Trends in the greenhouse and Smarthouse
It is concluded that, in the greenhouse, trends can occur down its length in even approximately 3 weeks of growth (Figure 2A). We believe that, in this case, the higher growth at the eastern end of this greenhouse, particularly on the southern side, was because these plants are next to an external eastern wall and so they received more light in the early morning. On the other hand, differences over the short distance encompassed by three rows of pots are unlikely, although there was evidence of a difference between sides.
The results of the analysis for the PA experiment (Figure 2) established that there is an east–west trend in the Smarthouse for the same-lane tactic, and that this has overshadowed minor column trends in the north-west of the greenhouse. One contributing factor to a Smarthouse position trend is the greater exposure of plants in the western half to the effects of the air conditioners. Presumably, the same is true for the bench tactic, although it cannot be confirmed because there is no data from day 21 for this tactic. For the half-lane tactic, the minor column trend in the north-east of the greenhouse has been also overshadowed in the Smarthouse, but in this case to produce no position trend for reasons discussed below. In contrast, the more pronounced column trend for total area in the south-east of the greenhouse is paralleled by a similar position trend in the day 51 total area for the next-lane tactic. The evidence for this is the disappearance of the position trend when the total area for day 51 is adjusted for the total area for day 21 using an analysis of covariance. It is not possible to be certain of the source of the position trend in total area from day 51. In particular, the contribution of the column trend in the greenhouse to it cannot be determined. On the other hand, it seems most likely that, like for the same-lane tactic, there is a contribution by the Smarthouse phase to the position trend in the day 51 total area for the next-lane tactic, although the trend might not be as great as in other tactics because of the suppressed growth for this tactic in the Smarthouse phase. Ultimately, the origin of the position trend is of little import here, because column trends in the greenhouse are aligned with position trends in the Smarthouse: whatever measures are taken to deal with one will deal with the other.
The three multiline experiments have shown that there is a trend for growth to decrease from south to north in the Smarthouse (Figure 4). This is in large part due to shading of some of the lanes at the northern end of the Smarthouse by the equipment in the adjoining imaging room, the number of shaded lanes being a maximum in winter. However, the PA experiment revealed that there were no differences within sets of three lanes in Smarthouse and the multiline experiments confirm this, although perhaps even sets of four lanes are homogeneous.
Thigmomorphogenic or other movement effects
Predicted averages and variances generally differed between tactics in the PA experiment (Table 2). However, there was no average or variability difference between the bench and same-lane tactics for any of the responses from day 51, in particular, height or density index. Thus the movement three times a week for imaging and watering had no effect over and above that associated with traditional greenhouse practices. We infer from this that there was no thigmomorphogenic or other effects of movement in the Smarthouse. The lack of a thigmomorphogenic effect is perhaps not surprising given that no such effect has been found in wheat when the plants were stimulated by rubbing . It would also appear that the potential effects of pot movement on the soil, and thence on plant growth, have been circumvented by the soil substrate chosen for use in this experiment (see the Methods section).
Relocation of plants versus experimental design and statistical analysis
The results of the half-lane and next-lane tactics are informative in considering the issue of how to deal with microclimate variation: relocation of plants or experimental design and statistical analysis. At first sight, it may seem that relocation of plants is the better option because, as seen in the half-lane and next-lane tactics, trends can be reduced and perhaps nullified by appropriate movement. We now discuss why this may not be the case.
The half-lane tactic differed from the other tactics in displaying no east–west trend over positions (Figure 2B), because plants spent half their time in the each half of the Smarthouse. However, in order for plant relocation to be successful, it must result in plant variability that is similar to that for plants that maintain their position, as in the same-lane tactic, after lane and position trends have been removed in a statistical analysis of the data. This did not happen for the half-lane tactic; instead, while no east–west trend was detected, the variability of plants was inflated, relative to that for the other tactics. The magnitude of this inflation was similar to the amount of variation that is removed by a position trend in the bench and same-lane tactics. It is noted that, while plants have spent time in both the east and west halves of the Smarthouse, there are still differences between plants in the exposure to the east–west trend. Within a set of 12 plants that start in the same half, plants retain their east–west order for the whole experiment. Also, plants that start together in the middle of a lane spend half their time at opposite ends of the lane. That is, while the half-lane tactic does reduce the trend to the extent that it was not detectable, it does not eliminate it because plants are not equalized with respect to the trend. Further, the tactic increases the inequality in exposure.
The next-lane plants, compared to same-lane plants, have smaller total area on day 51, are less variable for total area on day 51, are significantly shorter on average and have a lower density index (Table 2). This is consistent with the next-lane plants having been shaded during their growth. Further, evidence for this shading effect comes from the three multiline experiments, for which we argue that some of the lanes at the northern end of the Smarthouse are shaded by the equipment in the adjoining imaging room. At the time of the year that the PA experiment was run, it would have been the 6 most northern lanes at most that were shaded during it. That is, the plants in the next-lane tactic would have been shaded during only part of their time in the Smarthouse. They would have entered the shaded area sometime after the 6th time point, depending on how many lanes were shaded. However, all would have been shaded for the same amount of time, the number of time points spent in the shade being equal to the number of shaded lanes. The first lane of the tactic would have entered and left the shaded area two time points after the third lane, which is 5 days or less. So, any retardation in growth would begin after at least the 6th time point (day 32) and this is what is observed in Figure 3. There is also evidence of an increased growth rate after time point 12, time point 13 being the point at which all lanes have emerged from the shade. The lack of a difference between the three lanes for the next-lane tactic confirms that the effect of shading during the Smarthouse phase was similar for all the plants in this tactic. The variance of plants in this tactic was smaller than for the same-lane or bench tactics. A smaller variance for this zone was also observed in multiline experiments 2 and 3, in which carts were always returned to the same position. This suggests that the smaller variance for plants in the next-lane tactic is most likely due to the reduced growth of plants in this tactic, rather than the more equal exposure of plants to the microclimates in the Smarthouse leading to reduced variability. In any case, this decrease in variance would only be beneficial in an experiment involving multiple lines if there was not a matching reduction in the differences between lines.
Clearly, both half-lane and next-lane tactics have had the effect of spreading microclimate effects across all the plants in these tactics, position trends in the first case and lane trends in the other. However, while the half-lane tactic does not equalize the plants experience of the east–west trend, the next-lane tactic evens out the exposure of the plants to the north–south trend. This demonstrates that for rearrangement of plants during the experiment to be an effective strategy requires that the plants experience equally every microclimate in the experimental area. Even if this is achieved, the precision of the experiment will be no better than can be achieved by adjusting for trends in the analysis. The reason for this is that the effect of rearrangement is limited to removing microclimate differences, such as can be adjusted for in the statistical analysis, but has no effect on the other sources of variation in the experiment, such a soil and plant variability.
Attaining equal exposure to microclimates is probably easiest with systematic relocation, such as was used with the half-lane and next-lane tactics. Even so, while accomplishing equalization in small experiments may well be practicable, it is likely to be difficult to achieve in large experiments. For example, consider an experiment to be conducted in a Smarthouse that occupies 24 lanes by 24 positions. We have identified that areas of 4 lanes by 6 positions are reasonably homogeneous in our Smarthouse, which means that in the proposed experiment there are 6 by 4 or 24 such areas. The relocation strategy would need to rearrange the plants in the experiment so that each of 24 groups of 24 plants is located for the same amount of time in each of these 24 areas. This is not possible in a 31 day experiment. It would be for a 24 day experiment, but then, for each area, some plants would start the experiment in that area and other plants would finish in it; these plants would be at different stages in their growth. On the assumption of the same east–west trend for all lanes, it would only be necessary to ensure that plants spent the same amount of time in each of the 4 sets of 6 positions and the 6 sets of 4 lanes. This could be done in 12 days. Our data support such an assumption.
On the other hand, random or haphazard relocation of plant during an experiment will not equalize plant exposure to microclimates. Rather it will make it difficult, if not impossible, to adjust for microclimate differences and so will almost certainly result in greater variance than if adjustment can be made.
Which experimental design and statistical analysis?
Given that microclimate differences are to be accounted for by experimental design and statistical analysis, rather than relocation of the plant during an experiment, the question that arises is which experimental designs and statistical analysis are best as far as minimizing the variance of treatment differences is concerned. In answering this question, our investigation of alternative designs using total area from the PA experiment is relevant to dealing with the east–west trend, while the three multiline experiments provide information about the north–south trend. The result of these investigations (Figures 4, 5 and 6) is that, in general, blocks should be as small as possible, consisting of 4 lanes by 4 or 6 positions. It might appear that small blocks are the obvious solution, but this is not necessarily the case. While one would expect smaller blocks to be more homogeneous, and so be preferred, there are other elements of an experiment that may result in greater efficiency for larger blocks. In particular, with larger blocks, the amount of information estimated from within blocks will be higher and the error variance will be more precisely estimated, thereby counterbalancing the superior homogeneity of smaller blocks. Our results show that alternatives to small blocks are to use (nearly) trend-free designs with larger blocks and fit position trends as equal slopes for blocks or, as a last resort, blocks of several complete rows with trend terms for position in the analysis.
In the PA experiment, the exposure of plants to the increasing trend in total area from west to east in the greenhouse was aligned with their exposure to a trend from west to east in the Smarthouse. Consequently, the PA experiment conforms to Principle 8 (Big with big) in  in that comparisons between greenhouse columns and between Smarthouse positions are confounded with each other. This means that whatever steps are taken to adjust for east–west trend will do so simultaneously for the greenhouse and the Smarthouse. It also has the advantage of keeping the design simple and so observing Principle 5 (Simplicity desirable) in .
How many replicates?
An important issue in designing an experiment is the number of replicates for each treatment. Unfortunately it is impractical to give general guidelines because the number of replicates for each response variable depends on the amount of variation to be expected, the size of the difference to be detected, the number of treatment to be employed, how the error degrees of freedom are calculated, the significance levels to be used and the power required. Many different combinations of the values for these quantities occur, even in greenhouse experiments, and so the number of replicates will vary between experiments. The contribution of this paper is in suggesting ways in which the amount of variation to be expected can be minimized. Further, the results in this paper suggest that a CV in the range 20% to 30% can be expected in total area for day 51 in such experiments (see Tables 2 and 5). If one expresses the difference to be detected as a percentage of the expected mean value, then this value can be used in calculating the number of replicates required.
A limitation of the PA experiment is that each tactic was applied in only one zone, this being a necessary, practical restriction. We are of the opinion that this is unlikely to have affected our comparison of the bench and same-lane tactics, these being located next to each other and covering no more than 6 lanes at the unshaded, southern end of the room. Our main results for the half-lane and next-lane tactics are concerned with the position trend. It would appear that the position trend is consistent across the whole Smarthouse as the slope does not differ significantly between the bench, same-lane and next-lane tactics. However, while we also consider it unlikely, we cannot rule out that the extra variability associated with the half-lane tactic is due to its being in a zone that is inherently more variable than the other zones.