the semi-arid zone of southwestern Kenya,, Medical and Veterinary Entomology, 3 (1989), 83.

[5]

J. W. Hargrove, Age-dependent changes in the probabilities of survival and capture of the tsetse fly Glossina morsitans morsitans Westwood,, Insect Science and its Application, 11 (1990), 323.

[6]

J. W. Hargrove, Age-dependent sampling biases in tsetse flies (Glossina). Problems associated with estimating mortality from sample age distributions,, in, (1993), 549.

[7]

J. W. Hargrove, Lifetime changes in the nutritional characteristics of female tsetse flies Glossina pallidipes caught in odour-baited traps,, Medical and Veterinary Entomology, 13 (1999), 165.

[8]

J. W. Hargrove, Reproductive abnormalities in field tsetse flies in Zimbabwe,, Entomologia Experimentalis et Applicata, 92 (1999), 89.

[9]

J. W. Hargrove, Factors affecting density-independent survival of an island population of tsetse flies in Zimbabwe,, Entomologia Experimentalis et Applicata, 100 (2001), 151. doi: 10.1046/j.1570-7458.2001.00858.x.

[10]

J. W. Hargrove, Tsetse eradication; sufficiency, necessity and desirability,, DFID Animal Health Programme, (2003).

[11]

J. W. Hargrove, "Everybody lies". [But thinking about all the data might get you to the truth]. An example from tsetse biology,, PowerPoint Presentation of a Talk Delivered at: Mathematical Methods in Systems Biology and Population Dynamics (4-7 January 2012, (2012), 4.

[12]

J. W. Hargrove, R. Ouifki and J. E. Ameh, A general model for mortality in adult tsetse (Glossina spp.),, Medical and Veterinary Entomology, 25 (2011), 385.

[13]

M. Jarry, J. P. Gouteux and M. Khaladi, Are tsetse fly populations close to equilibrium?,, Acta Biotheoretica, 44 (1996), 317. doi: 10.1007/BF00046536.

[14]

M. Jarry, J. P. Gouteux and M. Khaladi, Estimation of age-dependent survival rates of female tsetse flies (Diptera: Glossinidae) from ovarian age distributions,, Bulletin of Entomological Research, 89 (1999), 515.

[15]

G. M. Jolly, Explicit estimates from capture-recapture data with both death and immigration - stochastic model,, Biometrika, 52 (1965), 225.

[16]

A. M. Jordan and C. F. Curtis, Productivity of Glossina austeni Newst. maintained on lop-eared rabbits,, Bulletin of Entomological Research, 58 (1968), 399.

[17]

A. M. Jordan and C. F. Curtis, Productivity of Glossina morsitans Westwood maintained in the laboratory, with particular reference to the sterile-insect release method,, Bulletin of the World Health Organisation, 46 (1972), 33.

[18]

R. J. Phelps, The effect of temperature on fat consumption during the puparial stages of Glossina morsitans morsitans Westw. (Dipt., Glossinidae) under laboratory conditions, and its implication in the field,, Bulletin of Entomological Research, 62 (1973), 423.

[19]

R. J. Phelps and P. M. Burrows, Puparial duration in Glossina morsitans orientalis under conditions of constant temperature,, Entomologia Experimentalis et Applicata, 12 (1969), 33. doi: 10.1111/j.1570-7458.1969.tb02494.x.

[20]

R. J. Phelps and G. P. Y. Clarke, Seasonal elimination of some size classes in males of Glossina morsitans morsitans Westw. (Diptera, Glossinidae),, Bulletin of Entomological Research, 64 (1974), 313.

[21]

G. A. F. Seber, A note on the multiple recapture census,, Biometrika, 52 (1965), 249.

[22]

G. A. F. Seber, "The Estimation of Animal Abundance and Related Parameters,", Charles Griffin & Co, (1982).

[23]

G. A. Vale, The responses of tsetse flies (Diptera: Glossinidae) to mobile and stationary baits,, Bulletin of Entomological Research, 64 (1974), 545.

[24]

G. A. Vale, The trap-orientated behaviour of tsetse flies (Glossinidae) and other Diptera,, Bulletin of Entomological Research, 72 (1982), 71.

[25]

J. Van Sickle and R. J. Phelps, Age distributions and reproductive status of declining and stationary populations of Glossina pallidipes Austen (Diptera: Glossinidae) in Zimbabwe,, Bulletin of Entomological Research, 78 (1988), 51.

show all references

References:
[1]

G. Caughley, "Analysis of Vertebrate Populations,", John Wiley & Sons, (1977).

[2]

A. Challier, Amélioration de la méthode de détermination de l'âge physiologique des glossines. Études faites sur Glossina palpalis palpalis Vanderplank, 1949,, Bulletin de la Société de Pathologie Exotique, 58 (1965), 250.

[3]

C. F. Curtis and A. M. Jordan, Calculations on the productivity of Glossina austeni Newst.maintained on goats and on lop-eared rabbits,, Bulletin of Entomological Research, 59 (1968), 651.

[4]

R. D. Dransfield, R. Brightwell, J. Kiilu, M. F. Chaudhury and D. A. Adabie, Size and mortality rates of Glossina pallidipes in the semi-arid zone of southwestern Kenya,, Medical and Veterinary Entomology, 3 (1989), 83.

[5]

J. W. Hargrove, Age-dependent changes in the probabilities of survival and capture of the tsetse fly Glossina morsitans morsitans Westwood,, Insect Science and its Application, 11 (1990), 323.

[6]

J. W. Hargrove, Age-dependent sampling biases in tsetse flies (Glossina). Problems associated with estimating mortality from sample age distributions,, in, (1993), 549.

[7]

J. W. Hargrove, Lifetime changes in the nutritional characteristics of female tsetse flies Glossina pallidipes caught in odour-baited traps,, Medical and Veterinary Entomology, 13 (1999), 165.

[8]

J. W. Hargrove, Reproductive abnormalities in field tsetse flies in Zimbabwe,, Entomologia Experimentalis et Applicata, 92 (1999), 89.

[9]

J. W. Hargrove, Factors affecting density-independent survival of an island population of tsetse flies in Zimbabwe,, Entomologia Experimentalis et Applicata, 100 (2001), 151. doi: 10.1046/j.1570-7458.2001.00858.x.

[10]

J. W. Hargrove, Tsetse eradication; sufficiency, necessity and desirability,, DFID Animal Health Programme, (2003).

[11]

J. W. Hargrove, "Everybody lies". [But thinking about all the data might get you to the truth]. An example from tsetse biology,, PowerPoint Presentation of a Talk Delivered at: Mathematical Methods in Systems Biology and Population Dynamics (4-7 January 2012, (2012), 4.

[12]

J. W. Hargrove, R. Ouifki and J. E. Ameh, A general model for mortality in adult tsetse (Glossina spp.),, Medical and Veterinary Entomology, 25 (2011), 385.

[13]

M. Jarry, J. P. Gouteux and M. Khaladi, Are tsetse fly populations close to equilibrium?,, Acta Biotheoretica, 44 (1996), 317. doi: 10.1007/BF00046536.

[14]

M. Jarry, J. P. Gouteux and M. Khaladi, Estimation of age-dependent survival rates of female tsetse flies (Diptera: Glossinidae) from ovarian age distributions,, Bulletin of Entomological Research, 89 (1999), 515.

[15]

G. M. Jolly, Explicit estimates from capture-recapture data with both death and immigration - stochastic model,, Biometrika, 52 (1965), 225.

[16]

A. M. Jordan and C. F. Curtis, Productivity of Glossina austeni Newst. maintained on lop-eared rabbits,, Bulletin of Entomological Research, 58 (1968), 399.

[17]

A. M. Jordan and C. F. Curtis, Productivity of Glossina morsitans Westwood maintained in the laboratory, with particular reference to the sterile-insect release method,, Bulletin of the World Health Organisation, 46 (1972), 33.

[18]

R. J. Phelps, The effect of temperature on fat consumption during the puparial stages of Glossina morsitans morsitans Westw. (Dipt., Glossinidae) under laboratory conditions, and its implication in the field,, Bulletin of Entomological Research, 62 (1973), 423.

[19]

R. J. Phelps and P. M. Burrows, Puparial duration in Glossina morsitans orientalis under conditions of constant temperature,, Entomologia Experimentalis et Applicata, 12 (1969), 33. doi: 10.1111/j.1570-7458.1969.tb02494.x.

[20]

R. J. Phelps and G. P. Y. Clarke, Seasonal elimination of some size classes in males of Glossina morsitans morsitans Westw. (Diptera, Glossinidae),, Bulletin of Entomological Research, 64 (1974), 313.

[21]

G. A. F. Seber, A note on the multiple recapture census,, Biometrika, 52 (1965), 249.

[22]

G. A. F. Seber, "The Estimation of Animal Abundance and Related Parameters,", Charles Griffin & Co, (1982).

[23]

G. A. Vale, The responses of tsetse flies (Diptera: Glossinidae) to mobile and stationary baits,, Bulletin of Entomological Research, 64 (1974), 545.

[24]

G. A. Vale, The trap-orientated behaviour of tsetse flies (Glossinidae) and other Diptera,, Bulletin of Entomological Research, 72 (1982), 71.

[25]

J. Van Sickle and R. J. Phelps, Age distributions and reproductive status of declining and stationary populations of Glossina pallidipes Austen (Diptera: Glossinidae) in Zimbabwe,, Bulletin of Entomological Research, 78 (1988), 51.

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