Developmental biology and population growth parameters

Freshly laid eggs of C. zastrowi sillemi were taken from maintained pure culture under controlled environmental conditions and individually placed in 9 cm diameter, 1.5 cm high Petri plates. The hatching period of the eggs was monitored at 24-hour intervals. After hatching, counted numbers of P. persicae aphids were provided daily to the individual C. zastrowi sillemi larvae until pupation in the Petri plates. Each set was replicated 20 times. Pupae thus obtained were observed daily of adult emergence. After emergence of adults they were kept in pairs in glass chimneys (10 × 14.5 cm) for mating and honey solution (50%), protinex mixture (protinex, yeast, pollen and honey) and water were provided for foraging (Chandana et al, Reference Chandana, Sood and Sharma2020a). The chimneys were covered with black muslin cloth to create favourable conditions for egg deposition and after every 24 h, the fecundity was recorded. Observations on the duration of each development stage, survival, longevity and fecundity were recorded. Total pre-ovipositional period (TPOP), adult pre-ovipositional period (APOP), and fecundity rate were calculated using age-stage, two-sex life table theory (Chi, Reference Chi1988) and the TWOSEX MS-Chart computer program (Chi, 2018). The population growth parameters were calculated using the following formulas:

s_xj = It indicates the likelihood that a newly emerged egg will survive to reach age x and stage j.

f_xj = It indicates the number of eggs that hatch from an adult female at age x.

\begin{equation*}{l_x} = \sum\limits_{j = 1}^m {{s_{xj}}} \end{equation*}

\begin{equation*}{m_x} = \frac{{\sum\limits_{j = 1}^m {{s_{xj}}} {f_{xj}}}}{{{l_x}}}\end{equation*}

Different population growth parameters were calculated using the variables mentioned above.

1. 1. Net Reproductive rate (R₀): The average number of offspring per female over her lifetime was calculated as:

   \begin{equation*}{R_0} = \sum\limits_{x = 0}^\infty {\sum\limits_{j = 1}^m {{s_{xj}}} } {f_{xj}}\end{equation*}

   \begin{equation*}{m_x} = \sum\limits_{x = 0}^\infty {{l_x}} \end{equation*}

2. 2. Gross reproductive rate (GRR): The cumulative number of female eggs deposited per female was calculated as:

   \begin{equation*}GRR = \sum\nolimits_{x = 0}^\infty {{m_x}} \end{equation*}

3. 3. True generation time (T): The average time interval from the birth of parents to that of off-springs was estimated using the following formula:

   \begin{equation*}T = \frac{{\ln {R_0}}}{r}\end{equation*}

4. 4. True intrinsic rate of increase (r_m): The rate of increase of a population under ideal environmental conditions in which food and space are unlimited was estimated as follows:

   \begin{equation*}\sum_{x=0}^\infty e^{-r\left(x+1\right)}l_xm_x=1\end{equation*}

5. 5. The finite rate of natural increase ( $\lambda $): The finite rate of natural increase representing the number of times the population multiplies per unit time, was computed using the following equation:

   \begin{equation*}\lambda = {e^r}\end{equation*}

6. 6. The doubling time (DT): The time taken by a species to double its population it was computed as follows:

   \begin{equation*}DT = \frac{{\ln 2}}{r}\end{equation*}

7. 7. Reproductive value (v_xj): The contribution of individuals at age x and stage j to future population growth (Yang et al, Reference Yang, Li, Xie, Wu, Xu, Wang, Li and Zhang2015) was calculated as follows:

   \begin{equation*}v_{xj}=\frac{e^{r(x+1)}}{s_{xj}}\sum_{i=x}^\infty{e^{-r(i+1)}}\sum_{y=j}^ms'_{iy}f_{iy}\end{equation*}

8. 8. Age-stage specific life expectancy (e_xj): The expected remaining lifespan of an organism at age x and stage j was calculated by the method proposed by Chi and Su (Reference Chi and Su2006) as presented below:

   \begin{equation*}e_{xj}=\sum_{i=x}^\infty\sum_{y=j}^ms'_{iy}\end{equation*}

   where s’ _iy is the probability that organisms of x and j were survive to age i and stage y.

Predatory potential

The predatory potential of all three C. zastrowi sillemi larval instars against P. persicae was investigated by recording daily survival and prey consumption data for each instar and this was replicated twenty times. The CONSUME-MS Chart (Chi, Reference Chi2020) was used to analyze the data and predator-prey kill parameters were determined using methods of van Lenteren et al (Reference van Lenteren, Bueno, Burgio, Lanzoni, Montes, Silva, de Jong and Hemerik2019).

s_xj = likelihood that a newly laid egg will survive to reach age x and developmental stage j.

c_xj = average consumption rate of an individual of age x and developmental stage j.

1. 1. Age-specific predation rate (k_x): It is defined as the number of hosts killed by the predators at age x and was determined as follows:

   \begin{equation*}{k_x} = \frac{{\sum\nolimits_{j = 1}^\beta {{s_{xj}}{c_{xj}}} }}{{\sum\nolimits_{j = 1}^\beta {{s_{xj}}} }}\end{equation*}

2. 2. Age-specific net predation rate (q_x): The age-specific survival rate represents the number of individuals surviving to age x, the net age-specific predation rate was calculated as follows:

   \begin{equation*}{q_x} = {l_x}{k_x}\end{equation*}

3. 3. Net consumption rate (C₀): It represents the number of hosts killed by a predator from the birth to age x, this parameter was determined as follows:

   \begin{equation*}C_{0=}\sum\nolimits_{x=0}^\infty\sum\nolimits_{j=1}^\infty s_{xj}c_{xj}\end{equation*}

4. 4. Transformation rate (Q_p): It represents the average number of prey required to be killed by a predator to produce one offspring and was computed as:

   \begin{equation*}Q_p=\frac{C_0}{R_0}\end{equation*}

5. 5. Stable host kill rate (Ѱ): It denotes the proportion of individuals at age x and stage j within the stable age distribution (a_xj).

   \begin{equation*}\psi = \sum\nolimits_{x = o}^\infty {\sum\nolimits_{j = 1}^\beta {{a_{xj}}{c_{xj}}} } \end{equation*}

6. 6. Finite Host kill rate (ω): The finite host killing rate was calculated to assess host-killing potential, was determined as follows:

   \begin{equation*}\omega = \lambda \psi \end{equation*}

Statistical analysis

To assess developmental biology and population growth parameters, TWOSEX-MS Chart was used with bootstrap method with 100,000 replications to estimate population mean and standard error (Efron & Tibshirani, 1993). Predation rate and prey-kill parameters for C. zastrowii sillemi were determined using the CONSUME-MS Chart (Chi, Reference Chi2020).