Understanding complex spatial dynamics from mechanistic models through spatio-temporal point processes

Landscape heterogeneity affects population dynamics, which determine
species persistence, diversity and interactions. These relationships can
be accurately represented by advanced spatially-explicit models (SEMs)
allowing for high levels of detail and precision. However, such approaches
are characterised by high computational complexity, high amount of data
and memory requirements, and spatio-temporal outputs may be difficult to
analyse. A possibility to deal with this complexity is to aggregate
outputs over time or space, but then interesting information may be masked
and lost, such as local spatio-temporal relationships or patterns. An
alternative solution is given by meta-models and meta-analysis, where
simplified mathematical relationships are used to structure and summarise
the complex transformations from inputs to outputs. Here, we propose an
original approach to analyse SEM outputs. By developing a meta-modelling
approach based on spatio-temporal point processes (STPPs), we characterise
spatio-temporal population dynamics and landscape heterogeneity
relationships in agricultural contexts. A landscape generator and a
spatially-explicit population model simulate hierarchically the
pest-predator dynamics of codling moth and ground beetles in apple
orchards over heterogeneous agricultural landscapes. Spatio-temporally
explicit outputs are simplified to marked point patterns of key events,
such as local proliferation or introduction events. Then, we construct and
estimate regression equations for multi-type STPPs composed of event
occurrence intensity and magnitudes. Results provide local insights into
spatio-temporal dynamics of pest-predator systems. We are able to
differentiate the contributions of different driver categories ( i.e.,
spatio-temporal, spatial, population dynamics). We highlight changes in
the effects on occurrence intensity and magnitude when considering drivers
at global or local scale. This approach leads to novel findings in
agroecology where, for example, we show that the organisation of
cultivated patches and semi-natural elements play different roles for pest
regulation depending on the scale considered. It aids to formulate
guidelines for biological control strategies at global and local scale.