## Life cycle graph

A life cycle graph is a way to graphically represent a stage structured model. Drawing a life cycle graph of the spotted knapweed will help us understand what is happening, and will make writing down model equations much simpler.

### How to draw a life cycle graph

#### STEP 1: drawing nodes

In our life cycle graph, each stage is represented by a circle, called a node. Our life cycle graph contains one node for each of the seed (S), rosette (R), and flower (F) stages. These nodes represent the number of individuals in each stage.

#### STEP 2: drawing transition arrows

Next, we can use arrows to show how individuals may move between classes in a given year, the movement probabilities associated with these yearly stage transitions correspond to these arrows. We write to represent the probability of moving from stage to stage in a year.

#### STEP 3: drawing fecundity arrows

Next, we need to include a seed production arrow. This arrow will go from the flower class to the seed class, since flowers produce seed. The arrow will represent the spotted knapweed flower fecundity, denoted by .

Definition: Fecundity refers to the average number of new individuals produced by a reproducing individual per year.

To determine fecundity for the spotted knapweed, we need to know the average number of seeds produced, and the fraction of produced seeds that are viable. Then

So the fecundity of a spotted knapweed flower is 432 individuals.

#### STEP 4: determining numerical values

Now we can replace our symbols for the transition and reproduction events with the transition probabilities and the fecundity.