Design of Spatial and Temporal Experiments to Estimate Pest

D ESIGN OF S PATIAL AND T EMPORAL EXPERIMENTS TO ESTIMATE PEST
POPULATION .
{J ENNIFER B RAMWELL } D ATA A NALYSIS A USTRALIA ; {M ARYANN P IRIE } A G R ESEARCH
I NTRODUCTION
Pests, such as black beetle,
can cause damage to pastures resulting in the loss of
profitability. Therefore, it is
of interest to use the prior
season adult population
to estimate future populations.
B EETLES ’ R ANDOM WALK
is to use a spade to dig
a square of soil and to
count the number of beetles within the sample. This
process is time consuming
and not a suitable solution
for farmers.
We propose setting pitfall
traps. We want to design an
The current practice for esexperiment
that
will
allow
timating beetle populations
us to estimate the scale and
location of damage based
on trap counts. The idea is
that environmental data is
used to produce a map of
the area including temperature, moisture and land
use. From this map we decide on the optimal locations to place traps so that
they are near to the pests’
preferred habitat, reducing
the likelihood of getting
nil catch. The trap data
can then be measured over
time and added to the map
to provide predictions of
damage to pastures.
B ACKGROUND
Catches of adult beetles ber of eggs laid, Neggs , is
tend to be relatively regu- estimated by E(Neggs ) =
lar and have low clustering. NSept × 0.52 × 10.
The females lay eggs singularly and the dispersion
of larvae is based on the
availability of food sources.
In September, the number
of adult beetles, NSept can
be assumed to follow a
Poisson distribution, with
mean 23.4 per m2 as indicated by a study conducted
in Northern New Zealand
[3]. Of all beetles, 52% of
these can be assumed to
be female, and each female
beetle can lay on average
ten eggs [3]. The num-
ture levels. Let the mortality rate of larvae be
mort, then E(NFeb ) =
E(Nhatch ) × (1 − mort),
where NFeb is the number
of young beetles in February. If the temperature is
less than 15◦ , the mortality
rate is high. Each 1◦ increase in the average daily
temperature above the
We assume a hatch rate threshold of 15◦ is related
of 0.96 [3].
The num- to a 0.008 unit increase in
ber of eggs that hatch, population [2]. When the
Nhatch , is estimated by soil moisture is near 50%
E(Nhatch ) = E(Neggs )×0.86. then the mortality has been
Summer mortality of lar- recorded as 0.27. Whereas
vae is dependent on the when the soil moisture is
proximity of food, tem- near 18% the mortality has
perature, and soil mois-
been recorded as 0.13 [3].
Beetles walk for about 8.3
hours per day. Their speed
is dependent on temperature.
In cool temperatures they are slow (about
1cm/s at 10◦ ) and in warm
temperatures they move
quicker (5cm/s at 21◦ ) [4].
Having an accurate estimate of February population densities is important
as high densities can cause
large scale damage to pastures. Population densities
of more than 40-60 larvae
per m2 has the potential to
cause damage [1].
I NITIAL S IMULATED FARM
The farm is simulated to be;
• 600m by 400m, divided in plots of 20m by 20m.
• Temperature on the x axis from 14◦ to 20◦ .
• Moisture on the y axis from 15% to 50%.
• Due to computational difficulties the farm was split
into two subsets; x ∈ [0, 300) and x ∈ [300, 600].
• Mortality = f (Temperature, Moisture).
Shown is the simulated farm with temperature and moisture contours, and mortality rate shown by the heat
colours. This is lowest for high temperature and low
moisture.
R EFERENCES
limitation of the simulation (the farm is simulated as two
subsets, x = 300 and x = 600 are the rightmost boundary of those subsets). Apart from the above, the trapping
counts are higher for hotter temperatures. This is as expected as the beetles are more active in hotter temperatures.
F EBRUARY POPULATION ESTIMATION
D ISCUSSION AND CONCLUSIONS
At the end of the trapping period, we assume the beetles
stop moving and the females proceed to lay eggs. The
beetle population of newly hatched beetles that survived
until February, si , for plot i is estimated as follows:
• Number of females at the end of the trapping period, fi ∼ Binomial(bi , 0.52).
• Number of eggs, ei = fi × 10.
• Number of hatched eggs, hi ∼ Binomial(ei , 0.96).
• Mortality Rate of young beetles from hatching till
February, morti = 0.226+0.004moisti −0.008tempi .
• si ∼ Binomial(hi , 1 − morti ).
Assuming that the path of
the beetles is random then
placing the traps in the
centre of each plot results
in very low catch numbers. To reduce the likelihood of getting nil catch
it is recommended that
more traps be placed in
warmer areas of the farm
using stratified sampling.
When placing these traps
it is also recommended to
consider land use, not included here, as large animals and vehicles can disturb traps.
This figure shows si . High February populations occurred for low temperature and moisture (ignoring the
‘boundary effect’). This suggests that beetles densities
are higher in dry conditions and that in higher temperature the beetles are more active and more likely to leave
the study area. The contours show the February densities per m2 estimated using ti , moisti and tempi (scaled
to account for beetles leaving farm and no arrivals).
Our computer power was
limited with each simulation taking several days.
Because of memory issues
we had reduce the size
of the farm and split into
two subsets. This caused
a ‘boundary effect’ where
the trapped counts were
high at the right most
boundaries of both subsets. This requires further
investigation.
The beetles moved long
distances, especially in
high temperatures. Hence,
a large number of beetles
left the farm (less than 8%
remaining) and we did not
assume any arrivals into
the study area.
Therefore, this model could be
improved by either modelling arrivals or modelling a larger area.
C ONTACT I NFORMATION
[1] N. L. Bell, R. J. Townsend, A. J. Popay, C. F. Mercer, and T. A. Jackson. Black beetles: lessons from the past and
options for the future. Pasture Persistence - Grassland research and practice series 15, pages 119–124, 2011.
[3] P. D. King, C. F. Mercer, and J. S. Meekings. Ecology of black beetles, Heteronychus arator (Coleoptera:
Scarabaeidae)-population studies . New Zealand Journal of Agriculture Research, 24(1):87–97, 1981.
[2]
[4] D. A. Raworth and M. Choi. Determining numbers of active carabid beetles per unit area from pithfall-trap
data. Entomologia Experimentalis et Applicata, 98:95–108, 2001.
P. D. King, C. F. Mercer, and J. S. Meekings. Ecology of black beetles, Heteronychus arator (Coleoptera:
Scarabaeidae)-population modelling . New Zealand Journal of Agriculture Research, 24(1):99–105, 1981.
Initial values for September
• µi ∼ Gamma(10, 10/23.4).
• yi ∼ Poisson(400 × µi ).
• Generate yi beetles located uniformly in plot i
Random walk
• 28days × 8.3hours/day = 232hours
• Straight line one hour at a time
• Direction random, speed temperature dependent
Trapping of the beetles
• Centre of each plot, radius 0.1m
• Beetle falls into trap then stops moving
End data for each plot
• Number of beetles in trap i, ti
• Total number of beetles in plot i, bi
The figure shows the proportion of beetles in each plot
that end up in the trap (pi = ti /bi ). The vertical bands
at x = 290 and x = 590 are ‘boundary effects’ due to the
Jennifer Bramwell
[email protected]
+61 8 9386 3304
Maryann Pirie
[email protected]
+64 7 838 5537