DOI: 10.5061/dryad.np5hqc06x
title: Survival, development, and reproductive data for <em>Hippodamia convergens</em> that provide the basis for cannibalism simulations

description: We used life tables to model rates of population growth when egg
 cannibalism by specific life stages increases developmental rate and/or
 fecundity, using aphidophagous coccinellids as a model system. The
 uploaded files contain the raw data used to delimit parameters of the
 model, data obtained from previously published observations on Hippodamia
 convergens (RawData). The oviposition period and daily fecundity followed
 Weibull and negative binomial distributions (see uploaded CSV files),
 respectively. The uploaded files do not contain the data generated by life
 table model simulations, as these can be obtained by anyone choosing to
 run the simulations.
description: The probability that a female survives and oviposits on a given
 day was defined as a Weibull function:
 <em>P(t)</em>= exp(- t/b)<sup>c</sup> 
      
                                                                                                             Eq. 1 where <em>t</em> is female age at oviposition, <em>p</em> denotes probability, <em>b</em> and <em>c</em> are parameters, and <em>exp</em> is the base of natural logarithms. <em>b</em> and <em>c</em> were estimated to be 24.9 and 1.77, respectively (<em>F</em><sub>1,53</sub> = 50.50, <em>p</em> &lt; 0.001, <em>R</em><sup>2</sup> = 0953, Suppl. Figure 1). To fit a suitable function to fecundity data, the age-dependence of per capita daily fecundity data was characterized by regressing the number of eggs laid over female age. A very poor, but significant, linear relationship was observed (<em>F</em><sub>1,460</sub> = 5.25, <em>p</em> = 0.0223, <em>R</em><sup>2</sup> = 0.0113) and, for the sake of simplicity, was ignored in the simulation. The observed frequency distribution of female daily fecundities was then fitted to a negative binomial function, which was used to predict the probability of observing x number of eggs (x = 0, 1, 2, …) (Suppl. Figure 1B). First, the sample mean ( and variance (<em>S<sup>2</sup></em>) of the daily per capita fecundities was obtained, and then parameters <em>K</em> and <em>C</em> of the negative binomial function were obtained from Eqs. 2 and 3: <strong>Equation 2:</strong> <code>K = \frac{\bar{X}^2}{S^2 - \bar{X}}</code> <strong>Equation 3:</strong> <code>C = K/\bar{X}</code> The probability of observing X eggs was then obtained using Eq. 4 (Southwood & Henderson, 2009): <em>p</em><sup>k</sup>{1, <em>kq</em>, [<em>k</em>(<em>k</em>+1)/2!]<em>q</em><sup>2</sup>, [<em>k</em>(<em>k</em>+1)(<em>k</em>+2)/3!]<em>q</em><sup>3</sup>...} where <em>p</em> = <em>c</em>/(<em>c</em>+1), and <em>q</em> = 1-<em>p</em>. For the first observation, <em>P</em>(0) = <em>p</em><sup>k</sup> was calculated, and subsequent probabilities were obtained using Eq. 5: <em>P</em>(x) = <em>p</em>(x-1)(k+x-1)<em>q</em>/(x!) Cumulative probabilities were then obtained by summing simple probabilities over ages to achieve unity and, for simulation purposes, random probabilities were assigned for each female from a cohort as large as 100, with the number of eggs randomly assigned. For example, the cumulative probabilities of observing 15 and 16 eggs were 0.21871, and 0.24798, respectively; therefore, a random intermediate value suggests an individual will lay 15 eggs. In order to construct a cohort-life table, stage-specific immature survival rates and developmental times were similarly assigned by random probabilities and a normal function for developmental time was assigned a value of 20 ± 0.7 d (mean ± SD). Immature development was split into 3.0 ± 0.2, 3.2 ± 0.2, 2.2 ± 0.2, 2.2 ± 0.2 and 4.4 ± 0.2 and 5.0 ± 0.25 d for eggs, L1, L2, L3, L4, and pupa, respectively, approximating median values observed for <em>H. convergens</em> fed <em>S. graminum</em> at 24 °C (Stowe et al., 2021). A 3.8 ± 0.2 d pre-oviposition period was added which corresponds to the mean time required for egg maturation when females have immediate access to aphid prey post-emergence (Vargas et al., 2012). Stage-specific survival rates, <em>p</em><sub>x</sub> were considered to be 93.2, 86.0, and 98.5% for survivorship of eggs, larvae and pupae, respectively (typical values observed under laboratory conditions), and were multiplied sequentially to obtain l<sub>x</sub> (per-radix-survival).
description: # Survival, development, and reproductive data for *Hippodamia convergens*
 that provide the basis for cannibalism simulations Dataset DOI:
 [10.5061/dryad.np5hqc06x](10.5061/dryad.np5hqc06x) ## Description of the
 data and file structure **File 1: "RawData.csv"** Rows: 1. 
 First row is reference, 2.     second and third row are heading of columns
 (numbers of days), 3.      Data of daily reproduction of 21 females
 extracted from Michaud & Qureshi (2006) are presented in 21 rows (rows
 4 to 24). 4.     Rows 26-31 represents sum, average, Sd, variance (var),
 number of females alive at each age, and survival rate (lx value of life
 table), below the data the fecundity curve of Michaud and Qureshi is
 presented. Colomns: * ID of each female, and then title of variables
 appears in column A, - No. females in column B, * C to BE: daily fecundity
 of each female at days 1 to 55 appears in columns C to BE, - BH to BK:
 oviposition period (OP), Total life time eggs of a female, corresponding
 average daily fecundity, and standard deviation (SD) of it are presented
 in so called columns. Average, minimum and maximum of all data appears in
 bottom of these columns. **File 2: "WeibullSurvival.csv"** Data
 appears in columns: * Ages of simulated individuals age 1 to 115 (over
 final age of 55 of the observed data) - Number of live females at each age
 (obsereved data, Michaud & Qureshi, 2006) * Observed survival rates
 (lx) - Expected survival rate calculated by b and c parameters of Weibull
 function from cells D3 and E3 * Expected number of females for a cohort as
 large as 21 females (simulated by Weibull function) - Columns H to L, the
 procedure of selecting OP values by a random manner from Weibull function,
 including number of females (1 to 21 in column H), random values in column
 I, probability (column J) of having an OP as long as values presented in
 column K, random value of OP chosen per female by random selection. * In
 righthand of calculations, the curve of observe vs. expected Weibull
 function of OP values is presented. **File 3:
 "NegativeBinomial.csv"** 1. Reproductive data of Hippodamia
 convergens, observed by  Michaud & Qureshi, 2006, as well as fecundity
 expected from a negative binomial function. 2. Parameters of negative
 binomial function appears in first to fifth rows (1 to 5, columns K to O),
 calculations appear in columns in subsequent rows (row 8, upward) *
 Columns A and B: number of eggs (column B), corresponding to age of female
 (column A), for 21 females of Michaud & Qureshi, 2006, overall 462
 pairs of data (data extracted from table in first sheet, "Raw
 data"). - Columns D to F: daily number of eggs from 0 to 139 appeared
 in column D, cumulative, and simple frequency distribution of each number
 appears in columns E and F respectively, * Column G: expected from
 negative binomial probability function for observing number of eggs
 delineated in column D, referring to parameters appears in rows 1 to 5. -
 Column H: cumulative expected probability, * Columns I to O: calculations
 for random selecting fecundity per female per day, including column I
 number of eggs per day per female (0 to 139), column J expected frequency
 (from negative binomial function) for a sample as large as 462 ovipositing
 insect-days, column K the same data rounded for integer, column O random
 set of data for choosing daily per capita fecundity (extended for 139
 insect-days, but can extend for any given number of insect-days, for
 example 462 or more), column M the selected number of daily per capita
 eggs by referring to random value of column O and probability table of
 columns H and I, ## Code/software Microsoft Excel can be used to view the
 files.