. 2024 May 15;14(5):e10903. doi: 10.1002/ece3.10903

TABLE 1.

The main notation used here.

Notation

Definition

Indices

t

Index for time;

t = 1,2,3, \dots, T

T

Number of time steps

t^{*}

Focal time at which we know the state of the system and want to predict the state at

t^{*} + 1

Variables

N_{t}

Value, such as population size, at

t = 1, \dots, T

Y_{t}

First‐difference value

Y_{t} = N_{t + 1} - N_{t}

\hat{\cdot}

Estimate of

\cdot

EDM calculations

{\tilde{x}}_{t}

Vector of length

E

defining the axes of the lagged state space, for example,

{\tilde{x}}_{t} = (Y_{t}, Y_{t - 1}, Y_{t - 2})

x_{t}

Realised values of the components of

{\tilde{x}}_{t}

, for example,

x_{t} = (3, - 5, 1)

; each element of

x_{t}

is the value along each axis of the

E

‐dimensional space, where the axes are defined by components of

{\tilde{x}}_{t}

x_{t^{*}}

Realised values of the components of

{\tilde{x}}_{t}

at the focal time

t = t^{*}

E

Embedding dimension, the number of dimensions of the state space in which the system is being embedded to look for the nearest

E + 1

neighbours to the focal point

x_{t^{*}}

;

E

is the length of

{\tilde{x}}_{t}

X

Matrix with rows representing time and columns representing each of the

E

components of

{\tilde{x}}_{t}

; row

t

represents the system state at time

t

with the jth element representing the jth component of

x_{t}

ℒ (E, t^{*})

Library for a given

E

and

t^{*}

, consisting of the set of

x_{t}

that are candidates to be considered as nearest neighbours of

x_{t^{*}}

C_{E, t^{*}}

The number of vectors

x_{t}

in the library

ℒ (E, t^{*})

C_{E}

The usual value of

C_{E, t^{*}}

for a given

E

, defined as

C_{E} = T - 2 (E + 1)

;

C_{E, t^{*}} \geq C_{E}

ψ_{i}

After calculating the distance between

x_{t^{*}}

and each

x_{t}

in the library,

ψ_{1}

gives the time index of the

x_{t}

that is the nearest neighbour to

x_{t^{*}}

ψ_{2}

corresponds to the second nearest neighbour, etc.