Combinatorial Maps, a New Framework to Model Agroforestry Systems.

Agroforestry systems are complex due to the diverse interactions between their elements, and they develop over several decades. Existing numerical models focus either on the structure or on the functions of agroforestry systems. However, both of these aspects are necessary, as function influences structure and vice versa. Here, we present a representation of agroforestry systems based on combinatorial maps (which are a type of multidimensional graphs), that allows conceptualizing the structure-function relationship at the agroecosystem scale. We show that such a model can represent the structure of agroforestry systems at multiple scales and its evolution through time. We propose an implementation of this framework, coded in Python, which is available on GitHub. In the future, this framework could be coupled with knowledge based or with biophysical simulation models to predict the production of ecosystem services. The code can also be integrated into visualization tools. Combinatorial maps seem promising to provide a unifying and generic description of agroforestry systems, including their structure, functions, and dynamics, with the possibility to translate to and from other representations.

Disease spread across multiple scales in a spatial hierarchy: effect of host spatial structure and of inoculum quantity and distribution.

Spatial patterns of both the host and the disease influence disease spread and crop losses. Therefore, the manipulation of these patterns might help improve control strategies. Considering disease spread across multiple scales in a spatial hierarchy allows one to capture important features of epidemics developing in space without using explicitly spatialized variables. Thus, if the system under study is composed of roots, plants, and planting hills, the effect of host spatial pattern can be studied by varying the number of plants per planting hill. A simulation model based on hierarchy theory was used to simulate the effects of large versus small planting hills, low versus high level of initial infections, and aggregated versus uniform distribution of initial infections. The results showed that aggregating the initially infected plants always resulted in slower epidemics than spreading out the initial infections uniformly. Simulation results also showed that, in most cases, disease epidemics were slower in the case of large host aggregates (100 plants/hill) than with smaller aggregates (25 plants/hill), except when the initially infected plants were both numerous and spread out uniformly. The optimal strategy for disease control depends on several factors, including initial conditions. More importantly, the model offers a framework to account for the interplay between the spatial characteristics of the system, rates of infection, and aggregation of the disease.

Linear relationship between Gaeumannomyces graminis var. tritici (Ggt) genotypic frequencies and disease severity on wheat roots in the field.

In order to investigate potential links existing between Gaeumannomyces graminis var. tritici (Ggt) population structure and disease development during polyetic take-all epidemics in sequences of Ggt host cereals, seven epidemics in fields with different cropping histories were monitored during the seasons 2001/2002 (two fields), 2002/2003 (two fields) and 2003/2004 (three fields). Take-all incidence and severity were measured at stem elongation and Ggt populations were characterized. The 73 isolates collected in the two fields in 2001/2002 were distributed into two multilocus genotypes, G1 and G2 according to amplified fragment length polymorphism analysis. A monolocus molecular marker amplified by F-12 random amplification polymorphism DNA primer sizing between 1.9 and 2.0 kb that gave strictly the same distinction between the two multilocus genotypes was further applied to measure G1/G2 frequencies among Ggt populations in all fields (266 isolates). The ratios of G1 to G2 differed between fields with different cropping histories. A linear relationship between G2 frequency among Ggt populations and disease severity at stem elongation was measured during the three cropping seasons. When take-all decline was observed, G2 frequencies were low in first wheat crops, highest in short-term sequences and intermediate in longer sequences of consecutive crops of Ggt host cereals. This pattern could be the result of population selection by environmental conditions, in particular by microbial antagonism during the parasitic phase of the fungus. In order to better understand take-all epidemic dynamics, the distinction between these two genotypes could be a basis to develop models that link approaches of quantitative epidemiology and advances in population genetics of Ggt.