Population size models based on cumulative size, with application to aphids

Bayesian Inference for Generalized Stochastic Population Growth Models with Application to Aphids

“…In this paper we have considered the task of inference for a stochastic population growth model of aphid numbers. Although such models are well known, interest has usually focused on their deterministic counterparts (Matis et al , 2006; Matis, Kiffe, Matis, Jackman and Singh, 2007). The model that is considered here is formulated as a Markov jump process with an unobserved component representing cumulative population size.…”

“…As discussed in Prajneshu (1998), aphids excrete honeydew, forming a cover on the leaf surface and causing aphid starvation. As the area that is covered by excretion at time t is proportional to the cumulative population size at time t , C ( t ), we assume a death rate of μ N ( t ) C ( t ) and, for simplicity, assume that there is no removal or decomposition of honeydew (Matis et al , 2006, 2008; Matis, Kiffe, Matis, Jackman and Singh, 2007). The model can be represented by the coupled (pseudo‐)reactions, since, clearly, an occurrence of reaction (1) will lead to a unit increase in both N and C whereas reaction (2) will give a unit decrease in N but leave C unchanged.…”

“…Consequently, accurate modelling of cotton aphid populations is of economic importance (Rummel et al , 1995; Xia et al , 1999). In the recent literature, attempts to model cotton aphid dynamics have included the use of dispersion models (Celini and Vaillant, 2004), computer simulation models (Giarola et al , 2006) and non‐linear regression models (Matis, Kiffe, Matis, Jackman and Singh, 2007).…”

“…Consequently, accurate modelling of cotton aphid populations is of economic importance (Rummel et al, 1995;Xia et al, 1999). In the recent literature, attempts to model cotton aphid dynamics have included the use of dispersion models (Celini and Vaillant, 2004), computer simulation models (Giarola et al, 2006) and non-linear regression models (Matis, Kiffe, Matis, Jackman and Singh, 2007). Whereas deterministic population growth models for insect counts are reasonably well developed (see for example Matis et al (2006Matis et al ( , 2008) little work has taken into account stochastic effects that are particularly important when population sizes are small (Zheng and Ross, 1991).…”

Reparameterization of nonlinear statistical models: a case study

“…Reparameterization of an aphid model Prajneshu [7] developed a deterministic model for the relationship between aphid population density and time when the death rate is density-dependent. An excellent description of this model, along with study of corresponding stochastic model, is given by Matis et al [4,5]. The deterministic model was in terms of interpretative (mechanistic) parameters λ, the intrinsic birth rate per capita, γ , the death rate divided by the cumulative population density and N 0 , the initial population density at time 0.…”