Density estimation of Heterodera schachtii populations by hyperspectral sensors on a biological time scale

What is the origin objective of this project? Is it possible, just and only by remote sensing technology and hyperspectral information from sugar beet canopies ( as shown in the icon picture right) to establish at least a rough density estimator of the underlying H. schachtii population?

To test the hypothesis and solve the given challenge all components of the Nemaplot H. schachtii project are going to be combined. Hyperspectral information and given multivariate statistical procedures as the discriminant analysis (DA) and General Linear Modeling (GLM) have been tools to check their potential to derive and quantify the soil borne pest from remote sensing data from crop canopies. The target E&J/100 ml soil is masked by several superior factors due to multiple interactions within the host - nematode system. In fact, the nematode impact on the hyperspectral signal in lab as well as in field trials is unexpected small, despite high population densities. These superior factors are variety, year effect (i.e. weather) and date of measurement during the season. While the variety effect is fixed by the chosen variety, the introduced host-parasite model standardize the two other factors. For the required transformation the Leslie model is not running on a real time scale, but based on the biological time concept, i.e. Degree Days, derived from the temperature response functions of the host (fig. 1, 2) and nematode development (temperature sums at base 8 as an approximation is doing fine as well). The alternative time scale summarizes the (temperature) events of all years, providing a normalized development of both the host and the nematodes. The advantages are obvious, it allows not only the comparison of the dynamics of several years, but combines all data of four years of the hyperspectral field experiment within one analysis. Finally, the transformation provides a data set of sufficient size for the GLM procedure, which transform the weak hyperspectral signal of H. schachtii into a numerical dimension. The analysis of the field trials has already shown that the ability to find a more or less linear correlation with sufficient performance from hyperspectral signal to nematode density varied with the date of measurement in every year. In conclusion, not the E&J/100 ml soil are the target (in fact a number, which is long gone when measurement are taken in July/August), but the current nematode stage density in the crop (there is no need to stress the obvious, nevertheless the number of nematodes in the crop is not easily to diagnose). By using the Leslie model we can identify some population numbers at any time of the season. Even they are simulated only, and have possibly no reference to reality, they are repeatable and and can be referred to the hyperspectral signature. In fact, the Leslie model is used as the calibration tool for the hyperspectral information.

Normalized nematode development — Fig. 1: Normalized system dynamics of all simulated development stages in the host; dots are measurement dates

Normalized cyst development — Fig. 1: Normalized system dynamics of all simulated development stages in the host; dots are measurement dates

The transformation of the host-parasite system results in the following charts for a Pi of 1000 E&J/100 ml soil. The dots represent the dates of hyperspectral measurements in each year: The bottom chart of fig. 1 & 2 presents the trajectories of the sugar beet canopy (Unit Green Area Index, GAI) as a result of the temperature files of 2011 to 2014 (with the assumption of planting when a DD₈ of 60°C is completed). The population dynamics of H. schachtii based on the Leslie model correspond similar. Up to a biological time (BT) of 60 the development rate is completely controlled by temperature, i.e. it is possible to establish a standardized nematode development as for the crop (fig. 1, 2 top). At end of season (BT>60) the massive population increase is a function of the host and not anymore solely controlled by temperature. To focus the results we distinguished between all nematode stages (fig. 1) and the dynamics of the cysts (fig. 2). Taking the Leslie model as the tool for the determination of the biological time, three dates of interest for hyperspectral measurements exist. At a BT of ~35, relates approximately to the J3 stages in the root tips (fig. 1 top), at a BT of ~50, when a temporary maximum of cysts in the root is noticed (fig. 2 top) and finally at a BT of ~60, a second maximum of all stages (fig. 1). In fact the GLM procedure have not been able to identify a significant correlation between hyperspectral signature and the number of nematode stages at BT 35 as well as BT 60. Only at BT 50 the procedure approximates with a sufficient precision (fig. 3), i.e. the hyperspectral signature corresponds with a certain number of (simulated) cysts, how they would have been expected with the temperature files from 2011 to 2014. The resulting parameter estimates are depicted in the following table:

Table of the General Linear Modeling procedure

Constant	A	B1	AC1	BC1	AL1	B1	B2	AC2	BC2	AL2	BE2	B3	Acrit3	Bcrit2	al3	be3	b4	Acrit3	al4
-3391.25	287.05	-3.78	11.17	6.3	4.39	1526.51	-1.56	-0.96	-38.28	9.04	-172.42	3.37	1.01	1.017	1.98	-0.12	145.03	-2.11	5.70

For explanation of the model parameters AC1, BC1, ... etc. and how they are estimated? We refer to the top project of hyperspectral data analysis forward

Cysts predicted — Fig. 3: Comparison of observed/simulated number of cysts in the root, r²=0.63

What does the table mean? It presents the one specific vector, which has to be multiplied with the fitted parameter vector of the hyperspectral signature and results in a numerical value characterizing the wanted target. In this case the number of simulated cysts in the root at a given biological time. A r² value of 0.6 is obviously poorer than the example r² - values within one year . But this model is valid for "all" years, as the abstract factor "year" is defined by the specific temperature pattern. Therefore all four years have been usable for the parameter estimation problem, and the parameter estimates are supported by a much larger data set. Some critics are seen: 1^st) at low population density (~detection limit) the population might be overestimated disproportionately high and 2^nd very high densities (values in the range of 50 and more) have to be more cautious. That is not related to the model procedure, but to the underlying experiments. No year did show the typical wilting. That means nematode related growth limitations at very high Pi values are considered in the Leslie model (50-55 cysts at BT 50 are some upper boundary in the model, corresponding to a complete suppression of beet growth, as seen in middle picture at the top of this page), but did not occur in any of the year 2011 to 2014.

Two examples chosen by chance from the current data set summarize the procedures as follows: Both plots have been scanned by hyperspectral sensors with a given number of repetitions (20). The results are the characteristic reflectance patterns of a green canopy with related variance (fig. 4). The position of the medians compared to the variance indicate a right skewed distribution. The underlying nematode density, taken from soil samples at pre-planting sugar beets, are in the range of 550 and 800 E&J/100 ml soil respectively. The spectra were fitted to the Nemaplot standard model, multiplied by the vector above, and the products provide estimates of the (simulated) cysts in the beet. Estimators are in the range of 30 (26-36) for the first and 23 (17-46) cysts for the second example, which are influencing the hyperspectral signal at given Biological Time. The cyst numbers relate to a Pi of 800 (700-1100) soil for plot 33 and 700 (500-2700) E&J/100 ml for plot 34. Numbers in brackets are the confidence ranges. The deviance is tolerable and has been expected by the achieved precision of the linear model.

Cyst calibration — Fig. 5: Calibration isolines of discrete density classes of E&J at given BT

To get the original Pi value from the numbers of cysts at a given BT, the Leslie model can run for each Pi. To avoid too much complexity we have build density classes beforehand, while it is important to differentiate between above the threshold levels (> 800 E&J) and below. Fig. 5 provides the related isolines for some Pi classes. Deviation from the ideal date (the point we never met) lead to minor changes in the number of cysts and therefore some more correction for a density class. Changes at very high cyst densities are part of the host-parasite system again, as both the crop and cyst develop over time. It is quite important to maintain the optimum measurement date at a BT of around 48 to 52. The application is limited to susceptible varieties in the moment, using resistant or tolerant varieties other isolines would be applicable. Their size is not determinable from the underlying data set. It is assumed, changes with respect to resistant varieties vary the abundance only, not the development time.

Hyperspectral RGB Image — Fig. 6a: Cubert aerial RGB image of a
plot in 2013 with 4000 E&J

Density plot of Heterodera schachtii cysts — Fig. 6a: Cubert aerial RGB image of a
plot in 2013 with 4000 E&J

It is necessary to refer to the chapter "image analysis" again. It can be shown by a small adaption of the transformation vector to the wave length specification of the Cubert camera to estimate the cysts distribution (fig. 6 b) from a hyperspectral aerial image of a field plot (fig. 6a), which again leads to the following E&J distribution at spring (fig. 6c). Numerical artifacts are noticed in the area of pathways, it should be ignored. There is no hard evidence about the distribution shown in fig. 6c, but the GLM vector calculates very high cysts or E&J numbers, they in fact correspond with the soil samples of the plot in the range of more than 4000 E&J/100 ml soil.

Resume: Yes, the system does the job, and that is more than fascinating. Measuring a sugar beet canopy at the right date with a hyperspectral sensor provides a numerical estimator about the nematode population in the soil. Error levels are high for sure, but, as usual in nematology, certainly not larger than soil sample based decisions. No counteraction is possible for the current crop (is that true? Are systemic nematicides out there?), but integrated nematode control deals with long term decision making and sustainability. Similar as the backward calculation of the original Pi the Leslie model and Difference model calculates forward, from Pf to Pi at next sugar beet. The concept introduced here implement a complete system for the H. schachtii control. The host-parasite model is certainly not perfect and mimic just parts of the reality (how ever that reality looks like), but only the combined application of both model types results in a perhaps hypothetical population density number at a time of the season when hyperspectral signatures respond with structural changes indicating the nematode impact. Exactly at that date the Leslie model correspond with a temporal maximum of cysts in the crop, which is more than plausible. The complexity and intensity, as female adults or cysts deter the crop physiology for the production of new eggs, let expect a change in the signature. The physiological process have been part of the underlying working hypothesis right from the beginning of the project. Based on the information about the dynamics of the host-parasite interaction model this critical date have had been expected in the range of a BT of ~35. No decent linearity or other meaningful structure from spectrum to population density (i.e. number of J3) were possible at this date.
We introduce a technique which have been developed to observation data in conjunction with local temperature pattern of the Rhineland, Germany. Although a common applicability of the system is wanted and likely, further investigations on other sites are required.
One more practical hint to the current end of the project: The importance of the right date for hyperspectral measurement has been sufficient described, but it is also crucial to measure in not wilting canopies and without water stress, when leaves are flattened. The changed reflections would focus on soil reflections and would mask the weak nematode impact again.

The hyperspectral data have been measured as part of a Nemaplot initiated and EU financed Project at the JKI Elsdorf (EU-funding no.: z1011bc001a)