# Design of Spatial and Temporal Experiments to Estimate Pest

## Transcription

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