Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/BioGeoBEARS_detection_v1.R

This function calculates P(data|presence,parameters),
i.e. the probability of some detection and taphonomic
control counts, given the true geographic range/state,
and parameters such as `dp`

, a detection probability
(and, optionally, a false detection probability,
`fdp`

).

1 2 | ```
calc_obs_like(truly_present = TRUE, obs_target_species,
obs_all_species, mean_frequency = 0.1, dp = 1, fdp = 0)
``` |

`truly_present` |
Is the OTU of interest
known/conditionally assumed to be truly present
( |

`obs_target_species` |
A count of detections of your
OTU of interest, e.g. as produced from a cell of the
matrix output from |

`obs_all_species` |
A count of detections of your
taphonomic controls, e.g. as produced from a cell of the
output from |

`mean_frequency` |
This is the proportion of samples from the taphonomic control group that will truly be from this OTU, GIVEN that the OTU is present. This could be estimated, but a decent first guess is (total # samples of OTU of interest / total # of samples in the taphonomic control group where the OTU is known to be present). All that is really needed is some reasonable value, such that more sampling without detection lowers the likelihood of the data on the hypothesis of true presence, and vice versa. This value can only be 1 when the number of detections = the number of taphonomic control detections, for every OTU and area. This is the implicit assumption in e.g. standard historical biogeography analyses in LAGRANGE or BioGeoBEARS. |

`dp` |
The detection probability. This is the per-sample probability that you will correctly detect the OTU in question, when you are looking at it. Default is 1, which is the implicit assumption in standard analyses. |

`fdp` |
The false detection probability. This is
probability of falsely concluding a detection of the OTU
of interest occurred, when in fact the specimen was of
something else. The default is 0, which assumes zero
error rate, i.e. the assumption being made in all
historical biogeography analyses that do not take into
account detection probability. These options are being
included for completeness, but it may not be wise to try
to infer |

The idea of taphonomic controls dates back at least to work of Bottjer & Jablonski (1988). The basic idea is that if you have taxa of roughly similar detectability, then detections of other taxa give some idea of overall detection effort. Obviously this is a very simple model that can be criticized in any number of ways (different alpha diversity in each region, different detectability of individual taxa, etc.), but it is a useful starting point as there has been no implementation of any detection model in historical/phylogenetic biogeography to date.

One could imagine (a) every OTU and area has a different count of detections and taphonomic control detections, or (b) the taphonomic control detections are specified by area, and shared across all OTUs. Situation (b) is likely more common, but this function assumes (a) as this is the more thorough case. Behavior (b) could be reproduced by summing each column, and/or copying this sum to all cells for a particular area.

`lnlike_allobs_given_absence`

The natural
log-likelihood of the data, given the model & assumption
of true presence or absence.

Go BEARS!

Nicholas J. Matzke matzke@berkeley.edu

http://phylo.wikidot.com/matzke-2013-international-biogeography-society-poster

Matzke_2012_IBS

Bottjer_Jablonski_1988

`mapply_calc_post_prob_presence`

,
`calc_post_prob_presence`

,
`mapply_calc_obs_like`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 | ```
# Example: 10 observations of the species mean dramatically higher likelihood of the
# data on the hypothesis that it is truly present.
# With zero error rate
obs_target_species = 10
obs_all_species = 100
mean_frequency=0.1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# Note that the probability of getting detections, under the hypothesis of
# true absence, is -Inf
# With a small error rate, there is some small but positive probability of
# falsely getting 10 detections
obs_target_species = 10
obs_all_species = 100
mean_frequency=0.1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# i.e. the prob. of the data is 1 under the hypothesis of presence, and 0
# under the hypothesis of absence (ln(prob) = 0 & -Inf, respectively)
# Note that with very high error rates, your conclusion could reverse
obs_target_species = 10
obs_all_species = 100
mean_frequency=0.1
dp=0.5
fdp=0.3
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# Example #2 -- what if you have ZERO detections, but lots of detections
# of your taphonomic control?
obs_target_species = 0
obs_all_species = 1
mean_frequency=0.1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# With a slight error rate
obs_target_species = 0
obs_all_species = 1
mean_frequency=0.1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
obs_target_species = 0
obs_all_species = 2
mean_frequency=0.1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# With a slight error rate
obs_target_species = 0
obs_all_species = 2
mean_frequency=0.1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# Example #3 -- what if you have ZERO detections, but only a few
# detections of your taphonomic control?
obs_target_species = 0
obs_all_species = 100
mean_frequency=0.1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# With a slight error rate
obs_target_species = 0
obs_all_species = 100
mean_frequency=0.1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# Special cases -- e.g., no data
# Prob(data)=1, ln(prob)=0
obs_target_species = 0
obs_all_species = 0
mean_frequency=0.1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
obs_target_species = 0
obs_all_species = 0
mean_frequency=0.1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# What if, for some reason, you put in identical detections and taphonomic control
# counts? (e.g., you load in a standard tipranges file)
obs_target_species = 1
obs_all_species = 1
mean_frequency=1
dp=1
fdp=0
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
# What if, for some reason, you put in identical detections and taphonomic control
# counts? (e.g., you load in a standard tipranges file)
obs_target_species = 1
obs_all_species = 1
mean_frequency=1
dp=0.99
fdp=0.001
LnL_under_presence = calc_obs_like(truly_present=TRUE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_absence = calc_obs_like(truly_present=FALSE, obs_target_species,
obs_all_species, mean_frequency, dp, fdp)
LnL_under_presence
LnL_under_absence
``` |

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