Marbled White

Melanargia galathea is a common grassland specialist butterfly. This animal model is one component of the nature submodel of Persefone.jl.

The model description follows the ODD (Overview, Design concepts, Details) protocol (Grimm et al., 2006; 2010; 2020):

1. Purpose

The purpose of this animal model is to simulate the abundance and distribution of a population of Melanargia galathea in response to climate and farm management in Central European agricultural landscapes.

2. Entities, state variables, and scales

2.1 Landscape

The simulated landscapes consist of a grid of pixels with a resolution of 10m and have an extent of 270km²-370km² (approximately; depending on the chosen input map). Each pixel is assigned a land cover class. It may also be associated with a farm plot, in which case it will contain information about the type and growth stage of the crop planted here. Farm management determines which crops are grown when, and when disturbance (e.g. mowing, harvesting, tillage) takes place.

The landscape is also associated with daily weather data, taken from the nearest weather station. This provides the daily mean temperature and daily precipitation as input to this species model (other variables are available, but not used).

2.2 Animals

The simulated individuals (a.k.a. agents) are female marbled whites. (It is assumed that all females mate, and males therefore do not need to be simulated to capture population dynamics.) Each individual is characterised by the following variables:

• ID A unique identifier for this individual, which can be used to link it to its parent and its offspring.

• phase The individual's current stage in the life cycle. May be one of: egg, larva, pupa, adult.

• age The individual's age in days.

• position The individual's position in the simulated landscape.

3. Process overview and scheduling

The simulation proceeds in time steps of one day. Every day, each individual executes the function associated with their current life phase:

• Juveniles (phases egg, larva, and pupa) check whether they are in a field that has been tilled or harvested, and if so, die with a certain probability (100% for tillage, by default 0% for harvest - the latter probability is configurable). They also check whether they are old enough to advance to the next phase. No movement or other activity takes place.
• Adults move around quasi-randomly and lay eggs. Distance moved and number of eggs laid is temperature-dependent (for details, see below). Individuals die once they reach their maximum age, which is determined using a linear distribution at birth.

4. Design concepts

4.1 Basic principles

This model assumes that marbled white distribution is primarily shaped by habitat availability, while abundance is most affected by weather. Thus, the model's representation of their biology focuses on habitat requirements and activity levels in response to weather. Accordingly, the only behavioural mechanisms that are simulated in the model are movement and oviposition.

Movement is assumed to be largely random, although with a strong preference for habitat that is suitable for oviposition (i.e. unmanaged grassy areas, extensively managed grassland, and fallows; cf. section 7.2). The representation of movement chosen here is coarser than that found in dedicated movement models of butterflies (e.g. Evans et al., 2019), as we are primarily interested in larger-scale processes (over seasons and kilometers) for which very fine-grained movement decisions (over seconds and meters) are less relevant.

The model assumes that marbled white population growth is limited by fecundity not mortality. Fecundity in turn is understood to be limited by the available time for oviposition, as determined by the daily weather (Gotthard et al., 2007). Therefore, a central part of the model is the calculation of the number of eggs that can be laid in a given day (section 7.1).

Agricultural management is of secondary importance to the modelled population trends, but can still influence them on two levels. The first concerns the availability of habitat, as the amount of fallow land and the proportion of extensively managed grassland can vary in different model scenarios. The second is additional mortality caused by tillage and harvest/mowing, which can be configured but is generally assumed to be negligible (Ebert & Rennwald, 1991).

4.2 Emergence

Multiple patterns emerge from the basic principles outlined above. The most important are listed here:

• Individual lifetime stats: The combination of individual behaviour, weather, and landscape structure lead to characteristic distributions of different measured individual-level variables (cf. section 4.11), which can be compared to known distributions of these variables from the literature (e.g. Baguette et al., 2000; Vandewoestijne et al., 2004). These variables include the individual fecundity (i.e. total eggs laid per female), the local population density experienced by each individual, the lifetime displacement (i.e. distance of the location at death from the birth location), and the relative use of different habitats while moving through the landscape.
• Population trends: Kühn et al. (2024) show the population trends of Melanargia galathea in Germany for the period 2006-2023. In the first time period (2006-2015), this shows a strongly fluctuating, overall slightly decreasing trend, followed by a marked increase after 2015. Comparing this to the summer temperatures over these years shows that the abundance in one year is correlated with the mean temperature of the previous summer, a pattern that was also shown for British butterflies by Roy et al. (2001). In addition, the introduction of the CAP Greening measures in 2015 may have contributed to the positive trend over the past years.

4.3 Adaptation

Marbled whites respond to the landscape by mostly restricting their movement to suitable habitat. The movement rules were chosen to reproduce lifetime and landscape-scale patterns, rather than conform to mechanistic principles of movement behaviour (see sections 7.2, 8.2).

4.4 Objectives

Marbled whites' only "objective" is to stay on or close to suitable habitat, in order to allow them to lay their eggs (see section 7).

4.5 Learning

The model includes no learning by individuals.

4.6 Prediction

The model includes no predictions by individuals.

4.7 Sensing

Marbled whites can perceive the landscape structure in a given radius around them (land cover, crop type, vegetation height and cover). They can see nearby conspecifics and sense the day's weather (temperature and precipitation).

4.8 Interaction

By default, there are no interactions between individual marbled whites. Optionally, a maximum local population density can be set, with individuals less likely to visit a landscape pixel as the number of conspecifics already on it approaches this maximum.

4.9 Stochasticity

Stochasticity is used when modelling mortality and movement. Juvenile mortality is modelled as a one-time probability of death, applied when an adult butterfly lays an egg. (Only eggs that pass this probability check and will therefore mature into adults are actually instantiated, in order to save computational resources.) The amount of time in days that an individual spends in each development phase is drawn at random during its initialisation, using a normal distribution for the larval phases and a linear distribution for the adult lifetime. Movement proceeds in quasi-random jumps (for details see below).

Persefone.jl includes a seed parameter, which is used to initialise the random number generator. This can be used to ensure reproducibility (simulation runs of the same model version with the same parameter values will be identical in outcome). The model saves all input files used for a simulation run alongside the run's output data, so that all run's can be repeated if necessary.

4.10 Collectives

The model includes no collectives.

4.11 Observation

The model collects three sets of data. The first set gathers daily abundance data, listing the number of individuals currently alive in each life phase. The second set is updated every time an individual dies, and shows that individual's lifetime values of fecundity, displacement, and habitat use, as well as the local population density at its last location. The third set is updated annually and lists that year's adult abundance, average fecundity, and average temperature. All data are saved as CSV files, with several figures automatically created from these at the end of the run.

5. Initialisation

The simulation is initialised with one individual per hectare placed at random on suitable habitat, defined as unmanaged grassy areas, extensive grassland, or fallow land. The starting population density can be modified with the initialdensity parameter. Individuals are created as eggs (whether at birth or at initialisation), and then calculate how much time they will spend in each juvenile phase in order to ensure eclosure during the known flying period. (As juvenile phases are functionally identical in the model, the amount of time in each is irrelevant for model outcomes.)

For details, see the source code and the associated documentation.

6. Input data

The general input to Persefone (i.e. land use maps and weather data) is described here.

The following extract from the source code lists the species parameters and values used by the Marbled White model, based on the literature cited below:

@species MarbledWhite begin
    ## SPECIES PARAMETERS
    # (parameters that are not `const`ants can be changed via the configuration file)

    # habitat/environmental requirements
    # (Height parameters from Vandewoestijne et al. 2004. For temperature parameters
    #  see Ebert & Rennwald 1991, Gotthard et al., 2007, and Evans et al. 2019)
    const minheight = 30cm # minimum height of vegetation for egg-laying
    const maxheight = 60cm # maximum height of vegetation for egg-laying
    mintemp = 18 # minimum temperature for activity (°C)
    maxtemp = 30 # maximum temperature for activity (°C)
	rainactive = false # allow activity on days with precipitation?

    # movement parameters
    movement = "random" # movement algorithm ("proximity" or "random")
    maxstepsperday = 100 # daily movement steps under optimal temperatures
    selfavoidance = 0.9 # likelihood of avoiding a spot already visited today (only relevant with "proximity" movement)
    habitatpreference = 0.95 # likelihood of avoiding a non-habitat spot
    const perception = 100m # perceptual range (cf. Cant et al. 2005)
    maxindperpixel = Inf # maximum population density in individuals/pixel (1px = 0.01ha)

    # lifecycle parameters
    # (eggsperday and time parameters from Reinhardt et al. 2007)
    maxeggsperday = 8 # number of eggs laid under optimal conditions
    const eggtime = 18:22 # days as egg
    const larvatime = 290:320 # days as larva
    const pupatime = 16:29 # days as pupa
    const maxadulttime = 34 # maximum lifespan in days as adult
    const maturationtime = 5:8 # days from hatching to first oviposition
    juvenilemortality = 0.95 # proportion of butterflies that die before hatching
    mowingmortality = 0.0 # juvenile mortality from mowing events
    const earliesteclosure::AnnualDate = (June, 15) # (Ebert & Rennwald 1991)
    const latesteclosure::AnnualDate = (August, 15) # (Ebert & Rennwald 1991)
    
    const enforceflyingperiod = true # make sure all pupa eclose in the flying period?
end

7. Submodels

7.1 Weather

Temperature affects both the distance moved and the number of eggs laid each day. The optimal temperature is taken to be the midway point between the species' minimum and maximum temperatures (i.e. 24°C). Outside the species' temperature range (18-30°C), neither movement nor oviposition take place. Within that range, the number of steps each day peaks at the optimum temperature and declines linearly on either side of it. (cf. Evans et al., 2019). The number of eggs laid declines linearly if the temperature is below the optimum, but stays stable above it (cf. Gotthard et al., 2007). The daily mean temperatures are used as the basis for calculation (using the maximum temperature produces wrong model results during heat waves). In addition, the model can be configured so that no activity takes place on days with rainfall (i.e. precipitation > 0, configured with rainactive).

7.2 Movement

Adults move a given number of steps each day, depending on the temperature (see above). Each step, an individual randomly scans landscape pixels within its perceptual range of 100m. If the pixel is suitable habitat, i.e. either arable or extensive grassland with plant heights within the required range (30-60cm), it moves to this pixel. In this case, the individual also lays an egg if it has not yet laid all its eggs for that day. If the pixel is not suitable habitat, it may nevertheless move there with a certain probability (given by the habitatpreference parameter). Otherwise, it looks at the next randomly chosen pixel in its perceptual range.

8. Testing & validation

8.1 Alternate weather parameters

We tested different temperature ranges (16-32°C, 18-30°C, 20-28°C), with and without rain sensitivity. Smaller ranges produce stronger population fluctuations, but also more frequently lead to populations dying out due to insufficient reproduction. The option 18-30°C with rain sensitivity was found to reproduce the selected patterns best.

8.2 Alternate movement

We tested an alternative movement submodel, but this gave worse pattern fits than the random movement described above:

Adults move a given number of steps each day, depending on the temperature (see below). Each step, an individual scans its surroundings in concentric circles, looking for the closest spot that offers suitable habitat which it hasn't visited today. (Depending on the habitatpreference and selfavoidance parameters, spots that are not suitable habitat or have been visited before may also be selected.) Spots with higher population densities are more likely to be avoided (avoidance increases linearly up to 100% at maxindperpixel). If no suitable spot is found, the individual moves to a random location on the periphery of its vision. After each step, if it is in a suitable habitat, the individual lays an egg, up to the number determined by the temperature for that day.

8.3 Other parameters

We also tested different values of the parameters habitatpreference, juvenilemortality, mowingmortality, and maxeggsperday. Juvenile mortality proved to have the strongest influence and the highest sensitivity. For each parameter, we selected values to give the optimal fit in the pattern-oriented modelling process (see main text).

9. References

• Baguette et al. (2000). Population spatial structure and migration of three butterfly species within the same habitat network: Consequences for conservation. Journal of Applied Ecology, 37(1), 100–108. https://doi.org/10.1046/j.1365-2664.2000.00478.x
• Dennis (Ed.). (1992). The ecology of butterflies in Britain. Oxford University Press.
• Ebert & Rennwald (1991). Die Schmetterlinge Baden-Württembergs, Bd.2, Tagfalter: Satyridae, Libytheidae, Lycaenidae, Hesperiidae. Verlag Eugen Ulmer.
• Evans et al. (2019). Integrating the influence of weather into mechanistic models of butterfly movement. Movement Ecology, 7(1), 24. https://doi.org/10.1186/s40462-019-0171-7
• Gotthard et al. (2007). What Keeps Insects Small? Time Limitation during Oviposition Reduces the Fecundity Benefit of Female Size in a Butterfly. The American Naturalist, 169(6), 768–779. https://doi.org/10.1086/516651
• Hannappel & Fischer (2020). Grassland intensification strongly reduces butterfly diversity in the Westerwald mountain range, Germany. Journal of Insect Conservation, 24(2), 279–285. https://doi.org/10.1007/s10841-019-00195-1
• Kühn et al. (2024). Tagfalter-Monitoring Deutschland: Auswertung 2005-2023. Oedippus, 42, 12–45. https://www.ufz.de/export/data/6/298835298188Oedippus42klein.pdf
• Lenda & Skórka (2010). Patch occupancy, number of individuals and population density of the Marbled White in a changing agricultural landscape. Acta Oecologica, 36(5), 497–506. https://doi.org/10.1016/j.actao.2010.07.002
• Reinhardt et al. (2007): Tagfalter von Sachsen. In: Klausnitzer & Reinhardt (Hrsg.) Beiträge zur Insektenfauna Sachsens Band 6. – Entomologische Nachrichten und Berichte, Beiheft 11, 696 + 48 Seiten. Dresden.
• Roy et al. (2001). Butterfly numbers and weather: Predicting historical trends in abundance and the future effects of climate change. Journal of Animal Ecology, 70(2), 201–217. https://doi.org/10.1111/j.1365-2656.2001.00480.x
• Schulte et al. (2007). Die Tagfalter der Pfalz—Band 2. Gesellschaft für Naturschutz und Ornithologie Rheinland-Pfalz.
• Vandewoestijne et al. (2004). Dispersal, landscape occupancy and population structure in the butterfly Melanargia galathea. Basic and Applied Ecology, 5(6), 581–591. https://doi.org/10.1016/j.baae.2004.07.004