Evolutionary constraints and optimality
Adaptation and acclimation have intrigued scientists ever since Darwin (1872) proposed his postulates of natural selection.

It has become common practise to use evolutionary arguments to account for the form and behaviour of living organisms, and the scientific community has widely accepted the underlying principles as a cornerstone in modern biology.

In modelling, evolutionary arguments can be formulated as optimisation problems. These models assume that 1) individuals vary in particular structures/functions, 2) at least part of such phenotypic variation is heritable, 3) individuals vary in fitness (the rate at which they produce viable offspring per unit time) at least partly as a function of their heritable phenotypic differences (Lewontin 1970), and further, that newly emerging structures/functions are constrained to some domain of variation, as a result of limits to biological variation and fundamental physical and chemical laws. From these premises, if heritable structures and/or functions arise that increase the fitness of their bearers relative to others, individuals bearing such structures/functions will increase in frequency and the population as a whole will evolve toward a greater average in relative fitness.

As a quantitative approach, optimality models can provide an important means for analysing the consequences of different plant forms and functions. Often, such models ask how variation in one or more traits would affect carbon gain and, hence, plant growth and presumed competitive ability in a particular environment. The Forest Modelling Group have used the optimisation approach especially in deriving models for growth allocation in different environments (see References), and also in models for balanced metabolic function (see References).

Picture: Example of a situation calling for optimization: Tradeoffs in carbon allocation between foliage and branches.


Franklin O., Harrison S.P., Dewar R., Farrior C.E., Brännström Å., Dieckmann U., Pietsch S., Falster D., Cramer W., Loreau M., Wang H., Mäkelä A., Rebel K.T., Meron E., Schymanski S.J., Rovenskaya E., Socker B.D., Zaehle S., Manzoni S., van Oijen M., Wright I.J., Ciais P., van Bodegom P.M., Peñuelas J., Hofhansl F., Terrer C., Soudzilovskaia N.A., Midgley G., Prentice I.C. 2020. Organizing principles for vegetation dynamics. Nature Plants https://www.nature.com/articles/s41477-020-0655-x

Dewar, R., Mauranen, A., Makela, A., Holtta, T.,Medlyn, B., Vesala, T. 2018. New insights into the covariation of stomatal, mesophyll and hydraulic conductances from optimisation models incorporating non-stomatal limitations to photosynthesis. New Phytologist 217: 571–585

Valentine H.T, Mäkelä, A. 2012. Modeling forest stand dynamics from optimal balances of carbon and nitrogen. New Phytologist. 194: 961–971

Dewar R.C., Franklin O., Mäkelä A., McMurtrie R.E., Valentine H.T. 2009. Optimal function explains forest responses to global change. Bioscience 59:127-139

Mäkelä A., Valentine H., Helmisaari H.-S.. 2008. Steady state solutions of forest stand foliage and fine root biomass as trade-offs between nitrogen uptake and use. New Phytologist 180.

Mäkelä A., Givnish TJ, Berninger F, Buckley TN, Farquhar GD and Hari P (2002) Challenges and opportunities of the optimality approach in plant ecology. Silva Fennica 36: 605–614

Mäkelä, A. and Sievänen, R. (1992). Height growth strategies in open-grown trees. Journal of Theoretical Biology 159, 443-467.

Mäkelä, A. and Sievänen, R. (1987). Comparison of two shoot-root partitioning models with respect to substrate utilization and functional balance. Annals of Botany 59, 129-140.

Hari, P., Mäkelä, A., Korpilahti, E. and Holmberg, M. (1986). Optimal control of gas exchange. Tree Physiology 2, 169-175.
Mäkelä, A. (1985). Differential games in evolutionary theory: height growth strategies of trees. Theoretical Population Biology 27, 239-267