I think that Mathematical modeling would play a significant role in ecological studies....as we understand that the mathematical models are just a simplified descriptions of the actual intricate ecological process/system....the mathematical model is incapable of capturing every possible aspects/properties of the ecological system, therefore understanding the limitations/drawbacks of the constructed mathematical model and the conditions under which this model is a good approximation, are some important aspects that needs to be looked into.

From experience I can say that probability and statistics are quite important as well.

La matemática es la explicación comprensible al ser humano de la naturaleza, es capaz de modelar no solo lo cuantificable, si no, las relaciones entre sistemas e individuos a travéz de algebras específicas, es capaz de modelar la complegidad a travez de los procesos aleatorios que se aplican en la inteligencia artificial. Los procesos de transferencia de masa y calor, el fluido de los diferentes líquidos se modelan con sistemas de ecuaciones diferenciales, pero tambien el comportamiento de las manchas de peces y el migrar de las aves, las rutas de los huracanes y las corrientes marinas. No fue hasta que se modeló matemáticamente, que se obtuvo la descripción del genoma humano. ¿tendrá sentido seguir enumerando la presencia de la matemática en la naturaleza?

In fine modeling, we've abstracted nature into simpler form so that we've some chance of understanding it. Mathematical ecology helps us understand the sense of our allowing about nature to help us avoid making presumptive arguments that may not be true or only true under certain restrictions

A matemática faz parte do cotidiano de todo cidadão, em qualquer idade, como a ecologia também. não é possível separar estas duas ciências.

Hello Panli

I am more doubtful about usage of Mathematic applied in theoretical ecology and eco-evolution.

For example all mathematics studies I saw concerning predator-prey coevolution are facing the same issue of asymmetry of population size.

Indeed, prey population size are systematically much more larger than predators

The extinction of predators is then systematic and consequence of the prey phenotypic evolution in long term.

To prevent this unavoidable evolutionary murder in mathematical models, I could see some solution like "increase the mutation probability of predators: P = 5p and choose smaller mutations steps."

For me this kind of studies does not bring any progress in our understanding of real life.

I really believe that ecological interactions are too complex and intertwined to be understood by simplified mathematical modeling.

(Simplification is mandatory to solve the very hard equations involved in all those studies)

I highly prefer computer multi-agent modeling that is for me the only solution to covers a large part of the structuring factors of ecosystems and simulates spatial and temporal mechanisms that affect their evolution.

A mensuração de vários aspectos da ecologia

Tudo deve ser previsto, logo,medido.qualquer projeto de intervenção no.meio ambiente tem que dar grande importância aos aspectos matemáticos.

The self-thinning rule, describing plant mortality because of competition in crowded even-aged stands, is the only process in ecology that has true mathematical support :)

It is the process whereby the number of plants per unit area (p) decreases as average plant (or mean individual) above-ground weight (w) increases as time t progresses.