Moving window growth—A method to characterize the dynamic growth of crops in the context of bird abundance dynamics with the example of Skylark (Alauda arvensis)

Abstract Agricultural field crops differ in their vegetation height, coverage, and temporal development, affecting the abundances of bird species, which are often used as bioindicators. Although this relationship has been observed, no significant methodology exists to describe the dynamics of field crop growth on a landscape scale in connection with the abundance of indicator bird species that allows meaningful interpretation of bird abundance data with respect to crop vegetation parameters during the breeding season. In a field observation program, we monitored 2,900 ha of agricultural landscape to represent both the crop growth processes and the bird abundances. We measured these two parameters in the study area, dominated by winter wheat, winter rapeseed, maize, and fallow fields, and adapted the moving window approach to a new method of “moving window growth” to describe the dynamic development of height and coverage of the crops over time. Simultaneously, Skylarks (Alauda arvensis) territorial behavior was measured concurrently on the same fields and crops. Their dynamic abundance was documented over the breeding season. To test the relationship between crop growth and development and bird abundance, we applied a generalized linear model (GLM) in two ways: (a) without differentiation of crop species and (b) with differentiation of crop species. We found significant relationships between bird abundance and vegetation height and coverage with respect to both individual parameters and their interactions, even without differentiation of the agricultural crops. In general, increasing vegetation height and coverage, especially the interaction, led to decreasing bird abundance values. The model quality increased significantly by including differentiation of specific crops as an explanatory variable indicating a non‐homogenous situation between crops. Separate models for individual crop species revealed larger differences in model quality with best and least goodness of fit values for fallow fields and winter rapeseed, respectively. Because of the clear interactions between bird abundance, type of field crop, and vegetation height and coverage, it follows that both habitat suitability assessments of arable fields and the definition of favorable vegetation structures for farmland birds should be crop species‐specific.

tion with the abundance of indicator bird species that allows meaningful interpretation of bird abundance data with respect to crop vegetation parameters during the breeding season. In a field observation program, we monitored 2,900 ha of agricultural landscape to represent both the crop growth processes and the bird abundances. We measured these two parameters in the study area, dominated by winter wheat, winter rapeseed, maize, and fallow fields, and adapted the moving window approach to a new method of "moving window growth" to describe the dynamic development of height and coverage of the crops over time. Simultaneously, Skylarks (Alauda arvensis) territorial behavior was measured concurrently on the same fields and crops. Their dynamic abundance was documented over the breeding season. To test the relationship between crop growth and development and bird abundance, we applied a generalized linear model (GLM) in two ways: (a) without differentiation of crop species and (b) with differentiation of crop species. We found significant relationships between bird abundance and vegetation height and coverage with respect to both individual parameters and their interactions, even without differentiation of the agricultural crops. In general, increasing vegetation height and coverage, especially the interaction, led to decreasing bird abundance values. The model quality increased significantly by including differentiation of specific crops as an explanatory variable indicating a non-homogenous situation between crops. Separate models for individual crop species revealed larger differences in model quality with best and least goodness of fit values for fallow fields and winter rapeseed, respectively.
Because of the clear interactions between bird abundance, type of field crop, and vegetation height and coverage, it follows that both habitat suitability assessments of arable fields and the definition of favorable vegetation structures for farmland birds should be crop species-specific.
Progress in plant breeding and agricultural management has led to high-yield crops in arable areas; however, individual crop species often differ significantly in phenology and growth patterns. In Central Europe, the main crop growth period in spring and summer coincides with the time of territorial occupation and reproduction by farmland birds. Plant growth leads to continuous changes in the vegetation structure of crops, influencing the suitability of crop fields as bird breeding habitats, as shown by Weibel (1999), Weibel, Jenny, Zbinden, and Edwards (2001), and Schön (2011) with regard to nesting and feeding. Height and coverage are important characteristics of vegetation structure, and temporal crop development can be described with these parameters (Toepfer & Stubbe, 2001).
If bird abundance values can be related to specific vegetation structures, the suitability of crops as habitat for farmland bird species can be inferred. For example, Jenny (1990) found that vegetation coverage of over 50% strongly limits the ability of Skylarks to move on the ground as well as to fly into the vegetation. Similarly, Toepfer and Stubbe (2001) acknowledge the influence of vegetation height and coverage, especially temporal development, on bird abundance.
Typically, Skylarks emigrate from habitats if the vegetation becomes too high and too dense, and the birds then switch to areas with less dense vegetation (Stöckli, Jenny, & Spaar, 2006). Therefore, some empirical approaches to enhance the habitat quality of crop fields aim at less high and dense plant coverage, e.g., in some parts of the crop fields (Dicks et al., 2011;Donald & Morris, 2005;Fischer, Jenny, & Jenni, 2007;Morris, Holland, Smith, & Jones, 2004;Stöckli et al., 2006).
In order to gather the appropriate information, empirical data on both vegetation structure and bird abundance are needed, taken simultaneously on identical arable fields.
There are many models used to describe crop growth (Asseng et al., 2013;Mirschel & Wenkel, 2007;Nendel et al., 2011;Poluektov & Terlev, 2007;Wenkel & Mirschel, 1991); however, most crop growth models focus only on anthesis, maturity, and especially on crop yield. They do not model the habitat structures characteristics like height and coverage of the vegetation. On the other hand, many bird monitoring programs in agricultural landscapes do exist without a parallel documentation or measurements of crop vegetation characteristics. As a consequence, the relations between crop growth dynamics and abundance dynamics of farmland birds are unclear, apart from some observations on very local and short time bases.
To solve this problem, a method is needed which encompasses (a) a data acquisition scheme, simple enough to be applied on a larger scale, i.e., on an appropriate number of fields; and (b) a crop growth model which characterizes the structural parameters of maize, winter rapeseed, etc., and allows to relate these to bird abundance data.
To this end, we propose a novel crop growth model approach, which describes the growth process of the vegetation structures of specific crop species with a high temporal resolution. To assess the effects of crop vegetation parameters on the habitats of farmland birds, the time range of the breeding season should be covered.
The received vegetation parameters (height, coverage) should be analyzed in relation to the simultaneously observed bird individuals with territorial behavior on the same fields. We take as an example the Skylark (Alauda arvensis; Figure 1), a typical farmland bird (BirdLife International, 2004;Gedeon et al., 2014), which is also an indicator species of the biodiversity of Central European farmland areas (Achtziger, Stickroth, & Zieschank, 2004;EBCC 2012

| Study area
The study area is located in Central Europe within the federal state of Brandenburg, Germany. The average annual temperature is 8.4°C, and the average annual precipitation is 520 mm. Fifty-five percent of the total land area in Brandenburg is covered by agricultural landscapes, 69% of which is dominated by arable land, including 5%-7% semi-natural small biotope structures. The main crops are winter cereals, winter rapeseed, and maize.  Table 1. Field maps were prepared based on the field geometries of all of the sampling plots using aerial photographs and field maps from the farms. The maps included the contours of all arable fields and small structures (biotopes), which were digitized and stored as polygon shapes (Hoffmann et al., 2016).  Table 2). The assignments of Vh and Vc in these classes were achieved by visual assessment while conducting line transects within the plots, with a distance of approximately 100 m between the transects. Small fields (10 fields <1 ha) were included by direct sampling, field by field. The spatial heterogeneity of the vegetation structures of the agricultural crops, e.g., due to variable soil conditions in the single fields or management effects such as tractor lanes, was recognized by estimating the share (%) of the field area that belonged to each of the Vh resp. Vc classes (see Tables 2 and 3). Data collection on one plot at one survey was thus linked to a transect survey length of approximately 8-10 km. The results were stored in databases (MS Access ™ ).

| Investigating bird data
The data surveys on Skylark were performed on the 29 1-km² plots using mapping of bird individuals or pairs with territorial behavior (Hoffmann, Wittchen, Stachow, & Berger, 2013;Hoffmann et al., 2012Hoffmann et al., , 2016. This method is based on the "territory mapping method" (Dornbusch, Grün, König, & Stephan, 1969;Fischer, Flade, & Schwarz, 2005;Oelke, 1968). All detected birds which did not exhibit territorial behavior, probably guests and resting birds, were excluded from the subsequent analyses. The field surveys for birds were conducted by the same person on the same days as the vegetation surveys, as described above. Then we applied the "moving TA B L E 1 Crops (number of fields (nf); ha) and other habitats (ha; ∑4.95%) found in the 29 plots (1 km² each) window abundance" (Hoffmann et al., 2016) approach to the Skylark data for winter wheat, winter rapeseed, maize, and fallow fields.

| Calculation of vegetation structures in the time course
We modified the "moving window abundance" method (Hoffmann et al., 2016) to be applicable to plant growth, which we termed "moving window growth" (MWG). MWG characterizes the growth of study crops within a time interval (a, b) ( Figure 2); in our case, the growth period was between March 16th and July 18th, which covers the breeding period of Skylarks. MWG was used to calculate daily values for the structural vegetation parameters Vh and Vc based on the field data (see above). It was necessary to compare the parameters to standardize the data for height (m) and coverage (%) to a dimensionless index between 0 and 1 for each parameter.
The time window in MWG was five days, and the average was assigned to the 3rd day. The shift of consecutive windows was one day, according to the specific overlapping moving window method (Hoffmann et al., 2016). The results are crop-specific daily Vhindex (VIh) and Vc -index (VIc) values for the 121-day time period from March 18th to July 16th. Finally, the functions that fit the values were calculated using SAS ™ (NLIN procedure).
Based on this, the analyses were conducted in three steps, (a) to (c), as described below. Combining all classes into vegetation indices (VIh for height, VIc for coverage) is accomplished using Equations (1) and (2).
VIh for height: [n = 4 = number of the vegetation height classes, see Table 2; i = individual height class (i = 1-4); rAh = relative proportion (% of the area) of height class I].
and VIc for coverage: [n = 4 = number of the vegetation cover classes, see Table 2; j = individual cover class (j = 1-4); rAc = relative proportion (% of the area) of cover class j].
The indices are standardized so that all of the values are between 0 and 1. If all of the vegetation belonged to class 1, then the vegetation index would be 0; if all of the vegetation belonged to class 4, then the vegetation index would be 1 (see Table 2 TA B L E 3 Theoretical example to characterize the height of a crop in a study area (plot) on one date. Seven fields of this crop were found (columns 1-7), each with a specific distribution of areas belonging to the four height classes. For example, in field 1, 70% of the area had a crop height between 0.25 and 0.5 m (class 2) and 30% had heights between 0.5 and 0.75 m (class 3). The values in the columns add up to 100%. This was performed similarly for the vegetation coverage for the analysis period that resulted in the highest ranked habitat quality class (1) (see Table 4).

| Vegetation structures of field crops during the growth course
With the MWG growth model for the time interval (a, b), we collected data on vegetation height and coverage for 95% of all possible days in wheat, winter rapeseed, and maize and 97% in fallow fields (Table 5). The table also shows that approximately 1/3 of the areas covered by the respective crops are represented by each of the daily data.
The growth curves of the agricultural crops differed clearly, as shown in Figure 3 for vegetation height (VIh as MWG) for WW, WR, MA, and FF. The functions of the MWG resulted in daily values for the whole monitoring period (77th to 197th day).
The function for WW follows an arctan curve, whereas WR and MA have a tangens hyperbolicus shape. In all field crops, a time period of little or no growth in height (VIh from 0 to approximately 0.1) is followed by a short phase of intensive growth, when VIh is >0.05 to approximately 0.8-0.9. However, the time periods of rapid growth differed between the crops (Figure 3, Table 6).

| Vegetation structures as determining factors for Skylark abundances
The GLM showed significant main effects and interactions for vegetation height and coverage on Skylark abundance even when the crop species were not included ( Table 7). The parameter estimates revealed negative regression coefficients for the VIh and VIc interaction.
When the crop species (WW, WR, MA, and FF) were included as variables, the model fit was further enhanced (Table 8). Facing this higher model complexity the penalizing BIC value decreased and the deviance ratio was much lower and closer to 1, indicating a better goodness of fit.
The separate GLMs of the four crops were significant but reveal large differences between model qualities (

| Vegetation coverage and Skylark abundance at similar vegetation heights for different field crops
To identify the impact of crop-specific vegetation structures on Skylark abundance, we compared the vegetation coverage and Skylark abundance at a similar vegetation height (VIh) for the crops.
This was the case for a VIh of 0.12-0.13 for the three crops and the fallow fields. The coverage (VIc) differed significantly between the crops, as did the Skylark abundances (Table 10)

| Abundance courses of Skylark in relation to the course of the vegetation structure development
The relationship between Skylark abundance and the development of crop vegetation structures, expressed as MWA resp. MWG, is shown in Figure 5. The parameters for vegetation structure were restricted to VIh and VIc.

| Comparison of the potential habitat quality of four agricultural crops during the Skylark breeding season
Using the functional equation for MWA and MWG, the time periods for the five classes for the potential habitat quality (Hq1-Hq5, see Table 4) could be identified for each crop according to Skylark abundance ( Figure 6). Moreover, three con-

| Method to describe the growth patterns of agricultural crops
The new moving window growth (MWG) method, a modification of the MWA (moving window abundance) method (Hoffmann et al., 2016), may have the potential to closing the knowledge gap about interrelations between crop vegetation structures and farmland bird abundances in field crops. To this end, the synchronized collection of vegetation and bird data on identical fields seems to be of paramount importance.
With the MWG method, the daily values of the vegetation structures throughout the growth period were calculated and thus made usable to characterize the growth patterns. Height and coverage were thus expressed quantitatively for each day and thus for any time interval within the growth period, and thus allow for comparisons between different crop species.
The vegetation on fallow fields, which was not disturbed by any agricultural measure during the growth period, is composed of a variety of grass and herb species (Berger, Pfeffer, Kächele, Andreas, & Hoffmann, 2003;Hoffmann et al., 2012;Jüttersonke, Arlt, & Rischewski, 2008) and is a special case compared to the agricultural crops investigated

| Habitat qualities of vegetation structures and Skylark abundance
The common method to characterize the suitability of a habitat for breeding birds is the determination of a single value for abundance, e.g., territories per 10 ha (Bauer, Fiedler, & Bezzel, 2005 are not based on a classification of crops (e.g., spring-sown vs. autumn-sown) but describe the development as a process that is individual for each crop species within a time interval (a, b). The application of the methods requires an appropriate sample size of both the study areas and bird individuals exhibiting territorial behavior to allow for statistical analysis of the differences between the growth dynamics of crops and bird abundances. The data and methods that do not accommodate these dynamics have limited explanatory value.
The results point to the importance of suitable vegetation structures and of crop diversity within a landscape for Skylarks.
The diversity relies on a temporal aspect, i.e., the crop-specific periods of high habitat suitability rotated between the crops within the breeding period, and a spatial aspect, i.e., respective crops are within the Skylark's flight distance. This also means that the theory that high crop diversity automatically leads to high abundance of Skylark (Daunicht, 1998;Engel, Huth, & Frank, 2012;EU, 2007;Tucker & Heath, 1994) can thus be attained only within limits set by the specific crops within the agricultural area (Chamberlain, Vickery, & Gough, 2000;Chamberlain, Wilson, Browne, & Vickery, 1999;Vepsäläinen, 2007). In areas with low crop diversity, temporally or spatially, land use types such as fallow fields, which have very high habitat suitability for Skylarks, obviously have the potential to partly buffer these deficits.
F I G U R E 6 Time periods of potential habitat quality levels (Hq1 -very high, Hq2 -high, Hq3 -medium, Hq4 -low, Hq5 -very low) for Skylark in fallow fields (FF), maize (MA), winter rapeseed (WR), and winter wheat (WW); three successive breeding cycles (BC1, BC2, and BC3), each of 40 days, which are theoretically possible, are marked The temporal differences in maximum Skylark abundance values and the different potential habitat suitability classes identified in the crops clarify the appropriate time frame for optimized Skylark monitoring, in order to use bird species and their abundance dynamics as indicator for biodiversity components. In Germany, the suggested time period spans approximately 40 days, from the beginning of April to the beginning of May (Suedbeck et al., 2005). However, to adequately grasp crop-specific habitat suitability dynamics, a longer monitoring period is necessary. As shown for winter rapeseed, high Skylark abundances (in our terminology: "Habitat suitability class 2") can be found within a time interval of only 3 weeks. This indicator of high suitability, if taken alone, would suggest that winter rapeseed is a favorable crop for Skylarks. Taking into account the declining abundance in May and June, the overall assessment of this crop would be dramatically altered.

| CON CLUS ION
Of all of the factors that affect bird populations on agricultural landscapes, the crop species that are being grown and the spatialtemporal appearance of the respective vegetation structures are of significant importance. Therefore, methods that are applicable on the landscape scale are required to quantify and assess the habitat suitability of the crops and thus be able to better evaluate their functions for farmland birds and the potential to use data on bird abundances as ecological indicator for agricultural landscapes. Important Finally, the generation of the empirical data on crop vegetation should be performed and doable on a landscape scale, similar to typical bird monitoring schemes, so that data collections can be combined.
In our view, this would significantly broaden the basis for fact-based interpretation of bird abundance data, thereby creating appropriate hypotheses and experimental designs, and finally well-based recommendations to support biological diversity in agricultural landscapes.