Asymmetrical response surface designs in the presence of neighbour effects

In this article, we have discussed a general methodology for constructing Asymmetrical Response Surface Designs in the presence of Neighbour Effects. Methodology of form 2n´3 has been derived. Conditions have been derived for the near orthogonal estimation of coefficients of response model. Further, conditions for rotatability under these models have also been obtained. A method of constructing asymmetrical response surface designs i.e.2n´3 for fitting second order response surface in the presence of neighbour effects has been developed.

Statistical designs for fitting response surfaces incorporating neighbour effects

Response Surface Methodology (RSM) approximates the relationship between one or more response variables and a set of experimental variables or factors. In RSM, it is generally assumed that the observations are independent and there is no effect of neighbouring units. But under the situation when the units are placed linearly with no gaps there is high possibility of overlapping or neighbour effects from the adjacent units. So including these effects into the model is of great importance in deciding the precision of the experiment. Further, availability of resources and size of the experiment is important factor in conducting an experiment. As the size increases, cost involved in conducting the experiment increases, thereby decreasing the precision of the experiment. In this study, response surface designs incorporating neighbour effects have been considered. Method of constructing First Order Rotatable Designs with Differential Neighbour Effects (FORDDNE) has been developed in smaller number of runs.

Resolvable block designs balanced for non-directional neighbour effects

When there is a constraint of cultivable land, experimental units are to be arranged side by side in compact blocks without gaps in between, the treatment applied to one experimental plot may affect the response on neighbouring plots besides the response to which it is applied. Neighbour-balanced designs, where in the allocation of treatments is such that every treatment occurs equally often with every other treatment as neighbours, can be advantageously used in such situations. These designs ensure that no treatment is unduly disadvantaged by its neighbours and also helps in estimating the neighbour effects besides the direct effects of treatments. Resolvable neighbour balanced designs are advisable if continuous area is not available for all replications. Methods for constructing a new series of resolvable block designs balanced for non-directional neighbour effects for prime or prime power of number of treatments (v) have been developed. The methods are discussed in detail along with appropriate examples in following section.

Neighbouring plants and perception of predation risk modulate winter browsing by white-tailed deer (Odocoileus virginianus)

The presence of neighbouring plants and predation risk can affect trophic interactions between plants and herbivores. We hypothesized that the relative preference for neighbouring species would determine winter herbivory and that predation risk would modulate browsing pressure. We tested these hypotheses using feeding trials in two regions with high white-tailed deer (Odocoileus virginianus (Zimmermann, 1780)) densities: Outaouais and Anticosti Island (Quebec, Canada). In each, we selected a species of interest and compared browsing rates and time spent foraging with neighbours relatively preferred or avoided. In a subexperiment, we included coyote (Canis latrans Say, 1823) urine to test for threat-sensitive foraging and interactions with neighbour effects. In Outaouais, time spent foraging on the focal species was reduced by the presence of potentially avoided neighbours and deer reduced browsing with increased perceived predation risk. On Anticosti, browsing rates on the focal species increased with avoided neighbours, with no effect of the predator urine. Anticosti deer have been in a predator-free environment for more than 120 years, likely reducing antipredator behaviours. This study demonstrates both neighbour effects and threat-sensitive foraging, phenomena that could interact and thus would benefit from being studied together to better represent trophic interactions in natural environments.