Some theoretical notes on agrobiodiversity: spatial heterogeneity and population interactions
Diego Griffon and Maria-Josefina Hernandez
Ecological interactions are fundamental in ecological pest management,
and these interactions form networks. The properties of these networks,
where interactions of all possible nature (positive, neutral, negative)
coexist, are key for management, but little is known about them. The
main reasons for this lack of knowledge are the difficulties in
obtaining empirical evidence. These problems may be partially bypassed
using a theoretical approach. Here, by means of mathematical models that
represent networks of ecological interactions in agroecosystems, we
characterize some architectural features that promote the
self-regulation of population densities in these networks. The results
show that the key features are: spatial heterogeneity and a high
proportion of positive interactions.
Biodiversity and spatial heterogeneity strongly benefit agricultural landscapes. Among others, these benefits are related to population regulation of organisms that feed on cultivated plants (Duflot et al. 2015; Fahrig et al. 2011; Letourneau et al. 2011; Rusch et al. 2016, 2010; Tscharntke et al. 2002, 2012; Vandermeer 1989). However, there is a need for further theoretical development to help us understand the processes behind these empirical observations, particularly from a mechanistic point of view. In a very general sense, in the agroecological literature it is proposed that increasing agricultural biodiversity involves an increase in the number of trophic interactions of the ecological community, which in turn promotes the stability of the whole system (Altieri 1983; Altieri and Nicholls 2000, 2004; Nicholls and Altieri 2002). On the other hand, we acknowledge that the ecological evidence concerning the relationship between the number of species (richness) and the number of trophic interactions in natural ecosystems is ambiguous (Hall and Raffaelli 1997) and, that from a theoretical point of view, the relationship between complexity and stability is an issue far from resolved (Allesina and Tang 2015; Bersier 2007; Ings et al. 2009; Namba 2015). However, when it comes to contrasting a monoculture with a multidiverse agroecosystem, these topics may have clearer answers (Griffon and Hernández 2014; Griffon and Rodríguez 2017; Rusch et al. 2016, 2010; Tscharntke et al. 2012).
In a conventional monoculture, the system is explicitly designed and managed to reduce as much as possible the unplanned associated biodiversity(typically by using insecticides, herbicides, etc.). Paradoxically this may contribute(among other things) to the long term establishment of phytophagous organisms in the system, eradicating at the same time their biological controllers (Jonsson et al. 2015; Landis, Wratten, and Gurr 2000; Levins and Vandermeer 1990). In this type of farming system most species are related directly to one (the monoculture) by a victim-exploiter relationship (i.e., predation, parasitism, parasitoidism and herbivory), where the monoculture species (the crop) typically plays the role of the victim. So, the system has a star-like architecture (i.e., many nodes connected to a central hub) with the monoculture in the center (Griffon and Torres-Alruiz 2008), which is a structure that favours the occurrence of pest situations and crops losses (Griffon and Hernández 2014; Griffon and Rodríguez 2017).
Alternatives to the ecological oversimplification of monocultures are companion crops. One of the aims of this cropping strategy is the population regulation of phytophagous and phytopathogenic species by means of ecological interactions (Altieri and Nicholls 2004). The success of this approach not only depends on the occurrence of a more complex trophic web, but also on the occurrence of other ecological interactions (competition, mutualism, amensalism and commensalism) that together make up the ecological network system, i.e., a network consisting of all types of ecological interactions (Ings et al. 2009). We have very little information on the structure of ecological networks (Pocock et al. 2012) and we also lack knowledge on how ecological networks promote the regulation of phytophagous population densities. Given the need of information, coupled with the difficulty and effort involved in achieving it in the field, this paper addresses the issue from a theoretical perspective. In order to do this, we build and numerically evaluate mathematical models that simulate networks of hypothetical ecological interactions associated with agricultural ecosystems. This is done with the objective of finding patterns that can provide guidelines on architectural features associated with self-regulation in populations.
Another related topic must be considered. There is abundant field information that shows the positive effects of spatial heterogeneity (Batáry et al. 2011; Duflot et al. 2015; Fahrig 2013; Fahrig et al. 2011, 2015; Jonsson et al. 2015; Landis, Wratten, and Gurr 2000; Rusch et al. 2016; Tscharntke et al. 2012; Tuck et al. 2014) on the maintenance of associated agricultural biodiversity (sensu Vandermeer and Perfecto 1995; Altieri et al. 2005). In some cases, space heterogeneity may even play a more important role than intra-farm diversity in the regulation of phytophagous population densities (Fahrig et al. 2011, 2015). But surely the two components (intra and inter farm diversity) relate synergistically.
For the spatial heterogeneity to have a positive effect on the internal dynamics of agroecosystems it is necessary, on the one hand, an insidefarm design that attracts biological controllers (e.g., flower strips or beetle banks) (Altieri, Ponti, and Nicholls 2005; Nicholls and Altieri 2002) and on the other, the existence of nearby sources of organisms with enough internal complexity to provide the necessary control agents (Rusch et al. 2016, 2010; Tscharntke et al. 2012).
So, metapopulation and metacommunity dynamics seem to be crucial for the long term survival of species in heterogeneous environments (Alfonzo et al. 2009; Aberg et al. 1995; Cantrell, Cosner, and Fagan 1998; Delin and Andren 1999; Griffon, Alfonzo, and Hernandez 2010; Griffon and Hernández 2014; Gustafson and Gardner 1996; Perfecto, Vandermeer, and Wright 2009; Sisk, Haddad, and Ehrlich 1997; Tejat et al. 2002; Vandermeer and Carvajal 2001; Vandermeer and Perfecto 2007). In general terms, the spatial structure of populations, along with processes of dispersal, migration and colonization, allows the emergence of dynamics that make possible the persistence and coexistence of species (Hanski 1994, 1998; Hanski and Gilpin 1997; Hanski et al. 1996; Leibold et al. 2004). Thus, spatial heterogeneity may enhance the configuration of the complex ecological networks needed for a successful ecological pest management program (Batáry et al. 2011; Fahrig et al. 2011; Rusch et al. 2016, 2010; Tejat et al. 2002; Tscharntke et al. 2002, 2012). For this reason, in the mathematical approach used here we also include the effect of spatial heterogeneity on population dynamics.
In short, the objective of this work is to find architectural features that promote the self-regulation of population densities in ecological networks associated to agroecosystems. To do this, we built mathematical models that represent ecological networks, both for a single community and for metacommunitarian systems. We must make clear that whenever we say ‘ecological network’, we are considering the potential presence of ‘all’ types of interactions, i.e., competition, mutualism, victim-exploiter, amensalism and commensalism.
Biodiversity and spatial heterogeneity strongly benefit agricultural landscapes. Among others, these benefits are related to population regulation of organisms that feed on cultivated plants (Duflot et al. 2015; Fahrig et al. 2011; Letourneau et al. 2011; Rusch et al. 2016, 2010; Tscharntke et al. 2002, 2012; Vandermeer 1989). However, there is a need for further theoretical development to help us understand the processes behind these empirical observations, particularly from a mechanistic point of view. In a very general sense, in the agroecological literature it is proposed that increasing agricultural biodiversity involves an increase in the number of trophic interactions of the ecological community, which in turn promotes the stability of the whole system (Altieri 1983; Altieri and Nicholls 2000, 2004; Nicholls and Altieri 2002). On the other hand, we acknowledge that the ecological evidence concerning the relationship between the number of species (richness) and the number of trophic interactions in natural ecosystems is ambiguous (Hall and Raffaelli 1997) and, that from a theoretical point of view, the relationship between complexity and stability is an issue far from resolved (Allesina and Tang 2015; Bersier 2007; Ings et al. 2009; Namba 2015). However, when it comes to contrasting a monoculture with a multidiverse agroecosystem, these topics may have clearer answers (Griffon and Hernández 2014; Griffon and Rodríguez 2017; Rusch et al. 2016, 2010; Tscharntke et al. 2012).
In a conventional monoculture, the system is explicitly designed and managed to reduce as much as possible the unplanned associated biodiversity(typically by using insecticides, herbicides, etc.). Paradoxically this may contribute(among other things) to the long term establishment of phytophagous organisms in the system, eradicating at the same time their biological controllers (Jonsson et al. 2015; Landis, Wratten, and Gurr 2000; Levins and Vandermeer 1990). In this type of farming system most species are related directly to one (the monoculture) by a victim-exploiter relationship (i.e., predation, parasitism, parasitoidism and herbivory), where the monoculture species (the crop) typically plays the role of the victim. So, the system has a star-like architecture (i.e., many nodes connected to a central hub) with the monoculture in the center (Griffon and Torres-Alruiz 2008), which is a structure that favours the occurrence of pest situations and crops losses (Griffon and Hernández 2014; Griffon and Rodríguez 2017).
Alternatives to the ecological oversimplification of monocultures are companion crops. One of the aims of this cropping strategy is the population regulation of phytophagous and phytopathogenic species by means of ecological interactions (Altieri and Nicholls 2004). The success of this approach not only depends on the occurrence of a more complex trophic web, but also on the occurrence of other ecological interactions (competition, mutualism, amensalism and commensalism) that together make up the ecological network system, i.e., a network consisting of all types of ecological interactions (Ings et al. 2009). We have very little information on the structure of ecological networks (Pocock et al. 2012) and we also lack knowledge on how ecological networks promote the regulation of phytophagous population densities. Given the need of information, coupled with the difficulty and effort involved in achieving it in the field, this paper addresses the issue from a theoretical perspective. In order to do this, we build and numerically evaluate mathematical models that simulate networks of hypothetical ecological interactions associated with agricultural ecosystems. This is done with the objective of finding patterns that can provide guidelines on architectural features associated with self-regulation in populations.
Another related topic must be considered. There is abundant field information that shows the positive effects of spatial heterogeneity (Batáry et al. 2011; Duflot et al. 2015; Fahrig 2013; Fahrig et al. 2011, 2015; Jonsson et al. 2015; Landis, Wratten, and Gurr 2000; Rusch et al. 2016; Tscharntke et al. 2012; Tuck et al. 2014) on the maintenance of associated agricultural biodiversity (sensu Vandermeer and Perfecto 1995; Altieri et al. 2005). In some cases, space heterogeneity may even play a more important role than intra-farm diversity in the regulation of phytophagous population densities (Fahrig et al. 2011, 2015). But surely the two components (intra and inter farm diversity) relate synergistically.
For the spatial heterogeneity to have a positive effect on the internal dynamics of agroecosystems it is necessary, on the one hand, an insidefarm design that attracts biological controllers (e.g., flower strips or beetle banks) (Altieri, Ponti, and Nicholls 2005; Nicholls and Altieri 2002) and on the other, the existence of nearby sources of organisms with enough internal complexity to provide the necessary control agents (Rusch et al. 2016, 2010; Tscharntke et al. 2012).
So, metapopulation and metacommunity dynamics seem to be crucial for the long term survival of species in heterogeneous environments (Alfonzo et al. 2009; Aberg et al. 1995; Cantrell, Cosner, and Fagan 1998; Delin and Andren 1999; Griffon, Alfonzo, and Hernandez 2010; Griffon and Hernández 2014; Gustafson and Gardner 1996; Perfecto, Vandermeer, and Wright 2009; Sisk, Haddad, and Ehrlich 1997; Tejat et al. 2002; Vandermeer and Carvajal 2001; Vandermeer and Perfecto 2007). In general terms, the spatial structure of populations, along with processes of dispersal, migration and colonization, allows the emergence of dynamics that make possible the persistence and coexistence of species (Hanski 1994, 1998; Hanski and Gilpin 1997; Hanski et al. 1996; Leibold et al. 2004). Thus, spatial heterogeneity may enhance the configuration of the complex ecological networks needed for a successful ecological pest management program (Batáry et al. 2011; Fahrig et al. 2011; Rusch et al. 2016, 2010; Tejat et al. 2002; Tscharntke et al. 2002, 2012). For this reason, in the mathematical approach used here we also include the effect of spatial heterogeneity on population dynamics.
In short, the objective of this work is to find architectural features that promote the self-regulation of population densities in ecological networks associated to agroecosystems. To do this, we built mathematical models that represent ecological networks, both for a single community and for metacommunitarian systems. We must make clear that whenever we say ‘ecological network’, we are considering the potential presence of ‘all’ types of interactions, i.e., competition, mutualism, victim-exploiter, amensalism and commensalism.
Species
survivals. Initial richness, for six different initial conditions
(defined in Fig 3). Blue: survival percentage in one community (no
spatial heterogeneity). Grey: survival percentage of one community in a
metacommunitarian background. The curves are averages of 40 simulations
for each initial condition.
Uniform
perturbation (example). A persistent network obtained under the
20:10:10:60 initial condition is perturbed by a little increase in the
densities of each population. Left: dynamics after the perturbation. Two
populations reach very low (but non zero) densities. Right: network
before and after the perturbation. Notice that both networks are the
same.
The more relevant results of the models evaluated and discussed in this article can be summarized as follows: (i) The conditions under which persistent networks are obtained after the iterative process are very restricted. However, when persistent networks are obtained, they are fundamentally resilient to perturbations. (ii) Mutualistic (and positive in general) interactions have an important and extensive effect under certain (very specific) conditions. (iii) Spatial heterogeneity increases the possibility of persistence in hypothetical communities. (iv) Ecological interactions that somehow have been neglected in the past (commensalism and amensalism, the forgotten sisters), may be: 1- More frequent than generally thought, and 2- Important for the persistence of communities.
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