Health

Carrying Capacity Estimator (Fit K from Time-Series Data)

Least-squares logistic fit of K, r, t₀ from `time, population` observations, with fitted curve, residuals, and plateau warnings.

html· HTML resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/carrying-capacity-estimator' \
  -H 'Content-Type: application/json' \
  -d '{"data":"0, 9.6\n2, 29.0\n4, 71.1\n6, 174.6\n8, 352.0\n10, 513.3\n12, 594.8\n14, 640.8\n16, 655.9\n18, 661.8"}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/carrying-capacity-estimator

Parameters

Name	Type	Required	Description
data	textarea	Yes	One `time, population` pair per line (separator: comma, space, semicolon, or tab). At least 5 points with strictly increasing times and positive populations that approach a plateau.

Response format

HTML result

JSON

{
  "result": "<div>Processed HTML content</div>",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-carrying-capacity-estimator": {
      "name": "carrying-capacity-estimator",
      "description": "Least-squares logistic fit of K, r, t₀ from `time, population` observations, with fitted curve, residuals, and plateau warnings.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=carrying-capacity-estimator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "carrying-capacity-estimator",
    "arguments": {
  "data": "0, 9.6\n2, 29.0\n4, 71.1\n6, 174.6\n8, 352.0\n10, 513.3\n12, 594.8\n14, 640.8\n16, 655.9\n18, 661.8"
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

Browse tools Open tool

curl -X POST 'https://api.elysiatools.com/en/api/tools/carrying-capacity-estimator' \ -H 'Content-Type: application/json' \ -d '{"data":"0, 9.6\n2, 29.0\n4, 71.1\n6, 174.6\n8, 352.0\n10, 513.3\n12, 594.8\n14, 640.8\n16, 655.9\n18, 661.8"}'

Name

Type

Required

Description

data

textarea

Yes

One `time, population` pair per line (separator: comma, space, semicolon, or tab). At least 5 points with strictly increasing times and positive populations that approach a plateau.

{ "mcpServers": { "elysiatools-carrying-capacity-estimator": { "name": "carrying-capacity-estimator", "description": "Least-squares logistic fit of K, r, t₀ from `time, population` observations, with fitted curve, residuals, and plateau warnings.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=carrying-capacity-estimator", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "carrying-capacity-estimator", "arguments": { "data": "0, 9.6\n2, 29.0\n4, 71.1\n6, 174.6\n8, 352.0\n10, 513.3\n12, 594.8\n14, 640.8\n16, 655.9\n18, 661.8" } } }