Spatial Structure in population dynamics

Most weed population dynamics models ignore the within-field distribution of the weed and generally simulate the average density per area (Holstet al., 2007). However, some studies include the spatial distribution of weeds. Developing spatially explicit models is difficult due to the necessity of obtaining dispersal data and data on the impact of environmental heterogeneity on individual performance (Freckletonet al., 2008) yet, as many weed species are patchy, it is often desirable to include their spatial distribution in models of their population dynamics. These models often only include intrinsic demographic parameters and dispersal. These features alone are often not sufficient to describe the degree of patchiness observed. It is thought that this may be due to the omission of soil variables (Paiceet al., 1998; Rew & Cousens, 2001). Also, dispersal models are often weak predictors as it is difficult to determine the exact shape of the dispersal kernel; an important part of modelling patch spread (Rew & Cousens, 2001).

The incorporation of spatial structure into weed population dynamics models can also have an important stabilizing effect, yet it is often ignored (Freckletonet al., 2008). The densities within individual patches can be relatively high despite low densities across the whole field. This makes the error in estimation of model parameters becomes less problematic as the problems associated with small errors in parameter estimates when a population is close to an extinction boundary will be buffered by the high population densities in the centre of patches and so stability is maintained (Freckletonet al., 2008).

Paice et al. (1998), considered the need for a spatial component to models of A. myosuroidespopulation dynamics. Building on basic models of the A. myosuroides life-cycle they incorporated elements of stochasticity into the life-cycle processes as well as binomial probability of herbicide survival. They included both isotropic and anisotropic dispersal processes derived from Howardet al. (1991) and modelled this in a rectangular area of a field defined by square cells scalable to real units of distance. They showed that when dispersal only occurs over short distances, patchiness can be maintained and even if the field is initialised with a uniform seed bank the population will develop toward a more patchy distribution.

Gonzalez-Andujaret al. (1999) also considered spatial patterns in the modelling ofA. myosuroides in an array of hexagons representing part of a field. The centre of each cell was spaced 1 m from its neighbours. Dispersal was assumed to be isotropic

and followed an exponential distribution truncated at 2.5 m. Isotropic dispersal by the combine was also considered. They demonstrated through simulations that there was some evidence for patch longevity (<10 years) under these conditions but that without further intervention a uniform distribution would be reached eventually.

6.2.3 Environment

The abiotic environment is often ignored in weed population models, despite the importance of factors such as light, water and nutrients, and intra- and interspecific competition (Holstet al., 2007). Often, the importance of the environment is outweighed by its complexity. Models usually operate on a yearly time-step. This precludes much environmental variation, which generally operates at shorter time steps.

Dunker et al. (2002) took steps toward including soil in a spatial model of A. myosuroides population dynamics. They included nutrients, soil pH and particle size in their model, based on the results of a pot experiment where these were manipu- lated in artificial soils. They verified this model in one field whereA. myosuroidescounts and soil properties were measured on a 50 x 50 m grid. Their model was based on the demographic data from Moss (1990). Only germination probability and probability of survival were affected by soil in their model as their experiment on which these were based was only conducted for 5 weeks post germination. The model arena consisted of a 20 x 20 m grid and the population dynamics continued independently in each cell. One percent of seeds from each cell were dispersed equally into the 4 adjoining cells. They found their simulations to be only weakly correlated with the real data and only 4 out of 20 showed a significant correlation, yet 18 out of the 20 simulations produced stronger correlations when soil properties were included.

6.3

Introduction

Alopecurus myosuroidesHuds. (black-grass), is a common grass weed of winter cereals in north-west Europe (Holmet al., 1997). It is particularly problematic in the UK due to its fast reproductive rate and strong competitive ability with the crop (Mar´echalet al., 2012). Its life-cycle is largely synchronised with that of winter cereals allowing it to compete at all stages of growth (Mar´echalet al., 2012). Alopecurus myosuroidesplants

can produce vast amounts of seeds (Moss, 1980) meaning small failures in control can lead to rapid population growth and dense infestations within some fields. As such, control of the population is of great importance to farmers. Currently, the main means by which farmers choose to control this pernicious weed is through broadcast application of herbicides. However, many farmers have seen a decline in the levels of control achieved because of the evolution of herbicide resistance. This together with the decreasing number of chemical products available for use and increasing economic and environmental pressures to reduce herbicide use puts a growing emphasis on the optimisation of current techniques and finding alternative approaches (Grundy, 2003).

Approaches for reducing the amount of herbicide on farm are wide ranging, from the introduction of additional cultural control methods focussing on the species’ biology and ecology, to the introduction of economic thresholds or particular densities of weeds below which there is little economic reason to spray herbicides as the cost of inputs will exceed yield losses. Another option, which is gathering interest, is precision management, including the spatially variable application of herbicides, or patch spraying.

The within-field distribution of A. myosuroidesis patchy (Wilson & Brain, 1991; Krohmann et al., 2006; Metcalfeet al., 2016 and 2017c (Chapters 2 and 3)) and as such this presents an opportunity for site-specific management. There are currently two main approaches to patch management: real-time detection of weeds and treatment maps. Each of these approaches has merit but also associated problems. The use of real-time sensors is an approach that is still in development, and whilst already feasible it is not yet at the stage of widespread commercialization (e.g. Murdochet al., 2010 and 2014), whereas treatment maps can be created more easily from manually sampled data on weed distributions, but can sometimes be of inadequate quality, often because the sampling on which they are based was too sparse (Metcalfeet al., 2016 (Chapter 2)). Both approaches are based on the mapping of easily detectable seed heads in the summer. However, Metcalfeet al.(2017c (Chapter 3)) showed that the distribution of seed heads in the summer is a contraction of the initialA. myosuroidespatch and so spray maps based upon these distributions present a risk of missing the true extent of the seedling patch. This risk of missing individuals that fall outside of mapped zones is perhaps the biggest hurdle in the implementation of patch spraying on farms due to the inherent and understandable conservativeness of farmers when it comes to weed control. Given the consequences of a control failure, the concept of leaving some areas of the field

unsprayed is currently seen as an unacceptable risk.

A possible extension to current techniques which addresses concerns about indi- viduals establishing outside of mapped patches is to identify parts of the field that are vulnerable toA. myosuroides. These “weed vulnerable zones”, once identified could be used in the creation of spray maps to guide the precision application of herbicides. As there is some indication that the patchy distribution ofA. myosuroidesin fields is related to variation in soil properties (Holmet al., 1997; Lutmanet al., 2002, Murdochet al., 2014, Metcalfeet al., 2016 and 2017c (Chapters 2 and 3)). This may provide a basis upon which to identify weed vulnerable zones within fields. If it is possible to identify a deterministic link between the soil and the location ofA. myosuroidespatches then soil maps could be used as a basis for patch spraying. Many farmers will already have soil maps for their farms and may already be using these in other forms of precision management such as the variable application of fertiliser within-field.

6.3.1 Objectives

Our aim was to develop a spatially explicit model of the life-cycle model ofA. myosuroides. The model was based on the work of Moss (1990), Colbachet al. (2006a) and Paice et al.(1998) but extended to include the direct and indirect effect of soil on the weed based on experimental data. By modifying the life-cycle of the plant according to known responses to variation in soil properties we tested the hypothesis that scale-dependent relationships between soil properties and the density ofA. myosuroidesobserved in fields by Metcalfeet al. (2017c (Chapter 3)) can be modelled according to the changes to each aspect of the weed’s life-cycle caused by different soil properties.