Table 2 Definitions of variables and parameters

Random variables, observed values

Λ, λ

Per host net egg output

eggs gram^-1

W, w

Per host mean weight of female Ascaris

grams

n

Per host female worm burden

worms host^-1

a

Host age group (a = 0 for age ≤ 12, a = 1 for age > 12,)

Unobserved random variables

M

Per host unobserved true mean weight of female Ascaris

grams

Unobserved values

μ _W

Expected value of the per host mean weight of female Ascaris

grams

μ _Λ

Expected value of the per host net egg output

eggs gram^-1

p

The probability of observing a zero count from the Bernoulli process

-

Estimated parameters

${\alpha }_a=\{{\alpha }_{1a},{\alpha }_{2a},{\alpha }_{3a}\}$

Describe the form of density-dependence of the expected value

of the per host mean weight of female Ascaris in age group a

-

$\sigma =\{{\sigma }_1^2,{\sigma }_2^2\}$

Describe the relationship between the variance of the per host

mean weight of female Ascaris and the female worm burden

-

λ ₁

Exponential of the intercept term of statistical models fitting

the expected value of the per host net egg output to data

-

β

Describes the effect of host age category on the expected

value of the per host net egg output

-

c

An inverse measure of the severity of density dependence (0 <c ≤ 1)

on the expected value of the per host net egg output

-

$\gamma =\{{\gamma }_1,{\gamma }_2,{\gamma }_3\}$

Describe the form of the relationship between the expected value

of the per host net egg output and female Ascaris mean weight

-

$\delta =\{{\delta }_0,{\delta }_1,{\delta }_2,{\delta }_3\}$

Describe the age-dependent relationship between the logit of the probability

of observing a zero egg count, the natural logarithm of female worm burden and

the natural logarithm of the mean weight of female Ascaris

-

k

Inverse measure of the degree of overdispersion in egg output data

-