Gompertz growth in number dead confirms medflies and nematodes show excess oldster survival

For prediction of elder survival by a Gompertz model, number dead is preferable to number alive

The standard Gompertz equation for human survival fits very poorly the survival data of the very old (age 85 and above), who appear to survive better than predicted. An alternative Gompertz model based on the number of individuals who have died, rather than the number that are alive, at each age, tracks the data more accurately. The alternative model is based on the same differential equation as in the usual Gompertz model. The standard model describes the accelerated exponential decay of the number alive, whereas the alternative, heretofore unutilized model describes the decelerated exponential growth of the number dead. The alternative model is complementary to the standard and, together, the two Gompertz formulations allow accurate prediction of survival of the older as well as the younger mature members of the population.

Modelling the colonisation of maize by toxigenic and non-toxigenic Aspergillus flavus strains: implications for biological control

To successfully exploit biological control it is desirable to understand how the introduced agent colonises the host and interferes with establishment of the pest. This study assessed field colonisation of maize by Aspergillus flavus strains as biological control agents to reduce aflatoxin contamination. Maize (corn, Zea mays L.) ears were inoculated with A. flavus using a pin-bar technique in 2004 and 2005. Non-aflatoxigenic strains K49 (NRRL 30797) & CT3 (NRRL 30798) and toxigenic F3W4 (NRRL 30798) were compared against a carrier control (0.2% aqueous Tween 20). Ten ears were sampled over 12 to 20 days, visually assessed, and curves fit to a three compartment Gompertz equation or other best appropriate regressions. Aflatoxin was determined by HPLC and cyclopiazonic acid (CPA) by LC/MS. The Gompertz model describes growth parameters, e.g. growth constant, lag phase and maximum colonisation characterised patterns of maize colonisation for most inoculated treatments. Aflatoxin accumulation in maize inoculated with F3W4 was about 35,000 ng/g in 2004 and 2005, with kinetics of aflatoxin accumulation in 2005 well described by the Gompertz equation. Less than 200 ng/g was observed in maize inoculated with strains CT3 & K49 and accumulation was described by a linear or logistic model. Maize inoculated with strains CT3 and F3W4 accumulated a maximum of 220 and 169 µg/kg CPA, respectively, compared to 22 and 0.2 µg/kg in the control and K49 inoculated, respectively. This technique can be used to elucidate colonisation potential of non-toxigenic A. flavus in maize in relation to biological control of aflatoxin. The greatest reduction of aflatoxin and CPA in maize inoculated with strain K49 and Gompertz parameters on colonisation indicates its superiority to CT3 as a biological control agent. The dynamics of maize colonisation by A. flavus strains and subsequent mycotoxin accumulation generated by using the pin-bar technique has implications for characterising the competence of biocontrol strains for reducing aflatoxin contamination.

Age invariant of Gompertz function and exponential decay of populations commensuration with CLOV experiments

The exponential decay law of populations is further examined on the basis of new observations of Japanese and Swedish cohorts. It is shown that the populations decrease exponentially at higher ages in accordance with the theoretical prediction, which confirms the previous conclusion. The theory is applied to recent experiments on Mediterranean fruit flies by Carey et al., (1992, Science, 258, 457-460), the results showing that the exponential decay law holds in sufficient approximation. All the evidences accumulated so far suggest that the decay law is a general theorem. On the basis of this information, we derive a general expression that estimates the limit age as a function of population. The predicted curve is in excellent agreement with the observed limit ages in Japan.