New Horizons in Insect Science Towards Sustainable Pest Management

422 B. B. Fand et al.

Spatial Simulation and Risk Mapping in

Geographic Information System (GIS)

Climate Data

Climate data required for spatial simulations at
current climatic scenario were obtained from
Worldclim database (http://www.worldclim.org/).
The current data comprised interpolated monthly
minimum and maximum temperatures obtained
from long-term time series (1950–2000) from a
global network (Hijmans et al. 2005 ). For simu-
lating P. solenopsis risk under climate change
scenario, we used downscaled data (Ramirez
and Jarvis 2010 ) (freely downloadable at http://
gisweb.ciat.cgiar.org/GCMPage) of the SRES-
A 1 B emission scenario for the year 2050 (IPCC
2007 ). The climate data were used at a resolution
of 10 arc minutes. For simulating within year
variability of P. solenopsis population increase at
different locations, i.e., point-by-point analyses,
we used actual temperature data obtained from
two weather stations in India, viz., Ludhiana
(Punjab State) and Akola (Maharashtra State).

Temperature Simulations

Daily minimum and maximum temperature data
are used by insect life cycle modeling (ILCYM)
for simulating pest population growth potential
for each 15 min time step using a cosine func-
tion for half-day temperature predictions. For the
first half-day predictions, the following equation
is used:

where Ti is the temperature (°C) of time step i
( i = 1, 2, 3, ... 48) and Min and Max are the daily
minimum and maximum temperatures.
The same procedure was then repeated to es-
timate Ti for the second half day using minimum
temperature of the next day in the equation. As
worldclim database only include monthly aggre-
gates of temperature data, ILCYM replaces the
daily minimum and maximum temperatures in
above equation with monthly averages for half-
day temperature predictions in each 15 min time
step. In this case, a value of Ti remains constant

( ) cos ( 0.5) ( ),

2 48 2

Ti

Max Min π i Min Max

=

−×−+×+



for all days of the month, except for the last day

that employs minimum temperature of first day

of next month to calculate Ti for second half day

(for details see Sporleder et al. 2008 ; Kroschel

et al. 2013 ).

Estimation of Life Table Parameters

Based on the simulated temperatures and model

outputs, the life table parameters, viz., net re-

productive rate (R 0 ), mean generation time (T),

intrinsic rate of natural increase (rm), finite rate

of increase (λ), and doubling time (Dt) were esti-

mated at range of constant temperatures using life

table simulation function of ILCYM (Sporleder

et al. 2008 , Kroschel et al. 2013 ). The estimated

life table parameters were plotted against Julian

days to visualize variability in pest potentials due

to seasonal climate variation.

Estimation of Pest Risk Indices

Based on the estimated life table parameters

and simulated temperatures, following three

indices for pest risk at each data point were cal-

culated.

a. Establishment risk index (ERI)or survival risk

index

This index characterizes the geographical areas

having risk of survival and establishment of the

pest insect. The survival index is calculated by

the following formula:

where

b. Generation index (GI)

This index represents the mean number of gener-

ations that a given pest can produce within a year.

It is calculated by averaging the sum of estimated

ERI

NymphNymph Nymph

=

() 11 −×xx() 12 −×() 13 −x ,

x=

∑

Numberofdays,aspecificimmature

lifestagedoesnotsurvive

3655

.