geotrait.md 3.92 KB
 Victor committed Oct 07, 2020 1 2 3 # The geotrait > This note has been taken from 2Y/articles/geotrait/mathematical_notes.md  Victor committed Oct 07, 2020 4 5 6 !!! note "'note' admonition" In Landscape Ecology, it is of particular interest to study the geographical position of the lineage through time. This is because richness patterns are thought to arise through allopatric speciation, where populations get separated in space and time. This is the topic of the following section.  Victor committed Oct 07, 2020 7 8 9 10 11 ## Julia accessors An agents of type Agent{Ancestors{true}} stores the values of its ancestors traits. From it, one can thus study the history of the lineage. ## Projection of the geographic history  Victor committed Oct 07, 2020 12 Consider a set of individuals which lineage geographical history has been stored in a vector x^{(i)}(t). If individual i was born at time t^* then x^{(i)}(t>t^*) represents its geographical position, while x^{(i)}(t_t \\ = \frac{1}{N} \sum_i \int_0^t \partial_s x^{(i)}(s) ds \\ = \frac{1}{N} \sum_i [x^{(i)}(t) - x^{(i)}(0))]  But one could also have a moving average, that is, averaging math \frac{1}{N} \sum_i \sum_j \int_{j\tau}^{j(\tau+1)} \frac{1}{\tau} \partial_s x^{(i)}(s) ds  Victor committed Oct 07, 2020 93 `