Trait-based models for functional groups Jorn Bruggeman Theoretische biologie Vrije Universiteit Amsterdam

Context: the project Title – “Understanding the ‘organic carbon pump’ in meso-scale ocean flows” 3 PhDs – biology, physical oceanography, numerical mathematics Aim: – quantitative prediction of global organic carbon pump from 3D models My role: – ‘detailed’ biota modeling in 1D water column, parameterization for 3D models

Issue: biological complexity Marine ecosystems are complex: – Many functional groups (phytoplankton, zooplankton, bacteria) – Large species variety within functional groups Option: large, detailed models – ERSEM: 46 state variables, >100 parameters But: – Few data  little information on biota parameters – Global 3D models need simple models (<10 state variables) Alternatives?

Trait ‘quantifiable, species-bound entity’ Here: trait = trade-off Environment-dependent advantage … – ‘nutrient affinity’ – ‘light harvesting ability’ – ‘detritus consumption’ – ‘predation’ … and environment-independent cost – increase in maintenance cost – increase in cost for growth

Trait-based population model Marr-Pirt based (food uptake, maintenance, growth) Trait implementation: – ‘trait biomass’, fixed fraction κ > 0 of ‘structural biomass’ – benefit: substrate availability ~ trait biomass – cost in maintenance/growth: sum of cost for structural- and trait biomass structural biomass nutrient + maintenance nutrient uptake +

Dynamic behavior 1 trait, 1 substrate, closed system symbolunitmeaning MVMV biomassstructural biomass MTMT biomasstrait biomass κ -trait value as fraction of structural biomass X substrate KXKX substrate half-saturation j X,Am substrate/time/biomassmaximum structure-specific substrate uptake jX,M,VjX,M,V substrate/time/biomassmaintenance for structural biomass jX,M,TjX,M,T substrate/time/biomassmaintenance for trait biomass y X,V substrate/biomasssubstrate req. per structural biomass y X,T substrate/biomasssubstrate req. per trait biomass

‘Natural’ limits on κ Extinction at small trait value: Extinction at very high trait value: κ bounds easily calculated (roots of parabola)

Functional group One trait-based population = species Functional group: collection of species Assumption: infinite biodiversity – within system, for any trait value, a species is present Then: continuous trait distribution For simulation: discretization of trait distribution

Setting: ‘chaotic’ water column 1D water column depth-dependent turbulent diffusion, surface origin: – Buoyancy (evaporation, cooling) – Shear (wind friction) Chaotic surface forcing: meteorological reports – Light intensity – Wind speed – Temperature – Humidity Closed for mass, open for energy (surface) weather: light air temperature air pressure relative humidity wind speed biotaturbulence biotaturbulence biotaturbulence biotaturbulence z = 0 z = -1 z = -2 z = -3 z = -4

Sample simulation Functional group: ‘phytoplankton’ – trait 1: ‘light affinity’ – trait 2: ‘nutrient affinity’ Start in end of winter: – deep mixed layer – little primary productivity – uniform trait distribution, low biomass: all ‘species’ start with same low biomass No predation or explicit mortality (but Marr- Pirt maintenance) nutrient uptake structural biomass nutrient light + + maintenance light harvesting

Results 1 log(turbulent diffusion)total biomass Forcing effect:Biota response:

Results 2 structural biomass light harvesting biomassnutrient harvesting biomass

Discussion Possible interpretation: – Deep chlorophyll maximum (observed in ocean) – Succession: large species replaced by small species (observed in ocean) However: – Long term behavior (50 years): dominance of species with high trait values – Why? Trait biomass serves as reserve, needed in winter

Reflecting: key components Trait cost/benefit function – maintenance/growth cost linear in κ – substrate availability linear, assimilation hyperbole in κ Continuous trait distribution – initial distribution? Chaotic environment – Long-term behavior (paradox of the plankton: competitive exclusion?)

Plans Add explicit reserves to base model Study 0D (long-term) behavior – Competitive exclusion? Other traits – Direct measure of body size – Heterotrophy – Predation Aggregation – 1 adapting population with flexible/constant trait value?

The end…

‘Natural’ limits on κ Trait value cannot be negative Negative growth at high trait value: