el nicho ecológico y la abundancia de las especies

Enrique Martínez Meyer

Instituto de Biología Universidad Nacional Autónoma de México

El Nicho Ecológico y la Abundancia de las Especies

Contopus virens

Fuente: Breeding Bird Survey

La abundancia poblacional de las especies varía enormemente a lo largo de sus distribuciones

1. La mayoría de los sitios de ocupación de una especie tienen pocos individuos, mientras que pocos sitios tienen órdenes de magnitud más de individuos (‘hot spots’)

Fuente: Brown et al. 1995. Ecology 76: 2028-243

Algunas generalidades

2. La abundancia presenta una fuerte autocorrelación espacial: sitios cercanos entre sí tienen abundancias más similares que sitios más alejados


Spiza americana

3. La variación geográfica de la abundancia tiende a ser mayor hacia el centro de la distribución, donde hay números altos y bajos. Hacia la periferia, la abundancia tiende a ser constantemente baja (Hipóteisis Centro-Abundante).


La Hipótesis Centro-Abundante …sin embargo, la validez misma de la HCA no ha sido suficientemente documentada empíricamente y los resultados de algunos meta-análisis ponen en duda su ‘generalidad’

Fuente: Sagarin et al. 2006. TREE 9: 524-530

Por ejemplo, sólo 39% de 145 bases de datos independientes de diversos grupos taxonómicos mostraron un patrón centro-abundante

¿En dónde le gusta más vivir al león?

Panthera leo

y = 3.7152Ln(x) + 8.4987R2 = 0.0495

P = 0.05

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1 1.2

Maxent Probability

Abu

ndan

ce

El poder explicativo de este MNE sobre la distribución de la abundancia de esta especie es muy bajo

La información que aportan los valores de favorabilidad generados por MexEnt sobre la abundancia de las especies permite, en el mejor de los casos, conocer los límtes máximos de abundancia

vol. 174, no. 2 the american naturalist august 2009 !

Abundance and the Environmental Niche: EnvironmentalSuitability Estimated from Niche Models Predicts

the Upper Limit of Local Abundance

Jeremy VanDerWal,* Luke P. Shoo, Christopher N. Johnson, and Stephen E. Williams

Centre for Tropical Biodiversity and Climate Change, School of Marine and Tropical Biology, James Cook University, Townsville,Queensland 4811, Australia

Submitted June 6, 2008; Accepted February 20, 2009; Electronically published June 11, 2009

Online enhancements: appendixes.

abstract: Ecologists seek to understand patterns of distributionand abundance of species. Studies of distribution often use occur-rence data to build models of the environmental niche of a species.Environmental suitability (ES) derived from such models may beused to predict the potential distributions of species. The ability ofsuch models to predict spatial patterns in abundance is unknown;we argue that there should be a positive relationship between ES andlocal abundance. This will be so if ES reflects how well the species’physiological and ecological requirements are met at a site and ifthose factors also determine local abundance. However, the presenceof other factors may indicate that potential abundance is not attainedat all sites. Therefore, ES should predict the upper limit of abundance,and the observed relationship with ES should be wedge shaped. Wetested the relationship of ES with local abundance for 69 rain forestvertebrates in the Australian wet tropics. Ordinary least squares andquantile regressions revealed a positive relationship between ES andlocal abundance for most species (184%). The relationships for thesespecies were wedge shaped. We conclude that ES modeled from pres-ence-only data provides useful information on spatial patterns ofabundance, and we discuss implications of this in addressing im-portant problems in ecology.

Keywords: abundance, conservation biology, distribution of abun-dance, ecological niche model, environmental suitability, presence-only model.

Introduction

Knowledge of patterns of distribution and abundance ofspecies is fundamental to ecology. A large body of workon species-distribution patterns uses predictive habitatmodels to derive estimates of the environmental suitabilityfor a species across available sites within an area of interestand, thus, to infer likelihood of occurrence. Models can

* Corresponding author; e-mail: [email protected].

Am. Nat. 2009. Vol. 174, pp. 282–291. ! 2009 by The University of Chicago.0003-0147/2009/17402-50524$15.00. All rights reserved.DOI: 10.1086/600087

be as simple as correlations between occurrence data (i.e.,locations where a species has been observed) and climaticvariables or as complex as mechanistic relationships be-tween the physiology of an organism and its surroundingenvironment (Elith et al. 2006; Kearney 2006). Either way,estimates of environmental suitability can be used to mappotential geographic ranges, and they can be applied topredict many aspects of distribution such as the locationof new populations of species in poorly known areas (e.g.,guided search effort; Fleishman et al. 2003; Raxworthy etal. 2003; Bourg et al. 2005; Guisan et al. 2006), patternsof occupancy beyond the native range for invasive species(Thuiller et al. 2005; Steiner et al. 2008), and occupancyin different time periods (e.g., distributional shifts underclimate change; Araujo et al. 2005; VanDerWal et al. 2009a)or absence from some environments (e.g., ecophysiologicalconstraints; Kearney and Porter 2004).

Distributions of many species may be predicted usingbasic occurrence data and models of environmental suit-ability. However, data on spatial variation in abundancewithin a species’ distribution are much more difficult toobtain, and prediction of patterns of spatial abundanceremains elusive for most taxa (Sagarin et al. 2006). Abun-dance is often highly variable among sites within the dis-tribution of a species, typically being high in relatively fewsites and low in the majority (Murphy et al. 2006). Siteswith high abundance may be clustered in the core of thedistribution range, while those with low abundance aremore widely distributed around the margins (e.g., Brown1984), but this pattern does not always hold (e.g., Sagarinand Gaines 2002; Sagarin et al. 2006). For very few speciesare there data available on local abundance and its cor-relates from a large enough number of sites to producemodels that are able to predict abundance in the way thatpresence-only models can be used to predict distributions.

It is possible that models of environmental suitabilityderived from occurrence data could also capture infor-

Fuente: VanderWal et al. 2009. The American Naturalist 172: 282-291

La relación de la abundancia con la favorabilidad modelada por diferentes métodos, es moderada en algunos de éstos y baja o nula en otros

because this was the model that showed the strongest positive

relationship with density values (Table 4).

However, the variances of suitability in localities with high

and low density values were different (higher in localities with

low densities) for many SDM models (significant Levene’s F

for Maxent, GARP, CTA, GBM and RF for the 37 local density

data set; and for Maxent, MD, GARP, CTA and GBM, for the

data set with 17 local densities) (Table 4). This indicates that

very frequently low jaguar densities can occur in areas with low

or high suitability, whereas high density values are restricted to

areas where the suitability is also high. This result indicates that

the relationship between density and suitability could be better

described as a triangular constraint envelope than by a straight

positive relationship.

Quantile regressions, however, revealed that only a few

methods presented any positive relationship. GBM and CTA

showed positive relationships for the 17 data set, but both

must be related to the presence of few influential points with

low suitability (see Table 3 and Appendix S4). On the other

hand, RF generated positive results for the 37 data set, but an

inconsistent negative relationship for the 17 data set. All

analysis for MDA and the 90th quantile for MARS also

showed negative relationships, which is unexpected and could

represent complex or nonlinear relationships. Note that

BIOCLIM already showed a linear and significant positive

relationship between suitability and population density and

thus is not expected to present a significant quantile

regression (except at the lower quantile, as shown in

Table 3).

The linear regression between AUC values and the OLS

slope between suitability and densities, for each SDM, did not

show any significant relationship (R2 = 0.06; P = 0.448). These

results were obtained for the 37 density data set, and a similar

pattern was observed using the more conservative 17 density

data set.

DISCUSSION

Predictions from SDMs are usually assumed as indicators of

habitat or environmental suitability and consequently of

species’ performance (Albert & Thuiller, 2008; Thuiller et al.,

2010). Nonetheless, this assumption has rarely been properly

evaluated (Wright et al., 2006; Elmendorf & Moore, 2008;

VanDerWal et al., 2009; Thuiller et al., 2010), mainly because

it is difficult to obtain empirical measures of species perfor-

mance throughout species’ range and along environmental

gradients.

Table 3 Ordinary linear regression (OLS) and quantile regressionconsidering 80th, 85th, 90th and 95th percentiles for the rela-tionship between jaguar (Panthera onca) local population densityand suitability measures derived from 11 SDM, for two sets ofjaguar population density data. Methods’ name abbreviationfollows article’s text

SDM

OLS Quantile regression slope

R2 P 80th 85th 90th 95th

37 data group

BIOCLIM 0.24** 0.00 0.03* 0.02 0.02 0.03

MD 0.03 0.31 )1.23 )1.19 )1.27 0.21

DOMAIN 0.03 0.29 0.95 0.97 1.08 1.18

MAXENT 0.13* 0.03 0.06 0.08 0.09 0.10

CTA 0.06 0.16 11.84 12.17 15.79 15.79

RF 0.04 0.26 12.78* 12.00* 14.33* 14.81

GBM 0.11* 0.05 13.08 16.54 16.63 17.48

MARS 0.00 0.95 19.13 9.38 5.96 7.14

MDA 0.00 0.90 7.81 9.70 9.79 10.19

ANN 0.03 0.33 7.29 9.63 10.30 4.97

GARP 0.09 0.06 0.19 0.24 0.27 0.31

17 data group

BIOCLIM 0.33* 0.02 0.03 0.02 0.02 0.02

MD 0.13 0.16 )1.12 )1.17 )1.46 )1.77

DOMAIN 0.05 0.37 1.25 1.30 1.81 2.06

MAXENT 0.07 0.30 0.10 0.12 0.13 0.15

CTA 0.03 0.51 9.61 9.61 15.66* 17.60*

RF 0.00 0.94 )11.92 )19.32 )19.32 )27.51*

GBM 0.05 0.42 11.18 11.61* 18.16* 14.82*

MARS 0.00 0.95 20.73* 20.73* )36.20* 28.60*

MDA 0.16 0.11 )23.08* )23.08* )17.83* )15.38*

ANN 0.06 0.37 8.16 8.46 9.56 )6.80

GARP 0.26* 0.04 0.40 0.40 0.53 0.60

*P < 0.05; **P < 0.01.

BIOCLIM suitability values0 – 0.000010.00001 – 0.50.5 – 0.750.75 – 11 – 115.75115.75 – 230.5230.5 – 345.25345.25 – 460 0 500 1000 2000 KM

Figure 2 Map showing potential geographical distribution forjaguar (Panthera onca) accordingly with BIOCLIM, which was themethod that showed the strongest relationship between model-based suitability estimate and jaguar density. Suitability valuesabove the lowest predicted value threshold (LPV) are shown in redand below the LPV threshold in blue tones.

Distribution models and population density

Diversity and Distributions, 18, 615–627, ª 2012 Blackwell Publishing Ltd 621

Fuente: Tôrres et al. 2012. Diversity & Distribution 18: 615-627 because this was the model that showed the strongest positive

relationship with density values (Table 4).

However, the variances of suitability in localities with high

and low density values were different (higher in localities with

low densities) for many SDM models (significant Levene’s F

for Maxent, GARP, CTA, GBM and RF for the 37 local density

data set; and for Maxent, MD, GARP, CTA and GBM, for the

data set with 17 local densities) (Table 4). This indicates that

very frequently low jaguar densities can occur in areas with low

or high suitability, whereas high density values are restricted to

areas where the suitability is also high. This result indicates that

the relationship between density and suitability could be better

described as a triangular constraint envelope than by a straight

positive relationship.

Quantile regressions, however, revealed that only a few

methods presented any positive relationship. GBM and CTA

showed positive relationships for the 17 data set, but both

must be related to the presence of few influential points with

low suitability (see Table 3 and Appendix S4). On the other

hand, RF generated positive results for the 37 data set, but an

inconsistent negative relationship for the 17 data set. All

analysis for MDA and the 90th quantile for MARS also

showed negative relationships, which is unexpected and could

represent complex or nonlinear relationships. Note that

BIOCLIM already showed a linear and significant positive

relationship between suitability and population density and

thus is not expected to present a significant quantile

regression (except at the lower quantile, as shown in

Table 3).

The linear regression between AUC values and the OLS

slope between suitability and densities, for each SDM, did not

show any significant relationship (R2 = 0.06; P = 0.448). These

results were obtained for the 37 density data set, and a similar

pattern was observed using the more conservative 17 density

data set.

DISCUSSION

Predictions from SDMs are usually assumed as indicators of

habitat or environmental suitability and consequently of

species’ performance (Albert & Thuiller, 2008; Thuiller et al.,

2010). Nonetheless, this assumption has rarely been properly

evaluated (Wright et al., 2006; Elmendorf & Moore, 2008;

VanDerWal et al., 2009; Thuiller et al., 2010), mainly because

it is difficult to obtain empirical measures of species perfor-

mance throughout species’ range and along environmental

gradients.

Table 3 Ordinary linear regression (OLS) and quantile regressionconsidering 80th, 85th, 90th and 95th percentiles for the rela-tionship between jaguar (Panthera onca) local population densityand suitability measures derived from 11 SDM, for two sets ofjaguar population density data. Methods’ name abbreviationfollows article’s text

SDM

OLS Quantile regression slope

R2 P 80th 85th 90th 95th

37 data group

BIOCLIM 0.24** 0.00 0.03* 0.02 0.02 0.03

MD 0.03 0.31 )1.23 )1.19 )1.27 0.21

DOMAIN 0.03 0.29 0.95 0.97 1.08 1.18

MAXENT 0.13* 0.03 0.06 0.08 0.09 0.10

CTA 0.06 0.16 11.84 12.17 15.79 15.79

RF 0.04 0.26 12.78* 12.00* 14.33* 14.81

GBM 0.11* 0.05 13.08 16.54 16.63 17.48

MARS 0.00 0.95 19.13 9.38 5.96 7.14

MDA 0.00 0.90 7.81 9.70 9.79 10.19

ANN 0.03 0.33 7.29 9.63 10.30 4.97

GARP 0.09 0.06 0.19 0.24 0.27 0.31

17 data group

BIOCLIM 0.33* 0.02 0.03 0.02 0.02 0.02

MD 0.13 0.16 )1.12 )1.17 )1.46 )1.77

DOMAIN 0.05 0.37 1.25 1.30 1.81 2.06

MAXENT 0.07 0.30 0.10 0.12 0.13 0.15

CTA 0.03 0.51 9.61 9.61 15.66* 17.60*

RF 0.00 0.94 )11.92 )19.32 )19.32 )27.51*

GBM 0.05 0.42 11.18 11.61* 18.16* 14.82*

MARS 0.00 0.95 20.73* 20.73* )36.20* 28.60*

MDA 0.16 0.11 )23.08* )23.08* )17.83* )15.38*

ANN 0.06 0.37 8.16 8.46 9.56 )6.80

GARP 0.26* 0.04 0.40 0.40 0.53 0.60

*P < 0.05; **P < 0.01.

BIOCLIM suitability values0 – 0.000010.00001 – 0.50.5 – 0.750.75 – 11 – 115.75115.75 – 230.5230.5 – 345.25345.25 – 460 0 500 1000 2000 KM

Figure 2 Map showing potential geographical distribution forjaguar (Panthera onca) accordingly with BIOCLIM, which was themethod that showed the strongest relationship between model-based suitability estimate and jaguar density. Suitability valuesabove the lowest predicted value threshold (LPV) are shown in redand below the LPV threshold in blue tones.

Distribution models and population density

Diversity and Distributions, 18, 615–627, ª 2012 Blackwell Publishing Ltd 621

A partir de esto surgen dos preguntas:

1. ¿Qué significan los valores de probabilidad, de similitud, de favorabiliad que dan las salidas de los MNE?

2. ¿Es posible modelar la distribución de la abundancia de las especies?

“… the spatial variation in abundance largely reflects the extent to which local sites satisfy the niche requirements of a species” (Brown et al. 1995, Ecology 76: 2028-2043)

Concepto Hutchinsoniano de Nicho El hipervolumen n-dimensional en el que cada punto corresponde a un estado del ambiente que permite la existencia de la especie indefinidamente.

¿Qué mecanismos causan estos patrones? La Hipótesis del Nicho Ecológico

Respuesta de una población a una variable fundamental

Variable importante (ej. Temperatura)

Abu

ndan

cia

Letal Letal

Subóptimo Subóptimo

Óptimo

El nicho ecológico y la abundancia de las especies

La estructura interna del nicho ecológico (Maguire 1973, Am. Nat. 107: 213-246)

En el espacio ecológico, teóricamente existe un óptimo en donde las poblaciones tenderían a ver maximizada su tasa de natalidad y minimizada su tasa de mortalidad; que se reducen conforme se alejan de dicho óptimo

Algoritmo de modelado

(Bioclim, GLM, GAM, ANN, GARP, MAxEnt, etc.)

Temperatura

Hum

edad

......

+

Datos de entrada

Registros de presencia de una especie

El modelado de nichos ecológicos (MNE) permite caracterizar las condiciones ecológicas que determinan la distribución geográfica

de las especies y representarlas en forma de mapa

......

Mapa de distribución

potencial

Producto

Entonces, una hipótesis que surge es:

Existiría una relación inversa entre la distancia al óptimo del nicho y la abundancia de las poblaciones de una especie

Distancia al centroide

Abu

ndan

cia

Temperatura

Pre

cipi

taci

ón

In Honoris

1917 The Auk, Vol. 34, 427-433

Cuitlacoche de California (Toxostoma redivivum)

Requerimientos de datos 1. Datos de abundancia a lo largo de la distribución de una especie

(US Breeding Bird Survey)

2. Conjunto de variables ambientales relevantes en la distribución de la especie

1. Annual mean temperature 2. Mean diurnal range 3. Isothermality 4. Temperature seasonality 5. Max temp of the hottest month 6. Min temp of the coldest month 7. Annual range temp 8. Mean temp of the wettest quarter 9. Mean temp of the driest quarter 10. Mean temp of the hottest quarter 11. Mean temp of the coldest quarter 12. Annual precipitation 13. Precipitation of the wettest month 14. Precipitation of the driest month 15. Precipitation seasonality 16. Precip of the wettest quarter 17. Precip of the driest quarter 18. Precip of the hottest quarter 19. Precip of the coldest quarter 20. Elevation 21. Slope 22. Aspect 23. Topographic Index

Cuitlacoche de California (Toxostoma redivivum)

© Dick Cannings

Métodos 3. Reconstrucción del nicho ecológico

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Esp

acio

Geo

gráf

ico

Registros de presencia de una especie

Algoritmo de modelado ANN, ENFA, GAM, GARP, GLM, MaxEnt

Temperatura

Hum

edad

Modelo de Nicho Ecológico

Predicción de distribución

Producto

Esp

acio

Eco

lógi

co

Información Ambiental

Proyección de vuelta al espacio geográfico

Datos de entrada

4. Extraer los pixeles que representan la distribución modelada y estandarizar las variables ambientales

Modelo GARP

La obtención de un modelo de distribución adecuado indica que también se tiene una buena caracterización del nicho de la especie

Métodos

5. Calcular el centroide del nicho en espacio ecológico

6. Calcular la distancia Euclidiana multidimensional de cada punto poblacional al centroide del nicho

Métodos

Temperatura P

reci

pita

ción

y = 49.107x-1.9078

R2 = 0.5745P < 0.001

n = 48

0

10

20

30

40

50

60

0 2 4 6 8 10

Distance to centroid

Abu

ndan

ce (i

nd/ro

ute)

© Dick Cannings

Relación Distancia Ecológica vs Abundancia

Distancia Geográfica

y = 0.533x0.3278

R2 = 0.0361P = 0.196

n = 48

0

10

20

30

40

50

60

0 100 200 300 400 500 600

Geographic distance (km)

Abu

ndan

ce (i

nd/ro

ute)

© Dick Cannings

Favorabilidad de MaxEnt

© Dick Cannings

Toxostoma redivivum

y = 1.7249e1.1729x

R2 = 0.0557P > 0.05

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Maxent Probability

Abun

danc

e

Hylocicla mustelina

y = 122.28x-2.0201

R2 = 0.3706P < 0.001

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10 11 12


Abu

ndan

ce

y = -2.9798Ln(x) + 26.024R2 = 0.0641

0

10

20

30

40

50

60

0 300 600 900 1200 1500Geographic distance (km)

Abun

danc

e (in

d/ro

ute)

Hylocicla mustelina

Hylocichla mustelina

y = 0.0511e7.911x

R2 = 0.2926P < 0.001

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8

Maxent Probability

Abun

danc

e

Calamospiza melanocorys

y = 1552e-1.1712x

R2 = 0.4196P < 0.001

050

100150200250300350400450

0 1 2 3 4 5 6 7


Abun

danc

eCalamospiza melanocornys

y = -28.825Ln(x) + 242.77R2 = 0.0459P < 0.01

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200Geographic distance (km)

Abu

ndan

ce (i

nd/ro

ute)


y = 1.9769e4.6759x

R2 = 0.1219 P < 0.001

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8

Maxent Probability

Abun

danc

e

y = 887.44e-0.6672x

R2 = 0.5621P < 0.001

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12 14


Abu

ndan

ce (i

nd/ro

ute)

y = 83.25e-0.0034x

R2 = 0.4353P < 0.001

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800

Geographic distance (km)

Abu

ndan

ce (i

nd/ro

ute)

Spiza americana

Canis lupus

y = 149.32x-1.485

R2 = 0.716P < 0.001

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10


Abu

ndan

ce

y = -0.2146x + 23.015R2 = 0.0467P = 0.197

0

5

10

15

20

25

30

35

40

45

50


Abu

ndan

ce (i

nd/ro

ute)

Canis lupus

Canis lupus

y = 4.3771e1.8151x

R2 = 0.2715P < 0.01

05

101520253035404550

0 0.2 0.4 0.6 0.8 1

Maxent Probability

Abun

danc

e

Alouatta palliata

y = -28.563x + 214.98R2 = 0.8622P < 0.001

20

40

60

80

100

120

3 4 5 6 7 8


Abu

ndan

ce

Alouatta palliata

Lineary = -0.0056x + 35.596

R2 = 0.0038P = 0.865

n = 10

102030405060708090

100

0 300 600 900 1200 1500


Dens

ity

Alouatta palliata

Alouatta palliata

y = 38.796x1.2363

R2 = 0.1068P > 0.05

0102030405060708090

100

0 0.2 0.4 0.6 0.8

Maxent Probability

Abun

danc

e

Peromyscus maniculatus

y = 163.96e-1.5622x

R2 = 0.4233P < 0.001

0

10

20

30

40

50

0 1 2 3 4 5


Abun

danc

e

Peromyscus leucopus

y = 81.944e-1.3349x

R2 = 0.3683P < 0.05

0

5

10

15

20

25

30

0 1 2 3 4 5


Abun

danc

e

Panthera leo

y = -14.971Ln(x) + 22.816R2 = 0.3458P < 0.001

0

10

20

30

40

50

0 1 2 3 4 5 6


Abu

ndan

ce

Panthera tigris

y = 44.97e-0.7202x

R2 = 0.5044P < 0.001

0

5

10

15

20

0 1 2 3 4 5 6


Abu

ndan

ce

Más especies

Clemmys guttata

y = 103.45x-3.5903

R2 = 0.7842P < 0.01

0123456789

10

2 3 4 5 6 7


Abu

ndan

ce

y = 53007x-1.6695

R2 = 0.1939P = 0.194

0

10

20

30

40

50

60

70

80

90


Abu

ndan

ce (i

nd/ro

ute)

Clemys guttata

¿Y para qué sirve?

R = 0.827P < 0.05

0

2

4

6

8

10

0 2 4 6 8 10 12 14

Observed abundance (ind/route)

Mod

eled

abu

ndan

ce

Toxostoma redivivum

y = 5.0179e-0.0006x

R2 = 0.0008

0

2

4

6

8

10

12

0 20 40 60 80 100

Maxent Values (suitability)

Rank

ed a

bund

ance

(ind

/rout

e)

Es posible generar modelos espaciales predictivos de la abundancia relativa de las especies usando las ecuciones de regresión.

Modelos en escenarios alternos

Modelo predictivo de abundancia Modelo predictivo de presencia

Presente

2050 bajo el escenario CCM3 A1

Modelación de abundancias en escenarios de cambio climático

Sin embargo, en la revisión del artículo hubo la necesidad de repetir los análisis, y las cosas no fueron tan lindas ¿viste?

y = 49.107x-1.9078

R2 = 0.5745P < 0.001

n = 48

0

10

20

30

40

50

60

0 2 4 6 8 10


Abu

ndan

ce (i

nd/ro

ute)

En lugar de esto: Salió esto:

Toxostoma redivivum

R2 = 0.312; P = 0.001


Spiza americana

A b

u n

d a

n c

e

Environmental distance

R2 = 0.161; P < 0.001

R2 = 0.081; P < 0.001


y = 1552e-1.1712x

R2 = 0.4196P < 0.001

050

100150200250300350400450

0 1 2 3 4 5 6 7


Abun

danc

e

y = 887.44e-0.6672x

R2 = 0.5621P < 0.001

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12 14


Abu

ndan

ce (i

nd/ro

ute)

A b

u n

d a

n c

e

Hylocichla mustelina

Peromyscus leucopus


R2 = 0.083; P < 0.001

R2 = 0.074; P = 0.045

Hylocicla mustelina

y = 122.28x-2.0201

R2 = 0.3706P < 0.001

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10 11 12


Abu

ndan

ce

Peromyscus leucopus

y = 81.944e-1.3349x

R2 = 0.3683P < 0.05

0

5

10

15

20

25

30

0 1 2 3 4 5


Abun

danc

e

A b

u n

d a

n c

e

Alouatta palliata

Clemmys guttata

Geographic distance


R2 = 0.691; P = 0.016

R2 = 0.440; P < 0.010

Clemmys guttata

y = 103.45x-3.5903

R2 = 0.7842P < 0.01

0123456789

10

2 3 4 5 6 7


Abu

ndan

ceAlouatta palliata

y = -28.563x + 214.98R2 = 0.8622P < 0.001

20

40

60

80

100

120

3 4 5 6 7 8


Abu

ndan

ce

¿Qué pasó?

En el primer análisis el cálculo del “centroide” no fue en realidad al centroide geométrico del nicho, sino al óptimo con base en el análisis de las curvas de respuesta de las especies a las variables ambientales, lo que favoreció el mayor ajuste de los modelos de regresión

A pesar de ello, unos análisis sí funcionan con el centroide, lo que indica que para ciertas especies o escalas, si no se tienen datos de abundancia, la estimación de la distancia al centroide a partir sólo de los datos de presencia informa más que las favorabilidades modeladas con métodos tradicionales

Fuente: Yáñez-Arenas et al. 2012. Oikos

EV-1

Modelling geographic patterns of population density of the white-tailed deer in central Mexico by implementing ecological niche theory

Carlos Yañez-Arenas, Enrique Martínez-Meyer, Salvador Mandujano and Octavio Rojas-Soto

C. Yañez-Arenas, Div. de Posgrado, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México. – E. Martínez-Meyer ([email protected]), Depto de Zoología, Inst. de Biología, Univ. Nacional Autónoma de México, Tercer Circuito Exterior s/n, Ciudad Universitaria, MX-04510 México City, México. – S. Mandujano, Red de Biología y Conservación de Vertebrados, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México. – O. Rojas-Soto, Red de Biología Evolutiva, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México.

Conservation and management of species require basic knowledge on their geographic distribution and abundance. Here, we propose a novel approach, based on the theory of the ecological niche, to model the spatial patterns of the white-tailed deer Odocoileus virginianus population density in two regions of central Mexico (Balsas Basin and Tehuacán-Cuicatlán Valley). We used an ecological niche model to generate binary geographic distribution maps of the white-tailed deer in each region based on occurrence data and a set of environmental variables. Then, the centroid of the distributions was calculated in ecological space (niche centroid) and the multidimensional Euclidian ecological distance of each pixel to the niche centroid was estimated. Finally, for each region the distance to the niche centroid (DNC) was regressed against 14 independent occurrence points in each site containing white-tailed deer density information to determine the function describing the DNC-density relationship, which was used to generate maps describing the distribution of white-tailed deer density. Our results indicated an inverse DNC-density relationship in both regions (Balsas Basin: r2 0.90 and Tehuacán-Cuicatlán: r2 0.76) that was validated via bootstrapping resulting in a predicting capacity of near 62% for Balsas Basin and 65% for Tehuacán-Cuicatlán Valley. Our results suggest that the distance to the niche centroid method is a robust, science-based correlative approach that resulted useful to predict the population density of the white-tailed deer in a spa-tially explicit fashion. The proposed approach is suitable for predicting the distribution of density for white-tailed deer for which occurrence data with accompanying density information exists, but relative abundance can also be estimated when no abundance data are available.

Oikos 000: 001–009, 2012 doi: 10.1111/j.1600-0706.2012.20350.x

© 2012 The Authors. Oikos © 2012 Nordic Society Oikos Subject Editor: Joseph Bailey. Accepted 28 March 2012

Conservation and management of species require some basic information regarding their geographic distribution and abundance (McShea et al. 1997). In recent years, eco-logical niche modeling (ENM) has been widely used to map the geographic distribution of species at different scales for conservation purposes, with reliable results (Peterson et al. 2011). However, despite that ENM methods have proven useful to adequately describe the geographic distribution of species, their capacity to inform about the distribution pat-terns of abundance is, in the best case, limited (VanDerWal et al. 2009, Tôrres et al. 2012).

Abundance is not evenly distributed across space (Brown 1984). In general, most sites hold relatively low abundances whereas few locations hold much higher abundances, and also, some species show a tendency to find higher abun-dances towards the center of the species’ range compared to its margins; this is called the ‘abundant-center hypothesis’ (Brown 1995, Sagarin and Gaines 2002). Although several

mechanisms have been invoked to explain these patterns, including population and dispersal dynamics (Pulliam 1988) or physiological tolerances (Brown 1984), none is fully satisfactory (Sagarin and Gaines 2002). Nevertheless, the theory of the ecological niche may shed some light on this regard. Hutchinson (1957) proposed that the ecological niche can be conceptualized as a multidimensional hyper-volume constructed with n-axes, each of which represents fundamental variables for the populations’ survival. Later on, Maguire Jr (1973) found that such hyper-volume has an internal structure in which optimal conditions, i.e. where birth rate is maximized and death rate minimized therefore the intrinsic population growth rate (r) is highest, are towards the centroid of the ecological niche. If this is true, population abundance patterns should be explained by their position with respect to the species’ ecological niche centroid: higher abundance should be found in populations closer to the niche centroid and it decreases monotonically EV-1

Modelling geographic patterns of population density of the white-tailed deer in central Mexico by implementing ecological niche theory

Carlos Yañez-Arenas, Enrique Martínez-Meyer, Salvador Mandujano and Octavio Rojas-Soto

C. Yañez-Arenas, Div. de Posgrado, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México. – E. Martínez-Meyer ([email protected]), Depto de Zoología, Inst. de Biología, Univ. Nacional Autónoma de México, Tercer Circuito Exterior s/n, Ciudad Universitaria, MX-04510 México City, México. – S. Mandujano, Red de Biología y Conservación de Vertebrados, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México. – O. Rojas-Soto, Red de Biología Evolutiva, Inst. de Ecología A. C., km 2.5 Camino Antiguo a Coatepec No. 351, Congregación del Haya, MX-91070 Xalapa, Veracruz, México.

Conservation and management of species require basic knowledge on their geographic distribution and abundance. Here, we propose a novel approach, based on the theory of the ecological niche, to model the spatial patterns of the white-tailed deer Odocoileus virginianus population density in two regions of central Mexico (Balsas Basin and Tehuacán-Cuicatlán Valley). We used an ecological niche model to generate binary geographic distribution maps of the white-tailed deer in each region based on occurrence data and a set of environmental variables. Then, the centroid of the distributions was calculated in ecological space (niche centroid) and the multidimensional Euclidian ecological distance of each pixel to the niche centroid was estimated. Finally, for each region the distance to the niche centroid (DNC) was regressed against 14 independent occurrence points in each site containing white-tailed deer density information to determine the function describing the DNC-density relationship, which was used to generate maps describing the distribution of white-tailed deer density. Our results indicated an inverse DNC-density relationship in both regions (Balsas Basin: r2 0.90 and Tehuacán-Cuicatlán: r2 0.76) that was validated via bootstrapping resulting in a predicting capacity of near 62% for Balsas Basin and 65% for Tehuacán-Cuicatlán Valley. Our results suggest that the distance to the niche centroid method is a robust, science-based correlative approach that resulted useful to predict the population density of the white-tailed deer in a spa-tially explicit fashion. The proposed approach is suitable for predicting the distribution of density for white-tailed deer for which occurrence data with accompanying density information exists, but relative abundance can also be estimated when no abundance data are available.

Oikos 000: 001–009, 2012 doi: 10.1111/j.1600-0706.2012.20350.x

© 2012 The Authors. Oikos © 2012 Nordic Society Oikos Subject Editor: Joseph Bailey. Accepted 28 March 2012

Conservation and management of species require some basic information regarding their geographic distribution and abundance (McShea et al. 1997). In recent years, eco-logical niche modeling (ENM) has been widely used to map the geographic distribution of species at different scales for conservation purposes, with reliable results (Peterson et al. 2011). However, despite that ENM methods have proven useful to adequately describe the geographic distribution of species, their capacity to inform about the distribution pat-terns of abundance is, in the best case, limited (VanDerWal et al. 2009, Tôrres et al. 2012).

Abundance is not evenly distributed across space (Brown 1984). In general, most sites hold relatively low abundances whereas few locations hold much higher abundances, and also, some species show a tendency to find higher abun-dances towards the center of the species’ range compared to its margins; this is called the ‘abundant-center hypothesis’ (Brown 1995, Sagarin and Gaines 2002). Although several

mechanisms have been invoked to explain these patterns, including population and dispersal dynamics (Pulliam 1988) or physiological tolerances (Brown 1984), none is fully satisfactory (Sagarin and Gaines 2002). Nevertheless, the theory of the ecological niche may shed some light on this regard. Hutchinson (1957) proposed that the ecological niche can be conceptualized as a multidimensional hyper-volume constructed with n-axes, each of which represents fundamental variables for the populations’ survival. Later on, Maguire Jr (1973) found that such hyper-volume has an internal structure in which optimal conditions, i.e. where birth rate is maximized and death rate minimized therefore the intrinsic population growth rate (r) is highest, are towards the centroid of the ecological niche. If this is true, population abundance patterns should be explained by their position with respect to the species’ ecological niche centroid: higher abundance should be found in populations closer to the niche centroid and it decreases monotonically

0

5

10

15

20

25

2.5 3 3.5 4 4.5 5 5.5 6 6.5

Torto

ise

abun

danc

e

Distance to niche centroid

¿Qué hemos aprendido?

La variación geográfica de la abundancia de las poblaciones de las especies está mejor explicada por las las condiciones del nicho en los sitios de ocupación que por su estructura geográfica. La integración de ambos factores explica mejor la variación de la abundancia

Existe una estructura interna del nicho que determina la adecuación de las poblaciones, y esto su abundancia; siendo máxima en torno a un óptimo, que puede o no ser el centroide geométrico. Además, estos óptimos pueden o no estar restringidos por la geografía en la que vive la especie


Es posible modelar y mapear la distribución de la abundancia, lo que representa un paso importante en la modelación de nichos y distribuciones geográficas de las especies, tanto teóricamente como en ciencia aplicada


1. Seguir haciéndo análisis sobre optimalidad ecológica y su interacción con la geografía que nos permita entender mejor la estructura interna del nicho y la abundancia

2. Probar el concepto del centroide para ciencia aplicada (e.g., probar si el rendimiento de maíz nativo responde al concepto de centroide [Carolina Ureta]; aprovechamiento cinegético de fauna [Dr. Salvador Mandujano])

3. Desarrollo de un conjunto de programas para modelar la distribución de la abundancia bajo el concepto del centroide

¿Para dónde vamos?

Desarrollo de un conjunto de programas para modelar la distribución de la abundancia bajo el concepto del centroide (Nichosfera)

el nicho ecológico y la abundancia de las especies

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